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

• Published in: European journal of operational research Vol. 211; no. 3; pp. 466 - 479
• Main Authors: Shah, Ruchit, Reed, Patrick
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.06.2011; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Algorithms; Applied sciences; Bayesian analysis; Combinatorial optimization; Combinatorial optimization Multiobjective optimization Knapsack problem Probabilistic model building evolutionary algorithms Hierarchical Bayesian networks; Comparative analysis; Correlation; Correlation analysis; Decision theory. Utility theory; Evolutionary algorithms; Exact sciences and technology; Flows in networks. Combinatorial problems; Genetic algorithms; Hierarchical Bayesian networks; Knapsack problem; Mathematical programming; Multiobjective optimization; Operational research; Operational research and scientific management; Operational research. Management science; Optimization; Optimization algorithms; Pareto optimality; Probabilistic model building evolutionary algorithms; Probability theory; Reliability theory. Replacement problems; Studies; Combinatorial optimization; Probabilistic model building evolutionary algorithms; Multiobjective optimization; Hierarchical Bayesian networks; Knapsack problem; Bayes estimation; algorithms; Statistical analysis; Probabilistic approach; Pareto optimum; Evolutionary algorithm; Multiobjective programming; Relative efficiency; Modeling; Genetic algorithm; Bayes network; Probabilistic model building evolutionary; Reliability; Algorithm analysis
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2011.01.030

This study analyzes multiobjective d-dimensional knapsack problems (MOd-KP) within a comparative analysis of three multiobjective evolutionary algorithms (MOEAs): the ε-nondominated sorted genetic algorithm II ( ε-NSGAII), the strength Pareto evolutionary algorithm 2 (SPEA2) and the ε-nondominated hierarchical Bayesian optimization algorithm ( ε-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 ε-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 ε-hBOA achieves superior performance relative to ε-NSGAII and SPEA2 with increasing number of objectives, number of decisions, and correlative linkages between the two. Performance of the ε-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.