Adaptive Strategy-Enhanced NSGA-II for Multi-Objective Optimization with Improved Convergence and Diversity Control

In modern society, sustainability has become an increasingly important issue. By solving multi-objective problems, decision-makers can make more sustainable decisions. To efficiently solve multi-objective problems, an adaptive strategy is proposed to optimize the crossover and mutation operators of the nondominated sorting genetic algorithm II (NSGA-II). Moreover, the multi-objective flexible job shop scheduling problem is modeled by incorporating worker fatigue factors. Finally, the algorithm performance was tested using ZDT and DTLZ series test functions, and the multi-objective solving performance of the algorithm was tested based on standard examples FMk01-FMk06.The results showed that in the ZDT1 and ZDT2 test functions, the solution set coverage of the proposed algorithm was 0.833 and 0.906, respectively, and the inverse generation distance was 0.006 and 0.0059, respectively, achieving better convergence and diversity. In the DTLZ1 test function, the inverse generation distance of the proposed algorithm did not exceed 2. In the FMk03 example, the inverse generation distance of the proposed algorithm was 0.009, which was lower than the traditional NSGA-II algorithm. In the FMk06 example, the proposed algorithm achieved a super volume of 0.37, which was higher than the multiobjective squirrel search algorithm and NSGA-III algorithm. The experiment has demonstrated the effectiveness of the improved algorithm in solving multi-objective issues. The research results contribute to improving the efficiency of addressing multi-objective optimization and complex problems in real life, enhancing the scientificity and effectiveness of decision-making.