Calculating the Complete Pareto Front for a Special Class of Continuous Multi-Objective Optimization Problems

Existing methods for multi-objective optimization usually provide only an approximation of a Pareto front, and there is little theoretical guarantee of finding the real Pareto front. This paper is concerned with the possibility of fully determining the true Pareto front for those continuous multi-objective optimization problems for which there are a finite number of local optima in terms of each single objective function and there is an effective method to find all such local optima. To this end, some generalized theoretical conditions are firstly given to guarantee a complete cover of the actual Pareto front for both discrete and continuous problems. Then based on such conditions, an effective search procedure inspired by the rising sea level phenomenon is proposed particularly for continuous problems of the concerned class. Even for general continuous problems to which not all local optima are available, the new method may still work well to approximate the true Pareto front. The good practicability of the proposed method is especially underpinned by multi-optima evolutionary algorithms. The advantages of the proposed method in terms of both solution quality and computational efficiency are illustrated by the simulation results.