Elementary Components of the Quadratic Assignment Problem
Francisco Chicano, Gabriel Luque, Enrique Alba
TL;DR
This paper decomposes the Quadratic Assignment Problem into three fundamental landscape components, providing formulas and bounds that enhance understanding of its structure and complexity.
Contribution
It introduces a novel decomposition of QAP into elementary landscapes with explicit formulas and autocorrelation bounds, advancing theoretical insights.
Findings
QAP can be expressed as the sum of three elementary landscapes
Closed-form formulas for each elementary component are provided
Bounds for the autocorrelation coefficient are derived
Abstract
The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when the swap neighborhood is used. We present a closed formula for each of the three elementary components and we compute bounds for the autocorrelation coefficient.
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