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A metaheuristic-based structural optimization method, whilst being popularly adopted due to its advantages in by-passing gradient function calculations, requires the use of time-consuming advanced analyses for constraint evaluation. To overcome this drawback, the present paper proposes a robust (machine learning-based) optimization method that combines the light gradient boosting machine (LightGBM) with the efficient p-best differential evolution (E p DE) method. In essence, the LightGBM classification model is constructed to assess the constraint (safety and integrity) satisfaction of structures. An efficient framework using a so-called safety parameter is proposed to prevent inaccurate predictions of the LightGBM model. The E p DE processes the optimization procedures on the constructed classification LightGBM model. This enables an enhanced machine learning-based optimization technique that not only maintains the sufficiently accurate optimal design of structures but also significantly reduces the required computing efforts, as compared to standard optimization schemes. Various examples of steel structure designs (i.e., two of which have been provided herein) have been successfully performed by the proposed approach. These illustrate the accuracy and robustness of the proposed method, where good comparisons with reference algorithms (including standard DE with "DE/rand/1" mutational strategy, Jaya, Rao-1 and CaDE) are evidenced. The statistical values collected present the accuracy and reliability of the proposed method in obtaining the minimum total weight designs with substantial (some 60%) reduction of computing efforts required to furnish optimal results. [ABSTRACT FROM AUTHOR]

To adapt to the uncertainty of the real environment and solve the problem of high efficiency and high quality, this study comprehensively considers a variety of uncertainty factors, focusing on modeling and solving a hybrid flow-shop scheduling problem by two-stage stochastic programming (HFSP-TSP). First, this paper uses a two-stage scenario tree to describe the uncertain factors, the probabilities and values are obtained under different discrete production scenarios, and stochastic programming theory is used to formulate a mixed-integer linear programming (MILP) model for HFSP-TSP. Second, based on a general discrete optimization algorithm framework, that is, pointer-based discrete differential evolution (PDDE) algorithm, a novel variant (H-PDDE) is proposed for effectively solving the HFSP-TSP. It adopts a permutation scheduling decoding method and introduces three new improvement strategies: the strategy of inconsistent code length of individuals in the population, adding local search in discrete mutation operation, using a heuristic algorithm to generate the initial population. Finally, computational experiments were conducted to illustrate the proposed mathematical model and optimization algorithm. The computational results show that the H-PDDE can solve the HFSP-TSP more effectively than existing algorithms and conventional PDDE variants. The stochastic programming model is increasingly superior to the deterministic model in an uncertain environment. The source code of the H-PDDE algorithm and its data files can be found at https://github.com/huangyiping-ai/H-PDDE-algorithm.git , which is publicly available. [ABSTRACT FROM AUTHOR]

The Gravitational Search Algorithm (GSA) has excellent performance in solving various optimization problems. However, it has been demonstrated that GSA tends to trap into local optima and are easy to lose diversity in the late evolution process. In this paper, a new hybrid algorithm based on self-adaptive Gravitational Search Algorithm (GSA) and Differential Evolution (DE) is proposed for solving single objective optimization, named SGSADE. Firstly, a self-adaptive mechanism based on GSA is proposed for improving the convergence speed and balancing exploration and exploitation. Secondly, the diversity of the population is maintained in the evolution process by using crossover and mutation operation from DE. Besides, to improve the performance of the algorithm, a new perturbation based on Levy flight theory is embedded to enhance exploitation capacity. The simulated results of SGSADE on 2017 CEC benchmark functions show that the SGSADE outperforms the state-of-the-art variant algorithms of the GSA. [ABSTRACT FROM AUTHOR]

