Solving the Hard Knapsack Problems with a Binary Particle Swarm Approach

Knapsack problems are important NP-Complete combinatorial optimization problems. Although nearly all the classical instances can be solved in pseudo-polynomial time nowadays, yet there are a variety of test problems which are hard to solve for the existing algorithms. In this paper we propose a new approach based upon binary particle swarm optimization algorithm (BPSO) to find solutions of these hard knapsack problems. The standard PSO iteration equations are modified to operate in discrete space. Furthermore, a heuristic operator based on the total-value greedy algorithm is employed into the BPSO approach to deal with constrains. Numerical experiments show that the proposed algorithm outperforms both the existing exact approaches and recent state-of-the-art search heuristics on most of the hard knapsack problems.