Li-Sen Wei

Summary: Although some many‐objective optimization algorithms (MaOEAs) have been proposed recently, Pareto dominance‐based MaOEAs still cannot effectively balance convergence and diversity in solving many objective optimization problems (MaOPs) due to insufficient selection pressure. To address this problem, a bi‐directional fusion niche domination is proposed. This method merges the strengths of cone and parallel decomposition directions in comparing dominations for nondominance stratification within the candidate population, augmenting the selection pressure of population. Subsequently, the crowding distance is introduced as an additional selection criterion to further refine the selection of nondominated individuals within the critical layer. Lastly, a MaOEA based on bi‐directional fusion niche dominance (MaOEA/BnD) is proposed, utilizing bi‐directional fusion niche dominance and crowding distance as important components of environmental selection. The performance of MaOEA/BnD was compared with five representative MaOEAs in 20 benchmark problems. Experimental results demonstrate that MaOEA/BnD effectively balances convergence and diversity when handling MaOPs with complex Pareto fronts.

Many‐objective evolutionary algorithms (MaOEAs) consisted of environmental selection and reproduction operator. However, few studies focus on how to design reproduction operators to improve the performance of MaOEAs. In this paper, a reproduction operator based on grey prediction is proposed for MaOEAs, named GPRS. Specifically, the grey prediction assisted by reference vector is first used to get the target location. Then, a fine regulation is designed to generate potential solutions by handling the different information further. Finally, a gene sharing strategy is executed to accelerate the convergence by information exchange. The effectiveness of the proposed reproduction strategy is validated by comparing it with five widely used reproduction operators by embedding into a classical framework NSGAIII. At the same time, an improved NSGAIIIGPRS is developed by embedding the proposed GPRS and compared with seven excellent algorithms on a number of benchmark problems and one practical application. The final experimental results show that the proposed GPRS has significant advantages over similar reproduction strategies, and the improved NSGAIIGRPS is more effective compared with other excellent algorithms in handling many‐objective optimization problem.

Pareto dominance-based many-objective evolutionary algorithms (MaOEAs) face a significant challenge from many-objective problems (MaOPs). The selection pressure reduces as the number of objectives rises, while the non-dominated solution grows exponentially. Pareto dominance-based MaOEA increases the selection pressure by designing diversity-related environmental strategies. However, it still struggles to strike a good balance between population diversity and convergence. Moreover, the diversity-selection method increases the likelihood that dominance-resistant solutions (DRSs) will be chosen, which is detrimental to the performance of MaOEAs. To address the aforementioned problems, a many-objective optimization algorithm based on population preprocessing and projection distance-assisted elimination mechanism (PPEA) is proposed. In PPEA, first, the population preprocessing method is designed to lessen the negative impacts of DRSs. Second, to further improve the ability to balance population diversity and convergence of Pareto dominance-based MaOEAs, a projection distance-assisted elimination mechanism is proposed to remove the poorer individuals one by one until the population size satisfies the termination condition. The performance of PPEA was compared with seven excellent MaOEAs on a series of benchmark problems with 3–15 objectives and a real-world application problem. The experimental results indicate that PPEA is competitive and can effectively balance the diversity and convergence of the population when dealing with MaOPs.

Aims: The main purpose of this paper is to achieve good convergence and distribution in different Pareto fronts. Background: Research in recent decades has shown that evolutionary multi-objective optimization can effectively solve multi-objective optimization problems with no more than 3 targets. However, when solving MaOPs, the traditional evolutionary multi-objective optimization algorithm is difficult to effectively balance convergence and diversity. In order to solve these problems, many algorithms have emerged, which can be roughly divided into the following three types: decomposition-based, indexbased, and dominance relationship-based. In addition, there are many algorithms that introduce the idea of clustering into the environment. However, there are some disadvantages to solving different types of MaOPs. In order to take advantage of the above algorithms, this paper proposes a manyobjective optimization algorithm based on two-phase evolutionary selection. Objective: In order to verify the comprehensive performance of the algorithm on the testing problem of different Pareto front, 18 examples of regular PF problems and irregular PF problems are used to test the performance of the algorithm proposed in this paper. Method: This paper proposes a two-phase evolutionary selection strategy. The evolution process is divided into two phases to select individuals with good quality. In the first phase, the convergence area is constructed by indicators to accelerate the convergence of the algorithm. In the second phase, the parallel distance is used to map the individuals to the hyperplane, and the individuals are clustered according to the distance on the hyperplane, and then the smallest fitness in each category is selected. Result: For regular Pareto front testing problems, MaOEA/TPS performed better than RVEA, PREA, CAMOEA and One by one EA in 19, 21, 30, 26 cases, respectively, while it was only outperformed by RVEA, PREA, CAMOEA and One by one EA in 8, 5, 1, and 6 cases. For the irregular front testing problem, MaOEA/TPS performed better than RVEA, PREA, CAMOEA and One by one EA in 20, 17, 25, and 21 cases, respectively, while it was only outperformed by RVEA, PREA, CAMOEA and One by one EA in 6, 8, 1, and 6 cases. Conclusion: The paper proposes a many-objective evolutionary algorithm based on two phase selection, termed MaOEA/TPS, for solving MaOPs with different shapes of Pareto fronts. The results show that MaOEA/TPS has quite a competitive performance compared with the several algorithms on most test problems. Other: Although the algorithm in this paper has achieved good results, the optimization problem in the real environment is more difficult, therefore, applying the algorithm proposed in this paper to real problems will be the next research direction.