Scheduling of a no-wait two-machine flow shop with sequence-dependent setup times and probable rework using robust meta-heuristics

This paper investigates the scheduling of a no-wait two-machine flow shop considering anticipatory sequence-dependent setup time and a probable rework for both machines to minimise mean completion time (MCT). To tackle the problem, a robust meta-heuristic algorithm, namely the adapted imperialist competitive algorithm (AICA), has been proposed and is compared with two common and popular meta-heuristic algorithms (i.e. genetic algorithm (GA) and population-based simulated annealing (PBSA)). In this study, we have adapted a traditional imperialist competitive algorithm (ICA) with some considerable changes. First of all, a revolution procedure is added to the algorithm for imperialists similar to colonies. Furthermore, the revolution is only performed when the new solution is better than the previous solution, and chief among them for preservation of premature convergence, the concept of global war is applied. However, the performance of AICA is sensitive to the choice of the best parameter values. Thus, to obtain optimal performance, a comprehensive calibration methodology called response surface methodology is employed to obtain the best combination of parameter values. In order to evaluate the effectiveness and efficiency of proposed algorithms, several test problems are generated and the results obtained from algorithms are then compared in terms of relative percentage deviation. Computational experiments indicate that AICA outperforms GA and PBSA in the MCT performance measure, and GA outperforms the others in terms of computational time.