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As an advanced optimization algorithm with a simple structure, the whale optimization algorithm is used to solve problems in many disciplines. Through in-depth research on the whale optimization algorithm, it is found that the algorithm has problems such as slow convergence speed, inability to escape local optima, low convergence accuracy, and inability to balance global exploration and local exploitation capabilities. To address these issues, a whale optimization algorithm integrating niche and hybrid mutation strategy (NHWOA) is proposed. NHWOA introduces adaptive weights to balance the global exploration and local exploitation capabilities of the algorithm and accelerate its convergence speed. It divides the population into three niches of the same size, and independently optimizes them to increase population diversity. It uses a hybrid mutation strategy to randomly perturb the population, helping the algorithm escape local optima. Simulation experiments on the CEC2017 benchmark suite and application to feature selection problems validate the superiority and effectiveness of NHWOA. NHWOA exhibits faster convergence speed, higher convergence accuracy, and better robustness. [ABSTRACT FROM AUTHOR]

To apply biogeography-based optimization (BBO) to large scale optimization problems, this paper proposes a novel BBO variant based on feedback differential evolution mechanism and steepest descent method, referred to as FBBOSD. Firstly, the immigration refusal mechanism is proposed to eliminate the damage of inferior solutions to superior solutions. Secondly, the dynamic hybrid migration operator is designed to balance the exploration and exploitation, which makes BBO suitable for high-dimensional environment. Thirdly, the feedback differential evolution mechanism is designed to make FBBOSD can select mutation modes intelligently. Finally, the steepest descent method is creatively combined with BBO, which further improves the convergence accuracy. Meanwhile, a sequence convergence model is established to prove the convergence of FBBOSD. Quantitative evaluations: FBBOSD is compared with BBO, seven BBO variants and seven state-of-the-art evolutionary algorithms, respectively. The experimental results on 24 benchmark functions and CEC2017 show that FBBOSD outperforms all compared algorithms, and the dimension of solving optimization problems can reach 10,000. Then, FBBPOSD is applied to engineering design problems. The simulation results demonstrate that it is also effective on constrained optimization problems. In short, FBBOSD has excellent performance and outstanding stability, which is a new algorithm worthy of adoption and promotion. [ABSTRACT FROM AUTHOR]

In this paper, we study swarm intelligence computation for constrained optimization problems and propose a new hybrid PSO-DE algorithm based on feasibility rules. Establishing individual feasibility rules as a way to determine whether the position of an individual satisfies the constraint or violates the degree of the constraint, which will determine the choice of the individual optimal position and the global optimal position in the particle population. First, particle swarm optimization (PSO) is used to act on the top 50% of individuals with higher degree of constraint violation to update their velocity and position. Second, Differential Evolution (DE) is applied to act on the individual optimal position of each individual to form a new population. The current individual optimal position and the global optimal position are updated using the feasibility rules, thus forming a hybrid PSO-DE intelligent algorithm. Analyzing the convergence and complexity of PSO-DE. Finally, the performance of the PSO-DE algorithm is tested with 12 benchmark functions of constrained optimization and 57 engineering optimization problems, the numerical results show that the proposed algorithm has good accuracy, effectiveness and robustness. [ABSTRACT FROM AUTHOR]

In order to solve the shortcomings of particle swarm optimization (PSO) in solving multiobjective optimization problems, an improved multiobjective particle swarm optimization (IMOPSO) algorithm is proposed. In this study, the competitive strategy was introduced into the construction process of Pareto external archives to speed up the search process of nondominated solutions, thereby increasing the speed of the establishment of Pareto external archives. In addition, the descending order of crowding distance method is used to limit the size of external archives and dynamically adjust particle parameters; in order to solve the problem of insufficient population diversity in the later stage of algorithm iteration, time-varying Gaussian mutation strategy is used to mutate the particles in external archives to improve diversity. The simulation experiment results show that the improved algorithm has better convergence and stability than the other compared algorithms. [ABSTRACT FROM AUTHOR]

In the financial market, investors must deal with uncertain risk, and they also face background risk and many uncertain factors caused by their own characteristics. Considering the fuzzy nature of these factors as well as investors' risk preferences, transaction costs, and so on, in order to reduce investment risk, an improved probability entropy measure is introduced, and a probability mean-lower semivariance-entropy model with different risk attitudes is established by using fuzzy sets and probability theory. To solve the portfolio model, an improved differential evolution algorithm is proposed and a numerical example is given. The numerical results show that the proposed algorithm is effective and that the model can disperse the financial risk to a certain extent and reasonably solve the portfolio problem under many different conditions. [ABSTRACT FROM AUTHOR]

