Breakout dynasearch for the single-machine total weighted tardiness problem

• BDS combines the dynasearch and an adaptive perturbation mechanism.
• The dynasearch is improved with a fast neighbourhood search.
• BDS is a competitive metaheuristic to solve 300-job instances in 252 s in average.

We present a breakout dynasearch algorithm (BDS) for solving the single-machine total weighted tardiness problem, in which a set of independent jobs with distinct processing times, weights, and due dates are to be scheduled on a single machine to minimize the sum of the weighted tardiness of all the jobs. BDS explores the search space by combining the dynasearch procedure and the adaptive perturbation strategy. Experimental results show that BDS virtually solves all the standard benchmark problem instances with 40, 50, and 100 jobs from the literature within 0.1 s. For 500 larger instances with 150, 200, 250, and 300 jobs, BDS obtains all the upper bounds with the same objective function of the optimal solutions within an average of 252 s, demonstrating the efficacy of BDS in terms of both solution quality and computational efficiency. We also analyze some key features of BDS to identify its success factors.