Multi-objective stochastic project scheduling with alternative execution methods: An improved quantum-behaved particle swarm optimization approach

This paper addresses the multi-objective resource-constrained project scheduling problems with stochastic activity durations and alternative execution methods. Three objectives are considered: minimizing expected makespan, expected cost and robustness. Chance constrained programming is applied for formulating this stochastic problem. A hybrid approach that integrates sample average approximation (SAA) and an improved multi-objective chaotic quantum-behaved particle swarm optimization (MOCQPSO) algorithm is proposed. To improve the diversity of solutions and enhance the global search ability, a two-stage learning strategy that balances the exploration and the exploitation is proposed for MOCQPSO. In addition, chaotic operators including chaotic initialization, crossover and mutation are also introduced. Six benchmark functions and an instance generator based on the RCPSP dataset of PSPLIB are designed to validate the performance of the proposed algorithm. The experimental results demonstrate that our proposed method outperforms the original algorithms in solution diversity and quality.