An improved discrete Harris Hawks optimization algorithm for the no-wait job shop problem to minimize total weighted tardinessAn improved discrete Harris Hawks optimization algorithm…J. Yin et al.

As an extension of the well-known job shop problem through introducing no-wait constraints, the no-wait job shop problem (NWJSP) is one of the most difficult combinatorial problems. In this study, we consider the NWJSP with the objective of minimizing total weighted tardiness and develop a mixed integer linear programming model (MILP) to formulate the problem. Furthermore, we propose an improved discrete Harris Hawks optimization (IDHHO) algorithm to efficiently explore the solution space. Firstly, to enhance solution quality during the initialization phase, we develop an improved apparent tardiness cost (IATC) rule and integrate it with the Nawaz–Enscore–Ham (NEH) heuristic, thereby constructing a new heuristic called IATC_PNEH. Secondly, six discrete operators are used to update the population during the iterative search phase. Finally, an insertion-based perturbation strategy is introduced to prevent falling into local optima. The computational results and statistical analyses based on benchmark sets show that the IATC_PNEH heuristic outperforms some other heuristics in most cases, and the proposed IDHHO algorithm is competitive to several other high-performing algorithms. Besides, optimal solutions for all small-size instances are obtained by implementing the Cplex solver on the MILP model.