2021 Volume 12 Issue 2 Pages 45-60
This paper proposes a decomposition-based multi-objective evolutionary algorithm that dynamically arranges weight vectors based on a Pareto front estimation. Evolutionary multi-objective optimization generally requires a solution set that uniformly approximates the Pareto front. Decomposition-based algorithms use a weight vector set specifying the target approximation points on the Pareto front. The distribution of solutions depends on the distribution of the weight vector set, and an appropriate weight vector distribution depends on the Pareto front. Conventional algorithms dynamically arranging the weight vector set have employed an archive of non-dominated solutions to estimate the Pareto front. However, the number of non-dominated solutions is limited, even if all of them are archived during the search. The proposed method estimates the Pareto front shape using the response surface methodology and the Pareto front range using the alpha shape based on the limited non-dominated solutions. The proposed method picks a representative set of objective vectors on the estimated Pareto front, converts it to the new weight vector set, and uses it for the search. Experimental results on three objective problems with concave, convex, inverted, and disconnected Pareto fronts show that the radial basis neural network, a response surface methodology, is suited for the Pareto front estimation. Also, results show that the proposed algorithm achieves better search performance than the conventional MOEA/D, S$^3$-CMA-ES, RVEA, MOEA/D-DCWV, -AWA, -URAW, and AR-MOEA.
