Decomposition-based interval multi-objective evolutionary algorithm with adaptive adjustment of weight vectors and neighborhoods

Abstract

Interval multi-objective optimization problems (IMOPs) are one of the most critical optimization problems in practical applications. However, compared to deterministic multi-objective optimization problems (MOPs), there are few researchs addressing IMOP. In addition, the uncertainty contained in the problem makes the distribution of the population more challenging. Therefore, this paper proposed a decomposition-based interval multi-objective evolutionary algorithm with adaptive adjustment of weight vectors and neighborhoods (IMOEA/D-AWN). Firstly, an interval sparsity level function (ISL) is constructed to measure the density of individuals, and a comprehensive ranking of interval sparsity ranking and interval uncertainty ranking is proposed. For the purpose of improving the distribution of the population while reducing its uncertainty, based on the above comprehensive ranking, a new adaptive adjustment weight vector strategy guided by interval elite population is designed. Besides, an adaptive adjustment neighborhoods strategy is designed. This strategy adjusts individuals' neighborhood size according to the number of iterations to improve the efficiency of evolution. Finally, the IMOEA/D-AWN is evaluated on 17 interval benchmark test problems and a collaborative computation offloading optimization problem, and compared with four advanced multi-objective evolutionary algorithms with interval parameters (IMOEAs). Experimental results show that this algorithm performs well in convergence, diversity, and uncertainty.