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• MMODE is developed as a new hybrid gene selection method for tumor identification. • MMODE combines multi-tasking and multi-objective frameworks. • MMODE uses a new elite strategy and a new guidance strategy. • MMODE selects a few genes and achieves high classification accuracy. A key preprocessing step in tumor recognition based on microarray expression profile data and machine learning is to identify tumor marker genes. Gene selection aims to select the most relevant gene subset from the original ultra-high dimensional microarray expression profile data to improve tumor identification performance. Inspired by evolutionary multitasking (EMT) and multi-objective optimization, this paper puts forward a novel multitasking multi-objective differential evolution gene selection algorithm (MMODE) which uses new elite and guidance strategies to select the best gene subsets. MMODE initializes two different populations according to different filtering criteria to increase the diversity of the search. These two populations guide their respective populations to search in the optimal direction through knowledge transfer in the evolutionary process. In addition, MMODE employs new elite and guidance strategies that enables individuals to narrow the search range and jump out of local optima. The proposed algorithm is validated on 13 publicly available microarray expression datasets in comparison with state-of-the-art gene selection algorithms. The experimental results show that MMODE can find smaller gene subsets and achieve higher classification accuracy compared with other algorithms. [ABSTRACT FROM AUTHOR]

The differential evolution (DE) algorithm is widely regarded as one of the most influential evolutionary algorithms for addressing complex optimization problems. However, the fixed mutation strategy limits the adaptive ability of DE, and the lack of utilization of historical information limits the optimization ability of DE. In this paper, an indicator-based self-learning differential evolution algorithm (ISDE) is proposed. A jump out mechanism based on deep reinforcement learning is adopted to control the mutation intensity of the population. The neural network in the jump out mechanism is designed as a decision maker. The mutation intensity of the population is controlled by the neural network, and the neural network are trained by a double deep Q network algorithm based on the continuous data generated during the evolution process. A population range indicator (PRI) is utilized to describe individual differences in the population. A diversity maintenance mechanism is designed to maintain individual differences according to the value of PRI. The experimental results reveal that the comprehensive performance of ISDE is superior to comparison algorithms on CEC 2017 real-parameter numerical optimization. [ABSTRACT FROM AUTHOR]

Adversarial sample generation problem is a hot issue in the security field of deep learning. Evolutionary algorithm has been widely used to solve this problem in recent years because of its good global search ability. However, existing methods still suffer from the "curse of dimensionality" when attacking high-resolution images. In this paper, a two-stage frequency domain generation algorithm of black-box adversarial samples based on differential evolution is proposed. In the first stage, a representative image-guided differential evolution method is proposed to quickly generate a universal adversarial perturbation with a high attack success rate in the frequency-domain. In the second stage, a space reduction strategy based on frequency-domain pixel blocks is designed to reduce the search space and alleviate the problem of "curse of dimensionality". In addition, a new space–frequency interaction sensitivity measure is introduced to evaluate the similarity between the adversarial samples and the original images. The adversarial perturbations obtained by the measure are more in line with the subjective perception of the human eye. Finally, compared with several typical black-box adversarial sample generation algorithms, experimental results show that the proposed algorithm can achieve higher attack success rate with less prediction times. • Proposing a two-stage evolutionary generation framework of adversarial samples. • Developing a space–frequency interaction sensitivity measure. • Presenting a representative image-guided differential evolutionary algorithm. • Designing an individual adversarial perturbation generation algorithm. [ABSTRACT FROM AUTHOR]

Population-based algorithms aim to explore the entire solution space in global numerical optimization problems. However, it is important to acknowledge that the solution spaces of different problems possess distinct characteristics, and even distinct regions within the same solution space can vary significantly. Efficient exploration of these diverse regions necessitates the utilization of distinct search models. To address this challenge, this study proposes a new variant of the Differential Evolution (DE) algorithm called MHDE. The MHDE algorithm introduces hash clustering technology combined with adaptive mutation strategies. The integration of hash clustering technology enables fast population clustering, significantly enhancing clustering efficiency. Additionally, a method for evaluating the population state is designed that allows for an adaptive clustering quantity to adapt the clustering quantity to the population state. Furthermore, a novel method is devised to calculate individual improvements considering the varying levels of difficulty that individuals face in achieving improvements within a population. This method is combined with a parameter adaptive mechanism, resulting in a weighted parameter adaptive mechanism. Experiments are conducted on the CEC2017 benchmark suite to evaluate the performance of the MHDE algorithm. The experimental results demonstrate that MHDE exhibits competitive performance compared with other efficient DE variants. Moreover, the MHDE algorithm is applied to the node deployment problem in wireless sensor networks (WSNs). The MHDE algorithm demonstrates efficient performance in node deployment problems through simulation experiments in different scenarios. • Introducing a BLSH technique for population clustering. • Designing a new method to evaluate population states. • Presenting a novel approach for calculating individual contributions. • Utilizing an external population to accelerate algorithm convergence. [ABSTRACT FROM AUTHOR]

In bioinformatics, biclustering is a crucial optimization task that can reveal hidden patterns and identify groups of genes that behave similarly under certain conditions. This study aims to efficiently identify high-quality and cohesive biclusters that share common characteristics across two data dimensions. To achieve this, we propose the first biclustering approach that utilizes Multi-objective Differential Evolution (DE), which is a novel technique for gene group discovery. Additionally, we introduce the Biclustering Binary Differential Evolution (BBDE), a new mutation operator that combines node addition and deletion, guided by an adaptive factor F. We thoroughly tested our method's effectiveness taking into account biological relevance, noise, overlap resistance, and statistics. We compared our results to state of the art algorithms using both synthetic and real datasets like Yeast Cell Cycle, Saccharomyces cerevisiae, and Human B Cell. Our algorithms outperformed the comparisons and effectively identified significant biclusters. • Multi-objective evolutionary biclustering approach using differential evolution. • BBDE: An adaptive mutation operator to adjust DE for biclustering. • A powerful approach for identifying multiple large biclusters simultaneously. [ABSTRACT FROM AUTHOR]

Unmanned surface vessel (USV) has a wide range of applications in oceanographic research, resource development, environment detection, and security rescue due to its advantages of maneuverability, flexibility, fast response, and intelligence. The ability of USVs to autonomously and effectively avoid obstacles in highly dynamic and uncertain marine environments is a prerequisite for the successful completion of their tasks. Therefore, in this article, a USV collision avoidance based on International Regulations for Preventing Collisions at Sea and the Collision Risk Model with the Improved Differential Evolution Algorithm (CRI-DE) has been considered. Based on the International Regulations for Preventing Collisions at Sea (COLREGs) and common practices of seafarers, an improved ship collision risk model is proposed. Specifically, the model is innovatively combined with the differential evolution algorithm (DE) as a constraint condition to further realize path planning in complex situations. Moreover, chaotic multi-population parallel optimization, parameter adaptive adjustment strategy, and the construction of fitness function based on individual path points are added to the DE. In this way, the ability to escape from local optima and enrich population diversity can be guaranteed. Finally, experiments based on the proposed CRI-DE are conducted and the results indicate the efficiency and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) and flower pollination algorithm (FPA) are efficient and novel meta -heuristic algorithms, which are effective tools for solving global optimization problems (GOPs). However, a single algorithm is always restricted to its own principle and mechanism, and even suffers from the imbalance of global and local search ability when solving large-scale GOPs. The organic combination of the two algorithms with a certain strategy can improve the performance of the hybrid algorithm. Motivated by this idea, a hybrid global optimization algorithm based on DE and FPA is proposed. Firstly, an improved initial population generation method is provided for improving the quality of the initial population. Secondly, an improved DE is given, and the parameters F and CR are adjusted in an adaptive and dynamic fashion, and a combined mutation operator is designed. Thirdly, an improved FPA is proposed, and a method for adaptively and dynamically adjusting the switch probability p is given, and formulas for updating the global and local position are introduced. Lastly, a hybrid strategy of organically combining DE and FPA is proposed to form a hybrid algorithm of differential evolution and flower pollination (HADEFP). To demonstrate the performance of the hybrid algorithm, the proposed hybrid algorithm is tested against other algorithms in the literature on CEC 2017 test functions (10- D , 50- D and 100- D) and practical optimization problem, respectively. The results show that the proposed HADEFP outperforms other comparison algorithms and has better robustness. [ABSTRACT FROM AUTHOR]

