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Aiming at the shortcomings of whale optimization algorithm (WOA) when solving problems such as high dimension, multi-peak and non-origin of optimal value, such as low convergence accuracy and easy to be captured by local optimum, this paper proposed a whale optimization algorithm based on multi-dimensional variation learning and distributed optimization (MLDOWOA) . Firstly, this algorithm introduced adaptive weights and dominant individual interference to dynamically adjust the direction of individual spiral surround, which improved the global search ability and convergence accuracy of the algorithm. Then, in order to further expand the search range of the algorithm, the improved algorithm used a multi-dimensional variation learning mechanism to adaptively plan the direction of population variation. Finally, it put forward the distributed optimization mechanism to coordinate the step size of search, so as to help the population break through the limitation of search stagnation in the middle and late stage. The test results on 8 high dimensional benchmark functions and 4 fixed dimensional benchmark functions show that, compared with the basic WOA, SSA and the improved WOA algorithms ACWOA, AWOA, MSIWOA, ADWOA, the proposed algorithm has significant advantages in convergence accuracy and ability to cope with high dimensional functions. This paper used the algorithm to tune the parameters of the FOPID controller, and compared the control results with the research results of this engineering problem in recent years, which prove the excellent performance of the proposed algorithm in FOPID parameter tuning problems. [ABSTRACT FROM AUTHOR]

The moth-flame algorithm shows some shortcomings in solving the complex problem of optimization, such as insufficient population diversity and unbalanced search ability. In this paper, an IMFO (Improved Moth-Flame Optimization) algorithm is proposed to be applied in solving the optimization problem of function. First, cat chaotic mapping is used to generate the initial position of moth to improve the population diversity. Second, cosine inertia weight is introduced to balance the global and local search abilities of the algorithm. Third, the memory information in the particle swarm algorithm is introduced into the iterative process of the algorithm to speed up the convergence of the population. Finally, Gaussian mutation strategy is used in the current optimal solution to avoid the algorithm from falling into the local optimum. Simulation experiments are conducted on 11 benchmark test functions, compared with other improved MFO (Moth-Flame Optimization) algorithms and classical optimization algorithms. The results show that the IMFO has higher accuracy and stability in solving the above-mentioned test functions. The proposed algorithm is experimented and verified by optimizing the KELM (Kernel Extreme Learning Machine) in an engineering example and exhibits a better optimization performance. [ABSTRACT FROM AUTHOR]

This paper presents an effective approach for solving economic load dispatch problems contemplating the scheduling a set of thermal generating units to produce a specific power at low consumption costs. These problems can be thought of as nonlinear, non-convex, and highly constrained optimization problems with a large number of local minima. To cope with the above issues in solving such problems, a new meta-heuristic named capuchin search algorithm was adopted. To boost the search performance of this algorithm as well as to mitigate its early convergence and regression to the local optimum, it was hybridized with another algorithm and improved using several positive amendments. First, a memory element was added to this algorithm to ameliorate its position and velocity update mechanisms in order to exploit the most encouraging candidate solutions. Second, two adaptive parametric functions were used to manage the exploration and exploitation features of this algorithm and balance them appropriately. Finally, the hybridization was made using the gradient-based optimizer to strengthen the intensification ability of this algorithm and balance its searching ability to fulfill sensible search performance. The proficiency of the proposed algorithm was divulged by assessing it on computationally difficult economic load dispatch problems under 6 different tests with a generator of 3, 13, 40, 80, and 140 units, each with different constraints and load conditions. The proposed algorithm provided the best performance among many other competitors. Its superiority and practicality were revealed by obtaining optimal solutions for large-scale test cases such as 40-unit and 140-unit test systems. [ABSTRACT FROM AUTHOR]

