Increasing the attraction area of the global minimum in the binary optimization problem

TL;DR

This paper proposes modifying the energy functional in binary quadratic minimization problems by raising the matrix to a power, which enlarges the attraction areas of deep minima and significantly improves the probability of locating the global minimum.

Contribution

It introduces a novel approach of transforming the energy functional to enhance the efficiency of random-search algorithms in binary optimization.

Findings

Deep minima displace slightly and become deeper with the new functional.

Attraction areas of minima grow significantly, aiding search.

Probability of finding the global minimum increases by up to 10^3 times.

Abstract

The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power the matrix it is based on. We demonstrate that this brings about changes of the energy surface: deep minima displace slightly in the space and become still deeper and their attraction areas grow significantly. Experiments show that this approach results in a considerable displacement of the spectrum of the sought-for minima to the area of greater depth, and the probability of finding the global minimum increases abruptly (by a factor of 10^3 in the case of the 10-by-10 Edwards-Anderson spin glass).