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Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The e-constrained method is a very effective one. In the literature, the e value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive e control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of e through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive e-constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive e control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method.

Some recent research reports that a dendritic neuron model (DNM) can achieve better performance than traditional artificial neuron networks (ANNs) on classification, prediction, and other problems when its parameters are well-tuned by a learning algorithm. However, the back-propagation algorithm (BP), as a mostly used learning algorithm, intrinsically suffers from defects of slow convergence and easily dropping into local minima. Therefore, more and more research adopts non-BP learning algorithms to train ANNs. In this paper, a dynamic scale-free network-based differential evolution (DSNDE) is developed by considering the demands of convergent speed and the ability to jump out of local minima. The performance of a DSNDE trained DNM is tested on 14 benchmark datasets and a photovoltaic power forecasting problem. Nine meta-heuristic algorithms are applied into comparison, including the champion of the 2017 IEEE Congress on Evolutionary Computation (CEC2017) benchmark competition effective butterfly optimizer with covariance matrix adapted retreat phase (EBOwithCMAR). The experimental results reveal that DSNDE achieves better performance than its peers.

Presents information on the 2021 IEEE Congress on Evolutionary Computation (IEEE CEC 2021).

In the last decade, many evolutionary computation (EC) algorithms with diversity enhancement have been proposed to solve large-scale optimization problems in big data era. Among them, the social learning particle swarm optimization (SLPSO) has shown good performance. However, as SLPSO uses different guidance information for different particles to maintain the diversity, it often results in slow convergence speed. Therefore, this article proposes a new region encoding scheme (RES) to extend the solution representation from a single point to a region, which can help EC algorithms evolve faster. The RES is generic for EC algorithms and is applied to SLPSO. Based on RES, a novel adaptive region search (ARS) is designed to on the one hand keep the diversity of SLPSO and on the other hand accelerate the convergence speed, forming the SLPSO with ARS (SLPSO-ARS). In SLPSO-ARS, each particle is encoded as a region so that some of the best (e.g., the top ${P}$ ) particles can carry out region search to search for better solutions near their current positions. The ARS strategy offers the particle a greater chance to discover the nearby optimal solutions and helps to accelerate the convergence speed of the whole population. Moreover, the region radius is adaptively controlled based on the search information. Comprehensive experiments on all the problems in both IEEE Congress on Evolutionary Computation 2010 (CEC 2010) and 2013 (CEC 2013) competitions are conducted to validate the effectiveness and efficiency of SLPSO-ARS and to investigate its important parameters and components. The experimental results show that SLPSO-ARS can achieve generally better performance than the compared algorithms.

Brain storm optimization (BSO) is an emerging global optimization algorithm. The primary idea is to divide the population into different clusters, and offspring are generated within a cluster or between two clusters. However, the problems of inefficient clustering strategy and insufficient exploration exist in BSO. In this paper, a novel and efficient BSO is proposed, called BSO20 (proposed in 2020). BSO20 pays attention to both the clustering strategy and the mutation strategy. First, we propose a hybrid clustering strategy, which combines two clustering strategies, i.e., nearest-better clustering and random grouping strategy. The size of the subpopulation clustered by two strategies is dynamically adjusted as the population evolves. Second, a modified mutation strategy is used in BSO20 to share information within a cluster or among multiple clusters to enhance the ability of exploration. BSO20 is tested on the problems of the 2017 IEEE Congress on Evolutionary Computation competition on real parameter numerical optimization. BSO20 is compared with several variants of BSO and two variants of particle swarm optimization, and the experimental results show that BSO20 is competitive.

Grey Wolf Optimizer represents a relatively new metaheuristic scheme for solving continuous optimization problems. In spite of its interesting characteristics, it presents several flaws such as lack of accuracy, low diversity, premature convergence and imbalance between exploitation and exploration. In this paper, a modified version of the Grey Wolf Optimizer called Group-based Synchronous-Asynchronous Grey Wolf Optimizer is introduced. The proposed scheme incorporates a synchronous-asynchronous processing scheme, a set of different nonlinear functions and an operation to increase diversity. With such mechanisms, the proposed algorithm presents a better balance between exploration and exploitation, an increment in the accuracy and the ability to avoid the convergence in local minima. Such capacities allow its use in complex engineering problems that involve highly multimodal objective functions with a difficult localization of their global optimum. To evaluate the performance of the proposed approach, it has been tested on a representative number of functions of the well-known IEEE Congress on Evolutionary Computation 2017 benchmark set of functions and real-world engineering problems. The results of our method have been compared against those produced by other states of the art metaheuristic algorithms. The results prove the effectiveness and accuracy of the proposed technique.

In this paper, a cooperative bat searching algorithm (CBA) is proposed by using a communication topology to share information among all the bats in bat algorithm (BA). Inspired by the cooperation mechanism in the distributed control theory, a cooperative term is added to the original BA to accelerate the searching process. The convergence issue is rigorously studied for CBA by using the Jury’s test. Moreover, numerical evaluation is conducted to compare CBA with other variants of BA by solving fifteen benchmark functions from IEEE congress on evolutionary computation. The results are provided to demonstrate the effectiveness of the proposed CBA. As an application, CBA and binary CBA are equipped as the real-time optimizers in a networked model predictive control strategy to solve a balanced coordination problem. The proposed CBA showed competitive performance.

For real parameter single objective optimization, Differential Evolution (DE) performs better than other types of population-based metaheuristic. Nevertheless, in the field of DE, it is impossible for a given combination of operators to perform well in all fitness landscapes. Practice has proved that assembling more than one combinations of operators may lead to improvement in solution. However, some DE algorithms with good performance, e.g., one of the best performers in competitions of real parameter single objective optimization among population-based metaheuristics held by the series of IEEE Congress on Evolutionary Computation - L-SHADE-EpSin, are still not involved in ensemble. Furthermore, ensemble based on similar DE algorithms is rarely reported. Based on such a background, we propose L-SHADE-E, ensemble of L-SHADE-EpSin and L-SHADE-RSP in this paper. The two constituent algorithms are both variants of L-SHADE and belong to similar DE algorithms. In our algorithm, L-SHADE-EpSin or L-SHADE-RSP is selected randomly to run at the beginning. If progress on fitness is low for generations, the other constituent algorithm takes over population immediately. Our experiments are based on the CEC 2014 and CEC 2017 benchmark test suites. Altogether, our algorithm is compared with nine DE algorithms and three population-based metaheuristics other than DE. Experimental results show that our algorithm is very competitive.

