Distributed permutation flowshop scheduling is an NP-hard problem that has become a hot research topic in the fields of optimization and manufacturing in recent years. Multimodal optimization finds multiple global and local optimal solutions of a function. This study proposes a harmony search algorithm with iterative optimization operators to solve the NP-hard problem for multimodal optimization with the objective of makespan minimization. First, the initial solution set is constructed by using a distributed NEH operator. Second, after generating new candidate solutions, efficient iterative optimization operations are applied to optimize these solutions, and the worst solutions in the harmony memory (HM) are replaced. Finally, the solutions that satisfy multimodal optimization of the harmony memory are obtained when the stopping condition of the algorithm is met. The constructed algorithm is compared with three meta-heuristics: the iterative greedy meta-heuristic algorithm with a bounded search strategy, the improved Jaya algorithm, and the novel evolutionary algorithm, on 600 newly generated datasets. The results show that the proposed method outperforms the three compared algorithms and is applicable to solving distributed permutation flowshop scheduling problems in practice.

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.

Credit risk transmission between cross‐platforms is an important issue in the construction of a credit service system. The effect of credit risk transmission between credit entities (nodes) is analyzed in this paper. A heuristic algorithm based on hybrid strategies (HAHS) is proposed to find risk transmission paths and calculate the influence of nodes. Besides, a novel community model is applied to predict the credit risk areas in advance. In detail, the mathematical association structure between credit entities is firstly given in the algorithm, and the breadth first search algorithm is used to find the hierarchical nodes on the credit risk transmission paths. Then, the characteristics of credit risk transmission are analyzed, and the calculation methods of single‐path and multipath influence are proposed. Finally, the credit entities are divided into communities based on a greedy strategy considering the characteristics of the credit entity association structure. The threshold control strategy is adopted to find global key nodes among all of the entities and local key nodes in communities, respectively, so as to realize the early warning of credit risk.