On Multiobjective Knapsack Problems with Multiple Decision Makers

Many real-world optimization problems require optimizing multiple conflicting objectives simultaneously, and such problems are called multiobjective optimization problems (MOPs). As a variant of the classical knapsack problems, multi-objective knapsack problems (MOKPs), exist widely in the real-world applications, e.g., cargo loading, project and investment selection. There is a special class of MOKPs called multiparty multiobjective knapsack problems (MPMOKPs), which involve multiple decision makers (DMs) and each DM only cares about some of all the objectives. To the best of our knowledge, little work has been conducted to address MPMOKPs. In this paper, a set of benchmarks which have common Pareto optimal solutions for MPMOKPs is proposed. Besides, we design a SPEA2-based algorithm, called SPEA2-MP to solve MPMOKPs, which aims at finding the common Pareto optimal solutions to satisfy multiple decision makers as far as possible. Experimental results on the benchmarks have demonstrated the effectiveness of the proposed algorithm.