Large-scale optimization has become a significant and challenging research topic in the evolutionary computation (EC) community. Although many improved EC algorithms have been proposed for large-scale optimization, the slow convergence in the huge search space and the trap into local optima among massive suboptima are still the challenges. Targeted to these two issues, this article proposes an adaptive granularity learning distributed particle swarm optimization (AGLDPSO) with the help of machine-learning techniques, including clustering analysis based on locality-sensitive hashing (LSH) and adaptive granularity control based on logistic regression (LR). In AGLDPSO, a master-slave multisubpopulation distributed model is adopted, where the entire population is divided into multiple subpopulations, and these subpopulations are co-evolved. Compared with other large-scale optimization algorithms with single population evolution or centralized mechanism, the multisubpopulation distributed co-evolution mechanism will fully exchange the evolutionary information among different subpopulations to further enhance the population diversity. Furthermore, we propose an adaptive granularity learning strategy (AGLS) based on LSH and LR. The AGLS is helpful to determine an appropriate subpopulation size to control the learning granularity of the distributed subpopulations in different evolutionary states to balance the exploration ability for escaping from massive suboptima and the exploitation ability for converging in the huge search space. The experimental results show that AGLDPSO performs better than or at least comparable with some other state-of-the-art large-scale optimization algorithms, even the winner of the competition on large-scale optimization, on all the 35 benchmark functions from both IEEE Congress on Evolutionary Computation (IEEE CEC2010) and IEEE CEC2013 large-scale optimization test suites.

In the last two decades, the field of global optimization has become very active, and, in this regard, many deterministic and stochastic algorithms were developed for solving various optimization problems. Among them, swarm intelligence (SI) is a stochastic algorithm that is more flexible and robust and has had the ability to find an optimum solution for high-dimensional optimization and search problems. SI-based algorithms are mainly inspired by the social behavior of fish schooling or bird flocking. Among the SI-based algorithms, Bat algorithm (BA) is one of the recently developed evolutionary algorithms. It employs an echolocation behavior of microbats by varying pulse rates of emission and loudness to perform their search process. In this paper, a modified Bat algorithm (MBA) is developed. The main focus of the MBA is to further enhance the exploration and exploitation search abilities of the original Bat algorithm. The performance of the modified Bat algorithm (MBA) is examined over the benchmark functions designed for evolutionary algorithms competition in the special session of 2005 IEEE Congress on Evolutionary Computation. The used benchmark functions include the unimodal, multimodal, and hybrid benchmark functions with high dimensionality. Furthermore, the impact analysis with respect to different values of temperatures is conducted by executing the proposed algorithm twenty-five times independently by using each benchmark function with different random seeds.

This article suggests a multimodal multiobjective evolutionary algorithm with dual clustering in decision and objective spaces. One clustering is run in decision space to gather nearby solutions, which will classify solutions into multiple local clusters. Nondominated solutions within each local cluster are first selected to maintain local Pareto sets, and the remaining ones with good convergence in objective space are also selected, which will form a temporary population with more than ${N}$ solutions ( ${N}$ is the population size). After that, a second clustering is run in objective space for this temporary population to get ${N}$ final clusters with good diversity in objective space. Finally, a pruning process is repeatedly run on the above clusters until each cluster has only one solution, which removes the most crowded solution in decision space from the most crowded cluster in objective space each time. This way, the clustering in decision space can distinguish all Pareto sets and avoid the loss of local Pareto sets, while that in objective space can maintain diversity in objective space. When solving all the benchmark problems from the competition of multimodal multiobjective optimization in the IEEE Congress on Evolutionary Computation 2019, the experiments validate our advantages to maintain diversity in both objective and decision spaces.

In this paper, we optimized PSO by quantum behavior and optimized KH by simulated annealing, so a new hybrid algorithm, named Annealing Krill Quantum Particle Swarm Optimization Algorithm (AKQPSO), is proposed, and it is based on annealing krill herd algorithm (AKH) and quantum particle swarm optimization algorithm (QPSO). QPSO has better performance in exploitation and AKH has better performance in exploration, so AKQPSO proposed on this basis increases the diversity of population individuals, and shows better performance in both exploitation and exploration. In addition, the quantum behavior increased the diversity of the population, and the simulated annealing strategy made the algorithm avoid falling into the local optimal value, which made the algorithm obtain better performance. The test set used in this paper is a classic 100-Digit Challenge problem, which is proposed at 2019 IEEE Congress on Evolutionary Computation (CEC 2019), and AKQPSO has achieved better performance on the benchmark problems.

As a meta-heuristic algorithm that simulates the intelligence of gray wolves, grey wolf optimizer (GWO) has a wide range of applications in practical problems. As a kind of local search, chaotic local search (CLS) has a strong ability to get rid of the local optimum due to its integration of chaotic maps. To enhance GWO, CLS is always incorporated into GWO to increase its population diversity and accelerate algorithm’s convergence. However, it is still unclear that how may chaotic maps should be used in CLS and how to embed them into GWO. To address these challenging issues, this paper studies both single and multiple chaotic maps incorporated GWOs. Extensive comparative experiments are conducted based on IEEE Congress on Evolutionary Computation (CEC) benchmark test suit. The results show that CLS incorporated GWOs generally perform better than the original GWO, suggesting the effectiveness of such hybridization. Moreover, a remarkable finding of this work is that the piecewise linear chaotic map (PWLCM) and Gaussian map have the most potential to improve the search performance of GWO. Additionally, CLS incorporated GWOs also perform significantly better than some other state-of-the-art meta-heuristic algorithms. This study not only gives more insights into the mechanism of how CLS makes influence on GWO, but also finds that the most suitable choice of chaotic map for it.

Rate of penetration (ROP) optimization is crucial for drilling processes due to its vital role in increasing efficiency. This article proposes a new hybrid bat algorithm (HBA) to achieve the maximum ROP accurately. A data-driven ROP model is established by combining the wavelet filtering and optimized support vector regression according to the drilling characteristics. After that, five modifications, namely, iterative local search, stochastic inertia weight, pulse rate and loudness improvement, directional echolocation, and modified local random walk are combined to further improve the global optimization performance of the bat algorithm. Extensive experiment results on the IEEE Congress on Evolutionary Computation 2005 standard benchmark problems show that the proposed algorithm has successful outcomes compared with ten conventional algorithms. Additionally, in the application of the HBA to a real-world drilling process in Shennongjia area, Central China, the ROP has been improved by 34.84%, which is the largest compared with the conventional popular ROP optimization methods.

