A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems

The particle swarm optimization (PSO) has been widely used to solve continuous problems. The discrete problems have just begun to be also solved by the discrete PSO. However, the combinatorial problems remain a prohibitive area to the PSO mainly in case of integer values. In this paper, we propose a combinatorial PSO (CPSO) algorithm that we take up challenge to use in order to solve a multi-mode resource-constrained project scheduling problem (MRCPSP). The results that have been obtained using a standard set of instances, after extensive experiments, prove to be very competitive in terms of number of problems solved to optimality. By comparing average deviations and percentages of optima found, our CPSO algorithm outperforms the simulated annealing algorithm and it is close to the PSO algorithm. © 2007 Elsevier Inc. All rights reserved.