Pareto Front Improvements Phase using linkage learning and mating restrictions for solving multi-objective industrial process planning problems with low-sized pareto fronts

Abstract

A thorough analysis of the features of real-world optimization problems is advantageous for many reasons. It helps in choosing an appropriate optimizer to solve the problem at hand. It allows to propose problem-dedicated mechanisms that improve the optimizer’s effectiveness and efficiency. Finally, it allows us to check if and which problems share similar features. In this work, we consider the multi-objective NP-hard production planning problem. We identify that its instances are characterized by the low-sized Pareto fronts, i.e., the best-known Pareto fronts for the instances of this problem are of low size when compared to problem size. To handle such problems, we propose two mechanisms. The first is the Pareto Front Improvement (PFI) phase, which joins objective space-based population clusterization, variable dependency utilization, mating restrictions, and elitism. The second is the solution comparing (CS) procedure that joins the dominance relation, crowding distance, and scalarization using weight vectors. These mechanisms are introduced into the Multi-Objective Parameter-less Population Pyramid (MO-P3), the state-of-the-art optimizer dedicated to multi-objective optimization in binary domains to propose MO-P3-SC-PFI. The experiments show that for the considered real-world problem, MO-P3-SC-PFI is highly competitive with other state-of-the-art optimizers. Additionally, we show that it is effective in solving typical benchmarks. Its advantage increases with the decrease of the ratio between the PF size and problem size.