Distributed flow shop scheduling of a camshaft machining is an important optimization problem in the automobile industry. The previous studies on distributed flow shop scheduling problem mainly emphasized homogeneous factories (shop types are identical from factory to factory) and economic criterion (e.g., makespan and tardiness). Nevertheless, heterogeneous factories (shop types are varied in different factories) and environment criterion (e.g., energy consumption and carbon emission) are inevitable because of the requirement of practical production and life. In this article, we address this energy-efficient scheduling of distributed flow shop with heterogeneous factories for the first time, where contains permutation and hybrid flow shops. First, a new mathematical model of this problem with objectives of minimization makespan and total energy consumption is formulated. Then, a hybrid multiobjective optimization algorithm, which integrates the iterated greedy (IG) and an efficient local search, is designed to provide a set of tradeoff solutions for this problem. Furthermore, the parameter setting of the proposed algorithm is calibrated by using a Taguchi approach of design-of-experiment. Finally, to verify the effectiveness of the proposed algorithm, it is compared against other well-known multiobjective optimization algorithms including MOEA/D, NSGA-II, MMOIG, SPEA2, AdaW, and MO-LR in an automobile plant of China. Experimental results demonstrate that the proposed algorithm outperforms these six state-of-the-art multiobjective optimization algorithms in this real-world instance.

Engineering optimization problems usually involve computationally expensive simulations and many design variables. Solving such problems in an efficient manner is still a major challenge. In this paper, a generalized surrogate-assisted evolutionary algorithm is proposed to solve such high-dimensional expensive problems. The proposed algorithm is based on the optimization framework of the genetic algorithm. This algorithm proposes to use a surrogate-based trust region local search method, a surrogate-guided genetic algorithm updating mechanism with a neighbor region partition strategy and a prescreening strategy based on the expected improvement infilling criterion of a simplified Kriging in the optimization process. The surrogate-guided genetic algorithm updating mechanism is a special characteristic of the proposed algorithm. This mechanism makes a fusion between surrogates and the evolutionary algorithm. The neighbor region partition strategy effectively retains the diversity of the population. Moreover, multiple surrogates used in the surrogate-guided genetic algorithm updating mechanism make the proposed algorithm optimize robustly. The proposed algorithm is validated by testing several high-dimensional numerical benchmark problems with dimensions varying from 30 to 100, and an overall comparison is made between the proposed algorithm and other optimization algorithms. The results show that the proposed algorithm is very efficient and promising for optimizing high-dimensional expensive problems.

This paper investigates an energy-efficient hybrid flowshop scheduling problem with the consideration of machines with different energy usage ratios, sequence-dependent setups, and machine-to-machine transportation operations. To minimize the makespan and total energy consumption simultaneously, a mixed-integer linear programming (MILP) model is developed. To solve this problem, a three-stage multiobjective approach based on decomposition (TMOA/D) is suggested, in which each solution is bound with a main weight vector and a set of its neighbors. Accordingly, a variable direction strategy is developed to ensure each solution along its main direction is thoroughly exploited and can jump to the neighboring directions using a proximity principle. To ensure an active schedule of arranging jobs to machines, a two-level solution representation is employed. In the first phase, each solution attempts to improve itself along its current weight vector through a developed neighborhood-based local search. In the second phase, the promising solutions are selected through the technique for order preference by similarity to an ideal solution. Then, they attempt to update themselves with a proposed global replacement strategy via incorporation with their closing solutions. In the third phase, a solution conducts a large perturbation when it goes through all its assigned weight vectors. Extensive experiments are conducted to test the performance of TMOA/D, and the results demonstrate that TMOA/D has a very competitive performance.