A Clustering Based Niching Method for Effectively Solving the 0-1 Knapsack Problem

Abstract

The 0-1 knapsack problem (01-KP) is a NP-hard combinatorial optimization problems (COPs) with several applications. Because of its non-convexity, its search space contains several local and/or global optimum solutions. In this situation, both the classical and metaheuristic global optimization approaches often failed to locate the optimal solution to the 01-KP. Therefore, this research develops a clustering-based niching (CBN) method for maintaining and locating multiple solutions within an optimization run, increasing the possibility of locating the global optimal solution to the 01-KP. To do this, CBN method divides the population individuals into a number of clusters (similar to niches in a biology or ecology system) by measuring the Hamming distance between individuals. During the optimization, the individuals in the formed clusters independently explore different regions of the combinatorial search space in order to find promising solutions. For simplicity, the proposed CBN method is implemented using a modified binary PSO (lbest-BPSO) method. The numerical results show that the CBN method is superior than the well-known metaheuristic methods on the basis of solution quality, with a better success rate and average function evaluations, over widely used sets of 0-1 knapsack instance. This guarantees that CBN method is a suitable optimization method for determining the optimal solution to combinatorial optimization problems.