O(1) Delta Component Computation Technique for the Quadratic Assignment Problem

TL;DR

This paper introduces a new O(1) delta computation method for the quadratic assignment problem, significantly reducing computational effort and improving heuristic algorithm performance by up to 25%.

Contribution

It presents a novel correlation-based formula that halves delta computations and reduces complexity from O(N) to O(1).

Findings

Up to 25% performance improvement in heuristics.

Halves the number of delta computations needed.

Reduces complexity from O(N) to O(1).

Abstract

The paper describes a novel technique that allows to reduce by half the number of delta values that were required to be computed with complexity O(N) in most of the heuristics for the quadratic assignment problem. Using the correlation between the old and new delta values, obtained in this work, a new formula of complexity O(1) is proposed. Found result leads up to 25% performance increase in such well-known algorithms as Robust Tabu Search and others based on it.