Energy-saving, one of the most significant strategies for green manufacturing, has become the focus of more and more scholars and enterprise managers. Hence, this work addresses the minimization of energy and cost requirements on mixed-model multi-manned assembly line balancing with multi-skilled workers. A new mixed-integer linear programming model is proposed to define the problem. Additionally, a novel multi-objective co-evolutionary algorithm is designed to achieve the trade-off between energy and cost requirements. This algorithm includes a two-layer solution representation to achieve full coverage of the solution space and a new decoding mechanism with idle time reduction. A collaborative initialization as the first stage of the algorithm is extended to get high-quality and great-diversity initial solutions. A self-learning evolution for each sub-population with four problem-specific evolutionary operators is developed to explore task or worker assignment sequences, and a dual-cooperation strategy is proposed to enhance the interaction between sub-populations. The final experiments, based on 269 instances, demonstrate that the improvement components are effective and the proposed algorithm is superior to seven latest multi-objective evolutionary algorithms from numerical, statistical and differential analyses. • Define the MALBP-MW by a MILP model to minimize the energy and cost requirements. • Design a new decoding with idle time reduction and a collaborative initialization. • Propose four problem-specific evolutionary operators for MOCEA. • Develop MOCEA with a self-learning selection and dual-cooperation. [ABSTRACT FROM AUTHOR]

This research studies the Share-a-Ride Problem (SARP) in which a set of taxis is used to serve a set of package and passenger requests at the same time. The goal is to maximize the profit from serving the requests without violating given constraints. We develop a new matheuristic algorithm that combines the simulated annealing with mutation strategy (SAMS) and the set partitioning (SP) approach to improve the reported solutions of SARP benchmark instances. The SAMS consists of a time-slack strategy, neighborhood moves, a mutation strategy that depends on the time-slack strategy, and a penalty mechanism for infeasible solutions. The first phase of the proposed matheuristic uses SAMS to generate a set of feasible candidate routes. A route accumulation mechanism is added to the SAMS to keep the candidate routes in the route pool. The second phase of the matheuristic focuses on solving the set partitioning model to find the best route combination as the final solution. The proposed matheuristic is tested on existing small and large SARP instances, and a set of newly generated large SARP instances and then compared with SAMS algorithm. The experimental results show that the proposed matheuristic obtains optimal solutions to all the small SARP benchmark instances. For large instances, the proposed matheuristic outperforms SAMS algorithm as it obtains several new best solutions to SARP. Lastly, our algorithm obtains high-quality solutions to the new large SARP instances generated in this study. [ABSTRACT FROM AUTHOR]

In this study, an energy efficiency study has been carried out through the moment values of a quadrotor applied in the position control with the differential evolution algorithm (DE), which is under the evolutionary algorithms among meta-heuristic algorithms particle swarm optimization (PSO) which is among swarm-based algorithms and gravity search algorithm (GSA) among physics-based algorithms and charged system search (CSS) algorithm, which are all well-known in the literature. The efficient use of energy in electrically powered flying mechanisms is important in terms of completing its task. The aim of this study is to obtain proportional–integral–derivative (PID) coefficients that minimize the energy consumption caused by quadrotor moments. First of all, 12 PID coefficients calculated with traditional Ziegler Nicholes, and trying-error methods for the control of the quadrotor have been trained with DE, PSO, GSA and CSS algorithms and their cost values have been found for this problem. In the study, optimum PID coefficients have been found separately with each algorithm and torque data giving energy efficiency have been obtained by applying them to the state equations. Although the cost minimization convergence value obtained from DE does not look good compared to other algorithms, it has been observed that the moment values of the obtained PID coefficients in the control program are lower. In the study, it has been shown that the PID coefficients obtained from DE reach the target with approximately less energy than the maximum-moment value of the PSO, which provides the closest moment value. It can be thought that this value contributes to energy consumption in each orbital movement of the quadrotor. The simulation results show that the coefficients obtained from DE provide better energy efficiency and are superior to other algorithms compared in terms of energy efficiency. • PID coefficients for quadrotor control are optimized with DE,PSO,CSS,GSA algorithms • The torque values to be applied to each motor were adjusted with these coefficients • The total force applied with DEPID in the z direction is smaller than others • DEPID consumes less energy than the other algorithms in the paper [ABSTRACT FROM AUTHOR]

In this study, an energy efficiency study has been carried out through the moment values of a quadrotor applied in the position control with the differential evolution algorithm (DE), which is under the evolutionary algorithms among meta-heuristic algorithms particle swarm optimization (PSO) which is among swarm-based algorithms and gravity search algorithm (GSA) among physics-based algorithms and charged system search (CSS) algorithm, which are all well-known in the literature. The efficient use of energy in electrically powered flying mechanisms is important in terms of completing its task. The aim of this study is to obtain proportional–integral–derivative (PID) coefficients that minimize the energy consumption caused by quadrotor moments. First of all, 12 PID coefficients calculated with traditional Ziegler Nicholes, and trying-error methods for the control of the quadrotor have been trained with DE, PSO, GSA and CSS algorithms and their cost values have been found for this problem. In the study, optimum PID coefficients have been found separately with each algorithm and torque data giving energy efficiency have been obtained by applying them to the state equations. Although the cost minimization convergence value obtained from DE does not look good compared to other algorithms, it has been observed that the moment values of the obtained PID coefficients in the control program are lower. In the study, it has been shown that the PID coefficients obtained from DE reach the target with approximately less energy than the maximum-moment value of the PSO, which provides the closest moment value. It can be thought that this value contributes to energy consumption in each orbital movement of the quadrotor. The simulation results show that the coefficients obtained from DE provide better energy efficiency and are superior to other algorithms compared in terms of energy efficiency. • PID coefficients for quadrotor control are optimized with DE,PSO,CSS,GSA algorithms • The torque values to be applied to each motor were adjusted with these coefficients • The total force applied with DEPID in the z direction is smaller than others • DEPID consumes less energy than the other algorithms in the paper [ABSTRACT FROM AUTHOR]

Reducing the number of lower-level function evaluations (LFEs) is crucial to designing a bilevel evolutionary algorithm (BLEA) for bilevel optimization. Direct neighbor solution transfer (DST) is regularly used in BLEA because it can improve the lower-level search efficiency and reduce the number of LFEs. But this method still faces the challenge of misleading searches to make the algorithm converge to the wrong optimum. This paper proposes a bilevel improved multi-operator differential evolution algorithm (BL-IMODE) for bilevel optimization, which uses the knowledge transfer and adaptive coordinate systems approach. Specifically, this paper proposes a lower-level search knowledge transfer (LLS-KT) and a lower-level (LL) optimal solution distribution information transfer (LLO-DIT) mechanism to implement knowledge transfer. In LLS-KT, transferring LL solutions to the LL optimizer is similar to DST, but the LLS-KT transfers multiple solutions and thus has less possibility of misleading searches than DST. Moreover, the LLO-DIT transfers the LL optimal solution distribution information to the LL optimizer for generating promising offspring solutions. Since this method does not directly transfer LL solutions, it avoids misleading searches. Additionally, the adaptive coordinate systems (ACS) approach is used in two-level optimizers to suit different fitness landscapes and further reduce the number of LFEs. In ACS, three differential evolution mutation operators are produced in two coordinate systems. An adaptive strategy is used to select the suitable differential evolution mutation operator to generate promising offspring solutions in the Eigen coordinate or original coordinate system. Experimental studies on three test suites benchmark problems for comparison with seven state-of-the-art algorithms are conducted. The results show BL-IMODE has a significant advantage over the comparative algorithms. Finally, BL-IMODE is applied to tackle the inverse optimal control problem. • We propose a bilevel improved multi-operator differential evolution algorithm. • We propose a knowledge transfer approach to avoid misleading search. • We propose an adaptive coordinate systems approach to improve search efficiency. • We outperform all existing approaches in most test instances. [ABSTRACT FROM AUTHOR]

