Symmetrical Generalized Pareto Dominance and Adjusted Reference Vector Cooperative Evolutionary Algorithm for Many-Objective Optimization

In Pareto-based many-objective evolutionary algorithms, performance usually degrades drastically as the number of objectives increases due to the poor discriminability of Pareto optimality. Although some relaxed Pareto domination relations have been proposed to relieve the loss of selection pressure, it is hard to maintain good population diversity, especially in the late phase of evolution. To solve this problem, we propose a symmetrical Generalized Pareto Dominance and Adjusted Reference Vectors Cooperative (GPDARVC) evolutionary algorithm to deal with many-objective optimization problems. The symmetric version of generalized Pareto dominance (GPD), as an efficient framework, provides sufficient selection pressure without degrading diversity, no matter of the number of objectives. Then, reference vectors (RVs), initially generated evenly in the objective space, guide the selection with good diversity. The cooperation of GPD and RVs in environmental selection in part ensures a good balance of convergence and diversity. Also, to further enhance the effectiveness of RV-guided selection, we regenerate more RVs according to the proportion of valid RVs; thereafter, we select the most valid RVs for adjustment after the association operation. To validate the performance of GPDARVC, we compare it with seven representative algorithms on commonly used sets of problems. This comprehensive analysis results in 26 test problems with different objective numbers and 6 practical problems, which show that GPDARVC outperforms other algorithms in most cases, indicating its great potential to solve many-objective optimization problems.