A class of convergent generalized hill climbing algorithms

• Published in: Applied mathematics and computation Vol. 125; no. 2; pp. 359 - 373
• Main Authors: Johnson, Alan W., Jacobson, Sheldon H.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 25.01.2002; Elsevier
• Subjects: Calculus of variations and optimal control; Convergence; Discrete optimization; Exact sciences and technology; Hill climbing algorithms; Local search; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Sciences and techniques of general use; Simulated annealing; Local search; Discrete optimization; Hill climbing algorithms; Simulated annealing; Convergence; Existence theorem; Linear complementarity problem; Uniqueness theorem; local search; Optimization; Search algorithm; Markov chain; Generalized hill climbing algorithm; Discretization; Erlang distribution; Local scope; Stationary process; Random variable
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/S0096-3003(00)00137-5

Generalized hill climbing (GHC) algorithms have been presented as a modeling framework for local search strategies applied to address intractable discrete optimization (minimization) problems. GHC algorithms include simulated annealing (SA), pure local search (LS), and threshold accepting (TA), among others, as special cases. A particular class of GHC algorithms is designed for discrete optimization problems where the objective function value of a globally optimal solution is known (in this case, the task is to identify an associated optimal solution). This class of GHC algorithms is shown to converge, and six examples are provided that illustrate the diversity of GHC algorithms within this class of convergent algorithms. Implications of these results are discussed.