Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems

This study analyzes multiobjective d-dimensional knapsack problems (MOd-KP) within a comparative analysis of three multiobjective evolutionary algorithms (MOEAs): the [epsilon]-nondominated sorted genetic algorithm II ([epsilon]-NSGAII), the strength Pareto evolutionary algorithm 2 (SPEA2) and the [epsilon]-nondominated hierarchical Bayesian optimization algorithm ([epsilon]-hBOA). This study contributes new insights into the challenges posed by correlated instances of the MOd-KP that better capture the decision interdependencies often present in real world applications. A statistical performance analysis of the algorithms uses the unary [epsilon]-indicator, the hypervolume indicator and success rate plots to demonstrate their relative effectiveness, efficiency, and reliability for the MOd-KP instances analyzed. Our results indicate that the [epsilon]-hBOA achieves superior performance relative to [epsilon]-NSGAII and SPEA2 with increasing number of objectives, number of decisions, and correlative linkages between the two. Performance of the [epsilon]-hBOA suggests that probabilistic model building evolutionary algorithms have significant promise for expanding the size and scope of challenging multiobjective problems that can be explored.