A parallel adaptive tabu search approach

This paper presents a new approach for parallel tabu search based on adaptive parallelism. Adaptive parallelism was used to dynamically adjust the parallelism degree of the application with respect to the system load. Adaptive parallelism demonstrates that high-performance computing using a hundred of heterogeneous workstations combined with massively parallel machines is feasible to solve large optimization problems. The parallel tabu search algorithm includes di€erent tabu list sizes and new intensi®cation/diversi®cation mechanisms. Encouraging results have been obtained in solving the quadratic assignment problem. We have improved the best known solutions for some large real-world problems. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Tabu search; Adaptive parallelism; Quadratic assignment problem 1. Motivation and goals Many interesting combinatorial optimization problems are NP-hard, and then they cannot be solved exactly within a reasonable amount of time. Consequently, heuristics must be used to solve real-world problems. Tabu search (TS) is a general purpose heuristic (meta-heuristic) that has been proposed by Glover [1]. TS has achieved widespread success in solving practical optimization problems in di€erent domains (such as resource management, process design, logistic and telecommunications). Promising results of applying TS to a variety of academic optimization problems (traveling salesman, quadratic assignment, time-tabling, job-shop scheduling, etc.) are reported in the literature [2]. Solving large problems motivates the development of a parallel implementation of TS. Parallel Computing 24 (1998) 2003±2019 * Corresponding author. E-mail: talbi@li ̄.fr 0167-8191/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 8 1 9 1 ( 9 8 ) 0 0 0 8 6 6 The proliferation of powerful workstations and fast communication networks (ATM, Myrinet, etc.) with constantly decreasing cost/performance ratio have shown the emergence of heterogeneous workstation networks and homogeneous clusters of processors (such as DEC Alpha farms and IBM SP/2) [3,4]. These parallel platforms are generally composed of an important number of machines shared by many users. In addition, a workstation belongs to an owner who will not tolerate external applications degrading the performance of his machine. Load analysis of those platforms during long periods of time showed that only a few percentage of the available power was used [5,6]. There is a substantial amount of idle time. Therefore, dynamic adaptive scheduling of parallel applications is essential. Many parallel TS algorithms have been proposed in the literature. In general, they don't use advanced programming tools (such as load balancing, dynamic recon®guration and checkpointing) to eciently use the machines. Most of them are developed for dedicated parallel homogeneous machines. Our aim is to develop a parallel adaptive TS strategy, which can bene®t greatly from a platform having combined computing resources of massively parallel machines (MPPs) and networks of workstations (NOWs). For this purpose, we use a dynamic scheduling system (MARS ) which harnesses idle time (keeping in mind the ownership of workstations), and supports adaptive parallelism to dynamically recon®gure the set of processors hosting the parallel TS. The testbed optimization problem we used is the quadratic assignment problem (QAP), one of the hardest among the NP-hard combinatorial optimization problems. The parallel TS algorithm includes di€erent tabu list sizes and intensi®cation/ diversi®cation mechanisms based on frequency based long-term memory and restricted neighborhood. The remainder of the paper is organized as follows. In Section 2, we describe existing parallel TS algorithms. The parallel adaptive TS proposed will be detailed in Section 3. Finally, Sections 4 and 5 will present respectively the application of the proposed algorithm to the QAP and results of experiments for several standard instances from the QAP-library. 2. Classi®cation of parallel TS algorithms We present in this section, respectively the main components of a sequential TS algorithm, and a classi®cation of parallel TS algorithms. A new taxonomy dimension has been introduced. 2.1. Sequential tabu search A combinatorial optimization problem is de®ned by the speci®cation of a pair …X ; f †, where the search space X is a discrete set of all (feasible) solutions, and the 1 Multi-user Adaptive Resource Scheduler. 2004 E.G. Talbi et al. / Parallel Computing 24 (1998) 2003±2019