Optimization algorithms are popular to solve different problems in many fields, and are inspired by natural principles, animal living habits, plant pollinations, chemistry principles, and physic principles. Optimization algorithm performances will directly impact on solving accuracy. The Crow Search Algorithm (CSA) is a simple and efficient algorithm inspired by the natural behaviors of crows. However, the flight length of CSA is a fixed value, which makes the algorithm fall into the local optimum, severely limiting the algorithm solving ability. To solve this problem, this paper proposes a Variable Step Crow Search Algorithm (VSCSA). The proposed algorithm uses the cosine function to enhance CSA searching abilities, which greatly improves both the solution quality of the population and the convergence speed. In the update phase, the VSCSA increases population diversities and enhances the global searching ability of the basic CSA. The experiment used 14 test functions,2017 CEC functions, and engineering application problems to compare VSCSA with different algorithms. The experiment results showed that VSCSA performs better in fitness values, iteration curves, box plots, searching paths, and the Wilcoxon test results, which indicates that VSCSA has strong competitiveness and sufficient superiority. The VSCSA has outstanding performances in various test functions and the searching accuracy has been greatly improved. [ABSTRACT FROM AUTHOR]

Optimization is the task of minimizing or maximizing an objective function f(x) parameterized by x. A series of effective numerical optimization methods have become popular for improving the performance and efficiency of other methods characterized by high-quality solutions and high convergence speed. In recent years, there are a lot of interest in hybrid metaheuristics, where more than one method is ideally combined into one new method that has the ability to solve many problems rapidly and efficiently. The basic concept of the proposed method is based on the addition of the acceleration part of the Gravity Search Algorithm (GSA) model in the Firefly Algorithm (FA) model and creating new individuals. Some standard objective functions are used to compare the hybrid (FAGSA) method with FA and the traditional GSA to find the optimal solution. Simulation results obtained by MATLAB R2015a indicate that the hybrid algorithm has the ability to cross the local optimum limits with a faster convergence than the luminous Fireflies algorithm and the ordinary gravity search algorithm. Therefore, this paper proposes a new numerical optimization method based on integrating the properties of the two methods (luminous fireflies and gravity research). In most cases, the proposed method usually gives better results than the original methods individually. [ABSTRACT FROM AUTHOR]

Cooperation search algorithm (CSA) is a new metaheuristic algorithm inspired from the team cooperation behaviors in modern enterprises and is characterized by fast convergence. However, for complex multimodal problems, it may get trapped into local optima and suffer from premature convergence for the shortcoming of population updating guided only by leading individuals. In this paper, the issue of low convergence efficiency and convergence accuracy of the CSA algorithm on complex multimodal problems is dramatically alleviated by integrating the mutation and crossover operators in DE algorithm. Experimental results demonstrate the better performance of CCSA on convergence speed and accuracy as compared to other existing optimizers. Furthermore, aiming at the problem that there is no universal approach for the multi-degree reduction in Ball Bézier surfaces under different interpolation constrains, we propose a new method to solve this problem by introducing metaheuristic methods, where the change of interpolation constrains is treated as the change of decision variables. The modeling examples show that the proposed method is effective and easy to implement under different interpolation constrains, which can achieve the multi-degree reduction in Ball Bézier surfaces at one time and can simplify the degree reduction procedure significantly. [ABSTRACT FROM AUTHOR]

In order to solve the problems of uneven resource utilization and long task completion time in complex task group scheduling, this paper constructed a complex task group resource scheduling model to minimize the mean square error of resource load and the task group completion time, and proposed a multi-objective optimization algorithm based on boundary range local search and NSGA-Ⅱ, called BRLSN. The algorithm used an effective coding method and cross mutation operator for iterative optimization, and constructed an elite retention strategy based on local search in boundary region to expand the search scope of the algorithm and preserved good individuals in the population. Experimental results show that compared with other multi-objective algorithms, the convergence and diversity of BRLSN are significantly improved. At the same time, the algorithm convergence speed is faster, the population quality is higher, and the result value of the final objective function is obviously optimized. [ABSTRACT FROM AUTHOR]

