Cooling schedules for optimal annealing
Mathematics of Operations Research
Simulated annealing: past, present, and future
WSC '95 Proceedings of the 27th conference on Winter simulation
On the convergence of generalized hill climbing algorithms
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Simulated Annealing: Searching for an Optimal Temperature Schedule
SIAM Journal on Optimization
Simulated Annealing With An Optimal Fixed Temperature
SIAM Journal on Optimization
A class of convergent generalized hill climbing algorithms
Applied Mathematics and Computation
INFORMS Journal on Computing
Analysis of static simulated annealing algorithms
Journal of Optimization Theory and Applications
Global Optimization Performance Measures for Generalized Hill Climbing Algorithms
Journal of Global Optimization
On the Explorative Behavior of MAX---MIN Ant System
SLS '09 Proceedings of the Second International Workshop on Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics
A framework for analyzing sub-optimal performance of local search algorithms
Computational Optimization and Applications
Using Markov chains to analyze the effectiveness of local search algorithms
Discrete Optimization
Hi-index | 0.00 |
Generalized hill climbing (GHC) algorithms provide a framework for modeling local search algorithms for addressing intractable discrete optimization problems. Current theoretical results are based on the assumption that the goal when addressing such problems is to find a globally optimal solution. However, from a practical point of view, solutions that are close enough to a globally optimal solution (where close enough is measured in terms of the objective function value) for a discrete optimization problem may be acceptable. This paper introduces β-acceptable solutions, where β is a value greater than or equal to the globally optimal objective function value. Moreover, measures for assessing the finite-time performance of GHC algorithms, in terms of identifying β-acceptable solutions, are defined. A variation of simulated annealing (SA), termed static simulated annealing (S2A), is analyzed using these measures. S2A uses a fixed cooling schedule during the algorithm's execution. Though S2A is provably nonconvergent, its finite-time performance can be assessed using the finite-time performance measures defined in terms of identifying β-acceptable solutions. Computational results with a randomly generated instance of the traveling salesman problem are reported to illustrate the results presented. These results show that upper and lower estimates for the number of iterations to reach a β-acceptable solution within a specified number of iterations can be obtained, and that these estimates are most accurate for moderate and high fixed temperature values for the S2A algorithm.