Latency and reliability are essential parameters for enabling ultra-reliable low-latency communication (URLLC). Therefore, an approach for node identification that satisfies the requirements of latency and reliability for URLLC based on the formation of swarms by dragonflies, called dragonfly node identification algorithm (DNIA), is proposed. This method maps bio-natural systems and legacy communication into metrics of URLLC, i.e., latency and reliability, for node identification. A performance analysis demonstrates that the new paradigm for mapping the metrics, i.e., latency and reliability, in terms of nodes (food source) and noise (predators) provides another dimension for URLLC. A comparative analysis proves that DNIA demonstrates significant impact on the improvement of latency, reliability, packet loss rate, as well as throughput. The robustness and efficiency of the proposed DNIA are evaluated using statistical analysis, convergence rate analysis, Wilcoxon test, Friedman rank test, and analysis of variance on classical as well as modern IEEE Congress on Evolutionary Computation 2014 benchmark functions. Moreover, simulation results show that DNIA outperforms other bioinspired optimization algorithms in terms of cumulative distributive function and average node identification errors. The conflicting objectives in the tradeoff between low latency and high reliability in URLLC are discussed on a Pareto front, which shows the improved and accurate approximation for DNIA on a true Pareto front. Further, DNIA is benchmarked against standard functions on the Pareto front, providing significantly superior results in terms of coverage as well as convergence.

In the evolutionary computing community, differential evolution (DE) is well appreciated as a simple yet versatile population-based, non-convex optimizer designed for continuous optimization problems. A simple two-phase DE algorithm is presented in this article, which aims to identify promising basins of attraction on a non-convex functional landscape in the first phase, and starting from those previously identified search regions, a success history-based switch parameter DE is employed to further fine tune the search process leading to the optima of the landscape. Our proposed framework has been validated on the well-known IEEE Congress on Evolutionary Computation (CEC) benchmark suites (CEC 2013, 2014 and 2017). Results of the proposed method are compared with corresponding CEC winners (SHADE for CEC 2013, L-SHADE for CEC 2014 and jSO for CEC 2017).

Differential evolution (de) is a popular population-based meta-heuristic that has been successfully used in complex optimization problems. Premature convergence is one of the most important drawbacks that affects its performance. In this paper, a novel replacement strategy that combines the use of an elite population and a mechanism to preserve diversity explicitly is devised. The proposal is integrated with de to generate the de with enhanced diversity maintenance. The main novelty is the use of a dynamic balance between exploration and exploitation to adapt the optimizer to the requirements of the different optimization stages. Experimental validation is carried out with several benchmark tests proposed in competitions of the well-known IEEE Congress on Evolutionary Computation. Top-rank algorithms of each competition, as well as other diversity-based schemes, are used to illustrate the usefulness of the proposal. The new method avoids premature convergence and significantly improves further the results obtained by state-of-the-art algorithms.

The bare bones particle swarm optimization (BBPSO) algorithm has been proved to be an effective tool for single-objective optimization problems over continuous search spaces. In this paper, a fission-fusion hybrid bare bones particle swarm optimizer (FHBBPSO) is proposed. The FHBBPSO combines a fission strategy and a fusion strategy to sample new positions of the particles. The fission strategy aims at splitting the search space. Particles are assigned to different local groups to sample the corresponding regions. On the other side, the fusion strategy aims at narrowing the search space. Marginal groups will be gradually merged by the central groups until there is only one group left. The two strategies work together for the theoretical optimal value. To confirm the searching ability of the FHBBPSO, the proposed method runs over the IEEE Congress on Evolutionary Computation 2014 (CEC2014) benchmark functions. Also, several famous evolutionary methods are used in the control group. The experimental results and analysis suggest that the FHBBPSO is a highly competitive optimization algorithm for single-objective functions.

Birogul, Serdar/0000-0003-4966-5970 WOS: 000510021700004 Harri's Hawk Optimization (HHO) algorithm manifests as a new meta-heuristic algorithm in literature. When we look at studies that have used with this algorithm, we can see that its results in test functions and in the solutions of some test functions in IEEE Congress on Evolutionary Computation (CEC) are much better compared to other heuristic and meta heuristic algorithm results. In this study, an algorithm has been developed which has been hybridized with the mutation operators of Differential Evolution (DE) to further improve the HHO algorithm. This algorithm is named as Hybrid Harris Hawk Optimization based on Differential Evolution (HHODE). Performance of the proposed HHODE algorithm has been first compared with HHO and then compared with the results of other algorithms which have been most commonly used in the literature. In this comparison process, the most commonly used test functions in the literature and some of the other test functions in CEC2005 and CEC2017 as a new application field, have been solved. When the results of the comparison of HHODE with other algorithms are analyzed, it is observed that the balance between the exploratory tendency and exploitative tendency of the algorithm is well consistent. Formula 1 ranking method is used in the order of HHODE according to HHO and other algorithms. When a general evaluation of HHODE was performed, it was found to be an even more powerful algorithm as a result of the combination of strong features of both HHO and DE. The optimal power flow (OPF) problem is one of the most important problems of the modern power system. The HHODE algorithm is proposed to solve the OPF problem, which is considered without valve-point effect and prohibited zones (1) and with prohibited zones (2) in this paper. The effectiveness of the HHODE hybrid algorithm is tested on modified IEEE 30-bus test system. The result of HHODE algorithms are compared with other optimization algorithms in the literature.

Simulated Kalman filter (SKF) is a new population-based optimization algorithm inspired by estimation capability of Kalman filter. Each agent in SKF is regarded as a Kalman filter. Based on the mechanism of Kalman filtering, the SKF includes prediction, measurement, and estimation process to search for global optimum. The SKF has been shown to yield good performance in solving benchmark optimization problems. However, the exploration capability of SKF could be further improved. From literature, current optimum opposition-based learning (COOBL) has been employed to increase the diversity (exploration) of search algorithm by allowing current population to be compared with an opposite population. By employing this concept, more potential agents are generated to explore more promising regions that exist in the solution domain. Therefore, this paper intends to improve the exploration capability of SKF through the application of COOBL. The COOBL is employed after the estimation process of SKF. Experimental results over the IEEE congress on evolutionary computation (CEC) 2014 benchmark functions indicate that current optimum opposition-based simulated Kalman filter (COOBSKF) improved the exploration capability of SKF significantly. The COOBSKF also has been compared with five other optimization algorithms and outperforms them all.