In order to fix the integer ambiguity quickly and accurately, this paper proposed a new ambiguity search algorithm based on measurement accuracy constraints to solve the problems of the LAMBDA algorithm, such as the wide search range of the integer ambiguity and the low search efficiency. When the least squares problem got optimally weighted, the algorithm took the carrier phase measurement accuracy as the constraint condition to test the fixed ambiguity solution on the basis of the stan-dard differential evolution （DE） algorithm. This algorithm solved the influence of different satellite altitude angles, and could achieve 99% success rate when solving 3D integer ambiguity. Compared with the MLAMBDA algorithm, the standard DE algorithm and the adaptive weighted differential evolution （AWDE） algorithm, the proposed algorithm further improves the efficiency and success rate of ambiguity resolution. [ABSTRACT FROM AUTHOR]

Targeting to the deficiency of sparrow search algorithm solved the multi-objective problems, and the problems can easily enter the partial optimization and inferior convergence in the counting process, this paper came up with a kind of improved multi-objective sparrow search algorithm. First of all, this paper used a new-type non-dominated sorting to find the Pareto front. Next, it integrated the polynomial mutation and cosine algorithm into species evolution strategy to strengthen its searching ability. It used the species selection method of competition mechanism to decrease the differentiation caused by partial optimized particle and overall optimized particle in the searching process. Finally, this paper compared the improved algorithm and various kinds of multi-objective algorithm in standard test function. The simulation results show that, the convergence and searching ability of the improved algorithm are all superior than other algorithm. Therefore, this algorithm can effectively address the multiple target optimization problem. [ABSTRACT FROM AUTHOR]

For the vehicle routing problem with time window, stochastic travel and service time, and customer classification, this paper constructed a chance constrained programming model, which considered two class customers (ordinary customers and priority customers) and adopted the chance constraint to guarantee the punctual service possibility of priority customers. Meanwhile, this paper designed a variable neighborhood iterated local search algorithm to solve the model, and proposed a minimum waiting time heuristic rule to generate initial solution. Based on Solomon benchmarks, it conducted series of simulation experiments. The results show that the initial solution generation method is valid, the given algorithm can get approximate optimal solutions for both of the deterministic and stochastic problems in a short time, and the customer ratio is positively relative to the number of vehicle usage . The results have a certain reference significance to solve the problem of low customer service level caused by the limited resources and uncertain factors. [ABSTRACT FROM AUTHOR]

In order to improve the safety and smoothness of flight, and solve the problems of excessive turning angle and too many search path nodes in the traditional A• algorithm, this paper proposed a synchronous bi-directional A• search algorithm based on sector field expansion. Firstly, this paper extended the hazardous area boundaries based on the raster map method. Secondly, it designed the A• algorithm based on synchronous bi-directional search, which dynamically defined the target nodes for forward and reverse search. Aiming at the problem of limiting search angles, this paper proposed a sector expansion strategy in 5 x 5 domain, and designed an evaluation function with double weight parameters to reduce the generation of redundant points. Finally, in order to verify the effectiveness of the improved algorithm, this paper selected square and irregular shape hazard areas for simulation. The results show that the improved algorithm searches for a smoother path. Compared with the results of the traditional bi-directional A• algorithm, the length of its search path reduce by 1. 65% and 13. 16%, and the number of its search path nodes reduce by 42. 6% and 46. 81 %, respectively, under different shapes of hazard areas, which has a strong search efficiency. [ABSTRACT FROM AUTHOR]

In order to solve the problem that the original sparrow search algorithm (Sparrow Search Algorithm, SSA) has reduced population diversity and the weak local development ability makes it difficult to jump out of the local optimum under the condition of approaching the global optimum. This paper proposes a sparrow search algorithm based on tangential flight (tangent flight Sparrow Search Algorithm, tanSSA). First of all, using adaptive t-distribution strategy to improve the finder location update formula can improve the individual sparrow’s optimization ability and prevent the algorithm from maturing. Then, the tangent flight strategy in the tangent search algorithm can enhance the search space ability of the algorithm, and can make the algorithm jump out of the advantage of the local optimal solution. In original sparrow search algorithm, using the tangent flight disturbance strategy to disturb the optimal solution. The combination of these two strategies can effectively improve the exploration and development performance of tanSSA algorithm. Finally, using 12 standard benchmark functions to test and verify the optimization performance of tanSSA algorithm combined with Wilcoxon rank sum test, and compared with the original SSA algorithm, whale optimization algorithm, particle swarm optimization algorithm and adaptive t-distribution SSA algorithm. The experimental results show that the optimization ability and convergence speed of the sparrow search algorithm based on tangent flight have a significant improvement. [ABSTRACT FROM AUTHOR]

