Hybrid Selection and Adaptive Strategies with Clustering Strategies for Solving Multi-Objective Optimization Problems

Abstract

In response to the shortcomings of the classic multi-objective optimization algorithm NSGA-II, such as slow convergence speed, difficulty in maintaining population diversity, and tendency to get trapped in local optima when solving complex problems, an improved fast elite multi-objective genetic algorithm (HSA-MOEA) that integrates hybrid initialization strategy, double-layer selection mechanism, adaptive crossover mutation, and particle swarm optimization (PSO) enhancement strategy is proposed. This algorithm improves in three core aspects: initial population construction, selection mechanism design, and evolutionary operator optimization. It adopts a hybrid initialization strategy combining Latin hypercube and boundary focused sampling to enhance the quality of the initial population; designs a double-layer selection mechanism including fast non-dominated sorting, adaptive crowding degree calculation, k-means++ clustering, and binary tournament selection to balance convergence and population diversity; constructs an adaptive operator combination of simulated binary crossover, uniform crossover, polynomial mutation, and Gaussian mutation to achieve a smooth transition between global exploration and local exploitation; combines PSO enhancement strategy to accelerate the convergence rate of elite individuals. Using the ZDT1-ZDT4 and DTLZ1-DTLZ8 series of standard test functions as verification carriers, the HSA-MOEA is compared with classic algorithms such as NSGA-II, NSGA-III, MOEA-D, and IBEA through experimental comparisons. The performance evaluation indicators used are reverse generation distance (IGD), generation distance (GD), and super volume (HV), and statistical verification is conducted using the Wilcoxon paired rank test. The experimental results show that HSA-MOEA significantly outperforms the comparison algorithms in terms of convergence accuracy, distribution uniformity of the solution set, and robustness, especially in complex multi-objective optimization problems with multiple peaks, non-convexity, and discontinuous frontiers. Applying this algorithm to the multi-objective path planning problem of robots, with path length, smoothness, and safety as optimization goals, the experimental results in a 20×20 grid map show that the optimized path length is shortened by 5.0%, the smoothness is increased by 89.4%, and the safety distance remains stable, verifying the effectiveness and practicality of HSA-MOEA in practical engineering problems. This algorithm provides a new effective approach for solving complex multi-objective optimization problems and has good application prospects in intelligent optimization and autonomous navigation fields.