Clustering of Local Optima in Combinatorial Fitness Landscapes

TL;DR

This paper investigates the structure of local optima in quadratic assignment problem instances, revealing distinct modular properties in real-like versus random uniform instances, which impacts heuristic search strategies.

Contribution

It introduces an analysis of local optima networks in quadratic assignment problems, highlighting differences in their modular structure across instance types.

Findings

Real-like instances have modular optima networks.

Random uniform instances are less clusterable.

Implications for heuristic search strategies.

Abstract

Using the recently proposed model of combinatorial landscapes: local optima networks, we study the distribution of local optima in two classes of instances of the quadratic assignment problem. Our results indicate that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the optima networks possess a clear modular structure, while the networks belonging to the class of random uniform instances are less well partitionable into clusters. We briefly discuss the consequences of the findings for heuristically searching the corresponding problem spaces.