Cluster Approach to the Domains Formation

TL;DR

This paper explores domain formation methods for optimizing quadratic functions of binary variables, emphasizing that aggregating strongly connected variables leads to better local minima in the optimization process.

Contribution

It introduces methods for forming variable domains based on their connectivity, demonstrating improved optimization results over traditional approaches.

Findings

Forming domains with strongly connected variables yields deeper local minima.

Aggregation of variables enhances the effectiveness of quadratic functional minimization.

Methods for domain formation improve optimization outcomes in binary variable problems.

Abstract

As a rule, a quadratic functional depending on a great number of binary variables has a lot of local minima. One of approaches allowing one to find in averaged deeper local minima is aggregation of binary variables into larger blocks/domains. To minimize the functional one has to change the states of aggregated variables (domains). In the present publication we discuss methods of domains formation. It is shown that the best results are obtained when domains are formed by variables that are strongly connected with each other.