In system design, the best system designed under a simple experimental environment may not be suitable for application in real world if dramatic changes caused by uncertainties contained in the real world are considered. To deal with the problem caused by uncertainties, designers should try their best to get the most robust solution. The most robust solution can be obtained by constrained min–max optimization algorithms. In this paper, the scheme of generating escape vectors has been proposed to solve the problem of premature convergence of differential evolution. After applying the proposed scheme to the constrained min–max optimization algorithm, the performance of the algorithm could be greatly improved. To evaluate the performance of constrained min–max optimization algorithms, more complex test problems have also been proposed in this paper. Experimental results show that the improved constrained min–max optimization algorithm is able to achieve a quite satisfied success rate on all considered test problems under limited accuracy. [ABSTRACT FROM AUTHOR]

Nature-inspired meta-heuristics have gained popularity for solutions to many real-world complex problems, and the artificial bee colony algorithm is one of the most powerful optimisation methods among meta-heuristics. However, inefficient exploitation of onlooker bees prevents the artificial bee colony algorithm from finding the final result accurately and efficiently for complex problems. In this paper, a novel optimisation method is proposed based on the artificial bee colony algorithm. The proposed optimisation method adaptively exploits onlooker bees over generations. In addition, the proposed optimisation method is applied to a stereo-matching problem to minimise the segment-based integer energy function, which is also introduced in this paper. The experimental results show that the proposed optimisation method outperforms state-of-the-art population-based meta-heuristics, such as the genetic algorithm, differential evolution, conventional artificial bee colony, and clonal selection algorithm, for benchmark functions as well as for the stereo-matching problem. [ABSTRACT FROM AUTHOR]

In this paper, an improved version of the Grey Wolf Optimizer (GWO) is proposed to improve the exploration and the exploitation ability of the GWO algorithm. This improvement is performed through using the chaotic logistic map, the Opposition-Based Learning (OBL), the differential evolution(DE), and the disruption operator (DO). Where, the chaotic logistic map and the OBL are used to initialize the candidate solutions and these approaches avoid the drawbacks of the random population and increase the convergence of the algorithm. Then, the DE operators are combined with the GWO algorithm, in which, the DE operators work as a local search mechanism to improve the exploitation ability of the GWO through updating the population. Also, after updating the solutions by using a hybrid between the GWO and the DE, the DO is used to enhance the exploration ability, in which, the DO is used to maintain the diversity of the population. Therefore, the combinations with chaotic logistic map, OBL, DE, and DO, provide the GWO with tools to better balance between the exploration and the exploitation of the search space without affecting the computational time required for this task. The proposed algorithm, called COGWO2D, is compared with other seven algorithms through a set of experimental series that have been performed over two benchmark functions, the classical CEC2005, and the CEC2014. Also, the performance of the proposed algorithm to improve the classification of the galaxy images is evaluated, where it is used as a feature selection method. The aim of this experiment is to select the optimal subset of features from the extracted features of the galaxy images. The experimental results support the efficacy of the proposed approach to find the optimal solutions of the global optimization problem, as well as, increase the accuracy of the classification of the galaxy images. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid version of marine predator algorithm (MPA) and naked mole-rat algorithm (NMRA) to aggregate the strengths of both algorithms. The new proposed algorithm is named as MpNMRA and designed to overcome the inherent drawbacks of MPA (slow exploitation) and NMRA (limited exploration). The algorithm adds the basic structure of MPA to the worker phase of NMRA, while keeping all the major parameters of both the algorithm. The major parameters of both the algorithms are subjected to four different mutation strategies namely, exponential, linear, simulated annealing and logarithmic mutation strategies. The concept of simulated annealing-based mutation is found to be best for most of the parameters, whereas in some cases exponentially decreasing weights provide better results. Leveraging on the best mutation strategies for all the parameters, the proposed MpNMRA is tested on CEC2005, CEC2014 and CEC 2019 benchmark problems. The experimental results demonstrate that MpNMRA provides best results when compared to other algorithms in the literature on higher-dimensional problems. This work also considers solving three real-world optimization problems and training of a multi-layer perceptron using the proposed algorithm. Statistical results obtained from Wilcoxon's rank-sum test, Freidman's test and computational complexity further proves that the proposed algorithm is highly efficient and provide superior results. 1 1 The link of source-code will be added after publishing. • Proposes new hybrid version of Marine predator naked mole-rat algorithm. • Four new mutation operators are added for adding the adaptive properties. • MpNMRA is tested on CEC 2005 and CEC 2014 benchmark functions. • MpNMRA is used to solve engineering design problems. • Experiments show that MpNMRA is efficient and effective. [ABSTRACT FROM AUTHOR]

