The Job Shop Scheduling Problem (JSSP) has enormous industrial applicability. This problem refers to a set of jobs that should be processed in a specific order using a set of machines. For the single-objective optimization JSSP problem, Simulated Annealing is among the best algorithms. However, in Multi-Objective JSSP (MOJSSP), these algorithms have barely been analyzed, and the Threshold Accepting Algorithm has not been published for this problem. It is worth mentioning that the researchers in this area have not reported studies with more than three objectives, and the number of metrics they used to measure their performance is less than two or three. In this paper, we present two MOJSSP metaheuristics based on Simulated Annealing: Chaotic Multi-Objective Simulated Annealing (CMOSA) and Chaotic Multi-Objective Threshold Accepting (CMOTA). We developed these algorithms to minimize three objective functions and compared them using the HV metric with the recently published algorithms, MOMARLA, MOPSO, CMOEA, and SPEA. The best algorithm is CMOSA (HV of 0.76), followed by MOMARLA and CMOTA (with HV of 0.68), and MOPSO (with HV of 0.54). In addition, we show a complexity comparison of these algorithms, showing that CMOSA, CMOTA, and MOMARLA have a similar complexity class, followed by MOPSO.

The Job Shop Scheduling Problem (JSSP) consists of finding the best scheduling for a set of jobs that should be processed in a specific order using a set of machines. This problem belongs to the NP-hard class problems and has enormous industrial applicability. In the manufacturing area, decision-makers consider several criteria to elaborate their production schedules. These cases are studied in multi-objective optimization. However, few works are addressed from this multi-objective perspective. The literature shows that multi-objective evolutionary algorithms can solve these problems efficiently; nevertheless, multi-objective algorithms have slow convergence to the Pareto optimal front. This paper proposes three multi-objective Scatter Search hybrid algorithms that improve the convergence speed evolving on a reduced set of solutions. These algorithms are: Scatter Search/Local Search (SS/LS), Scatter Search/Chaotic Multi-Objective Threshold Accepting (SS/CMOTA), and Scatter Search/Chaotic Multi-Objective Simulated Annealing (SS/CMOSA). The proposed algorithms are compared with the state-of-the-art algorithms IMOEA/D, CMOSA, and CMOTA, using the MID, Spacing, HV, Spread, and IGD metrics; according to the experimental results, the proposed algorithms achieved the best performance. Notably, they obtained a 47% reduction in the convergence time to reach the optimal Pareto front.