Distance-Based Bias in Model-Directed Optimization of Additively Decomposable Problems

TL;DR

This paper introduces a method that leverages problem-specific distance metrics and probabilistic models to improve the efficiency and accuracy of solving additively decomposable optimization problems.

Contribution

It proposes a novel approach combining distance metrics with probabilistic models to enhance model-directed optimization for similar problem instances.

Findings

Improved speed in solving problem instances.

Enhanced accuracy and reliability of solutions.

Broader applicability to various optimization techniques.

Abstract

For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the dependencies between variables that are closer to each other with respect to the metric are expected to be stronger than the dependencies between variables that are further apart. The purpose of this paper is to describe a method that combines such a problem-specific distance metric with information mined from probabilistic models obtained in previous runs of estimation of distribution algorithms with the goal of solving future problem instances of similar type with increased speed, accuracy and reliability. While the focus of the paper is on additively decomposable problems and the hierarchical Bayesian optimization algorithm, it should be straightforward to generalize the approach to other model-directed optimization techniques and other problem classes. Compared to other techniques for learning from experience put forward in the past, the proposed technique is both more practical and more broadly applicable.