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

Image thresholding is a process for separating interesting objects within an image from their background. An optimal threshold’s selection can be regarded as a single objective optimization problem, where obtaining a solution can be computationally expensive and time-consuming, especially when the number of thresholds increases greatly. This paper proposes a novel hybrid differential evolution algorithm for selecting the optimal threshold values for a given gray-level input image, using the criterion defined by Otsu. The hybridization is done by adding a reset strategy, adopted from the Cuckoo Search, within the evolutionary loop of differential evolution. Additionally a study of different evolutionary or swarm-based intelligence algorithms for the purpose of thresholding, with a higher number of thresholds was performed, since many real-world applications require more than just a few thresholds for further processing. Experiments were performed on eleven real world images. The efficiency of the hybrid was compared to the cuckoo search and self-adaptive differential evolution, the original differential evolution, particle swarm optimization, and artificial bee colony where the results showed the superiority of the hybrid in terms of better segmentation results with the increased number of thresholds. Since the proposed method needs only two parameters adjusted, it is by far a better choice for real-life applications. [ABSTRACT FROM AUTHOR]

Optimization methods have shown to be a very important approach for control engineers. They emulate the decision-making ability of a human expert to tune the control gains for a process or system with the formulation and solution of a mathematical optimization problem. In such formulation, evolutionary algorithms (EAs) have been widely used to obtain the control gains. Nevertheless a bad selection of the control gains through the optimization process can result in instability of the closed-loop control system such that the convergence and diversity in the EAs can be compromised. In this paper the PID control tuning for a planar parallel robot with a five-bar mechanism to follow a highly nonlinear trajectory is stated as an off-line nonlinear dynamic optimization problem (OLNLDOP). In order to promote individuals with a stable behavior in the closed-loop control system, a dynamic constraint and a method to handle such constraint is proposed into the OLNLDOP and into eight different variants of the differential evolution algorithm, respectively. Comparative analysis shows that the proposal finds suitable solutions for the OLNLDOP with a better convergence time. Laboratory testing with the optimum PID control gains on a real prototype validates the tuning optimization method. [ABSTRACT FROM AUTHOR]

• A new interdisciplinary metaheuristic derived from engineering field is proposed. • The new algorithm is developed based on the framework of the differential evolution. • Inspiration is derived from Proportional, Integral and Derivative control method. • CEC 2014 and CEC 11 functions are evaluated by the proposed optimizer. • CEC 2020 real-world constrained optimization problems are discussed. The proportional, integral, and derivative differential evolution algorithm (PID-DE) is proposed as a new type of interdisciplinary metaheuristic evolutionary algorithm in this paper. The inspiration of PID-DE is derived from the classical proportional, integral, and derivative control method in engineering, and it is used in the framework of the differential evolution (DE) algorithm. To begin, the mathematical models of proportional search, integral search, and derivative search are established as the fundamental search operations. Five different types of optimizers that use a combination of these three basic operations and an additional mutation operation are presented. The selection and crossover methods in DE are then modified to maintain population diversity while also improving global search capacity, and a feedback strategy is established to adaptively adjust the subgroup member of each optimizer. Following that, an integrated high-accuracy, rapid-convergence, and stable metaheuristic is invented using the comprehensive information utilization principle and flexible parameter determination method. Five groups of experiments are studied to assess the overall performance of the proposed algorithm. The first test comprises 12 standard benchmark functions with minimum optima. In Tests 2 and 3, the 52 functions of Congress on Evolutionary Computation (CEC) 2014 and CEC 11 are evaluated using PID-DE under standard test conditions. Besides, three classic real-world engineering design problems and the CEC 2020 test suit are studied for the constrained optimization test. The experimental tests validate PID-DE's higher accuracy and faster convergence speed in numerical optimization when compared with the representative approaches and top algorithms in the CEC competitions. [ABSTRACT FROM AUTHOR]

