MOEA/D with Uniform Design for Solving Multiobjective Knapsack Problems

The 0/1 knapsack problem is a well-known problem, which appears in many real domains with practical importance. The problem is NP-complete. The multiobjective 0/1 knapsack problem is a generalization of the 0/1 knapsack problem in which multiple knapsacks are considered. Many algorithms have been proposed in the past five decades for both single and multiobjective knapsack problems. A new version of MOEA/D with uniform design for solving multiobjective 0/1 knapsack problems is proposed in this paper. The algorithm adopts the uniform design method to generate the aggregation coefficient vectors so that the decomposed scalar optimization subproblems are uniformly scattered, and therefore the algorithm could explore uniformly the region of interest from the initial iteration. To illustrate how the algorithm works, some numerical experiments on the benchmark multiobjective knapsack problems are realized. Experimental results show that the proposed algorithm outperforms NSGA-II, SPEA2 and PESA significantly for the 2-objective, 3-objective and 4-objective knapsack problems.