A tri-objective preference-based uniform weight design method using Delaunay triangulation

User-preference based multi-objective evolutionary algorithms (MOEAs) have attracted much attention recently because it helps save computational cost, make better use of the knowledge offered by the decision-maker, and offer more insight into solutions in the region of interest (ROI). Weight vectors based MOEAs can be converted to their user-preference based versions by offering a set of evenly distributed weight vectors located in ROI. Yet existing weight design methods can only generate weight vectors in the whole unit plane in the weight space. To generate an arbitrary number of weight vectors in ROI, this paper proposes a tri-objective user-preference based uniform weight design method using Delaunay Triangulation (PUWD-DT), so that weight vectors can be fine-tuned to uniformity in ROI. Furthermore, the proposed PUWD-DT based preference method with the achievement scalarizing function is assembled into MOEA/D to convert it into its user-preference based version (MOEA/D+PUWD-DT) and the convergence of population in ROI for optimization problems with irregular shaped Pareto front is also promoted. Finally, the MOEA/D+PUWD-DT is applied to the reservoir flood control operation problem, and our experimental results indicate that the proposed preference-based MOEA method performs better than the state-of-the-art.