Constrained optimization problems are critical in optimization research owing to their prevalence in various fields such as engineering, management science, and economics. In this study, we develop an improved hybrid membrane algorithm based on the hormone modulation mechanism (IHMA-HMM), which combines differential evolution algorithm with the dynamic membrane structure of cell-like P systems, for constrained engineering design problems. In the IHMA-HMM, hormone modulation mechanism is developed to adjust the membrane structure in an adaptive manner. Experiments on 24 benchmark test functions and five well-known engineering design problems show that the proposed IHMA-HMM is capable of balancing exploration and exploitation well, and is competitive with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• A two-layer hierarchical differential evolution (DE) algorithm is proposed. • Success-history-based adaptive DE (SHADE) is implemented in the bottom layer. • Multi-cross operation (MCO) is implemented in the top layer. • The first-order stability is analyzed without a stagnation assumption. • The proposed DE yields more accurate solutions for 30- and 50-dimensional problems. In expert systems, complex optimization problems are always characterized by nonlinearity, nonconvexity, multi-modality, discontinuity, and high dimensionality. Although classical optimization algorithms are mature, they readily fall into a local optimum. The differential evolution (DE) algorithm has been successfully applied to solve numerous problems with expert systems. However, balancing the global and local search capabilities of the DE algorithm remains an open issue and has attracted significant research attention. Thus, a hierarchical heterogeneous DE algorithm that incorporates multi-cross operation (MCO) is proposed in this article. In the proposed algorithm, success-history-based adaptive DE (SHADE) is implemented in the bottom layer, while MCO is implemented in the top layer. The MCO search is based on the SHADE results, but its search results do not affect the bottom layer. First-order stability analyses conducted for the presented MCO showed that the individual positions are expected to converge at a fixed point in the search space. The accuracy and convergence speed of the proposed algorithm were also experimentally compared with those of eight other advanced particle swarm optimization techniques and DE variants using benchmark functions from CEC2017. The proposed algorithm yielded better solution accuracy for 30- and 50-dimensional problems than the other variants, and although it did not provide the fastest convergence for all of the functions, it ranked among the top three for the unimodal and simple multimodal functions and achieved fast convergence for the other functions. [ABSTRACT FROM AUTHOR]

Highlights • Differential evolution on islands of different sizes improves fitness dynamics. • Concept of multi-size island model facilitates the design of distributed algorithms. • No need to determine migration policy, topology and tune the size of population. • Multi-size island model shows high efficiency even without solution migration. • The concept of active islands reduces the demand for computing units to 3 at most. Abstract Computational intelligence methods can provide high-quality solutions to a variety of complex optimization problems where exact analytical solutions are impossible to obtain within a reasonable time and other resources used. The article proposes a novel concept of island model with islands of different sizes as well as differential evolution algorithms implementing this concept. Such a multi-size approach facilitates the design of island-based algorithms and brings a variety of benefits. Among them: improved fitness dynamics throughout the entire time of operation even without migration of solutions among the islands. The absence of migration eliminates the need to establish the topology and the policy of migration. It also makes the efficiency of multi-size island-based algorithms independent of the particular islands' size and practically eliminates the need of tuning the size of islands which is usually done in the case of the canonical island model. All these features indicate the superiority of the proposed multi-size island model over the canonical one. The efficiency of the proposed multi-size approach has been tested by solving one of the most difficult scheduling problems which is the discrete-continuous scheduling with continuous resource discretization. [ABSTRACT FROM AUTHOR]

The software module clustering problem (SMCP) aims to improve the internal quality of software while helping software engineers understand the system architecture and facilitating software system maintenance. However, most current methods ignore modular stability in software evolution and the topological properties of the software architecture and hence obtain decompositions much worse than the expert. Therefore, we propose a collaborative multi-objective information-sharing differential evolution (MOPISDE) algorithm for SMCP with global stability and path complexity as two new objective functions. Specifically, two new concepts are defined for SMCP as two objectives of populations and modular quality (MQ) as an objective of the third population. Population-sharing technology is designed to collaboratively exchange information among different populations to address the lack of diversity in a single population. An information-sharing three-stage differential evolution strategy is presented to reduce the search space and improve search performance by sharing good substructures among elite individuals. New mutation strategies are proposed to utilize the different substructures between two random individuals as a new community to further improve the search performance. Experiments on various projects demonstrate the superiority of the proposed algorithm. The proposed method not only has fast convergence but also provides stable and accurate modularity that is somewhat closer to expert decomposition than that of other methods. • We propose two key concepts in the software module clustering problem (SMCP). • We design a collaborative multi-objective information-sharing DE algorithm based on the new concepts for SMCP. • The experiment results of our method are significantly better than the SOTA methods. • We provide the source code of our proposed method and the datasets used. [ABSTRACT FROM AUTHOR]

Short-time traffic flow prediction plays an essential role in Intelligent Transportation System. Mixed flow is a common type of short-time traffic flow, with characteristics of small sample size, high temporal variability, and evident phase. To better predict the changes of mixed flow and speed, a new variable order fractional grey model (NVOFGM) is proposed by introducing the variable order fractional integro-differential (VO-FID) model into the grey model and extending the first accumulation generation to variable order fractional accumulation generation (VO-FAGO). The analytical expression of NVOFGM is obtained using Laplace transform. At the same time, considering that NVOFGM needs to optimize the parameters, and the objective function of the optimization is the nonlinear function with many parameters, a new grey prediction evolution algorithm (CDEGPEA) is obtained by improving the grey prediction evolution algorithm by the chaotic logistic map and the differential evolution algorithm (DE), and the superiority and effectiveness of its performance are validated on CEC2005 benchmark functions. Finally, based on the mixed flow and speed data from the M3 and M25 freeways in the UK, it is found that NVOFGM performs well in both fitting and testing and has good stability and stable generalization ability. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a novel fitness-value-independent Differential Evolution to tackle complex real-parameter single-objective optimization. There were three innovations in the algorithm: First, dimension improvements based adaptation schemes for control parameters F and C R were advanced in this paper. Different from those fitness value improvements based parameter control in the recent winner DE variants, our algorithm has fitness-value-independent characteristic, therefore, it can be applied in much wider optimization scenarios especially for those that the exact fitness values of the objectives are unavailable. Second, a combined parabolic–linear reduction scheme for population size is employed in the algorithm based on the observation that the slower reduction of population size at the earlier stage of the evolution usually helps to get better perception of the objectives while a linear reduction of population size in the later stage helps to get better exploitation. Third, an indicator is proposed to monitor the diversity of the population and a corresponding population enhancement technique is launched when the diversity is detected bad. The first two innovations have the P arameter a daptive characteristic of the DE algorithm while the third innovation refers to p opulation e nhancement t echnique, therefore, we name our algorithm "the PaDE-pet algorithm". Then, the algorithm is validated under a larger test suite containing 88 benchmarks from CEC2013, CEC2014 and CEC2017 test suites for real-parameter single objective optimization, which may avoid over-fitting problem in comparison with employing a test suite containing a small number of benchmarks. The experiments support the superiority of the novel PaDE-pet algorithm in comparison with several recently proposed powerful DE variants. • A black-box model reflecting complex optimization without available fitness values. • The model reveals the fitness-value-dependent weakness of recent winner DE variants. • A novel fitness-value-independent DE algorithm was proposed to tackle the model. • New adaptation schemes for control parameters and population enhancement technique. • To avoid over-fitting, a larger test suite is employed in algorithm validation. [ABSTRACT FROM AUTHOR]

