This paper presents a hybrid method of Simulated Annealing (SA) algorithm and Sine Cosine Algorithm (SCA) to solve unrelated parallel machine scheduling problems (UPMSPs) with sequence-dependent and machine-dependent setup times. The proposed method, called SASCA, aims to improve the SA algorithm using the SCA as a local search method. The SCA provides a good tool for the SA to avoid getting stuck in a focal point and improving the convergence to an efficient solution. SASCA algorithm is used to solve UPMSPs by minimizing makespan. To evaluate the performance of SASCA, a set of experiments were performed using 30 tests for 4 problems. Moreover, the performance of the proposed method was compared with other meta-heuristic algorithms. The comparison results showed the superiority of SASCA over other methods in terms of performance dimensions.

Scheduling can be described as a decision-making process. It is applied in various applications, such as manufacturing, airports, and information processing systems. More so, the presence of symmetry is common in certain types of scheduling problems. There are three types of parallel machine scheduling problems (PMSP): uniform, identical, and unrelated parallel machine scheduling problems (UPMSPs). Recently, UPMSPs with setup time had attracted more attention due to its applications in different industries and services. In this study, we present an efficient method to address the UPMSPs while using a modified harris hawks optimizer (HHO). The new method, called MHHO, uses the salp swarm algorithm (SSA) as a local search for HHO in order to enhance its performance and to decrease its computation time. To test the performance of MHHO, several experiments are implemented using small and large problem instances. Moreover, the proposed method is compared to several state-of-art approaches used for UPMSPs. The MHHO shows better performance in both small and large problem cases.