Generalized Hill Climbing Algorithms for Discrete Optimization Problems

Generalized hill climbing (GHC) algorithms are introduced, as a tool to address difficult discrete optimization problems. Particular formulations of GHC algorithms include simulated annealing (SA), local search, and threshold accepting (TA), among others. A proof of convergence of GHC algorithms is presented, that relaxes the sufficient conditions for the most general proof of convergence for stochastic search algorithms in the literature (Anily and Federgruen (1987)). Proofs of convergence for SA are based on the concept that deteriorating (hill climbing) transitions between neighboring solutions are accepted by comparing a deterministic function of both the solution change cost and a temperature parameter to a uniform (0,1) random variable. GHC algorithms represent a more general model, whereby deteriorating moves are accepted according to a general random variable. Computational results are reported that illustrate relationships that exist between the GHC algorithm's finite-time performance on three problems, and the general random variable formulations used. The dissertation concludes with suggestions for further research.Air Force Inst of Tech Wright-Patterson AFB OH is the author of 'Generalized Hill Climbing Algorithms for Discrete Optimization Problems', published 1997 under ISBN 9781423584315 and ISBN 1423584317.