On the Complexity to Approach Optimum Solutions by Inhomogeneous Markov Chains

We analyse the probability 1 − δ to be in an optimum solution after k steps of an inhomogeneous Markov chain which is specified by a logarithmic cooling schedule c(k) = Γ/ ln (k + 2). We prove that after k > (n/δ)O(Γ ) steps the probability to be in an optimum solution is larger than 1 − δ, where n is an upper bound for the size of local neighbourhoods and Γ is a parameter of the entire configuration space. By counting the occurrences of configurations, we demonstrate for an application with known optimum solutions that the lower bound indeed ensures the stated probability for a relatively small constant in O(Γ).

• Type: Conference
• Year: 2004
• Where: GECCO
• Authors: Andreas Alexander Albrecht
• Keywords: GECCO 2004, Inhomogeneous Markov Chain, Logarithmic Cooling Schedule, Optimum Solutions