A decomposition-based multiobjective evolutionary algorithm with weights updated adaptively

Abstract

• A new trigger is developed to control when the weight should be updated. • A new adaptive weighting method is proposed. • A new decomposition algorithm with weights updated adaptively is proposed. • The proposed algorithm is applied to solve various multiobjective optimization problems . Recently, decomposition-based multiobjective evolutionary algorithms (DMEAs) have become more prevalent than other patterns (e.g., Pareto-based algorithms and indicator-based algorithms) for solving multiobjective optimization problems (MOPs). They utilize a scalarizing method to decompose an MOP into several subproblems based on the weights provided, resulting in the performances of the algorithms being highly dependent on the uniformity between the problem’s optimal Pareto front and the distribution of the specified weights. However, weight generation is generally based on a simplex lattice design, which is suitable for “regular” Pareto fronts (i.e., simplex-like fronts) but not for other “irregular” Pareto fronts. To improve the efficiency of this type of algorithm, we develop a DMEA with weights updated adaptively (named DMEA-WUA) for the problems regarding various Pareto fronts. Specifically,the DMEA-WUA introduces a novel exploration versus exploitation model for environmental selection.The exploration process finds appropriate weights for a given problem in four steps: weight generation, weight deletion, weight addition and weight replacement. Exploitation means using these weights from the exploration step to guide the evolution of the population. Moreover, exploration is carried out when the exploitation process is stagnant; this is different from the existing method of periodically updating weights. Experimental results show that our algorithm is suitable for solving problems with various Pareto fronts, including those with “regular” and “irregular” shapes.