A simple migrating birds optimization algorithm with two search modes to solve the no-wait job shop problem

The no-wait job shop problem has important applications in various industries such as steel-making and chemical processes, and its mainstream approaches are metaheuristics with timetabling methods. Inspired by the characteristics of the problem, we consider both left and right shifts for some jobs and present an effective timetabling method called left-right shift (LRS) method. The LRS method schedules jobs as far left as possible and tries all the possible right shifts for some jobs to expand the search space. We propose a simple migrating birds optimization (SMBO) algorithm for searching the space of job sequences. The population of the proposed algorithm is equally divided into two subpopulations with two search modes, one for the original instance and the other for the inverse instance. Local exploitation and global exploration are well balanced in the population evolution scheme of the proposed algorithm. To enhance the run efficiency of the algorithm, we introduce a speedup method for left timetabling and employ the simultaneous multithreading technique for the parallel evolution of subpopulations. Experimental results show that the proposed SMBO algorithm outperforms the state-of-the-art by a significant margin and obtains new upper bounds for a large number of benchmark instances.