Computers & Operations Research 26 (1999) 481 — 503 A fast method for generalized starting temperature determination in homogeneous two-stage simulated annealing systems James M. Varanelli  *, James P. Cohoon  Bell Labs Design Automation, Lucent Technologies, 600 Mountain Ave., Rm 3B-426C, Murray Hill, NJ 07974, USA  Department of Computer Science, University of Virginia, Olsson Hall, Charlottesville, VA 22903-2442, USA Received October 1997; received in revised form July 1998 Scope and purpose The homogeneous simulated annealing algorithm is a general-purpose optimization paradigm that has proven to be quite effective for finding high-quality solutions to a diverse range of NP-hard combinatorial optimization problems. These types of problems are quite common in the field of operations research, and indeed simulated annealing has been used quite extensively to produce high-quality solutions to many of these problems. Two common examples are the graph partitioning problem and the traveling salesperson problem. Although the efficacy and robustness of the simulated annealing heuristic has been thoroughly demonstrated in the literature, the main drawback to the algorithm is its sometimes prohibitive run times. Two-stage simulated annealing is a technique introduced in the literature as a method for decreasing the run times of simulated annealing while maintaining its exceptional solution quality for many problems. The main drawback to the two-stage simulated annealing technique is its problem- and formulation-dependent nature. * Corresponding author. Tel.: (908) 582-3009; fax: (908) 582-5145; e-mail: varanell@mhcnet.lucent.com.  This work has been supported by the National Science Foundation under grants MIP-9107717 and CDA-8922545. Their support is greatly appreciated.  J.M. Varanelli received his B.A. in Mathematics from Franklin and Marshall College, his M.S. in Computer Science from Pace University, and Ph.D. in Computer Science from the University of Virginia. He is currently a Member of Technical Staff with the Bell Labs Design Automation unit of Lucent Technologies. His research interests include VLSI design automation algorithms, combinatorial optimization, heuristic search, evolutionary computation, and parallel computation.  J.P. Cohoon received his B.S. in Mathematics from Ramapo College, his M.S. in Computer Science from Pennsyl- vania State University, and Ph.D. in Computer Science from the University of Minnesota in 1982. He is a former member of AT&T Bell Laboratories and is currently an Associate Professor with the Department of Computer Science at the University of Virginia in Charlottesville, VA. His professional interests include VLSI design automation algorithms, computational geometry, probabilistic search, and computer science education. He is the author of more than 60 papers in these fields. He is past chair of SIGDA. He can be reached via email at cohoon@virginia.edu. 0305-0548/99/$ — see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S0305-0548(98)00062-8