Bound-constrained optimization has wide applications in science and engineering. In the last two decades, various evolutionary algorithms (EAs) were developed under the umbrella of evolutionary computation for solving various bound-constrained benchmark functions and various real-world problems. In general, the developed evolutionary algorithms (EAs) belong to nature-inspired algorithms (NIAs) and swarm intelligence (SI) paradigms. Differential evolutionary algorithm is one of the most popular and well-known EAs and has secured top ranks in most of the EA competitions in the special session of the IEEE Congress on Evolutionary Computation. In this paper, a customized differential evolutionary algorithm is suggested and applied on twenty-nine large-scale bound-constrained benchmark functions. The suggested C-DE algorithm has obtained promising numerical results in its 51 independent runs of simulations. Most of the 2013 IEEE-CEC benchmark functions are tackled efficiently in terms of proximity and diversity.

The main goal of this paper is to study the performance of two metaheuristics, that are classified as belonging to Swarm Intelligence, when dealing with complex optimization problems. In this case, the Algorithms are the Grey Wolf Optimizer (GWO) algorithm and Firefly Algorithm (FA). In this case study, we are presenting in this paper the Mathematical Benchmark Functions that were given in the IEEE Congress on Evolutionary Computation 2015 (CEC’ 15) competition, in order to compare these popular algorithms.

Metaheuristic optimization algorithms are a relatively new class of optimization algorithms that are widely used for difficult optimization problems in which classic methods cannot be applied and are considered as known and very broad methods for crucial optimization problems. In this study, a new metaheuristic optimization algorithm is presented, the main idea of which is inspired by models in kinematics. This algorithm obtains better results compared to other optimization algorithms in this field and is able to explore new paths in its search for desirable points. Hence, after introducing the projectiles optimization (PRO) algorithm, in the first experiment, it is evaluated by the determined test functions of the IEEE congress on evolutionary computation (CEC) and compared with the known and powerful algorithms of this field. In the second try out, the performance of the PRO algorithm is measured in two practical applications, one for the training of the multi-layer perceptron (MLP) neural networks and the other for pattern recognition by Gaussian mixture modeling (GMM). The results of these comparisons are presented in various tables and figures. Based on the presented results, the accuracy and performance of the PRO algorithm are much higher than other existing methods.

The particle swarm optimization algorithm (PSO) is not good at dealing with discrete optimization problems, and for the krill herd algorithm (KH), the ability of local search is relatively poor. In this paper, we optimized PSO by quantum behavior and optimized KH by simulated annealing, so a new hybrid algorithm, named the annealing krill quantum particle swarm optimization (AKQPSO) algorithm, is proposed, and is based on the annealing krill herd algorithm (AKH) and quantum particle swarm optimization algorithm (QPSO). QPSO has better performance in exploitation and AKH has better performance in exploration, so AKQPSO proposed on this basis increases the diversity of population individuals, and shows better performance in both exploitation and exploration. In addition, the quantum behavior increased the diversity of the population, and the simulated annealing strategy made the algorithm avoid falling into the local optimal value, which made the algorithm obtain better performance. The test set used in this paper is a classic 100-Digit Challenge problem, which was proposed at 2019 IEEE Congress on Evolutionary Computation (CEC 2019), and AKQPSO has achieved better performance on benchmark problems.

By performing data analysis, statistical approaches are highly welcome to explore the data. Nowadays with the increases in computational power and the availability of big data in different domains, it is not enough to perform exploratory data analysis (descriptive statistics) to obtain some prior insights from the data, but it is a requirement to apply higher-level statistics that also require much greater knowledge from the user to properly apply them. One research area where proper usage of statistics is important is multi-objective optimization, where the performance of a newly developed algorithm should be compared with the performances of state-of-the-art algorithms. In multi-objective optimization, we are dealing with two or more usually conflicting objectives, which result in high dimensional data that needs to be analyzed. In this paper, we present a web-service-based e-Learning tool called DSCTool that can be used for performing a proper statistical analysis for multi-objective optimization. The tool does not require any special statistics knowledge from the user. Its usage and the influence of a proper statistical analysis is shown using data taken from a benchmarking study performed at the 2018 IEEE CEC (The IEEE Congress on Evolutionary Computation) is appropriate. Competition on Evolutionary Many-Objective Optimization.

A key aspect of the design of evolutionary and swarm intelligence algorithms is studying their performance. Statistical comparisons are also a crucial part which allows for reliable conclusions to be drawn. In the present paper we gather and examine the approaches taken from different perspectives to summarise the assumptions made by these statistical tests, the conclusions reached and the steps followed to perform them correctly. In this paper, we conduct a survey on the current trends of the proposals of statistical analyses for the comparison of algorithms of computational intelligence and include a description of the statistical background of these tests. We illustrate the use of the most common tests in the context of the Competition on single-objective real parameter optimisation of the IEEE Congress on Evolutionary Computation (CEC) 2017 and describe the main advantages and drawbacks of the use of each kind of test and put forward some recommendations concerning their use., Spanish Ministry of Economy, Industry and Competitiveness, Spanish Ministry of Science

Although evolutionary algorithms (EAs) have been widely applied in static optimization problems (SOPs), it is still a great challenge for EAs to solve dynamic optimization problems (DOPs). This paper proposes a Cloudde-based differential evolution (CDDE) algorithm based on Message Passing Interface (MPI) technology to solve DOPs. During the evolutionary process, different populations are sent to different slave processes to perform mutation and crossover operations independently using different evolution strategies and then return to the master process to apply migration operation under an adaptive probability. Experimental studies were taken on several DOPs generated by the Generalized Dynamic Benchmark Generator (GDBG) which was used in 2009 IEEE Congress on Evolutionary Computation (CEC2009). The simulation result indicates that the proposed algorithm achieves promising performance in a statistical efficient manner.

