Cooling schedules for optimal annealing
Mathematics of Operations Research
On eigenvalues and annealing rates
Mathematics of Operations Research
Markov chains with rare transitions and simulated annealing
Mathematics of Operations Research
Note on the convergence of simulated annealing algorithms
SIAM Journal on Control and Optimization
Journal of Computational Physics
Convergence rates for Markov chains
SIAM Review
On the convergence of generalized hill climbing algorithms
Discrete Applied Mathematics
A class of convergent generalized hill climbing algorithms
Applied Mathematics and Computation
Analyzing the Performance of Generalized Hill Climbing Algorithms
Journal of Heuristics
Global Optimization Performance Measures for Generalized Hill Climbing Algorithms
Journal of Global Optimization
INFORMS Journal on Computing
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Simultaneous generalized hill climbing (SGHC) algorithms provide a framework for using heuristics to simultaneously address sets of intractable discrete optimization problems where information is shared between the problems during the algorithm execution. Many well-known heuristics can be embedded within the SGHC algorithm framework. This paper shows that the solutions generated by an SGHC algorithm are a stochastic process that satisfies the Markov property. This allows problem probability mass functions to be formulated for particular sets of problems based on the long-term behavior of the algorithm. Such results can be used to determine the proportion of iterations that an SGHC algorithm will spend optimizing over each discrete optimization problem. Sufficient conditions that guarantee that the algorithm spends an equal number of iterations in each discrete optimization problem are provided. SGHC algorithms can also be formulated such that the overall performance of the algorithm is independent of the initial discrete optimization problem chosen. Sufficient conditions are obtained guaranteeing that an SGHC algorithm will visit the globally optimal solution for each discrete optimization problem. Lastly, rates of convergence for SGHC algorithms are reported that show that given a rate of convergence for the embedded GHC algorithm, the SGHC algorithm can be designed to preserve this rate.