Multimodal multiobjective optimization problems (MMOPs) possess multiple equivalent Pareto optimal sets (PSs) corresponding to the same Pareto front (PF). Numerous multimodal multiobjective evolutionary algorithms (MMEAs) have been developed to solve MMOPs. However, how to locate multiple high quality equivalent PSs and obtain a uniformly distributed PF simultaneously remains a challenging task. This paper explores a novel multimodal multiobjective differential evolution algorithm, termed MMO_CDE, for solving MMOPs. In MMO_CDE, a neighborhood-based dual mutation strategy is proposed by developing two novel mutation operators. The two novel mutation operators provide a better tradeoff between exploration and exploitation in locating multiple equivalent PSs. In addition, a clustering-based environmental selection mechanism is designed by integrating an affinity propagation method. The affinity propagation method improves the distribution of solutions in decision and objective spaces, and a harmonic averaged distance is adopted to promote the diversity of a population. The proposed MMO_CDE is compared against state-of-the-art MMEAs on a test suite of CEC 2019 benchmark functions and a map-based practical application. Empirical results validate the superiority of the proposed MMO_CDE regarding locating multiple equivalent PSs and obtaining a well-distributed PF. • Propose a clustering differential evolution with neighborhood-based dual mutation. • Develop a neighborhood-based dual mutation for the proposed algorithm. • Develop a clustering-based environmental selection for the proposed algorithm. [ABSTRACT FROM AUTHOR]

• The position-updated function of GWO is extended to boost the exploitation of GWO. • A rank-based mutation operator is introduced into DE to enhance the exploration capacity. • A hybrid algorithm, HGWODE, is developed. • The HGWODE is used to solve the UAV path planning. Autonomous navigation is significant to UAVs, especially in disaster scenarios. A Hybrid GWO and Differential Evolution (HGWODE) algorithm is developed to solve UAV path planning. In HGWODE, GWO and DE algorithms cooperate well to balance exploitation and exploration. The position-updated equation of GWO is improved, which makes alpha, beta, and delta wolves search around the alpha wolf, and omega wolves search around the top three wolves to boost the exploitation. A rank-based mutation strategy is implemented in DE algorithm to promote exploitation while maintaining the exploration capacity. We test HGWODE on CEC 2014 and UAV path planning. The proposed HGWODE is superior to GWO and several GWO variants when solving test functions and UAV path planning models. UAV path from HGWODE is smoother and shorter than its rivals. [ABSTRACT FROM AUTHOR]

Driver pathways have been acknowledged to play critical roles in the initiation and progression of cancers►hence it is essential for precision medicine related studies to develop accurate and efficient methods to identify them. Although previous approaches have shown promising results by integrating multi-omics data, their preset artificial parameters may decrease the convenience to use and limit the application scalability. In this paper, a novel integration approach is proposed to incorporate four omics data, i.e., construct a weighted non-binary mutation matrix without presetting artificial parameters. A parameter-free identification model is put forward based on it. It takes advantage of the association between genes in the PPI network as well as balances the contribution of coverage and mutual exclusivity with the harmonic mean. Furthermore, a cooperative co-evolution algorithm is proposed for solving this model. In the algorithm, a particle swarm optimization algorithm suitable for solving combinatorial problems is presented. Three cooperative operators are devised to construct the cooperation among the populations and the swarm to increase the population diversity. Both real biological datasets and simulated ones were exerted to perform experimental comparisons among the proposed method and six other state-of-the-art ones. The gene sets identified by the presented method generally contain more genes involved in known signaling pathways than those obtained by the other methods. Simultaneously, both high accuracy and high efficiency of the proposed method were verified in experiments, making it practical in realistic applications and an effective supplementary tool to identify driver pathways. • A non-binary mutation matrix is constructed without artificial adjustable parameters. • The model incorporates gene association and balances coverage and mutual exclusivity. • A PSO algorithm suitable for solving combinatorial problems is presented. • A co-operative co-evolution algorithm is put forward for solving the presented model. • The performance is compared among the proposed method and seven state of the art ones. [ABSTRACT FROM AUTHOR]

In imperialist competition algorithm (ICA), the assimilation is an important step, which is responsible for exploring potential better position or solution for an optimization problem. In this paper, an improved ICA equipped with an adaptive differential mutation (ADM) assimilation strategy was proposed inspired by differential evolution (DE). The proposed algorithm is called ICA-ADM. The ADM assimilation strategy generates new positions for colonies in an empire using the "DE/best/1" mutation operator and crossover operator with adaptively varied mutation and crossover rate. Since the "DE/best/1" mutation and crossover can produce high quality solutions, ICA-ADM possesses good exploration capability. Meanwhile, since the mutation and crossover rates are adaptively varied, ICA-ADM also preserves a good population diversity. Thus, the performance of ICA-ADM is greatly increased. Optimization results on 16 well-known benchmark functions and comparisons verify that the proposed ICA-ADM exceeds the initial ICA and its several variants. • A new assimilation method was proposed for imperialist competitive algorithm. • The method generates new position using "DE/best/1" mutation and crossover operator. • The method has better global searching capability. • The method can maintain a good population diversity. [ABSTRACT FROM AUTHOR]

• A hybrid DESGO algorithm is developed to solve mixed-integer optimization problems. • An inventory model for deteriorating items over finite time horizonis developed. • DESGO algorithm isapplied to find the best found solution of the proposed model. • Statistical tests are performed to test the significance of the DESGO algorithm. This work presents an inventory model with partial backlogged shortages for deteriorating items over finite time horizon. Here, the deterioration rate is considered as a random variable which follows three-parameter Weibull distribution. Also, the demand rate is dependent on time and selling price of the product. The aim of this work is to determine the optimal selling price of the product, optimal number of replenishment cycle and maximum shortage level which maximize the retailer's total profit over the finite time horizon. To maximize the total profit, a new hybrid algorithm is proposed which is based on differential evolution and social group optimization algorithms. This algorithm is named as DESGO algorithm. In this context, a numerical problem, based on the proposed inventory model, is considered and solved by DESGO algorithm. To test the performance and efficiency of the proposed algorithm, the problem is solved by some other popular metaheuristic algorithms available in the existing literature and the obtained numerical results are compared with that of the DESGO algorithm. To justify the comparison, two different non-parametric statistical tests and also ANOVA test are conducted. From these tests, it is observed that the proposed hybrid algorithm performs well. Moreover, the impact of changes of different model parameters on the best-found policy is studied graphically through the sensitivity analysis. Finally, the work is concluded with some fruitful future scopes. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) algorithm is popular to tackle real-world optimization problems. The standard DE, however, is not able to solve constrained optimization problems (COPs) for their complicated linear or nonlinear constraints. The transformation of constraints, which is realized via constraint handling technique, has a great impact on dealing with constrained algorithms. In this paper, a lightweight and efficient variant of DE named C ε -LDE is proposed to solve constrained single-objective optimization problems. This study firstly introduces a combined constraint handling method, which is designed based on the difference and relationship between two different ε constrained methods and balances infeasible solution and feasible solution with rules from the perspective of probability allocation. In addition, an extra control parameter is redefined in terms of different initial ε level in consideration of the complexity and diversity of COPs. On the other hand, DE evolves by opposition-based learning initialization and modifications on mutation operator and crossover rate selection, respectively. Mutation strategies frequently named rand/1 and best/1 are adopted and Lévy flight is added to the mutation strategy as a multiplier with scale factor F for a long jump. The crossover rate CR tends to be a larger or smaller stochastic value according to the pros and cons of the selected vector. A set of 28 problems under different dimension settings (D = 10, 30, 50 and 100) used for the CEC 2017 Competition is employed to evaluate the performance of the proposed C ε -LDE. The computational results demonstrate the effectiveness and superiority of the proposed combined ε constrained method. A comparative study of C ε -LDE with state-of-art algorithms is conducted on the obtained experimental results under the rules of CEC 2017 Competition. The ranking outcomes reveal that C ε -LDE is equipped with high competitiveness. Furthermore, the applications in several standard real-life engineering problems verify the effectiveness and practicability of the proposed scheme. [ABSTRACT FROM AUTHOR]