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

Many real-world problems can be categorized as constrained optimization problems. So, designing effective algorithms for constrained optimization problems become more and more important. In designing algorithms, how to guide the individuals moving more efficiently towards the feasible region is one of the most important aspects on finding the optimum of constrained optimization problems. In this paper, we propose an improved ε constrained differential evolution, which combines with pre-estimated comparison gradient based approximation. The proposed algorithm uses gradient matrix to determine whether the trail vector generated by differential evolution algorithm is worth using the fitness function to evaluate it or not. Pre-estimated comparison gradient based approximation is used as a detector to find the promising offspring and in this way can we guide the individuals moving towards the feasible region. The proposed method is tested both on twenty-four benchmark functions and four well-known engineering optimization problems. Experimental results show that the proposed algorithm is highly competitive in comparing with other state-of-the-art algorithms. The proposed algorithm offers higher accuracy in engineering optimization problems for constrained optimization problems. [ABSTRACT FROM AUTHOR]

Recently, an improved ( μ + λ ) constrainted differential evolution (ICDE) has been proposed and proven to be robust and effective for solving constrainted optimization problems. However, so far, the ICDE has been developed mainly for continuous design variables, and hence it becomes inappropriate for solving layout truss optimization problems which contain both discrete and continuous variables. This paper hence fills this gap by proposing a novel discrete variables handling technique and integrating it into original ICDE to give a so-called Discrete-ICDE (D-ICDE) for solving layout truss optimization problems. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress, displacement and buckling limitations. Numerical examples of five classical truss problems are carried out and compared to other state-of-the-art optimization methods to illustrate the reliability and effectiveness of the proposed method. The D-ICDE’s performance shows that it not only successfully handles discrete variables but also significantly improves the convergence of layout truss optimization problem. The D-ICDE is promising to extend for determining the optimal solution of other structural optimization problems which contain both discrete and continuous variables. [ABSTRACT FROM AUTHOR]

Cuckoo search (CS) has been proven to be one of the most efficient metaheuristic algorithms in solving global optimization problems. However, it suffers from a slow convergence speed and premature convergence, especially when the complexity of the problem increases. To address these shortcomings, a ranking-based adaptive cuckoo search algorithm, called RACS, is proposed in this paper. Specifically, a novel ranking-based mutation strategy is designed at first, which is inspired by the natural phenomenon that good species or individuals always contain good information and thus have better odds of guiding others. In the proposed ranking-based mutation strategy, the global search equation is modified in combination with a ranking-based vector selection method, where some of the parent vectors are proportionally selected according to their rankings. The higher ranking a parent vector obtains, the more opportunity it will be chosen. Secondly, a crossover operation with parameter adaptation is employed after the Lévy flights random walk to preserve some good elements of the current solutions from being changed. Furthermore, a replacement strategy is designed to update the solutions not improved through pre-determined cycles by exploiting the beneficial information from the discarded solutions saved in the external archive. To evaluate the comprehensive performance of RACS, extensive experiments are conducted on three well-known test suites and an application problem of identifying unknown parameters of fractional-order nonlinear systems. Simulation results demonstrate that the presented strategies bring a significant improvement in effectiveness and efficiency on CS. Besides, RACS is verified to be superior or at least comparable to other CS variants and state-of-the-art algorithms on most of the benchmark problems, and thus, can be regarded as a useful and promising technique for solving real-world complex optimization problems. • A ranking-based adaptive cuckoo search algorithm is proposed. • A ranking-based mutation strategy is developed to enhance the exploitation ability. • The crossover operation is used to preserve some good elements from being changed. • A replacement strategy is designed to avoid stagnation. • RACS exhibits superior performance when solving various test problems. [ABSTRACT FROM AUTHOR]

