Scheduling of unrelated parallel machines considering sequence-related setup time, start time-dependent deterioration, position-dependent learning and power consumption minimization

Abstract

This research presents an optimization problem associated with scheduling of unrelated parallel machines considering the simultaneous effects of start-time-related deterioration, position-related learning and sequence-related setup times, with the aim to achieve an optimized value for the mean weighted tardiness and power consumption minimization. A workaround is proposed and served as the converter for solving the Mixed Integer Programming (MIP) problem by the continuous-based metaheuristic algorithms. Knowing the NP-hard nature of the problem, three metaheuristic algorithms, namely, Genetic Algorithm (GA), Cat Swarm Optimization (CSO) and Interactive Artificial Bee Colony (IABC), are employed to obtain quality solutions within acceptable computation time. A unique elitism strategy is introduced in the conventional CSO to reduce the computational time of its seeking mode and to provide improved solution, with the new algorithm form called CSO-Elit. Furthermore, a compact solution expression form is proposed for the use of GA, CSO-Elit and IABC to reduce the number of constraints. With the newly proposed model, many essential constraints are automatically built into the solution representation. Accordingly, the efficiency of algorithms is compared with LINGO regarding the quality of solutions, computational time, and overall power consumption using two sets of problems in small and large scales. In solving the small-scale cases, no statistically meaningful difference was observed between LINGO, GA and CSO-Elit, while in large-scale instances CSO-Elit demonstrated higher performance. The contributions of this paper lie in modeling a complex parallel machines problem considering power consumption minimization and proposing a new form of CSO algorithm with elitism strategy to reduce the computational time.