The initial population of an evolutionary algorithm is an important factor which affects the convergence rate and ultimately its ability to find high quality solutions or satisfactory solutions for that matter. If composed of good individuals it may bias the search towards promising regions of the search space right from the beginning. Although, if no knowledge about the problem at hand is available, the initial population is most often generated completely random, thus no such behavior can be expected. This paper proposes a method for initializing the population that attempts to identify i.e., to get close to promising parts of the search space and to generate (relatively) good solutions in their proximity. The method is based on clustering and a simple Cauchy mutation. The results obtained on a broad set of standard benchmark functions suggest that the proposed method succeeds in the aforementioned which is most noticeable as an increase in convergence rate compared to the usual initialization approach and a method from the literature. Also, insight into the usefulness of advanced initialization methods in higher-dimensional search spaces is provided, at least to some degree, by the results obtained on higher-dimensional problem instances—the proposed method is beneficial in such spaces as well. Moreover, results on several very high-dimensional problem instances suggest that the proposed method is able to provide a good starting position for the search. [ABSTRACT FROM AUTHOR]

Sine Cosine Algorithm (SCA), as a recently viral population-based meta-heuristic, which is in the extensive application for a variety of optimization cases. Regardless of the concerns on its novelty, SCA updates the population based on a simple updating rule with a basic structure and few parameters. However, it is considered that SCA remains the weakness of low diversity, slow convergence speed, stagnation in local optimum, and low accuracy of solutions. In that case, an attempt is made to design a new SCA version to overcome these shortcomings, namely FGSCA, combined with two strategies, including spiral motion and Gaussian mutation. Spiral motion is inspired by Moth-flame Optimization (MFO), which is employed to strengthen the capacity of exploitation based on the original SCA. The Gaussian mutation is adopted to increase the population's diversity generated by SCA and strengthen local exploration capability. The principle is to update the population generated by SCA, respectively, and then choose the best from these two new populations by greedy selection. Combining the two strategies effectively strengthens the original SCA's performance and maintains a proper exploitation and exploration balance. To examine the performance of FGSCA, it is used for making comparisons with eight well-known meta-heuristic algorithms (MAs), six reported SCA variants, and ten improved MAs on 23 well-known benchmark test problems and 30 standard IEEE CEC2014 benchmark test problems. Results indicate that the overall performance of FGSCA is superior to twenty-four comparative MAs on 53 benchmark test problems. Besides, FGSCA is employed to resolve three practical engineering problems. Results exhibit that FGSCA harvests the best results among twenty-four comparative MAs. Thus, FGSCA is expected to be a mighty and efficient tool for dealing with various complex optimization problems. [ABSTRACT FROM AUTHOR]

There are feasible and infeasible solutions in Constrained Multi-objective Optimization Problems (CMOPs). The feasible solutions with lower rank should be given more chances to generate offspring, while infeasible and worse solutions with higher rank should have fewer chances in these CMOPs. A constrained multi-objective Differential Evolution (DE) algorithm is developed by considering the selection pressure. The population is ranked based on the non-dominated crowd sort and constrained dominated principle. Then, a tournament operator is designed to extend the conventional mutation operator to boost the exploitation. The performances of the proposed algorithm are assessed on nineteen benchmark functions and industrial applications. Five representative algorithms are selected to make comparisons. The experiments have demonstrated that the algorithm can find well-distributed Pareto front, and the result of the performance indicator is superior. [ABSTRACT FROM AUTHOR]

• Optimal foraging algorithm with direction prediction & Gaussian oscillation is built. • New algorithm includes two update methods: prediction model and random model. • Prediction model mends exploitation ability by predicting the evolutionary direction. • Random model mends exploration by exploring the space with Gaussian distribution. • The superiority of algorithm is verified on benchmark set and engineering problems. Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G. [ABSTRACT FROM AUTHOR]

A Meta-evolutionary Selection of Constituents in Ensemble DE (MeSCEDE) framework is proposed in this paper to automate the design of high-level multi-population ensemble Differential Evolution (DE) algorithms. The automated design of high-level multi-population ensemble DE algorithms involves both automated selection of constituent DE algorithms for the ensemble and automated configuration of ensemble related parameters. Grammatical Evolution has been used as the meta-evolutionary algorithm in MeSCEDE to search the space of design choices so as to evolve effective ensemble design(s) for given problem(s). The simulation experiments carried out in this paper involve applying MeSCEDE to evolve ensemble DE designs for solving 30-dimensional CEC'17 benchmark functions. The effectiveness of the evolved designs are validated on 30 and 50-dimensional CEC'14 functions as well as on 22 real-world problem instances from CEC'11 benchmark suite. The MeSCEDE evolved designs have exhibited a competitive performance against state-of-the-art ensemble DE algorithms. In addition, the potential of MeSCEDE has been demonstrated against irace , a state-of-the-art algorithm configurator. All simulation experiments reiterate the potential of MeSCEDE towards evolving effective and robust ensemble DE designs. • Automated design of ensemble differential evolution (DE) algorithm is presented. • The proposed approach is Meta-evolutionary Selection of Constituents in Ensemble DE. • The approach uses grammatical evolution as the meta evolutionary algorithm. • The approach is demonstrated on CEC'17, CEC'14 and CEC'11 benchmark suites. • Relieves the practitioners from the difficult task of algorithm configuration. [ABSTRACT FROM AUTHOR]

• A flexible job shop scheduling problem with outsourcing and job priority is studied. • Resources that have different processing times to handle one operation are studied. • A sequence-based mathematical model which minimizes the overdue days is proposed. • A hybrid self-adaptive differential evolution algorithm (HSDE) is proposed. • Experiments are carried out to verify the effectiveness of the model and algorithm. Owing to the increasing complexity of products and the specialization of enterprises, production outsourcing has become a common practice in industrial manufacturing. Moreover, different jobs feature various priorities in actual production. The previous research that aims to minimize the makespan may not be applicable in real scenarios. Therefore, this study investigates a flexible job shop scheduling problem with outsourcing operations and job priority constraints. We propose a sequence-based mathematical model aiming at minimizing weighted overdue days, which considers the outsourcing constraints and different overdue weights of jobs with different priorities. An efficient hybrid self-adaptive differential evolution algorithm with heuristic strategies (HSDE) is proposed to address this problem. In HSDE, a well-designed chromosome encoding and decoding method is presented. To eliminate individuals that do not satisfy the outsourcing constraints, we add a penalty term to improve the objective function. By considering heuristic strategies for initial chromosome generation, the proposed approach is able to achieve a high-quality initial population. Crossover and mutation operators with self-adaptive control of the parameters are established to enlarge the search range and accelerate the convergence speed. Finally, several experiments are conducted to verify the effectiveness of the proposed model and algorithm. Experimental results confirm that the proposed algorithm outperforms other algorithms both in efficiency and accuracy. [ABSTRACT FROM AUTHOR]

