Green flexible job shop scheduling problem (FJSP) aims to improve profit and reduce energy consumption for modern manufacturing. Meanwhile, FJSP with type-2 fuzzy processing time is proposed to predict the uncertainty in timing constrain for better simulating the practical production. This study addresses the multi-objective energy-efficient flexible job shop scheduling problem with type-2 processing time (ET2FJSP), where the minimization of makespan and total energy consumption are considered simultaneously. The previous studies do not propose the model verification and energy-saving strategy. Moreover, the best parameters required by an algorithm in different stage is different. Therefore, we propose a mixed integer linear programming model and design a learning-based reference vector memetic algorithm (LRVMA). Its main features are: i) four problem-specific initial rules are presented for initialization to generate diverse solutions; ii) four problem-specific local search methods are incorporated to enhance the exploitation; iii) an effective solution selection method depending on the Tchebycheff decomposition strategy is utilized to balance the convergence and diversity; iv) a reinforcement learning-based parameter selection strategy is proposed to improve the diversity of nondominated solutions, and v) an energy-saving strategy is designed to reduce energy consumption. To verify the effectiveness of LRVMA, it is compared against other related algorithms. The results demonstrate that LRVMA outperforms the compared algorithms for solving ET2FJSP.

Solving constrained multi-objective optimization problems (CMOPs) with various features and challenges via evolutionary algorithms is very popular. Existing methods usually adopt an additional helper problem to simplify and solve them by divide-and-conquer. This paper proposes a new multitasking framework for CMOPs, borrowing the idea of evolutionary multitasking optimization. The main contributions are i) a multitasking framework is proposed, where a CMOP is modeled as a multitasking optimization problem with three tasks. Then, it is solved by constraint-first, constraint-ignored, and constraint-relaxed multi-objective evolutionary algorithms; ii) a knowledge expression and a transfer strategy are devised to transfer the knowledge among the tasks; and iii) based on the proposed framework, a new two-stage algorithm is presented to solve CMOPs. The effectiveness of our approach is validated through experiments on four CMOP benchmark suites and 19 real-world CMOPs.

Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention. Various constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been developed with the use of different algorithmic strategies, evolutionary operators, and constraint-handling techniques. The performance of CMOEAs may be heavily dependent on the operators used, however, it is usually difficult to select suitable operators for the problem at hand. Hence, improving operator selection is promising and necessary for CMOEAs. This work proposes an online operator selection framework assisted by Deep Reinforcement Learning. The dynamics of the population, including convergence, diversity, and feasibility, are regarded as the state; the candidate operators are considered as actions; and the improvement of the population state is treated as the reward. By using a Q-network to learn a policy to estimate the Q-values of all actions, the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance. The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems. The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.