Average complexity and the Bayesian heuristic approach to discrete optimization

Abstract

We apply some concepts of Infonnation-Based Complexity (mC) to global and discrete optimization. We assume that only partial infonnation on the objective is available. We gather this partial infonnation by observations. We use the traditional mc definitions and notions while defining fonnal aspects of the problem. We use the Bayesian framework to consider less fonnal aspects, such as expert knowledge and heuristics, We extend the traditional Bayesian Approach (BA) including heuristics. We call that a Bayesian Heuristic Approach (BHA). We discuss how to overcome the computational difficulties using parallel computing. We illustrate the theoretical concepts by three examples: by discrete problems of flow-shop sheduling and parameter grouping, and by a continuous problem of batch operations scheduling.