The performance of optimization algorithms significantly depends on the landscape of the problems. It is known that there is no single algorithm that outperforms others on problems with different fitness landscapes. One of the issues in metaheuristic algorithms is keeping the balance between exploration and exploitation. The features extracted from analysis of fitness landscapes can be used to select the suitable algorithm for the given problem. However, these features are usually expensive and extracted prior to the optimization process which leads to a single algorithm to be selected. In this work, we propose an intelligent switch mechanism that enjoys an efficient non-convex ratio (ENCR) feature extracted online during the optimization to switch between two choices of algorithms, each favoring a type of landscape in terms of modality. For this work, two case studies including a pair of Harris hawks optimizer (HHO) and differential evolution (DE) and another pair of multiverse optimizer (MVO) and moth-flame optimizer (MFO) are selected among several algorithms to evaluate the performance of this framework. The proposed one-way and two-way switch algorithms take advantage of the merits of the two base algorithms to reach better final solutions and higher convergence rates in the majority of case studies. The overall comparison and ranking of the algorithms, including a random switch baseline, demonstrates the superiority of the intelligent switch mechanisms over the baselines. • A switching mechanism is introduced for online algorithm selection. • The mechanism makes use of features extracted from the landscape analysis. • The efficient non-convex ratio feature describes modality. • The intelligent switch outperforms baseline algorithms in overall ranking. • The one-way and two-way smart switch are better than random switch. [ABSTRACT FROM AUTHOR]

• The proposed method can be applied for any non-linear ECM without pre-assumptions. • Parameters identification of battery was transformed into a LSOP. • A new m -decomposition method allots R 0 , R P and C P overlapped to each group. Parameters identification of battery is a significant task for lithium-ion batteries. Some widely used techniques usually simplify the electrical circuit model (ECM) with non-linearity to a linear model or local linear model. However, by using such a methodology, the parameters in ECMs are not globally optimal, since the parameters may be not consistent at different linearized points. To address this issue, this paper proposed a cooperative co-evolution differential evolution (CCDE) algorithm to identify parameters of lithium-ion battery, without any linearization or pre-assumption. First, to describe the dynamic behaviors of battery, we presented a first-order RC equivalent circuit model ECM. Without making any approximation, improved Euler's numerical method was utilized to solve the differential equations directly. Second, an optimizing objective function was built to minimize errors between the true and optimized terminal voltages. In that optimization model, parameters of battery (R 0 , R P and C P) and v OCV (t) at each sampling point were considered as variables to be optimized, resulting in a very high-dimension problem. Third, such an optimization problem was transformed into a large scale optimization problem (LSOP). Based on the character of parameters identification, we proposed a new m -decomposition method which is different from general grouping methods for benchmark functions and its corresponding differential evolution (DE) algorithm to solve this LSOP. Comprehensive experimental results demonstrated effectiveness of the proposed framework and methodology, compared with seven state-of-the-art cooperative co-evolution methods. [ABSTRACT FROM AUTHOR]

• A novel modified algorithm denoted "modified ABC by DE" (mABC) is introduced. • The exploitation ability of ABC is enhanced by modifying the onlooker bee phase. • mABC is even validated by bencmarking with recent ABC variants. • The mean ranks of mABC are 1.4 and 2.3 for benchmark functions and CEC 2014. • mABC outperforms the other variants averagely for 38 of 50 benchmark functions. Artificial bee colony (ABC) and differential evolution (DE) are the most powerful and operative meta -heuristic algorithms inspired by the nature. Although both algorithms are successful, their successes vary from phase to phase, i.e. while ABC is better in the exploration ability, DE is well in the exploitation capability. Because the diversity of mutation and exponential crossover operators is prominently better than that of onlooker bee; in this study, the exploitation ability of ABC is enhanced by replacing the onlooker bee operator with those of mutation and the crossover phases of DE in order to increase the accuracy and speed up the convergence. We hereby introduce a novel modified algorithm denoted "modified ABC by DE" (mABC). The precision performance of mABC is verified through 20 classical benchmark functions and CEC 2014 test suit by a comprehensive comparison with recent ABC variants and hybrids for 30 and 50 dimensions. The results are interpreted using various statistical evaluations such as Wilcoxon, Friedman, and Nemenyi tests. Moreover, mABC is comparatively examined over convergence plots. In concise, the mean ranks of mABC are 1.4 and 2.3 for classical benchmark functions and CEC 2014, respectively. mABC outperforms the other variants averagely for 14 of 20 classical benchmark functions and 24 of 30 CEC 2014 functions. The results manifest that the proposed mABC is a robust and reliable algorithm as well as better than the existing ABC variants and hybrids with regard to high optimization performance like precision and convergence. [ABSTRACT FROM AUTHOR]

• Proposing an effective multi-trial vector approach (EMTV) armed by diversity maintaining. • Developing a diversity-maintained differential evolution algorithm (DMDE) using EMTV. • Introducing an archiving mechanism to keep solutions and enhance population diversity. • Introducing a mechanism to track individuals' behavior and enrich population diversity. • DMDE is competitive to solve non-decomposition large-scale and real-world problems. DE algorithms have outstanding performance in solving complex problems. However, they also have highlighted the need for an effective approach to alleviating the risk of premature convergence and loss of population diversity, particularly for non-decomposition large-scale global optimization (N-LSGO) problems. In this study, first, the multi-trial vector (MTV) approach is improved by adding a population diversity component, then, a diversity-maintained multi-trial differential evolution (DMDE) algorithm is proposed using the improved approach for N-LSGO problems. The DMDE algorithm produces solutions during six phases: initializing, subpopulation constructing, movement, evaluating and updating, archiving, and diversity maintaining. In initializing, the population is located in the search space and partitioned into three subpopulations using a success-rate based policy. Then, the subpopulations are independently evolved using the proposed meaningful search strategies to decrease the risk of stagnation. The DMDE algorithm introduces an archiving mechanism to maintain population diversity, which prevents premature convergence. Finally, the individuals' behavior is analyzed using the diversity maintaining phase, and those dimensions that have lost their diversity will be enriched. The effectiveness and scalability of the DMDE algorithm are evaluated using benchmark functions CEC 2018 with dimensions 30, 50, and 100 and CEC 2013 with dimension 1000 as LSGO problems. Moreover, the performance of the proposed algorithm was statistically analyzed using Wilcoxon signed-rank sum, ANOVA, and the Friedman tests. In addition, the applicability of the DMDE was assessed by solving seven well-known real-world problems including large-scale problems selected mostly from test-suite CEC 2020. In all experiments and tests, several well-known and N-LSGO algorithms have competed with DMDE through which the comparison results prove that the proposed DMDE algorithm is superior to competitor algorithms. [ABSTRACT FROM AUTHOR]

• The optimization problem is formulated for CAA to achieve the desired FOM. • Meta-heuristic algorithm is proposed to generate quick, low cost and robust solutions. • Performance of the algorithm is verified for the different hard controlled variables. • The 3Dradiation pattern results are also tested to validate the desired FOM. In many wireless applications, circular antenna arrays are commonly used but managing the lower side lobe with high directivity is still challenging. Many typical methods could be used to synthesize the array in real time but lag behind to retain high directivity and the low sidelobe level. This study formulates an optimization problem to obtain the desired main lobe direction, suppress the subsidiary lobe, and maximizes the directivity. A modified optimization algorithm is proposed called Integrated Harmony Search with Differential Evolution based Naked Mole Rat Algorithm (IHDN) to rapidly and reliably refine control parameters. Simulations are performed, and results are compared to other traditional algorithms. The findings show that the proposed algorithm results in excellent side lobe minimization with good directivity. The size analysis indicates that good directivity values with low sidelobe levels can be obtained for a smaller number of antenna elements. [ABSTRACT FROM AUTHOR]

Although the customer order scheduling problem to minimize the total completion time has received a lot of attention from researchers, the literature has not considered so far the case where there are sequence-dependent setups between jobs belonging to different orders, a case that may occurs in real-life scenarios. For this NP-hard problem we develop a novel efficient approximate solution procedure. More specifically, we develop an innovative discrete differential evolution algorithm where differential mutations are performed directly in the permutation space and that uses a novel, parameter-free, restart procedure. The so-obtained solutions are improved by two proposed local search mechanisms that employ problem-specific, heuristic dominance relations. We carry out an extensive computational experience with randomly generated test instances to compare our proposal with existing algorithms from related problems. In these experiments, the proposed algorithm obtains the best results in terms of their average relative percentage deviation and success rate. Furthermore, an analysis of variance test, followed by a Tukey's test, confirms the excellent performance of the algorithm proposed. • We address the COSP with sequence-dependent setup times. • We propose a mixed-integer linear programming model for the problem under study. • We develop a hybrid DDE metaheuristic with an innovative restart operator. • We propose two local search procedures based on heuristic dominance rules. [ABSTRACT FROM AUTHOR]

