A diversity reserved quantum particle swarm optimization algorithm for MMKP

As a variant of the classical knapsack problem, the multi-dimension multi-choice knapsack problem (MMKP) is widely used in practical applications. It is a NP-complete problem, the exact solution of MMKP cannot be founded in polynomial-time. As one of the heuristic algorithms, quantum particle swarm optimization (QPSO) algorithm provides a sight to get the approximately optimal result for MMKP. However, due to the multiple constraints among dimensions and the dispersing feasible regions, QPSO tends to fall into local convergence. Hence a modified diversity reserved QPSO algorithm for MMKP is proposed in this paper: (i) to measure the availability of a particle by comparing the position between itself and the next alternative during the generation; (ii) import a position disturbance operator to increase the diversity of population. Experiments demonstrate that the proposed evolutionary algorithm could find better near-optimal results. And the analysis of convergence and execution time suggest that the probability of local convergence is declined in our algorithm.