Improving decomposition-based MOEAs for combinatorial optimisation by intensifying corner weights

In the real world, a class of common problems such as supply chain management, project scheduling, portfolio optimisation and facility location design are multi-objective combinatorial optimisation problems (MOCOPs), where there are multiple objectives and the set of feasible solutions is discrete. In MOCOPs, corner solutions are solutions in which at least one objective reaches the optimal value. Corner solutions are important as they are likely to be preferred by the decision maker and are able to help improve algorithm performance. In this paper, we first reveal that in decomposition-based MOEAs, improving the corner weights (as opposed to improving the middle weights) significantly enhances the generation of corner solutions, thereby enhancing the overall performance of algorithms. Based on this, we propose a method to enhance the search for corner solutions in MOCOPs. We act on a class of popular MOEAs, decomposition-based MOEAs, and in their evolutionary mechanism we intensify the weights in the corner areas. To verify the proposed method, we conduct experiments by incorporating the method into three decomposition-based MOEAs, MOEA/D, MOEA/D-DRA-UT and MOEA/D-LdEA (the latter two were designed specifically for enhancing the search of corner solutions). The experimental results demonstrate that the proposed method can improve the spread of solution sets found, without compromising the quality of internal solutions.