In the industrial Internet environment, concerning about poor cooperation efficiency and high production cost of intercell scheduling, this paper solved the problem in the case of overlapping placement of machines. Firstly, the paper used the hierarchical network design idea to construct a two-layer directed processing network with machines and manufacturing cells as nodes. And it proposed a multi-objective scheduling model aiming at minimizing the average degree, completion time and processing cost by analyzing the relationship among the global cooperation efficiency, redundant processing paths and the first-or der degree. Secondly, according to the strong local search ability of sparrow search algorithm, this paper designed a fusion strategy that based on nondominated sorting genetic algorithm and sparrow search algorithm, and an initial solution generation mechanism basing on clustering coefficient. Finally, the experiment illustrates the correlation between network characteristics and intercell scheduling objectives, so the proposed model and algorithm have higher quality of solution. [ABSTRACT FROM AUTHOR]

One of the main goals of network planners is the protection of important nodes in a network against natural disasters, security threats, attacks, and so on. Given the importance of this issue, a new model is presented in this paper for protecting an important node in a typical network based on a defensive location problem where the two agents threaten this node. The protecting facilities location problem with two agents is formulated as a three-level programming problem. The decision maker in the upper level is a network planner agent. The planner agent wants to find the best possible location of protecting facilities to protect the important node against threatening agents. The second and third levels problems are stated as the shortest path problems in the network in which the edges are weighted with positive values. In this work, the genetic, variable neighborhood search, simulated annealing algorithms are used to solve the problem. The performance of the used metaheuristic algorithms on this class of problems is investigated by a test problem that is generated randomly. Then, t-test are used to compare the performance of these algorithms. The best results are obtained by the variable neighborhood search algorithm. [ABSTRACT FROM AUTHOR]

The rapid growing number of web services has posed new challenges for service composition computing. How to combine services that meet the needs of users in the least amount of time from a huge number of candidate services is a hot topic of research today. As a meta-heuristic algorithm for solving optimization problems, salp swarm algorithm (SSA) has been widely applied to case scenarios in different fields due to its simple structure and high performance. However, QoS-aware service composition is a discrete problem and existing methods are not suitable for it. Therefore, in this paper, we propose an improved SSA integrating chaotic mapping method for QoS service composition selection, named CSSA. Through the randomness and ergodicity of chaos, reducing the possibility of falling into local optimum and strengthening the exploitation capability of the algorithm. In addition, a fuzzy continuous neighborhood search method is used to enhance the local search capability of the algorithm which makes the discrete space of service composition in a way similar to continuous space. Finally, two well-known datasets are used to verify the effectiveness of CSSA compared to three advanced algorithms and original SSA. The test results demonstrate that CSSA has significant advantages and it also has satisfactory performance in large scale scenarios. [ABSTRACT FROM AUTHOR]

The metaheuristic optimization algorithms are relatively new optimization algorithms introduced to solve optimization problems in recent years. For example, the firefly algorithm (FA) is one of the metaheuristic algorithms inspired by the fireflies' flashing behavior. However, its weakness in terms of exploration and early convergence has been pointed out. In this paper, two approaches were proposed to improve the FA. In the first proposed approach, a new improved opposition-based learning FA (IOFA) method was presented to accelerate the convergence and improve the FA's exploration capability. In the second proposed approach, a symbiotic organisms search (SOS) algorithm improved the exploration and exploitation of the first approach; two new parameters set these two goals, and the second approach was named IOFASOS. The purpose of the second method is that in the process of the SOS algorithm, the whole population is effective in the IOFA method to find solutions in the early stages of implementation, and with each iteration, fewer solutions are affected in the population. The experiments on 24 standard benchmark functions were conducted, and the first proposed approach showed a better performance in the small and medium dimensions and exhibited a relatively moderate performance in the higher dimensions. In contrast, the second proposed approach was better in increasing dimensions. In general, the empirical results showed that the two new approaches outperform other algorithms in most mathematical benchmarking functions. Thus, The IOFASOS model has more efficient solutions. [ABSTRACT FROM AUTHOR]

