## 2 Literature Review
The proposed HDE algorithm, a special encoding and decoding scheme, was constructed to deal with the machine-eligibility constraint, and chaos theory was applied to determine the parameter settings of the DE algorithm. [PERSON] et al. [17] presented the traditional DE with embedded heuristics to obtain near-optimal solutions in realistically sized machine scheduling, including capacitated machine restrictions and sequencing-independent setup-time considerations. Results revealed that the proposed method's performance tended to find a new optimal solution during the simulation, while the local-search-based heuristics were trapped at some local optima, and the DE was insufficient for search intensification. Variable neighborhood strategies adaptive search (VaNSAS) is a new type of metaheuristics that was first introduced by [PERSON] et al. [36], with the concept of solving combinatorial optimization problems. The primary idea of the VaNSAS is to allow for algorithms to search in many different areas to obtain the best possible solution by using several searching methods. VaNSAS is very flexible to use in many optimization problems, such as the location and routing problem (LRP). [PERSON] et al. [36] studied the LRP in the Thai rubber industry, and proposed VaNSAS to solve the problem with the objective function of fuel-cost minimization, including a realistic constraint that allowed for a vehicle to collect products by visiting rubber farms more than once in cases where they had more rubber than vehicle capacity. Computation results showed that VaNSAS could find solutions for all problem sizes in much less processing time than that needed by the exact method. After that, [PERSON] et al. [37] presented VaNSAS with another LRP, the green 2-echelon location-routing problem (G2 ELRP), which is a variant of the capacitated location-routing problem (CLRP) and the 2-echelon location routing problem (2 ELRP). The G2 ELRP aims to reduce overall fuel consumption on the basis of distance and road conditions in both echelons. A new constraint considered in the G2 ELRP is that a customer can be served more than once. The finding demonstrated that VaNSAS could solve this case and be applied to other industries. [PERSON] et al. [17] introduced another application of VaNSAS in a sugar mill as a computational tool for scheduling sugarcane-vehicle-unloading systems. The objective was to minimize the makespan of parallel-machine-capacity scheduling with a cyclic sequence, and machine restriction included sequencing-independent setup time. Numerical results showed that, during the simulation, VaNSAS could find optimal solutions. In a manufacturing case study regarding the garment industry, the VaNSAS proposed by [PERSON] et al. [22] presented a better solution and less computation time in order to minimize cycle time for a simple assembly line, balancing the Type 2 problem while considering the number and types of machines operated in each workstation. Recently, [PERSON] et al. [38] applied VaNSAS to minimize the cycle time while considering the limited number of machine types in a particular workstation for the special case of the simple assembly line balancing Type 2 problems, where multi-skilled workers have a set of competencies that allow them to work on more than one machine in a workstation. Results showed that VaNSAS was able to reduce the cycle time and increase assembly line effectiveness. The studies discussed above show that global search metaheuristics (e.g., VNS, GA, DE and VaNSAS) are effective in solving optimization problems such as parallel-machine scheduling. Due to the importance of the environmental and economic impact, studies on energy-cost concerns, job priority, and makespan control are obviously attractive and important in terms of theoretical and application value; however, no previous articles had investigated this kind of problem and employed the VaNSAS algorithm to find the solution.