Effective 2- and 3-Objective MOEA/D Approaches for the Chance Constrained Knapsack Problem

Ishara Hewa Pathiranage, Frank Neumann, Denis Antipov, Aneta Neumann

Abstract: Optimizing real-world problems often involves decision-making under uncertainty due to the presence of unknown or uncontrollable variables. Chance-constraints allow to model the optimization problem with stochastic components by ensuring the probabilistic constraint is satisfied with high probability. Multi-objective evolutionary algorithms (MOEAs) are successfully applied to chance constrained optimization problems to achieve high-quality results. Most of these algorithms are based on Pareto dominance for measuring the quality of solutions during their search. A very few algorithms are based on the decomposition approach which tries to optimize the aggregations of the objectives. Among them, multi-objective evolutionary algorithm based on decomposition (MOEA/D) is one of the efficient MOEAs which decomposes the multi-objective optimization problems (MOPs) into a number of scalar optimization problems and then optimizes these sub-problems simultaneously. In this paper, we investigate the effectiveness of the MOEA/D algorithm when solving 2- and 3-objective formulations of the chance constrained knapsack problem, where the weights of each item are stochastic. We compare its performance with global simple evolutionary multi-objective optimizer (GSEMO) across various benchmark scenarios. Overall, we demonstrate that the MOEA/D achieved high-quality solutions with lower computational complexity.