In recent years, many researchers have utilized metaheuristic optimization algorithms along with fuzzy logic theory in their studies for various purposes. The harmony search (HS) algorithm is one of the metaheuristic optimization algorithms that is widely employed in different studies along with fuzzy logic (FL) theory. FL theory is a mathematical approach to expressing uncertainty by applying the conceptualization of fuzziness in a system. This review paper presents an extensive review of published papers based on the combination of HS and FL systems. In this regard, the functional characteristics of models obtained from integration of FL and HS have been reported in various articles, and the performance of each study is investigated. The basic concept of the FL approach and its derived models are introduced to familiarize readers with the principal mechanisms of FL models. Moreover, appropriate descriptions of the primary classifications acquired from the coexistence of FL and HS methods for specific purposes are reviewed. The results show that the high efficiency of HS to improve the exploration of FL in achieving the optimal solution on the one hand, and the capability of fuzzy inference systems to provide more flexible and dynamic adaptation of the HS parameters based on human perception on the other hand, can be a powerful combination for solving optimization problems. This review paper is believed to be a useful resource for students, engineers, and professionals. [ABSTRACT FROM AUTHOR]

• Investigated a large-scale heterogeneous container loading problem. • Considered weight limits and suspension constraints in this problem. • Integrated ALNS and heuristic packing algorithm for the presented problem. • Performed experiments on real-world instances. • Verified the superiority of HALNS by comparing with existing methods. This paper aims to solve the large-scale heterogeneous container loading problem (HCLP), which is an extensive form of the multiple container loading problem, in a limited time. The target is to choose a set of containers of different sizes to accommodate all products and minimize the wasted space rate. Although the heterogeneous container selection problem is a general problem in the logistics industry, few related studies have been conducted. This study also considers some practical constraints, such as weight limits and suspension constraints. A hybrid adaptive large neighborhood search (HALNS) algorithm, which includes a set of original destroy-repair operators, especially for heterogeneous container selection problems, and integrates a heuristic packing algorithm, is proposed to solve the problem in an acceptable time. To verify the efficiency of the proposed algorithm, computational experiments on real-world instances from a multinational logistics company are performed, and the results are compared with those of other existing algorithms. The results indicate that the proposed algorithm outperforms other algorithms for the HCLP. [ABSTRACT FROM AUTHOR]

Dynamic economic dispatch with valve-point effects (DED_ vpe) is a high-dimensional constrained optimization problem with non-convex and non-smooth characteristics. Hybrid methods are one of the most advanced methods to solve the problem. However, most of these methods improve the solution accuracy at the expense of algorithm robustness. This paper proposes an adaptive hybrid backtracking search optimization algorithm (AHBSA) for solving the DED_ vpe. The core idea of AHBSA lies in designing a suitable coupling structure based on the current best individual (called optimal partial coupling). The structure hybridizes an improved BSA mutation operator and the DE/best/1 operator with equal probability. The improved BSA mutation operator uses the current best individual and the historical population to update individual position, called BSA/best/old. It is also the first research work of extending BSA to the problem. In addition, an adaptive parameter control mechanism is proposed to select an appropriate 'mixrate' value for achieving better coupling. The performance of AHBSA is validated on six DED test cases of three systems. Experimental results demonstrate that, compared with some representative methods, AHBSA not only reduces the fuel cost but also ensures the robustness of the algorithm. • A hybrid method AHBSA is proposed to solve DED problem with valve-point effects. • An optimal partial coupling structure is designed in AHBSA. • BSA is the first attempt at solving DED problem. • Results on six benchmark DED test cases show AHBSA is competitive. [ABSTRACT FROM AUTHOR]

