A worm optimization algorithm to minimize the makespan on unrelated parallel machines with sequence-dependent setup times

This paper addresses the unrelated parallel machine scheduling problem with setup times, with an objective of minimizing the makespan. The machines are unrelated in the sense that the processing speed depends on the job being executed and not the machine. Each job will have different processing times for each of the available machines, is available at the beginning of the scheduling horizon, and can be processed on any of the machines but needs to be processed by one machine only. Sequence-dependent and machine-dependent setup times are also considered. A Worm Optimization (WO) algorithm is introduced and is applied to this NP-hard problem. The novel WO is based on the behaviors of the worm, which is a nematode with only 302 neurons. Nevertheless, these neurons allow worms to achieve several intricate behaviors including finding food, interchanging between solitary and social foraging styles, alternating between dwelling and roaming, and entering a type of stasis/declining stage. WO’s performance is evaluated by comparing its solutions to solutions of six other known metaheuristics for the problem under study, and the extensive computational results indicated that the proposed WO performs best.