Gradient-based hybrid method for multi-objective optimization problems

How to strike a tricky balance between convergence and diversity is still an ever-present challenge in the field of multi-objective optimization. In this paper, a hybrid method of gradient-based and improved non-dominated sorting genetic algorithm is proposed to solve this complex problem (HMGB). Initially, we propose a partition clustering method under a new criterion to divide the individuals in the target space, which not only facilitates the construction of Pareto descent directions but also prevents the population from falling into local optima. Subsequently, we improve the finite-difference method to obtain gradient information for multiple objective functions, which are used to construct Pareto descent directions that can accelerate convergence. Finally, we replaced the simulated binary crossover in NSGA-II with a normally distributed crossover, and combined it with polynomial variation to generate offspring, which we used for global exploration to increase the diversity of the population. The HMGB algorithm was compared with several state-of-the-art algorithms on benchmark functions and real-world problems. Experimental results demonstrate that the HMGB algorithm possesses strong competitiveness and effectiveness.