Tracking Variable Fitness Landscape in Dynamic Multi-Objective Optimization Using Adaptive Mutation and Crossover Operators

Abstract

Many real-world problems are modeled as multi-objective optimization problems whose optimal solutions change with time. These problems are commonly termed dynamic multi-objective optimization problems (DMOPs). One challenge associated with solving such problems is the fact that the Pareto front or Pareto set often changes too quickly. This means that the optimal solution set at period $t$ may likely vary from that at $(t+1)$ , and this makes the process of optimizing such problems computationally expensive to implement. This article proposes the use of adaptive mutation and crossover operators for the non-dominated sorting genetic algorithm III (NSGA-III). The aim is to find solutions that can adapt to fitness changes in the objective function space over time. The proposed approach improves the capability of NSGA-III to solve multi-objective optimization problems with solutions that change quickly in both space and time. Results obtained show that this method of population reinitialization can effectively optimize selected benchmark dynamic problems. In addition, we test the capability of the proposed algorithm to select robust solutions over time. We recognize that DMOPs are characterized by rapidly changing optimal solutions. Therefore, we also test the ability of our proposed algorithm to handle these changes. This is achieved by evaluating its performance on selected robust optimization over time (ROOT) and robust Pareto-optimality over time (RPOOT) benchmark problems.