Solving constrained optimization problems (COPs) has been gathering attention from many researchers. In this paper, we defined the best fitness value among feasible solutions in current population as gbest . Then, we converted the original COPs to multi-objective optimization problems (MOPs) with one constraint. The constraint set the function value f ( x ) should be less than or equal to gbest ; the objectives are the constraints in COPs. A reverse comparison strategy based on multi-objective dominance concept is proposed. Compared with usual strategies, the innovation strategy cuts off the worse solutions with smaller fitness value regardless of its constraints violation. Differential evolution (DE) algorithm is used as a solver to search for the global optimum. The method is called multi-objective optimization based reverse strategy with differential evolution algorithm (MRS-DE). The experimental results demonstrate that MRS-DE can achieve better performance on 22 classical benchmark functions compared with several state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-agent type-2 fuzzy logic control (FLC) method optimized by differential evolution (DE) for multi-intersection traffic signal control. Type-2 fuzzy sets can deal with models' uncertainties efficiently because of its three-dimensional membership functions, but selecting suitable parameters of membership functions and rule base is not easy. DE is adopted to decide the parameters in the type-2 fuzzy system, as it is easy to understand, simple to implement and possesses low space complexity. In order to avoid the computational complexity, the expert rule base and the parameters of membership functions (MF) are optimized by turns. An eleven-intersection traffic network is studied in which each intersection is governed by the proposed controller. A secondary layer controller is set in every intersection to select the proper phase sequence. Furthermore, the communication among the adjacent intersections is implemented using multi-agent system. Simulation experiments are designed to compare communicative type-2 FLC optimized by DE with type-1 FLC, fixed-time signal control, etc. Experimental results indicate that our proposed method can enhance the vehicular throughput rate and reduce delay, queue length and parking rate efficiently. [ABSTRACT FROM AUTHOR]

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

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

• Developed a global optimization approach using cooperative meta-heuristic methods. • The proposed method inspired from the natural selection theory. • DE, GWO, WOA, SSA, SCA, and SOS are used to build the proposed method. • Three variants of proposed are developed based on strategy of updating solutions. • Results of proposed method compared with other methods using CEC2014 and CEC2017. This paper presents an alternative global optimization meta-heuristics (MHs) approach, inspired by the natural selection theory. The proposed approach depends on the competition among six MHs that allows generating an offspring, which can breed the high characteristics of parents since they are unique and competitive. Therefore, this leads to improve the convergence of the solutions towards an optimal solution and also, to avoid the limitations of other methods that aim to balance between exploitation and exploration. The six algorithms are differential evolution, whale optimization algorithm, grey wolf optimization, symbiotic organisms search algorithm, sine–cosine algorithm, and salp swarm algorithm. According to these algorithms, three variants of the proposed method are developed, in the first variant, one of the six algorithms will be used to update the current individual based on a predefined order and the probability of the fitness function for each individual. Whereas, the second variant updates each individual by permuting the six algorithms, then using the algorithms in the current permutation to update individuals. The third variant is considered as an extension of the second variant, which updates all individuals using only one algorithm from the six algorithms. Three different experiments are carried out using CEC 2014 and CEC 2017 benchmark functions to evaluate the efficiency of the proposed approach. Moreover, the proposed approach is compared with well known MH methods, including the six methods used to build it. Comparison results confirmed the efficiency of the proposed approach compared to other approaches according to different performance measures. [ABSTRACT FROM AUTHOR]

