A Many-Objective Evolutionary Algorithm Based on a Two-Round Selection Strategy

External archive guided radial-grid multi objective differential evolution

Differential evolution (DE) is a robust evolutionary algorithm for solving single-objective and multi-objective optimization problems (MOPs). While numerous multi-objective DE (MODE) variants exist, prior research has primarily focused on parameter control and mutation operators, often neglecting the issue of inadequate population distribution across the objective space. This paper proposes an external archive-guided radial-grid-driven differential evolution for multi-objective optimization (Ar-RGDEMO) to address these challenges. The proposed Ar-RGDEMO incorporates three key components: a novel mutation operator that integrates a radial-grid-driven strategy with a performance metric derived from Pareto front estimation, a truncation procedure that employs Pareto dominance in conjunction with a ranking strategy based on shifted similarity distances between candidate solutions, and an external archive that preserves elite individuals using a clustering approach. Experimental results on four sets of benchmark problems demonstrate that the proposed Ar-RGDEMO exhibits competitive or superior performance compared to seven state-of-the-art algorithms in the literature.

A Many-Objective Evolutionary Algorithm Based on Dual Selection Strategy

In high-dimensional space, most multi-objective optimization algorithms encounter difficulties in solving many-objective optimization problems because they cannot balance convergence and diversity. As the number of objectives increases, the non-dominated solutions become difficult to distinguish while challenging the assessment of diversity in high-dimensional objective space. To reduce selection pressure and improve diversity, this article proposes a many-objective evolutionary algorithm based on dual selection strategy (MaOEA/DS). First, a new distance function is designed as an effective distance metric. Then, based distance function, a point crowding-degree (PC) strategy, is proposed to further enhance the algorithm's ability to distinguish superior solutions in population. Finally, a dual selection strategy is proposed. In the first selection, the individuals with the best convergence are selected from the top few individuals with good diversity in the population, focusing on population convergence. In the second selection, the PC strategy is used to further select individuals with larger crowding distance values, emphasizing population diversity. To extensively evaluate the performance of the algorithm, this paper compares the proposed algorithm with several state-of-the-art algorithms. The experimental results show that MaOEA/DS outperforms other comparison algorithms in overall performance, indicating the effectiveness of the proposed algorithm.

A Multiobjective Framework for Many-Objective Optimization

It is known that many-objective optimization problems (MaOPs) often face the difficulty of maintaining good diversity and convergence in the search process due to the high-dimensional objective space. To address this issue, this article proposes a novel multiobjective framework for many-objective optimization (Mo4Ma), which transforms the many-objective space into multiobjective space. First, the many objectives are transformed into two indicative objectives of convergence and diversity. Second, a clustering-based sequential selection strategy is put forward in the transformed multiobjective space to guide the evolutionary search process. Specifically, the selection is circularly performed on the clustered subpopulations to maintain population diversity. In each round of selection, solutions with good performance in the transformed multiobjective space will be chosen to improve the overall convergence. The Mo4Ma is a generic framework that any type of evolutionary computation algorithm can incorporate compatibly. In this article, the differential evolution (DE) is adopted as the optimizer in the Mo4Ma framework, thus resulting in an Mo4Ma-DE algorithm. Experimental results show that the Mo4Ma-DE algorithm can obtain well-converged and widely distributed Pareto solutions along with the many-objective Pareto sets of the original MaOPs. Compared with seven state-of-the-art MaOP algorithms, the proposed Mo4Ma-DE algorithm shows strong competitiveness and general better performance.

An Indicator-Based Many-Objective Evolutionary Algorithm With Boundary Protection

Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the I_ϵ⁺ indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest I_ϵ⁺ value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., I _SDE⁺ , SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms.