Optimal parameters for search using a barrier tree Markov model

William Benfold, Jonathan Hallam, Adam Prügel-Bennett

Abstract: The performance, on a given problem, of search heuristics such as simulated annealing and descent with variable mutation can be described as a function of, and optimised over, the parameters of the heuristic (e.g. the annealing or mutation schedule). We describe heuristics as Markov processes; the search for optimal parameters is then rendered feasible by the use of level-accessible barrier trees for state amalgamation. Results are presented for schedules minimising “where-you-are” and “best-so-far” cost, over binary perceptron, spin-glass and Max-SAT problems. We also compute first-passage time for several “toy heuristics”, including constant-temperature annealing and fixed-rate mutation search.