• A new multi-objective optimization method used OBL strategy, WOA and DE algorithms • It combines DE and the OBL to improve the performance of the WOA • The MWDEO results outperformed all other algorithms in most of the test problems • 32 multi-objective test problems are used in the experiments and CEC2017 problems The optimization problems are divided into a single objective and multi-objective. Single objective optimization has only one objective function; whereas, multi-objective optimization has multiple objective functions that generate the Pareto set; therefore, solving a multi-objective problem is a challenging problem. This paper presents a new multi-objective optimization method (called MWDEO) based on improved whale optimization algorithm (WOA) by combining the differential evolution (DE) algorithm and the opposition-based learning (OBL). The MWDEO uses the WOA to perform a global exploration, whereas DE is used to exploit the search space; while the OBL is applied to improve the exploration and exploitation by generating the opposite values. The proposed algorithm is evaluated using 32 multi-objective test problems besides a set of benchmark problems of CEC'2017. The experimental results are compared with nine state-of-the-art multi-objective methods. The analysis of the results showed that the proposed MWDEO outperformed all other algorithms in most of the test problems which indicates that the proposed MWDEO is competitive and effective in solving different types of multi-objective problems. [ABSTRACT FROM AUTHOR]

• We consider both fuel costs and emissions, and find the best compromise value. • We introduce differential evolution operator into quantum particle swarm optimization (QPSO). • We introduce crossover operator into quantum particle swarm optimization (QPSO). • Adaptive control is adopted for crossover probability. Consumption of traditional fossil energy has promoted rapid economic development and caused effects such as climate warming and environmental degradation. In order to solve the problem of environmental economic dispatch (EED), this paper proposes a DE-CQPSO (Differential Evolution-Crossover Quantum Particle Swarm Optimization) algorithm based on the fast convergence of differential evolution algorithms and the particle diversity of crossover operators of genetic algorithms. In order to obtain better optimization results, a parameter adaptive control method is used to update the crossover probability. And the problem of multi-objective optimization is solved by introducing a penalty factor. The experimental results show that: the evaluation index and convergence speed of the DE-CQPSO algorithm are better than QPSO (Quantum Particle Swarm Optimization) and other algorithms, whether it is single-objective optimization of fuel cost and emissions or multi-objective optimization considering both optimization objectives. A good compromise value is verified, which verifies the effectiveness and robustness of the DE-CQPSO algorithm in solving environmental economic dispatch problems. The study provides a new research direction for solving environmental economic dispatch problems. At the same time, it provides a reference for the reasonable output of the unit to a certain extent. [ABSTRACT FROM AUTHOR]

• Selfish herd optimizer is refined without changing its basic concepts. • The refinements are verified with two benchmark suites. • The results show the refinements are efficient for improving selfish herd optimizer. The selfish herds optimizer (SHO) is a recently developed swarm optimization algorithm for solving global optimization problems. SHO mimics the widely observed selfish herd behaviors of avoiding predation risks. In SHO, a set of unique evolutionary operators inspired by the prey-predator relationship are used in dealing with optimization problems. Although SHO can provide a good performance when finding an optimal solution, this algorithm has some oversights that cause problems in the exploitation ability of SHO. Additionally, SHO still has some shortcomings that influence the performance of exploration and avoiding stagnation in local optima. In this paper, some refinements and modifications are proposed for these oversights and shortcomings. In order to validate whether the refinements and modifications are appropriate for improving the performance of SHO, two suites of benchmark functions are employed to compare the proposed method with the original SHO and other well-known and recently developed algorithms, such as Standard Particle Swarm Optimization, Artificial Bee Colony algorithm, Differential Evolution, and Crow Search Algorithm, etc. Finally, the efficiency of the proposed method is justified using the nonparametric Wilcoxon rank-sum test. The experimental results show that the proposed modifications are appropriate for improving the performance of the original SHO. In addition, the proposed method can also give competitive results in finding global optima when compared with other algorithms. [ABSTRACT FROM AUTHOR]