The effect of diversity maintenance on prediction in dynamic multi-objective optimization

Abstract

There are many dynamic multi-objective optimization problems (DMOPs) in real-life engineering applications whose objectives change over time. After an environmental change occurs, prediction strategies are commonly used in dynamic multi-objective optimization algorithms to find the new Pareto optimal set (POS). Being able to make more accurate prediction means the algorithm requires fewer computational resources to make the population approximate to the Pareto optimal front (POF). This paper proposes a hybrid diversity maintenance method to improve prediction accuracy. The method consists of three steps, which are implemented after an environmental change. The first step, based on the moving direction of the center points, uses the prediction to relocate a number of solutions close to the new Pareto front. On the basis of self-defined minimum and maximum points of the POS in this paper, the second step applies the gradual search to produce some well-distributed solutions in the decision space so as to compensate for the inaccuracy of the first step, simultaneously and further enhancing the convergence and diversity of the population. In the third step, some diverse individuals are randomly generated within the region of next probable POS, which prompts the diversity of the population. Eventually the prediction becomes more accurate as the solutions with good convergence and diversity are selected after the non-dominated sort on the combined solutions generated by the three steps. Compared with three other prediction methods on a series of test instances, our method is very competitive in convergence and diversity as well as the speed at which it responds to environmental changes.