Hybrid Particle Swarm Optimization and convergence analysis for scheduling problems

This paper proposes a hybrid particle swarm optimization algorithm and for solving Flow Shop Scheduling Problems (FSSP) and Job Shop Scheduling Problems (JSSP) to minimize the maximum makespan. A new hybrid heuristic, based on Particle Swarm Optimization (PSO), Tabu Search (TS) and Simulated Annealing (SA), is presented. By reasonablycombining these three different search algorithms, we develop a robust, fast and simply implemented hybrid optimization algorithm HPTS (Hybrid of Particle swarm optimization, Tabu search and Simulated annealing). On the other hand, we analyze the convergence of PSO algorithm with an optimum keeping strategy and TS, SA algorithms by Markov chain theory at a different aspect in this paper, and HPTS algorithm is proved to be convergent. This hybrid algorithm is applied to the standard benchmark sets and compared with other approaches. The experimental results show that the proposed algorithm could obtain the high-quality solutions within relatively short computation time. Meanwhile, the convergence of HPTS is proved. For example, in 30 and 43 benchmarks, 7 new upper bounds and 6 new upper bounds are obtained by the HPTS algorithm, respectively.