In adaptive DE, the parameter p is used to balance the algorithm exploration and exploitation ability. Selection of suitable p in the evolution process is an ongoing challenge for adaptive DE. Population diversity is an effective measure showing the distribution of individuals in the search space. In this paper, use of diversity as a search strategy selection criterion for calculating p in adaptive DE is proposed. The proposed algorithm normalizes the calculated diversity to [0, 1] and calculates p according to the normalized diversity using an exponential function. Higher diversity yields higher p, providing the proposal with higher exploration ability, and vice versa. The accuracy of the proposed algorithm was experimentally compared to those of five other advanced DE variants using benchmark functions from IEEE Congress on Evolutionary Computation 2017. The results show that the proposed algorithm achieved the best performance among all variants for most benchmark functions.

In adaptive DE algorithms, the parameter p is used to strike a balance between the algorithm’s exploration and exploitation abilities. In this paper, an effective method for generating a suitable p value is proposed. The probability distribution function (PDF) of p is viewed as a linear function. At the start of the evolutionary process, the PDF of p is a linearly increasing function. Hence, there is a high probability of p having a high value. With successive generations, the PDF of p changes to a linearly decreasing function, and there is a high probability of p having a smaller value. Furthermore, a method for allowing a variable archive size is also proposed. After each generation, the archive size for the next generation is computed. If the archive size has to be reduced, the worst-ranking individuals are deleted from the archive. The accuracy of the proposed method is computationally compared with those of eight other advanced DE variants using benchmark functions from the IEEE Congress on Evolutionary Computation 2017. The results show that the proposed algorithm achieves the best performance among all the variants for most of the benchmark functions in the case of 30-dimensional problems.

Grey wolf optimizer algorithm was recently presented as a new heuristic search algorithm with satisfactory results in real-valued and binary encoded optimization problems that are categorized in swarm intelligence optimization techniques. This algorithm is more effective than some conventional population-based algorithms, such as particle swarm optimization, differential evolution and gravitational search algorithm. Some grey wolf optimizer variants were developed by researchers to improve the performance of the basic grey wolf optimizer algorithm. Inspired by particle swarm optimization algorithm, this study investigates the performance of a new algorithm called Inspired grey wolf optimizer which extends the original grey wolf optimizer by adding two features, namely, a nonlinear adjustment strategy of the control parameter, and a modified position-updating equation based on the personal historical best position and the global best position. Experiments are performed on four classical high-dimensional benchmark functions, four test functions proposed in the IEEE Congress on Evolutionary Computation 2005 special session, three well-known engineering design problems, and one real-world problem. The results show that the proposed algorithm can find more accurate solutions and has higher convergence rate and less number of fitness function evaluations than the other compared techniques.

The recently introduced Marine Predators Algorithm (MPA) exhibits competitive performance in solving optimization problems. However, it often prematurely converges due to an imbalance between its exploration and exploitation capabilities. Therefore, in this paper, an improved MPA variant using a proposed Local Escaping Operator (LEO) is introduced. In the MPA, solution candidates are replaced by better candidates from the previous iteration, mimicking a memory of already visited prey-abundant areas. This indicates a weak inter-dependence between the candidates in the population and possible acceptance of new solution candidates created outside the algorithm without damaging the optimization process. Consequently, in the proposed approach, the worst candidates are replaced with solutions created by the LEO. The LEO is based on representative solutions, taking into account the relationship between predators and the characteristics of their population. The approach is experimentally compared with the state-of-the-art meta-heuristics on 82 test functions, including IEEE Congress on Evolutionary Computation test suites (CEC’14 and CEC’17) and three engineering problems. The results show the superiority of the LEO-MPA over the MPA and recent algorithms. Furthermore, in this paper, the suitability of the hybridization of meta-heuristics with the LEO is discussed and successful attempts with the best algorithms are shown.

Real-parameter optimisation is a prolific research line with hundreds of publications per year. There exists an impressive number of alternatives in both algorithm families and enhancements over their respective original proposals. In this work, we analyse if this growth in the number of publications is correlated with a real progress in the field. We have selected five approaches from one of the most significant journals in the field and compared them with the winner of the competition celebrated within the IEEE Congress on Evolutionary Computation 2005. We observe that not only these methods are unable to get the good results of the winner of the competition, published several years before, but that they often avoid this type of comparison. Instead, they usually compare with other approaches from the same family. We conclude that the comparison with the state-of-the-art of the field should be mandatory to promote a real progress and to prevent that the area becomes obfuscated for outsiders.

Many engineering design problems can be transformed into constrained optimization problems (COPs) which are usually very challenging for optimization algorithms. Differential Evolution (DE) has better global searching ability than traditional optimization algorithms. However, the drawbacks are also obvious: (1) The performance of DE depends largely on parameters. (2) Constraint handle technique (CHT) is necessary for COPs since DE is essentially an unconstrained optimization algorithm. This study sets up a stable optimization algorithm for COPs by combining Differential Evolution Algorithm with Strategy Adaptation (SADE) and a novel CHT. This paper proposes a simple and easy repair strategy (RP), which needn't to introduce other parameters or change the structure of algorithm. The specific operation is to repair the non-feasible solution by constructing sub-problems. To verify its superiority, the proposed Repair Strategy-Differential Evolution Algorithm with Strategy Adaptation (RP-SADE) was applied to the 2018 IEEE Congress on Evolutionary Computation (CEC2018) and one engineering application. The results show that the proposed RP-SADE has good comprehensive performance by considering computational efficiency and convergence accuracy.

Increased use of renewable energies in smart microgrids (SMGs) present new technical challenges to system operation. SMGs must be self-sufficient and operate independently; however, when more elements are integrated into SMGs, as distributed energy resources (DER), traditional explicit mathematical formulations will demand too much data from the network and become intractable. In contrast, tools based on optimization with metaheuristics can provide near optimal solutions in acceptable times. Considering this, this paper presents the variable neighborhood search differential evolutionary particle swarm optimization (VNS-DEEPSO) algorithm to solve multi-objective stochastic control models, as SMGs system operation. The goal is to control DER while maximizing profit. In this work, DER considered the bidirectional communication between energy storage systems (ESS) and electric vehicles (EVs). They can charge/discharge power and buy/sell energy in the electricity markets. Also, they have elements such as traditional generators (e.g., reciprocating engines) and loads, with demand response/control capability. Sources of uncertainty are associated with weather conditions, planned EV trips, load forecasting and the market prices. The VNS-DEEPSO algorithm was the winner of the IEEE Congress on Evolutionary Computation/The Genetic and Evolutionary Computation Conference (IEEE-CEC/GECCO 2019) smart grid competition (with encrypted code) and also won the IEEE World Congress on Computational Intelligence (IEEE-WCCI) 2018 smart grid competition (these competitions were developed by the group GECAD, based at the Polytechnic Institute of Porto, in collaboration with Delft University and Adelaide University). In the IEEE-CEC/GECCO 2019, the relative error improved between 32% and 152% in comparison with other algorithms.

