Journal of Heuristics, 10: 387–405, 2004 c  2004 Kluwer Academic Publishers. Manufactured in The Netherlands. Analyzing the Performance of Generalized Hill Climbing Algorithms * SHELDON H. JACOBSON Simulation and Optimization Laboratory, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801-2906, USA email: shj@uiuc.edu(netfiles.uiuc.edu/shj/www/shj.html) ENVER Y ¨ UCESAN Technology Management Area, INSEAD, Boulevard de Constance, 77305 Fontainebleau Cedex, France email: enver.yucesan@insead.edu(http://www.insead.edu/facultyresearch/tm/yucesan) Submitted in January 2003 and accepted by David Woodruffin February 2004 after 1 revision Abstract Generalized hill climbing algorithms provide a framework to describe and analyze metaheuristics for addressing intractable discrete optimization problems. The performance of such algorithms can be assessed asymptotically, either through convergence results or by comparison to other algorithms. This paper presents necessary and sufficient convergence conditions for generalized hill climbing algorithms. These conditions are shown to be equivalent to necessary and sufficient convergence conditions for simulated annealing when the generalized hill climbing algorithm is restricted to simulated annealing. Performance measures are also introduced that permit generalized hill climbing algorithms to be compared using random restart local search. These results identify a solution landscape parameter based on the basins of attraction for local optima that determines whether simulated annealing or random restart local search is more effective in visiting a global optimum. The implications and limitations of these results are discussed. Key Words: meta-heuristics, simulated annealing, performance evaluation, convergence 1. Introduction Discrete optimization problems are defined by a finite set of solutions and an objective function value associated with each solution (Garey and Johnson, 1979, p. 123). The goal when addressing such problems is to determine the set of solutions for which the objective function is optimized (i.e., minimized or maximized). Heuristic procedures are typically formulated with the hope of finding good or near- optimal solutions for hard (i.e., NP-hard) discrete optimization problems (Garey and Johnson, 1979). Generalized Hill Climbing (GHC) algorithms (Jacobson et al., 1998), such as simulated annealing (Kirkpatrick et al., 1983), the noising method (Charon and ∗ This research is supported in part by the Air Force Office of Scientific Research (F49620-01-1-0007, FA9550- 04-1-0110).