## 2 Literature Review
Although more attention is now paid to energy cost in parallel-machine-scheduling problems, some constraints for job priority and makespan control are also important, such as starting time, completion time, due date, and delivery time, since late-delivery cost and production-overhead cost per working hour impact manufacturers. Some studies attempted to avoid late- or express-delivery charges, such as lateness and tardiness issues. For instance, [PERSON] et al. [49] considered the minimization of total tardiness in identical parallel-machine-scheduling problems by using a genetic algorithm (GA), and compared it with branch-and-bound and particle-swarm-optimization methods. Then, [PERSON] et al. [50] demonstrated minimizing maximal earliness and number of tardy jobs in parallel-machine-scheduling problems. That article proposed the hybrid variable neighborhood search (VNS)-gravitational search algorithm (GSA), which is a combination of VNS and GSA to find a solution. Solution-search efficiency is also an attractive goal for many studies. [PERSON] and [PERSON] [51] also applied the VNS algorithm with the fast evaluation technique (FET) to improve the computational efficiency of solution finding in the identical parallel-machine problem with machine-dependent delivery times in order to minimize total weighted tardiness. In a continuous search space for function optimization, differential evolution (DE) is a type of evolutionary algorithm that is widely implemented [27]. The DE algorithm has gained much attention from scholars since it was first presented by [PERSON] and [PERSON] [28]. There are a variety of DE algorithms in industrial applications studied for optimization problems. For instance, the DE algorithm was implemented for solving production-scheduling problems. [PERSON] et al. [29] demonstrated hybrid differential evolution (HDE) in scheduling problems with splitting jobs. The study proposed a global search method with block mutation and block crossover. Experiment results revealed that the proposed HDE performed better than the traditional DE did. [PERSON] et al. [52] showed the performance of the hybrid DE algorithm for the uniform parallel-machine-scheduling problem with arbitrary job sizes, non-identical capacities, and different speeds. The objective was to minimize makespan. The HDE algorithm was proposed for solving large-scale problems. In this algorithm, individuals were represented as a discrete job sequence. The proposed algorithm and novel mutation were designed on the basis of this representative. [PERSON] and [PERSON] [53] proposed a memetic differential evolution algorithm for an energy-efficient bi-objective-unrelated parallel-machine-scheduling problem in order to minimize makespan and total energy consumption. Efficient speed adjusting and job machine swap heuristic were introduced and integrated into the algorithm as a local search method with an adaptive meta-Lamarckian learning strategy. [PERSON] et al. [19] presented a multi-objective DE algorithm for effectively solving the parallel-batch-processing machine-scheduling problem while considering energy cost on a large scale. In this algorithm, individuals were encoded into job permutations and discrete mutations; crossover operators were designed on the basis of the encoding structure, and a Pareto selection operator was proposed to select what the individuals for the next population are. Defining job permutation, a heuristic was employed to group jobs into batches and schedule them on BPMs. In addition, a procedure to minimize the total energy cost of a schedule without compromising the makespan was proposed by [PERSON] et al. [54]. They investigated the parallel-machine-scheduling problem with different-colored families, sequence-dependent setup times, and machine-eligibility restriction of the dyeing process in textile manufacturing. Generally, the dyeing optimization problem is NP-hard, and the HDE algorithm was proposed to solve real-world data problems.