Differential evolution (DE) has established itself as a simple but efficient population-based, nonconvex optimization algorithm for continuous search spaces. Unlike the conventional real-coded genetic algorithms (GAs) and evolution strategies (ESs), DE uses a mandatory self-referential mutation for its population members, each of which are perturbed with the scaled difference(s) of the individuals from the current generation (iteration). These difference vectors determine the direction of the search moves for the individuals. However, unlike the better individuals, they are not retained in the elitist evolution cycle of DE. In this paper, we show that by archiving the most promising difference vectors from past generations and then by reusing them for generating offspring in the subsequent generations, we can strikingly improve the performance of DE. This strategy can be integrated with any classical or advanced DE variant with no serious overhead in time or space complexity. We demonstrate that when combined with the DE-based winners of the IEEE Congress on Evolutionary Computation (CEC) 2013, 2014, and 2017 competitions on real parameter optimization, the simple reuse strategy leads to a statistically significant performance improvement in the majority of test cases. We further showcase the efficacy of our proposal on a practical optimization problem concerning the design of circular antenna arrays with a prespecified radiation pattern.

“Cyber-Physical Systems or “smart” systems are co-engineered interacting networks of physical and computational components. These systems will provide the foundation of our critical infrastructure, form the basis of emerging and future smart services, and improve our quality of life in many areas.” (National Institute of Standards and Technology: Cyber-physical systems. [Online]. Available: https://www.nist.gov/el/cyber-physical-systems. Accessed 31 Dec 2017, 2017). The concept of Smartness has been increasingly used as a marketing catchphrase. This study seeks to explain that smartness can be a serious indicator which can help to describe the machine intelligence level of different devices, systems or networks weighted by, among others, the usability index. The present study aims to summarize the implementation of complex, resilient and smart system on the level of devices, systems and complex system networks. The research should consider a smart device as a single agent, the system as a multi-agent system, and the network of complex systems has been envisaged as an ad hoc multi-agent system (Farid AM: Designing multi-agent systems for resilient engineering systems. In: Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), vol 9266, pp 3–8, 2015) organised in a network. The physical incarnations of this latter could be, for example, the subsystems of a smart city. In order to determine the smartness of a certain system, the Machine Intelligence Quotient (MIQ) (Iantovics LB, Gligor A, Georgieva V: Detecting outlier intelligence in the behavior of intelligent coalitions of agents. In: 2017 IEEE congress on evolutionary computation (CEC), pp 241–248, 2017; Park H-J, Kim BK, Lim KY: Measuring the machine intelligence quotient (MIQ) of human-machine cooperative systems. IEEE Trans Syst Man Cybern – Part A Syst Humans 31(2):89–96, 2001; Park HJ, Kim BK, Lim GY: Measuring machine intelligence for human-machine coop-erative systems using intelligence task graph. In: Proceedings 1999 IEEE/RSJ international conference on intelligent robots and systems. Human and environment friendly robots with high intelligence and emotional quotients (Cat. No.99CH36289), vol 2, pp 689–694, 1999; Ozkul T: Cost-benefit analyses of man-machine cooperative systems by assesment of machine intelligence quotient (MIQ) gain. In: 2009 6th international symposium on mechatronics and its applications, pp 1–6, 2009), Usability Index (UI) (Li C, Ji Z, Pang Z, Chu S, Jin Y, Tong J, Xu H, Chen Y: On usability evaluation of human – machine interactive Interface based on eye movement. In: Long S, Dhillon BS (eds) Man-machine-environment system engineering: proceedings of the 16th international conference on MMESE. Springer, Singapore, pp 347–354, 2016; Szabo G: Usability of machinery. In: Arezes P (ed) Advances in safety management and human factors: proceedings of the AHFE 2017 international conference on safety management and human factors, July 17–21, 2017, The Westin Bonaventure Hotel, Los Angeles, California, USA. Springer International Publishing, Cham, pp 161–168, 2018; Aykin N (ed): Usability and internationalization of information technology. Lawrence Erlbaum Associates, Inc., Publishers, Mahwah, 2005) and Usability Index of Machine (UIoM), Environmental Performance Index (Hsu A et al: Global metrics for the environment. In: The environmental performance index ranks countries’ performance on high-priority environmental issues. Yale University, New Haven, 2016) of Machine (EPIoM) indexes will be considered. The quality of human life is directly influenced by the intelligence and smart design of machines (Farid AM: Designing multi-agent systems for resilient engineering systems. In: Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), vol 9266, pp 3–8, 2015; Liouane Z, Lemlouma T, Roose P, Weis F, Liouane Z, Lemlouma T, Roose P, Weis F, Neu HMAG: A genetic neural network approach for unusual behavior prediction in smart home. In: Madureira AM, Abraham A, Gamboa D, Novais P (eds) Advances in intelligent systems and computing, vol 2016. Springer International Publishing AG, Porto, pp 738–748, 2017). Smartness of systems have an indispensable role to play in enabling the overall resilience of the combined cyber-physical system.

Dynamic optimization problems (DOPs) have been a subject of considerable research interest mainly due to their widespread application potential. In the literature, various mechanisms have been reported to cope with the challenges of DOPs. The proposed mechanisms have usually been adopted by well-known population-based optimization algorithms, such as genetic algorithms or particle swarm optimization. Although new generation swarm-intelligence algorithms are continuously being developed and have much to offer in DOPs, their performance is usually tested on stationary optimization problems. In this study, a recently introduced optimization algorithm, Harris Hawk Optimizer, is redesigned as a multi-population based algorithm to deal with possible multiple optima. Thus, the proposed modification is allowed to search diverse parts of the search space more efficiently, particularly in multimodal environments. Next, it is further enhanced by using quantum particles to tackle with diversification and intensification challenges in DOPs. As shown in the present work, this mechanism can maintain population diversity and intensification depending on a user-supplied parameter. Finally, based on different algorithmic components, four different variants of HHO are proposed. The performances of the developed algorithms are tested on both stationary and dynamic test problems. Dynamic test functions introduced in the IEEE Congress on Evolutionary Computation 2009 (CEC 2009) are used and further extended to test the proposed algorithms' performances. Finally, appropriate statistical analysis is conducted to demonstrate significant improvements over the existing algorithms.