According to our extensive investigation, Biogeography-based optimization (BBO) and its variants have not been applied to solve high-dimensional optimization problems. To make a breakthrough in this field, a new BBO variant with hybrid migration operator and feedback differential evolution mechanism, HFBBO, is proposed. Firstly, the example learning method is used to ensure the inferior solutions cannot destroy the superior solutions. Secondly, the hybrid migration operator is presented to balance the exploration and exploitation. It enables the algorithm to switch freely between local search and global search. Finally, the feedback differential evolution mechanism is designed to replace the random mutation operator. HFBBO can select the mutation mode intelligently by this mechanism to avoid getting stuck in local optima. Meanwhile, the Markov model is established to prove the convergence of HFBBO, and the complexity is also discussed. A series experiments are carried out on 24 benchmark functions, CEC2017 test suite and 12 real-world engineering problems. The results of the Wilcoxon's rank-sum test and Friedman's test show that HFBBO has better competitiveness and stability than the 27 compared algorithms. Furtherly, the performance of HFBBO is compared on 1000, 2000, 5000 and 10000 dimensions, respectively. Experimental results show that this method can effectively solve high-dimensional optimization problems. [Display omitted] • HFBBO can self-regulate mutation mode through the feedback mechanism. • The damage of the inferior solutions to the superior solutions is avoided. • The exploration and exploitation of the population can reach an equilibrium state. • The performance of HFBBO is tested on 1000, 2000, 5000 and 10000 dimensions. • 27 algorithms proposed in recent years are used to compare with HFBBO. [ABSTRACT FROM AUTHOR]

Opposition-based learning (OBL), which plays an important role in soft computing, has recently drawn attention. The paramount challenge of OBL is to design and find an OBL strategy that is suitable for the problem structure. Besides, for the OBL variants proposed so far, there is no clear taxonomy guideline. To solve these issues, this paper proposes a novel opposition, called dual opposition-based learning (DOBL), which contains two opposition strategies and a protective mechanism. Firstly, a diversity-based taxonomy is proposed, which categorizes existing state-of-the-art OBL variants according to dimension-wise diversity. The subpopulation strategy is used and embedded in the classified OBL variants to generate explorative opposition and exploitative opposition. Secondly, for a successful algorithm, a good ratio between exploration and exploitation is required. Therefore, a protective mechanism is designed to obtain a good equilibrium between exploration and exploitation. Finally, the performance of DOBL is compared with eight state-of-the-art OBL variants on DE and advanced DE named jSO to find the CEC 2017 test suite's best solution. Besides, DOBL is applied to CEC 2011 as well as CEC 2020 real-world optimization problems, and compared with nine novel metaheuristic algorithms as well as the top three algorithms in CEC 2020, respectively. Two statistical tests, the Wilcoxon rank-sum test and the Friedman test, are used to analyze the experiment results. The experiment results of 29 functions and 60 real-world problems demonstrate that the proposed DOBL is better than its competitors on CEC2011, CEC 2017, and CEC 2020 test suites. • The convergence behavior of OBL variants is analyzed according to dimension-wise diversity. • Two novel OBL variants are combined with a subpopulation framework to generate DOBL. • DOBL significantly improves performance on both DE and advanced DE named jSO. • The equilibrium state between exploration and exploitation is reached. • 89 problems from CEC 2011, CEC 2017 and CEC 2020 are used to test the performance of DOBL. [ABSTRACT FROM AUTHOR]

This paper presents a multiobjective differential evolution algorithm with multiple trial vectors. For each individual in the population, three trial individuals are produced by the mutation operator. The offspring is produced by using the crossover operator on the three trial individuals. Good individuals are selected from the parent and the offspring and then are put in the intermediate population. Finally, the intermediate population is sorted according to the Pareto dominance relations and the crowding distance, and then the outstanding individuals are selected as the next evolutionary population. Comparing with the classical multiobjective optimization algorithm NSGA-II, the proposed algorithm has better convergence, and the obtained Pareto optimal solutions have better diversity [ABSTRACT FROM AUTHOR]

There are some processing problems of imbalanced data such as imbalanced data sets being difficult to integrate efficiently. This paper proposes and constructs a mixed penalty function data integration screening criterion, and proposes Differential Evolution Integration Algorithm Based on Mixed Penalty Function Screening Criteria (DE-MPFSC algorithm). In addition, the theoretical validity and the convergence of the DE-MPFSC algorithm are analyzed and proven by establishing the Markov sequence and Markov evolution process model of the DE-MPFSC algorithm. In this paper, the entanglement degree and enanglement degree error are introduced to analyze the DE-MPFSC algorithm. Finally, the effectiveness and stability of the DE-MPFSC algorithm are verified by UCI machine learning datasets. The test results show that the DE-MPFSC algorithm can effectively improve the effectiveness and application of imbalanced data classification and integration, improve the internal classification of imbalanced data and improve the efficiency of data integration. [ABSTRACT FROM AUTHOR]