A reactive iterated greedy algorithm for the no-wait flowshop to minimize total tardiness

Abstract

This paper addresses a no-wait flowshop scheduling problem with total tardiness minimization. We present a mixed-integer linear programming formulation with positional decision variables and a new constraint programming model to solve the problem as exact approaches. As an alternative solution procedure, we develop an innovative Reactive Iterated Greedy (RIG) algorithm that presents a dynamic mechanism to adjust the number of jobs to be removed from the current permutation in the destruction phase. We carried out computational experiments on a set of 800 test instances available in the literature to evaluate the performance of the proposed RIG algorithm in comparison with five solution approaches (Mixed-Integer Linear Programming, Constraint Programming, Block Simulated Annealing, Variable Neighborhood Descent, and Iterated Greedy). The used performance criterion is the Relative Deviation Index (RDI). The RIG algorithm returned an average RDI of 5.0%, representing the best results among the solution procedures under comparison. Computational results pointed out that our proposal outperformed the mathematical model and other metaheuristics available in the literature with statistical significance.