This article presents a modified version of the Differential Evolution (DE) algorithm for solving Dynamic Optimization Problems (DOPs) efficiently. The algorithm, referred as Modified DE with Locality induced Genetic Operators (MDE-LiGO) incorporates changes in the three basic stages of a standard DE framework. The mutation phase has been entrusted to a locality-induced operation that retains traits of Euclidean distance-based closest individuals around a potential solution. Diversity maintenance is further enhanced by inclusion of a local-best crossover operation that empowers the algorithm with an explorative ability without directional bias. An exhaustive dynamic detection technique has been introduced to effectively sense the changes in the landscape. An even distribution of solutions over different regions of the landscape calls for a solution retention technique that adapts this algorithm to dynamism by using the previously stored information in diverse search domains. MDE-LiGO has been compared with seven state-of-the-art evolutionary dynamic optimizers on a set of benchmarks known as the Generalized Dynamic Benchmark Generator (GDBG) used in competition on evolutionary computation in dynamic and uncertain environments held under the 2009 IEEE Congress on Evolutionary Computation (CEC). The experimental results clearly indicate that MDE-LiGO can outperform other algorithms for most of the tested DOP instances in a statistically meaningful way.

An alternative adaptive DE algorithm is suggested.Two new mutation strategies are proposed.EI criterion is employed to identify scale factor adaptively.Cut-HDMR is used to determine crossover constant due to coupling characteristic.The suggested method is successfully applied to time-based sheet forming optimization. Differential Evolution (DE) is one of the most powerful stochastic real parameter optimizers. An alternative adaptive DE algorithm called Expected Improvement (EI)-High Dimensional Model Representation (HDMR)-DE is suggested. The EI criterion and the Kriging-HDMR are used to adjust scale factor F and crossover constant Cr, respectively. Considering the expensive computational cost of evaluation, the Kriging is integrated to evaluate the objective function when an accuracy criterion is met. To compare the performance, the suggested method, it has been compared with four popular adaptive DE algorithms over 25 standard numerical benchmarks derived from the IEEE Congress on Evolutionary Computation 2005 competition. To verify the feasibility of the suggested algorithm, a real-world application, time-dependent variable Blank Hold Force (BHF) optimization problem is also carried out by the EI-HDMR-DE. The results show that the EI-HDMR-DE improves the performance of adaptive DE and has potential capability to solve some complicated real-world applications.

Graphical abstractDisplay Omitted HighlightsThe proposed MMTD employs both Pareto dominance-based concept and decomposition strategy in the process of population evolution.The proposed algorithm employs these multimethod simultaneously based on dynamic resources allocation procedure.The proposed MMTD is flexible and many algorithms or multiple operators in their constituent algorithms can be integrated in their evolutionary process. The impact analysis of different operators in constituent algorithms of the MMTD framework is part of work in this paper.Experimental results demonstrate that MMTD has significantly performed better than state-of-the-art MOEAs such as MOEA/D, NSGA-II, AMALGAM, MOPSO: a proposal for multiple objective particle swarm optimization, MOSaDE, DECMOSA-SQP in terms of reducing the inverted generational distance (IGD) metric and time cost on both ZDT test problems 68 and CEC'09 test instances. In the last two decades, multiobjective optimization has become main stream and various multiobjective evolutionary algorithms (MOEAs) have been suggested in the field of evolutionary computing (EC) for solving hard combinatorial and continuous multiobjective optimization problems. Most MOEAs employ single evolutionary operators such as crossover, mutation and selection for population evolution. In this paper, we suggest a multiobjective evolutionary algorithm based on multimethods (MMTD) with dynamic resource allocation for coping with continuous multi-objective optimization problems (MOPs). The suggested algorithm employs two well known population based stochastic algorithms namely MOEA/D and NSGA-II as constituent algorithms for population evolution with a dynamic resource allocation scheme. We have examined the performance of the proposed MMTD on two different MOPs test suites: the widely used ZDT problems and the recently formulated test instances for the special session on MOEAs competition of the 2009 IEEE congress on evolutionary computation (CEC'09). Experimental results obtained by the suggested MMTD are more promising than those of some state-of-the-art MOEAs in terms of the inverted generational distance (IGD)-metric on most test problems.

This study developed a novel optimization algorithm, called Forensic-Based Investigation (FBI), inspired by the suspect investigation–location–pursuit process that is used by police officers. Although numerous unwieldy optimization algorithms hamper their usability by requiring predefined operating parameters, FBI is a user-friendly algorithm that does not require predefined operating parameters. The performance of parameter-free FBI was validated using four experiments: (1) The robustness and efficiency of FBI were compared with those of 12 representations of the top leading metaphors by using 50 renowned multidimensional benchmark problems. The result indicated that FBI remarkably outperformed all other algorithms. (2) FBI was applied to solve a resource-constrained scheduling problem associated with a highway construction project. The experiment demonstrated that FBI yielded the shortest schedule with a success rate of 100%, indicating its stability and robustness. (3) FBI was utilized to solve 30 benchmark functions that were most recently presented at the IEEE Congress on Evolutionary Computation (CEC) competition on bound-constrained problems. Its performance was compared with those of the three winners in CEC to validate its effectiveness. (4) FBI solved high-dimensional problems, by increasing the number of dimensions of benchmark functions to 1000. FBI is efficient because it requires a relatively short computational time for solving problems, it reaches the optimal solution more rapidly than other algorithms, and it efficaciously solves high-dimensional problems. Given that the experiments demonstrated FBI’s robustness, efficiency, stability, and user-friendliness, FBI is promising for solving various complex problems. Finally, this study provided the scientific community with a metaheuristic optimization platform for graphically and logically manipulating optimization algorithms.

Multipopulation is an effective optimization component often embedded into evolutionary algorithms to solve optimization problems. In this paper, a new multipopulation-based multiobjective genetic algorithm (MOGA) is proposed, which uses a unique cross-subpopulation migration process inspired by biological processes to share information between subpopulations. Then, a Markov model of the proposed multipopulation MOGA is derived, the first of its kind, which provides an exact mathematical model for each possible population occurring simultaneously with multiple objectives. Simulation results of two multiobjective test problems with multiple subpopulations justify the derived Markov model, and show that the proposed multipopulation method can improve the optimization ability of the MOGA. Also, the proposed multipopulation method is applied to other multiobjective evolutionary algorithms (MOEAs) for evaluating its performance against the IEEE Congress on Evolutionary Computation multiobjective benchmarks. The experimental results show that a single-population MOEA can be extended to a multipopulation version, while obtaining better optimization performance.

