Solving Many-Objective Optimization Problems via Multistage Evolutionary Search

Chen H, Cheng R, Pedrycz W, Jin Y. Solving Many-Objective Optimization Problems via Multistage Evolutionary Search. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2021;51(6):3552-3564.With the increase in the number of optimization objectives, balancing the convergence and diversity in evolutionary multiobjective optimization becomes more intractable. So far, a variety of evolutionary algorithms have been proposed to solve many-objective optimization problems (MaOPs) with more than three objectives. Most of the existing algorithms, however, find difficulties in simultaneously counterpoising convergence and diversity during the whole evolutionary process. To address the issue, this paper proposes to solve MaOPs via multistage evolutionary search. To be specific, a two-stage evolutionary algorithm is developed, where the convergence and diversity are highlighted during different search stages to avoid the interferences between them. The first stage pushes multiple subpopulations with different weight vectors to converge to different areas of the Pareto front. After that, the nondominated solutions coming from each subpopulation are selected for generating a new population for the second stage. Moreover, a new environmental selection strategy is designed for the second stage to balance the convergence and diversity close to the Pareto front. This selection strategy evenly divides each objective dimension into a number of intervals, and then one solution having the best convergence in each interval will be retained. To assess the performance of the proposed algorithm, 48 benchmark functions with 7, 10, and 15 objectives are used to make comparisons with five representative many-objective optimization algorithms

Solving Many-Objective Optimization Problems via Multistage Evolutionary Search

With the increase in the number of optimization objectives, balancing the convergence and diversity in evolutionary multiobjective optimization becomes more intractable. So far, a variety of evolutionary algorithms have been proposed to solve many-objective optimization problems (MaOPs) with more than three objectives. Most of the existing algorithms, however, find difficulties in simultaneously counterpoising convergence and diversity during the whole evolutionary process. To address the issue, this paper proposes to solve MaOPs via multistage evolutionary search. To be specific, a two-stage evolutionary algorithm is developed, where the convergence and diversity are highlighted during different search stages to avoid the interferences between them. The first stage pushes multiple subpopulations with different weight vectors to converge to different areas of the Pareto front. After that, the nondominated solutions coming from each subpopulation are selected for generating a new population for the second stage. Moreover, a new environmental selection strategy is designed for the second stage to balance the convergence and diversity close to the Pareto front. This selection strategy evenly divides each objective dimension into a number of intervals, and then one solution having the best convergence in each interval will be retained. To assess the performance of the proposed algorithm, 48 benchmark functions with 7, 10, and 15 objectives are used to make comparisons with five representative many-objective optimization algorithms

Ensemble of differential evolution variants

Differential evolution (DE) is one of the most popular and efficient evolutionary algorithms for numerical optimization and it has gained much success in a series of academic benchmark competitions as well as real applications. Recently, ensemble methods receive an increasing attention in designing high-quality DE algorithms. However, previous efforts are mainly devoted to the low-level ensemble of mutation strategies of DE. This study investigates the high-level ensemble of multiple existing efficient DE variants. A multi-population based framework (MPF) is proposed to realize the ensemble of multiple DE variants to derive a new algorithm named EDEV for short. EDEV consists of three highly popular and efficient DE variants, namely JADE (adaptive differential evolution with optional external archive), CoDE (differential evolution with composite trial vector generation strategies and control parameters) and EPSDE (differential evolution algorithm with ensemble of parameters and mutation strategies). The whole population of EDEV is partitioned into four subpopulations, including three indicator subpopulations with smaller size and one reward subpopulation with much larger size. Each constituent DE variant in EDEV owns an indicator subpopulation. After every predefined generations, the most efficient constituent DE variant is determined and the reward subpopulation is assigned to that best performed DE variant as an extra reward. Through this manner, the most efficient DE variant is expected to obtain the most computational resources during the optimization process. In addition, the population partition operator is triggered at every generation, which results in timely information sharing and tight cooperation among the component DE variants. Extensive experiments and comparisons have been done based on the CEC2005 and CEC2014 benchmark suit, which shows that the overall performance of EDEV is superior to several state-of-the-art peer DE variants. The success of EDEV reveals that, through an appropriate ensemble framework, different DE variants of different merits can support one another to cooperatively solve optimization problems