A multiobjective state transition algorithm based on modified decomposition method

Aggregation functions largely determine the convergence and diversity performance of multi-objective algorithms in decomposition methods. Nevertheless, the traditional Tchebycheff function does not consider the matching relationship between the weight vectors and candidate solutions. To deal with this issue, a new multiobjective state transition algorithm based on modified decomposition method (MOSTA/D) is proposed. According to the analysis of the relationship between the weight vectors and candidate solutions under the Tchebycheff decomposition scheme, the concept of matching degree is introduced which employs vectorial angles between weight vectors and candidate solutions. Based on the matching degree, a new modified Tchebycheff aggregation function is proposed in MOSTA/D. It can adaptively select the candidate solutions which are better matched with the weight vectors. This proposed MOSTA/D decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them in a collaborative manner. Each individual solution in the population of MOSTA/D is associated with a subproblem. Four mutation operators in STA are adopted to generating candidate solutions on subproblems and maintaining the population diversity. Relevant experimental results show that the proposed algorithm is highly competitive in comparison with other state-of-the-art evolutionary algorithms on tackling a set of benchmark problems with complicated Pareto fronts and a typical engineering optimization problem. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

The MOSTA/D algorithm proposes a new modified Tchebycheff aggregation function based on the concept of matching degree, which adaptively selects candidate solutions better matched with weight vectors, and optimizes subproblems collaboratively to maintain population diversity. Experimental results demonstrate the competitiveness of the proposed algorithm in solving benchmark problems with complex Pareto fronts and engineering optimization problems compared to other state-of-the-art evolutionary algorithms.