One of the issues that might affect the performance of Differential Evolution (DE) is premature convergence. In such cases, and especially in long-term executions, due to the nature of the reproduction phase of DE, computational resources might not be employed efficiently. In DE this issue is usually tackled by altering the reproduction phase or by attaching an external archive. However, in other fields such as in combinatorial optimization, methods that amend the replacement phase have been very successful. In this paper, two variants of DE are extended by including a replacement phase that explicitly relates the amount of diversity maintained in the population with the number of generations evolved and with the stopping criterion. One of the variants is the classic DE/rand/1/bin whereas the other one is Success-History based Adaptive DE (SHADE), a state-of-the-art approach. In the case of the classic variant, the principles employed in combinatorial optimization could be used straightforwardly. However, when integrating it with state-of-the-art techniques that already incorporate mechanisms to preserve diversity, additional modifications were required. Experimental validation has been performed with the benchmarks provided for the 2013 IEEE Congress on Evolutionary Computation competition on real parameter optimization. The results of the best-ranked DE in such a competition could be improved further. Additionally, some problems that had not been solved to optimality ever by any proposal, could be successfully solved.

JADE is an state-of-the-art adaptive differential evolution algorithm which implements “DE/current-to-pbest” as its mutation strategy, adapts its mutation factor and crossover rate, and uses an optional external archive to keep track of potential removed individuals in previous generations. This paper proposes MPADE, which extends JADE by using a multi-populated approach to solve high dimensional real-parameter optimization problems. This mechanism helps preventing the two well-known problems affecting the differential evolution algorithm performance, which are premature convergence and stagnation. The algorithm was tested using the benchmark functions in IEEE Congress on Evolutionary Computation 2014 test suite. MPADE was compared using Wilcoxon test to JADE algorithm and with other state-of-the-art algorithms that either use a multi-population approach or adapt their parameters. The experimental results show that the proposed new algorithm improves significantly its precursor and it is also suggested that other state-of-the-art algorithms could benefit from the multi-populated based approach.

The performance of many nature-inspired optimization algorithms (NIOAs) depends strongly on their implemented coordinate system. However, the commonly used coordinate system is fixed and not well suited for different function landscapes, NIOAs thus might not search efficiently. To overcome this shortcoming, in this paper we propose a framework, named ACoS, to adaptively tune the coordinate systems in NIOAs. In ACoS, an Eigen coordinate system is established by making use of the cumulative population distribution information, which can be obtained based on a covariance matrix adaptation strategy and an additional archiving mechanism. Since the population distribution information can reflect the features of the function landscape to some extent, NIOAs in the Eigen coordinate system have the capability to identify the modality of the function landscape. In addition, the Eigen coordinate system is coupled with the original coordinate system, and they are selected according to a probability vector. The probability vector aims to determine the selection ratio of each coordinate system for each individual, and is adaptively updated based on the collected information from the offspring. ACoS has been applied to two of the most popular paradigms of NIOAs, i.e., particle swarm optimization and differential evolution, for solving 30 test functions with 30D and 50D at the 2014 IEEE Congress on Evolutionary Computation. The experimental studies demonstrate its effectiveness.

In this paper we propose using interval type-2 fuzzy logic for the optimization of parameters the form dynamic using the Differential Evolution algorithm. For this particular work we use Benchmark mathematical functions for the experiments that were performed adhering to the rules of the competition for the IEEE Congress on Evolutionary Computation (CEC) benchmark set of 2015. We are presenting a comparison against the winning paper of the competition IEEE Congress on Evolutionary Computation (CEC) to verify how good the proposed method Fuzzy Differential Evolution algorithm really is.

The artificial bee colony (ABC) algorithm is one of popular swarm intelligence algorithms that inspired by the foraging behavior of honeybee colonies. To improve the convergence ability, search speed of finding the best solution and control the balance between exploration and exploitation using this approach, we propose a self adaptive hybrid enhanced ABC algorithm in this paper. To evaluate the performance of standard ABC, best-so-far ABC (BsfABC), incremental ABC (IABC), and the proposed ABC algorithms, we implemented numerical optimization problems based on the IEEE Congress on Evolutionary Computation (CEC) 2014 test suite. Our experimental results show the comparative performance of standard ABC, BsfABC, IABC, and the proposed ABC algorithms. According to the results, we conclude that the proposed ABC algorithm is competitive to those state-of-the-art modified ABC algorithms such as BsfABC and IABC algorithms based on the benchmark problems defined by CEC 2014 test suite with dimension sizes of 10, 30, and 50, respectively.

Genetic algorithm (GA) is a heuristic search technique that draws inspiration from principles and mechanisms of natural selection. Conventionally, parents selection takes place at every generation and offspring are reproduced through genetic operators like crossover and mutation. The process reiterates until some termination conditions are met. Until recently, little attention has been paid on the enduring relationship between parent solutions. In this paper, we take on and further extend the idea of monogamous genetic algorithm to solving real-coded numerical optimization problems. In this GA model, each monogamous pair of parents yields two offspring, and only the best two offspring survive into the next generation. Occasional infidelity generates variety and promotes diversity in the population. Simulation results over the IEEE-CEC'13 (IEEE Congress on Evolutionary Computation 2013) contest for real parameter single objective optimization with 28 benchmark functions demonstrate the effectiveness of the proposed approach.

For years, there have been organized single objective real-parameter optimization competitions on the IEEE Congress on Evolutionary Computation, in which the organizer define a common experimental, the researchers carry out the experiments with their proposals using it, and the obtained results are compared. It is a excellent way to know which algorithms (and ideas) can improve others, creating guidelines to improve the field. However, in several competitions the benchmark can change and the winners of previous benchmarks are not always introduced into the comparisons. Due to that, it could be not clear the improvement that new proposals offer against proposals of previous years. In this paper, we compare the winners in different years among them using the different proposed benchmarks, and we analyse the results obtained by all of them to observe whether there is an real improvement or not by the winner proposals of these competitions through the years.