## 6 Conclusions and Outlook  
Green machine-scheduling problems, such as optimization problem related to energy concerns, are paid more attention by a wide array of industries, since environmental awareness is part of industrial manufacturing sustainability. This paper presents a novel method called variable neighborhood strategy adaptive search (VaNAS) to solve the parallel-machine-scheduling problem in order to minimize energy consumption while considering job priority and makespan control. Although VaNAS successfully improved solution-search performance in previous studies [17; 22; 36; 37; 38], none had accounted for energy consumption, late delivery charge, and production overhead. The advantage of applying VaNAS in this study was that its algorithms search for the best possible solution in many different areas by using several searching approaches, thereby moving to find more diversification and intensification at all times depending on the designed black-box methods. In addition, we improved the solution-search performance of VaNAS by presenting new neighborhood search strategies: (1) solution destroy and repair (SDR); (2) track-transition method (TTM); and (3) multiplier factor (MF). The proposed methods were performed in three sets of test instances and one case study, and compared with the exact method.  
Computation results show that the proposed VaNAS outperformed all traditional and other proposed methods. It performed as well as the exact method did, illustrated in the small problem, while the traditional DE could find only 25%; CU, SDR, TTM, and MF could not find the optimal solution at all, while VaNAS could find 100% of the optimal solution. Even by increasing the problem size, VaNAS still gave promising results, as it could improve the solution quality by 16.35-19.55% of the solution obtained from the exact method with 30-45 min of computation time, while the exact method required 48-72 h. In the medium-sized and large samples, DE, SDR, TTM, and MF could also improve the solution quality by 7.89-14.59% more than the exact method. In addition, the current practice gave a worse solution than that of the exact method, including all proposed methods, by 1.42-4.37%.  
The excellent solution-search efficiency of VaNSAS in this study and its advantage of a flexible neighborhood search scheme allow researchers to further develop and design new mechanisms for improving solution quality. Additionally, it would be interesting to implement the proposed VaNSAS in various problem areas, such as production planning in a real manufacturing environment, while considering other additional factors or constraints, e.g., the study of the capability of each type of machine, job restriction, and customer-order scheduling.  
Conceptualization, R.N. and C.-H.L.; methodology, R.N.; software, S.P.; validation, C.-H.L., S.P. and K.N.; formal analysis, R.N.; investigation, K.N.; writing--original-draft preparation, R.N.; writing--review and editing, K.N.; project administration, C.-H.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Data Availability StatementData sharing not applicable.  
The authors declare no conflict of interest.