Decomposition based multiobjective evolutionary algorithm with adaptive resource allocation for energy-aware welding shop scheduling problem

Welding is an important industrial process that consumes a huge amount of energy. This paper addresses the energy-aware welding shop scheduling problem (EAWSSP) to minimize both makespan and energy consumption. A mathematical model is presented and a multiobjective evolutionary algorithm based on decomposition with adaptive resource allocation (MOEA/D-ARA) is proposed. Two initialization heuristics are designed to generate an initial population with certain quality and diversity. To effectively improve solutions located in different objective spaces, several objective-oriented search operators are designed. A cooperative search and a problemspecific local intensification are represented to balance the exploration and exploitation. An adaptive resource allocation strategy is developed to improve the computational efficiency of the algorithm. Computational experiments demonstrate the effectiveness of the adaptive resource allocation strategy, and statistical comparisons to the existing algorithms demonstrate the superiority of MOEA/D-ARA to solve EAWSSP. In addition, the application of MOEA/D-ARA to a real-world case also verifies the effectiveness of the proposed algorithm to minimize makespan and energy consumption of the EAWSSP.