Convergence in Probability of Compressed Annealing

Abstract

We consider combinatorial optimization problems for which the formation of a neighborhood structure of feasible solutions is impeded by a set of constraints. Neighborhoods are recovered by relaxing the complicating constraints into the objective function within a penalty term. We examine a heuristic called compressed annealing that integrates a variable penalty multiplier approach within the framework of simulated annealing. We refer to the value of the penalty multiplier as "pressure." We analyze the behavior of compressed annealing by exploring the interaction between temperature (which controls the ability of compressed annealing to climb hills) and pressure (which controls the height of the hills). We develop a necessary and sufficient condition on the joint cooling and compression schedules for compressed annealing to converge in probability to the set of global minima. Our work generalizes the results of Hajek (1988) in the sense that when there are no relaxed constraints, our results reduce to his.

Economic contribution of French serradella (Ornithopus sativus Brot.) pasture to integrated weed management in Western Australian mixed‐farming systems: an application of compressed annealing*

“…For example, there are around 2 395 possible solutions in the continuous‐cropping rotation described below. Accordingly, this analysis uses an innovative search algorithm, compressed annealing (Ohlmann et al . 2004), to identify near‐optimal management strategies.…”

“…Compressed annealing (Ohlmann et al . 2004; Doole and Pannell 2008a) is a recent derivative of simulated annealing that allows the explicit inclusion of resource constraints.…”

“…The steps of selection, evaluation, and comparison in this application are structured according to standard annealing theory (Aarts and Korst 1989; Ohlmann et al . 2004) to maximise the efficiency of the search.…”

Election Day Routing of Rapid Response Attorneys

“…We employ compressed annealing to solve problem (11) in search of high-quality solutions to problem (7)-(9). Compressed annealing varies the penalty multiplier λ, referred to as "pressure," within the framework of traditional simulated annealing (Ohlmann et al, 2004). Over the course of the heuristic search, pressure is increased, thereby biasing the solution landscape toward inequity-feasible solutions satisfying constraint (8).…”

“…We utilize compressed annealing to direct the search because of its success in other problem domains and because it provides a straightforward method for penalty-based local search. Further, unlike the vast majority of metaheuristic methods, compressed annealing converges in probability to the set of global minima (Ohlmann et al, 2004).…”