On Minimization of a Quadratic Binary Functional

TL;DR

This paper investigates methods for minimizing quadratic binary functionals, comparing three algorithms through simulations on spin-glass matrices, and finds that the greedy algorithm exhibits superior performance due to its maximal dynamics.

Contribution

It introduces a comparative analysis of three minimization procedures for quadratic binary functionals using computer simulations, highlighting the effectiveness of the greedy algorithm.

Findings

Greedy algorithm shows superior performance among tested methods.

The distribution of local minima depends critically on the initial distance from the ground state.

Performance varies with the initial conditions and the structure of the problem.

Abstract

The problem of minimization of a quadratic functional depending on great number of binary variables is examined. 3 variants of minimization procedure are studied with the aid of computer simulation for spin-glass matrices. It is shown that under other equal conditions evident superiority has the maximal dynamics (the greedy algorithm). The dependence of the results on a distance between start points and the ground state is investigated. It is determined that the character of distribution of local minima depends on this distance crucially.