A Many-Objective Optimization Algorithm Integrating Convergence and Diversity Metrics

Abstract Currently, many critical fields in science, society, and engineering involve Many-objective Optimization Problems (MaOPs) composed of numerous decision variables. A key challenge with such problems is the difficulty in simultaneously maintaining good diversity and convergence during the search process. To address this challenge, this paper proposes a dual-indicator-based multi-objective optimization framework (TDC-MOEA), which transforms the multi-objective space into a bi-objective space based on convergence and diversity metrics. Firstly, the population is clustered into multiple sub-populations according to reference points, shifting the focus of subsequent operations from individuals to sub-populations, and the convergence and diversity metrics for each sub-population are calculated. Secondly, to further enhance convergence and diversity, a selection process is applied to each sub-population, aiming to improve both the local convergence within sub-populations and the overall diversity. This algorithmic framework incorporates polynomial crossover and binomial mutation as core evolutionary operators, ultimately constructing the TDC-MOEA algorithm. Experimental results demonstrate that the TDC-MOEA algorithm can obtain Pareto solutions with good convergence and a wide distribution, while also acquiring multiple Pareto solution sets for the original multi-objective optimization problem. Comparative results against seven state-of-the-art MaOP algorithms on 39 test instances show that the TDC-MOEA algorithm possesses strong competitiveness and superior overall performance. In a practical application, the algorithm effectively optimized five objectives—power output, ecological function, thermal efficiency, power density, and efficient power—for a simple endoreversible closed Brayton cycle, achieving favorable results.