A Mahalanobis distance-based approach for dynamic multi-objective optimization with stochastic changes

In recent years, researchers have made significant progress in handling dynamic multi-objective optimization problems (DMOPs), particularly for environmental changes with predictable characteristics. However, little attention has been paid to DMOPs with stochastic changes. It may be difficult for existing dynamic multi-objective evolutionary algorithms (DMOEAs) to effectively handle this kind of DMOPs because most DMOEAs assume that environmental changes follow regular patterns and consecutive environments are similar. This paper presents a Mahalanobis Distance-based approach (MDA) to deal with DMOPs with stochastic changes. Specifically, we make an all-sided assessment of search environments via Mahalanobis distance on saved information to learn the relationship between the new environment and historical ones. Afterward, a change response strategy applies the learning to the new environment to accelerate the convergence and maintain the diversity of the population. Besides, the change degree is considered for all decision variables to alleviate the impact of stochastic changes on the evolving population. MDA has been tested on stochastic DMOPs with 2 to 4 objectives. The results show that MDA performs significantly better than the other latest algorithms in this paper, suggesting that MDA is effective for DMOPs with stochastic changes.