A Hybrid Harmony Search for Distributed Permutation Flowshop Scheduling with Multimodal Optimization

Multimodal optimization is to find multiple global and local optimal solutions of a function, rather than a single solution. This study proposes a harmony search algorithm with iterative optimizing operators to solve the NP-hard distributed permutation flowshop scheduling for multimodal optimization. First, the initial solution set is constructed by using a distributed NEH operator. Second, after generating new candidate solutions, efficient iterative optimizing operators are applied to optimize these solutions and the worst solutions in the harmony memory(HM) are replaced. The proposed operations are repeated until the stopping condition of the algorithm is met. Finally, the solutions satisfying multimodal optimization in the harmony memory are obtained. The constructed method is compared with two meta-heuristics, the iterative greedy meta-heuristic algorithm with a bounded search strategy and the improved Jaya algorithm, on 600 newly generated datasets. The results show that it runs stably and outperforms the two algorithms compared.