An effective hybrid heuristic for flow shop scheduling

In typical production scheduling problems, flow shop scheduling is one of the strongly NP-complete combinatorial optimisation problems with a strong engineering background. In this paper, after investigating the effect of different initialisation, crossover and mutation operators on the performances of a genetic algorithm (GA), we propose an effective hybrid heuristic for flow shop scheduling. First, the famous NEH heuristic is incorporated into the random initialisation of the GA to generate the initial population with a certain prescribed suboptimal quality and diversity. Secondly, muhicrossover operators are applied to subpopulations divided from the original population to enhance the exploring potential and to enrich the diversity of the crossover templates. Thirdly, classical mutation is replaced by a metropolis sample of simulated annealing with probabilistic jump and multiple neighbour state generators to enhance the neighbour search ability and to avoid premature convergence, as well as to avoid the problem of choosing the mutation rate. Simulation results based on benchmarks demonstrate the effectiveness of the hybrid heuristic.