• A novel objective function is proposed for land reallocation and land redistribution. • ABC, DE and PSO are used for land reallocation and land redistribution (LR). • Two different novel Parcel-based Crossover Operators are proposed for LR. • An expert system is proposed to make the result directly available in the real world. • The algorithms by expert system outperform technician in terms of solution quality. Land readjustment and reallocation (LR) applications are complex and difficult real-world problems involving many different criteria. By considering these criteria, it is very difficult and takes a long time to be solved manually by an expert. Since the search space of these problems is very large, solution of these problems requires meta -heuristic optimization algorithms instead of classical methods in order to acquire more robust, acceptable and qualified solutions. Considering the meta -heuristic approaches, the algorithm needs an objective function that can make the right decision and evaluate the solutions most reasonably among the candidate solutions. Using the proposed objective function, the quality of the distribution and subdivision plans will be automatically evaluated and compared without the need for an expert. In this study, an objective function which considers all the criteria in the LR problems is proposed. In addition, unlike the available crossover operators used in meta -heuristic algorithms in the literature, two different parcel-based crossover operators called Classical (CPC) and Intelligent (IPC) Parcel-Based Crossover Operators are proposed. While CPC performs the distribution of the owners to the predetermined parcel randomly, IPC makes this operation with a greedy approach rather than randomly. According to this approach, if the shareholder and distance values after the crossover operation would be better than the existing ones, the crossover operation is performed. Otherwise, this operation is cancelled. By using the proposed objective function and crossover operators, artificial bee colony (ABC), particle swarm optimization (PSO) and differential evolution (DE) algorithms are run under equal conditions on a real project site, and the obtained results are compared with the official results obtained by a technician in the study. In addition, since there will be so many zoning blocks of different sizes and shapes on a real project site, it is very possible to have gaps or overflows in the blocks of subdivision plans obtained from the algorithms. Therefore, the gaps and overflow areas in the blocks can be completely eliminated by utilizing an Expert System developed specifically for LR problems called LRES, and as a result, the solutions obtained from the algorithms can be directly applicable in real life by the LRES. It's clearly seen from the experimental studies that all of the results obtained by using the algorithms based on LRES are much more effective than the official results obtained by a technician in terms of both solution quality and speed. In addition, among the evaluated algorithms, it is observed that the PSO algorithm presents much more effective and robust results than results of the other algorithms. Moreover, as a consequence of the algorithms using the IPC presents much more successful results than the results of the algorithms using CPC, it can be used as a very effective alternative crossover operator for land use problems. [ABSTRACT FROM AUTHOR]

• A general mathematical model for the SSCGR problem is established. • The IMCHFA is proposed to solve the mixed-discrete SSCGR problem. • Mixed-coded method, new position update, and combined mutation are used in IMCHFA. • Some mixed-discrete test problems are employed to verify the performance of IMCHFA. Reducers play a particularly important role in mechanical transmission field, and even a slight reduction in the material consumption would bring considerable economic and social benefits. With the goal of the minimum volume of consumables, a general mathematical model for the widely used single-stage cylindrical gear reducer (SSCGR), is established. When some real and discrete parameters are selected as the design variables, the SSCGR problem becomes a mixed-discrete SSCGR problem. To minimize the mixed-discrete SSCGR problem and make discrete design variables always satisfy discrete constraints, an improved mixed-coded hybrid firefly algorithm (IMCHFA) is proposed. The proposed approach uses new mixed-coded method to encode the position structure, and uses sorting group selection to select paired fireflies for position update, then uses combinatorial mutation to accelerate convergence of the algorithm. Meanwhile, the rounding technique is adopted to make the position structure meet the coding rules. 28 modified CEC 2017 mixed-discrete problems and two practical mixed-discrete engineering optimization problems are tested by the IMCHFA and other improved algorithms. The results show that the solution quality of IMCHFA is significantly better than other improved algorithms examined in this study. Finally, the proposed IMCHFA is applied to optimize the mixed-discrete SSCGR problem. Compared to the solution quality of other improved algorithms examined in this study, the proposed IMCHFA can obtain more efficient and economic solutions. [ABSTRACT FROM AUTHOR]

In this paper, a new compact algorithm is proposed. Two sinusoidal formulas are used to automatically adjust the crossover rate and the mutation scaling factor in the compact Differential Evolution (cDE) metaheuristic. The proposed algorithm, called Compound Sinusoidal cDE, CScDE, is compared to seven state-of-the-art compact algorithms on the well-known BBOB test-bed, the CEC-2014 test suite for continuous optimisation, as well as five real-world optimisation problems chosen from the CEC-2011 benchmarks. The CScDE algorithm outperformed its competitors for most problem categories and over most dimensions. It is also compared to some well-established population-based metaheuristics. • A compact compound sinusoidal differential evolution, CScDE, is proposed. • CScDE uses sinusoidal formulas to adjust the parameters of compact DE. • Both binomial and exponential crossover are tested. • CScDE is applied on 89 reference problems with several dimensions. • CScDE outperformed state-of-the-art compact algorithms. [ABSTRACT FROM AUTHOR]

[Display omitted] • A contribution to drug repurposing using deep learning and optimization is proposed. • A novel deep learning model is developed to predict Drug-Target binding affinities. • The proposed model integrates a Convolutional Neural Network on the top of a BiLSTM. • The Hyperparameters of the model are set using a Differential Evolution algorithm. • The Differential Evolution-based learning framework outperformed baseline methods. The identification of drug-target interactions (DTIs) is an important process in drug repositioning and drug discovery. However, it is very expensive and time-consuming to determine all possible DTIs with experimental approaches. Most existing machine learning-based methods formulate the DTIs prediction problem as a binary classification problem. Nevertheless, the lack of experimentally validated negative samples results in imbalanced class distribution within the datasets, which may have a negative influence on the DTI prediction performance. Casting DTI prediction task as a regression problem seems an interesting alternative to avoid this issue especially with the recent increase in protein structural data and DTI datasets. Within this context, a twofold contribution is described in this paper. First, we propose a novel deep learning model for predicting drug-target binding affinities called "Convolution Neural Network with Attention-based bidirectional Long Short-Term Memory network" (CNN-AbiLSTM), which combines a CNN with an attention-based biLSTM. Second, building a powerful hybrid CNN-AbiLSTM model can be highly complicated and requires a suitable setting of the model's hyperparameters. To handle this problem, we propose an evolutionary algorithm-based framework more specifically a Differential Evolution (DE) algorithm to find the optimal configuration of the proposed model. Experimental results show that the proposed DE-based CNN-AbiLSTM model achieves better performance compared with baseline methods. [ABSTRACT FROM AUTHOR]

Moth–Flame Optimization (MFO) algorithm is widely used to solve real parameter global optimization problems. However, the original MFO algorithm has some problems. First, the global search ability of the algorithm is insufficient due to the lack of high-quality flames or the lack of diversity of the population. Moreover, due to the reduction of the number of flames mechanism and the simple transverse orientation flight mode of moths, the algorithm is easy to fall into local optimum. To overcome these difficulties, a new MFO called ODSFMFO is proposed in this paper, which consists of an improved flame generation mechanism based on Opposition-Based Learning (OBL) and Differential Evolution (DE) algorithm, and an enhanced local search mechanism based on Shuffled Frog Leaping Algorithm (SFLA) and death mechanism. The ODSFMFO firstly obtains a high-quality population through opposition-based learning, then enhances the diversity of the population through differential evolution algorithm, to improve the global search ability of the algorithm, and then, employs an improved shuffled frog leaping algorithm as a local search algorithm, and uses the death mechanism to eliminate the individuals with low fitness value, which not only make the algorithm easy to jump out of the local optimum, but also further improve the convergence speed. To demonstrate the effectiveness of the proposed algorithm, the ODSFMFO and other fourteen well-known optimization algorithms are tested and compared on 28 benchmark tasks of CEC 2013 and 30 benchmark tasks of CEC 2017. Simulation results show that the proposed algorithm obtains better results compared with other competitive algorithms. • An improved flame generation mechanism of MFO is proposed. • A new updating mechanism of SFLA is proposed to improve the local search ability. • The SFLA and death mechanism are applied in combination to MFO. • ODSFMFO is better than 14 compared algorithms. [ABSTRACT FROM AUTHOR]

