Multiple-Population Hybrid Evolutionary Algorithm for Solving Distributed Heterogeneous Lot-Streaming Hybrid Flowshop Scheduling Problem with Missing Operations

A Multi-Population Hybrid Evolutionary Algorithm (MPHEA) was proposed for the distributed heterogeneous lot-streaming hybrid flowshop scheduling problem with missing operations, aiming to minimize the makespan, total flow time, idle time of machines, and total weighted earliness and tardiness. Firstly, the calculation method for each optimization objective was provided, and an appropriate coding scheme was developed. Then, a parallel coevolutionary strategy was designed between the total population and the four subpopulations. After performing hybrid crossover and mutation operations on the population, the population was updated based on Pareto dominance and crowding distance to ensure diversity and preservation of high-quality solutions. Furthermore, partial solutions were extracted from the population to form four subpopulations, each focusing on optimizing a specific objective. The parallel evolution of the population and subpopulations allows subpopulations to avoid overly focusing on a particular objective when evolving in their respective directions, thereby achieving balanced optimization of multiple objectives. Considering the impact of missing operations on scheduling, corresponding heuristic rules of missing operations was designed. Finally, the effectiveness of MPHEA in solving the scheduling problem was verified through 400 instances. The results of four well-known algorithms were compared and the empirical results showed that MPHEA outperformed the compared algorithms.