With the development of cloud computing (CC), service-oriented architecture (SOA), and container technology, modeling and simulation (M&S) resources, such as simulation software and different sorts of models, can be shared and reused in a cloud environment. Modeling and Simulation as a Service (MSaaS), as a new paradigm, supports sharing simulation models or modeling tools and has enabled a wide range of model reuse. However, reusing or combining some immature models may result in inefficient M&S activities or even false simulation results. To make sure the appropriate reuse and composition of simulation models in cloud environments, which is also termed as model service composition for simulation (MSCS), this paper incorporates model maturity with service cooperation as a metric to evaluate the quality of model composition in cloud. Then, as a multi-objective optimization problem with multiple constraints, the MSCS problem and its process are described in detail. To solve the MSCS problem, a novel evolutionary algorithm named CA-AO-NSGAII is proposed. In the algorithm, adaptive crossover and mutation operators, as well as probabilistic initialization are developed. Furthermore, a half-local search algorithm in an elitist mechanism is designed for efficient decision-making. To validate the performance of CA-AO-NSGAII, experiments with respect to four different cases are conducted. Results show that the proposed method for addressing MSCS issue is effective and feasible. [ABSTRACT FROM AUTHOR]

Influence maximization (IM) is the problem of finding a set of nodes that can achieve the maximal influence spreads into the network, which faces two significant but intractable issues in latest studies: (i) Curse of scales: with the increase of the network scale, traditional methods cost extensive times in guaranteeing accuracy, which re-evaluate influence spread of every node in network, leading to significant computational overhead; (ii) Generalization issue: with more and more studies on various networks and propagation parameters, it is difficult to find a universally appropriate algorithm that performs well in each topology. In this paper, we propose a novel probability-driven structure-aware (PDSA) algorithm, which begins by cutting/updating network according to the edge activation probability parameters of the IC model, and then uses a graph traversal algorithm (e.g., breadth first search algorithm) to evaluate the influence spread scores of each node. Meanwhile, we adopt a kind of centrality-based independent cascade (CIC) model to approximate a more realistic propagation scenario. Through extensive experiments with six real-world/synthetic networks and six CIC/IC models, we demonstrate that PDSA achieves great performance over state-of-the-art algorithms in terms of effect and efficiency. Even facing various complex topologies and propagation parameters, PDSA exhibits excellent robustness in solving IM problems. • Efficient algorithm to solve the IM problem on large-scale networks. • The novel structure-aware algorithm adaptively finds the influential nodes. • A centrality-based IC model is applied to simulate more realistic social scenarios. • The proposed algorithm achieves great performance on both effect and efficiency. • Our methodology universes for various topologies and propagation parameters. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid algorithm that combines two prominent nature-inspired meta-heuristic strategies to solve the combined heat and power (CHP) economic dispatch. In this line, an innovative hybrid heap-based and jellyfish search algorithm (HBJSA) is developed to enhance the performance of two recent algorithms: heap-based algorithm (HBA) and jellyfish search algorithm (JSA). The proposed hybrid HBJSA seeks to make use of the explorative features of HBA and the exploitative features of the JSA to overcome some of the problems found in their standard forms. The proposed hybrid HBJSA, HBA, and JSA are validated and statistically compared by attempting to solve a real-world optimization issue of the CHP economic dispatch. It aims to satisfy the power and heat demands and minimize the whole fuel cost (WFC) of the power and heat generation units. Additionally, a series of operational and electrical constraints such as non-convex feasible operating regions of CHP and valve-point effects of power-only plants, respectively, are considered in solving such a problem. The proposed hybrid HBJSA, HBA, and JSA are employed on two medium systems, which are 24-unit and 48-unit systems, and two large systems, which are 84- and 96-unit systems. The experimental results demonstrate that the proposed hybrid HBJSA outperforms the standard HBA and JSA and other reported techniques when handling the CHP economic dispatch. Otherwise, comparative analyses are carried out to demonstrate the suggested HBJSA's strong stability and robustness in determining the lowest minimum, average, and maximum WFC values compared to the HBA and JSA. [ABSTRACT FROM AUTHOR]