An Efficient Multi-Indicator and Many-Objective Optimization Algorithm based on Two-Archive

Indicator-based algorithms are gaining prominence as traditional multi-objective optimization algorithms based on domination and decomposition struggle to solve many-objective optimization problems. However, previous indicator-based multi-objective optimization algorithms suffer from the following flaws: 1) The environment selection process takes a long time; 2) Additional parameters are usually necessary. As a result, this paper proposed an multi-indicator and multi-objective optimization algorithm based on two-archive (SRA3) that can efficiently select good individuals in environment selection based on indicators performance and uses an adaptive parameter strategy for parental selection without setting additional parameters. Then we normalized the algorithm and compared its performance before and after normalization, finding that normalization improved the algorithm's performance significantly. We also analyzed how normalizing affected the indicator-based algorithm and observed that the normalized $I_{ε+}$ indicator is better at finding extreme solutions and can reduce the influence of each objective's different extent of contribution to the indicator due to its different scope. However, it also has a preference for extreme solutions, which causes the solution set to converge to the extremes. As a result, we give some suggestions for normalization. Then, on the DTLZ and WFG problems, we conducted experiments on 39 problems with 5, 10, and 15 objectives, and the results show that SRA3 has good convergence and diversity while maintaining high efficiency. Finally, we conducted experiments on the DTLZ and WFG problems with 20 and 25 objectives and found that the algorithm proposed in this paper is more competitive than other algorithms as the number of objectives increases.