Population Decomposition-Based Greedy Approach Algorithm for the Multi-Objective Knapsack Problems

Despite the effectiveness of the decomposition-based multi-objective evolutional algorithm (MOEA/D-M2M) in solving continuous multi-objective optimization problems (MOPs), its performance in addressing 0/1 multi-objective knapsack problems (MOKPs) has not been fully explored. In this paper, we use MOEA/D-M2M with an improved greedy repair strategy to solve MOKPs. It first decomposes an MOKP into a number of simple optimization subproblems and solves them in a collaborative way. Each subproblem has its own subpopulation, and then an improved greedy strategy is introduced to improve the performance of the proposed algorithm on MOKPs. Therein, a weight vector chosen randomly from a corresponding subpopulation is utilized to repair infeasible individuals or improve feasible individuals to have a better fitness, which improves the convergence of the population. Experimental studies on a set of test instances indicate that the MOEA/D-M2M with the improved greedy strategy is superior to MOGLS and MOEA/D in terms of finding better approximations to the Pareto front.