An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem
Faculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ, UK Faculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ, UK Department of Decision and Information Sciences, Rotterdam School of Management, Erasmus University, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands Richard.Congram@paconsulting.com • C.N.Potts@maths.soton.ac.uk • S.Velde@fac.fbk.eur.nl

Richard K. Congram • Chris N. Potts • Steef L. van de Velde

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his paper introduces a new neighborhood search technique, called dynasearch, that uses dynamic programming to search an exponential size neighborhood in polynomial time. While traditional local search algorithms make a single move at each iteration, dynasearch allows a series of moves to be performed. The aim is for the lookahead capabilities of dynasearch to prevent the search from being attracted to poor local optima. We evaluate dynasearch by applying it to the problem of scheduling jobs on a single machine to minimize the total weighted tardiness of the jobs. Dynasearch is more effective than traditional first-improve or best-improve descent in our computational tests. Furthermore, this superiority is much greater for starting solutions close to previous local minima. Computational results also show that an iterated dynasearch algorithm in which descents are performed a few random moves away from previous local minima is superior to other known local search procedures for the total weighted tardiness scheduling problem. (Production Scheduling: Single Machine, Sequencing; Analysis of Algorithms; Dynamic Programming )

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A descent or iterative improvement algorithm is a simple and practical type of local search method for obtaining near-optimal solutions for a wide variety of NP-hard