A Tree-Based Multiobjective Evolutionary Algorithm for Energy-Efficient Hybrid Flow-Shop Scheduling

This paper studies an energy-efficient hybrid flowshop scheduling problem (EHFSP) considering variable machine speed (EHFSP-VMS). To minimize the makespan and total energy consumption simultaneously, a tree-based multiobjective evolutionary algorithm (TMOEA) is proposed. It decomposes a multiobjective optimization problem into multiple scalar optimization subproblems and optimizes them simultaneously. Moreover, different from existing multiobjective evolutionary algorithms (MOEAs), TMOEA maintains Pareto archive using a tree structure instead of a linear structure, which reduces the time complexity of updating Pareto solutions from O(P) to O(logP), where P is the size of Pareto archive. In TMOEA, the population evolution is performed in three stages. Stage one is responsible for local search, in which five different operators are combined in the form of a roulette wheel to explore promising solutions in neighboring regions. Stage two is responsible for the global search, which uses a technique for order preference by similarity to an ideal solution (TOPSIS) to select promising solutions for crossover to promote the population to evolve towards the Pareto front. Stage three is responsible for preventing local optimality, where a neighbor exchange method and opposition-based learning strategy are adopted to escape the local optimal. Computational experiments demonstrate that the tree structure is effective and TMOEA is superior to the existing algorithms in solving EHFSP-VMS.