A shuffled frog leaping algorithm with q-learning for distributed hybrid flow shop scheduling problem with energy-saving

Energy saving has always been a concern in production scheduling, especially in distributed hybrid flow shop scheduling problems. This study proposes a shuffled frog leaping algorithm with Q-learning (QSFLA) to solve distributed hybrid flow shop scheduling problems with energy-saving(DEHFSP) for minimizing the maximum completion time and total energy consumption simultaneously. The mathematical model is provided, and the lower bounds of two optimization objectives are given and proved. A Q-learning process is embedded in the memeplex search of QSFLA. The state of the population is calculated based on the lower bound. Sixteen search strategy combinations are designed according to the four kinds of global search and four kinds of neighborhood structure. One combination is selected to be used in the memeplex search according to the population state. An energy-saving operator is presented to reduce total energy consumption without increasing the processing time. One hundred forty instances with different scales are tested, and the computational results show that QSFLA is a very competitive algorithm for solving DEHFSP.