• The proportioned mean solution generator can avoid fast shrinkage of search space. • Two significant difference individuals are perturbed to provide more useful information. • Population diversity is increased. • A lifespan selection operator is used to enhance the ability to avoid local optimum. • Comparative results of engineering problems in welded beam design show the promise of our algorithms for real-world applications. Dynamic group optimization has recently appeared as a novel algorithm developed to mimic animal and human socialising behaviours. Although the algorithm strongly lends itself to exploration and exploitation, it has two main drawbacks. The first is that the greedy strategy, used in the dynamic group optimization algorithm, guarantees to evolve a generation of solutions without deteriorating than the previous generation but decreases population diversity and limit searching ability. The second is that most information for updating populations is obtained from companions within each group, which leads to premature convergence and deteriorated mutation operators. The dynamic group optimization with a mean–variance search framework is proposed to overcome these two drawbacks, an improved algorithm with a proportioned mean solution generator and a mean–variance Gaussian mutation. The new proportioned mean solution generator solutions do not only consider their group but also are affected by the current solution and global situation. The mean–variance Gaussian mutation takes advantage of information from all group heads, not solely concentrating on information from the best solution or one group. The experimental results on public benchmark test suites show that the proposed algorithm is effective and efficient. In addition, comparative results of engineering problems in welded beam design show the promise of our algorithms for real-world applications. [ABSTRACT FROM AUTHOR]

• A systematic literature review of meta-heuristics for truss optimization. • Application of a competitive algorithm for truss size optimization. • Behavior analysis of solution quality, diversity, and feasibility. • Release of a truss size optimization package (3 planar and 4 spacial structures). Truss optimization is an important class of engineering problems, with better solutions allowing for reduced material use and reduced construction costs. Due to its complexity, meta-heuristic algorithms are often applied to this problem, since these algorithms require no prior knowledge of the search space, being built upon stochastic rules. The present work has two main objectives: the elaboration of a systematic literature mapping on meta-heuristic algorithms applied to truss optimization, and the application of EB-A-SHADE, a self-adaptive algorithm based on Differential Evolution, to truss size optimization with continuous variables. The systematic mapping was made based on 179 articles published between 2010 and 2020 and analyzed the categories of truss optimization, the algorithms used, and parameter self-adaptation techniques. This mapping provided a snapshot of the current state of truss optimization research, showing that it is an active field, with an increasing number of publications each year, but that also includes gaps for potential future works. For the truss size optimization application, seven benchmark structures were used to evaluate the EB-A-SHADE algorithm, and the results obtained were compared to those of state-of-the-art algorithms with the use of statistical analysis. Convergence, constraints, and diversity plots were also employed to analyze the algorithm behavior on the problems studied, showing a stable convergence. The experiments showed that EB-A-SHADE achieved competitive results, having the statistical best results in most structures, and with the lowest standard deviation values. These results show that the algorithm can be applied to more complex approaches to the problem at hand. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes an optimization-based model for generic document summarization. The model generates a summary by extracting salient sentences from documents. This approach uses the sentence-to-document collection, the summary-to-document collection and the sentence-to-sentence relations to select salient sentences from given document collection and reduce redundancy in the summary. To solve the optimization problem has been created an improved differential evolution algorithm. The algorithm can adjust crossover rate adaptively according to the fitness of individuals. We implemented the proposed model on multi-document summarization task. Experiments have been performed on DUC2002 and DUC2004 data sets. The experimental results provide strong evidence that the proposed optimization-based approach is a viable method for document summarization. [Copyright &y& Elsevier]

Abstract: In the field of image analysis, segmentation is one of the most important preprocessing steps. One way to achieve segmentation is by mean of threshold selection, where each pixel that belongs to a determined class is labeled according to the selected threshold, giving as a result pixel groups that share visual characteristics in the image. Several methods have been proposed in order to solve threshold selection problems; in this work, it is used the method based on the mixture of Gaussian functions to approximate the 1D histogram of a gray level image and whose parameters are calculated using three nature inspired algorithms (Particle Swarm Optimization, Artificial Bee Colony Optimization and Differential Evolution). Each Gaussian function approximates the histogram, representing a pixel class and therefore a threshold point. Experimental results are shown, comparing in quantitative and qualitative fashion as well as the main advantages and drawbacks of each algorithm, applied to multi-threshold problem. [Copyright &y& Elsevier]

Abstract: Many problems occurring in engineering can be formulated as min–max optimization problems, for instance, in game theory, robust optimal control and many others. Min–max problems are considered difficult to solve, specially constrained min–max optimization problems. Approaches using co-evolutionary algorithms have successfully been used to solve min–max optimization problems without constraints. We propose a novel differential evolution approach consisting of three populations with a scheme of copying individuals for solving constrained min–max problems. Promising results have been obtained showing the suitability of the approach. [Copyright &y& Elsevier]

Abstract: The sale of electric energy generated by photovoltaic (PV) plants has attracted much attention in recent years. The installation of PV plants aims to obtain the maximum benefit of captured solar energy. The current methodologies for planning the design of the different components of a PV plant are not completely efficient. This paper addresses the optimization of the design of PV plants with solar tracking, which consists of the optimization of the variables that make up the PV plant to obtain the minimum electric (Joule) losses possible. These variables are the size and distribution of solar modules in the solar tracker, the distribution of the solar trackers in the field and the choice of inverter. Evolutionary algorithms (EAs) are adaptive methods based on natural evolution that may be used for searching and optimization. Four different EAs have been used for optimizing the design of PV plants: steady-state genetic algorithm, generational genetic algorithm, CHC algorithm and DE algorithm. In order to test the performance of these algorithms we have used different proposed fields to mount PV plants. The results obtained show that EAs, and specifically DE with rand mutation schemes, are promising techniques to optimize design of PV plants. Furthermore, the results are contrasted with nonparametric statistical tests to support our conclusions. [Copyright &y& Elsevier]

Abstract: A multiobjective optimisation engineering design (MOED) methodology for PI controller tuning in multivariable processes is presented. The MOED procedure is a natural approach for facing multiobjective problems where several requirements and specifications need to be fulfilled. An algorithm based on the differential evolution technique and spherical pruning is used for this purpose. To evaluate the methodology, a multivariable control benchmark is used. The obtained results validate the MOED procedure as a practical and useful technique for parametric controller tuning in multivariable processes. [Copyright &y& Elsevier]

Abstract: This paper proposes a differential evolution algorithm based on ε-domination and orthogonal design method (ε-ODEMO) to solve power dispatch problem considering environment protection and saving energy. Besides the operation costs of thermal power plant, contaminative gas emission is also optimized as an objective. In the proposed algorithm, ε-dominance is adopted to make genetic algorithm obtain a good distribution of Pareto-optimal solutions in a small computational time, and the orthogonal design method can generate an initial population of points that are scattered uniformly over the feasible solution space, these modify the differential evolution algorithm (DE) to make it suit for multi-objective optimization (MOO) problems and improve its performance. A test hydrothermal system is used to verify the feasibility and effectiveness of the proposed method. Compared with other methods, the results obtained demonstrate the effectiveness of the proposed algorithm for solving the power environmentally-friendly dispatch problem. [Copyright &y& Elsevier]