Meta-RaPS: a simple and effective approach for solving the traveling salesman problem Gail W. DePuy a, * , Reinaldo J. Moraga b , Gary E. Whitehouse c a Department of Industrial Engineering, University of Louisville, Louisville, KY 40292, USA b Department of Industrial Engineering, Universidad del B  ıo B  ıo Avenida Collao 1202, Casilla 5C, Concepci on, Chile c Industrial Engineering and Management Systems Department, University of Central Florida, Orlando, FL 32816-2450, USA Received 7 October 2003; received in revised form 4 February 2004; accepted 10 February 2004 Abstract This paper investigates the development and application of a general meta-heuristic, Meta-RaPS (meta- heuristic for randomized priority search), to the traveling salesman problem (TSP). The Meta-RaPS ap- proach is tested on several established test sets. The Meta-RaPS approach outperformed most other solution methodologies in terms of percent difference from optimal. Additionally, an industry case study that incorporates Meta-RaPS TSP in a large truck route assignment model is presented. The company estimates a more than 50% reduction in engineering time and over $2.5 million annual savings in trans- portation costs using the automated Meta-RaPS TSP tool compared to their current method. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Meta-heuristic; TSP; Cheapest insertion 1. Introduction The well-known traveling salesman problem (TSP), in its simplest form, involves finding an optimal route for visiting N cities and returning to the point of origin, where the inter-city dis- tances are symmetric and known. Regardless of the fact that TSP can be easily formulated, its nature exhibits all aspects of NP-hard combinatorial optimization (Reinelt, 1994). This is the * Corresponding author. Tel.: +1-502-852-0115; fax: +1-502-852-5633. E-mail addresses: depuy@louisville.edu (G.W. DePuy), rmoraga@ubiobio.cl (R.J. Moraga), whitehse@mail.ucf.edu (G.E. Whitehouse). 1366-5545/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2004.02.001 Transportation Research Part E 41 (2005) 115–130 www.elsevier.com/locate/tre