First-improvement vs. Best-improvement Local Optima Networks of NK Landscapes

TL;DR

This paper compares the structural properties of Local Optima Networks derived from first-improvement and best-improvement hill-climbing algorithms on NK landscapes, revealing key differences affecting search heuristic behavior.

Contribution

It introduces a model for Local Optima Networks using first-improvement hill-climbing and compares it to the best-improvement version, highlighting structural differences.

Findings

Structural differences in network connectivity

Distinct basin of attraction characteristics

Implications for search heuristic performance

Abstract

This paper extends a recently proposed model for combinatorial landscapes: Local Optima Networks (LON), to incorporate a first-improvement (greedy-ascent) hill-climbing algorithm, instead of a best-improvement (steepest-ascent) one, for the definition and extraction of the basins of attraction of the landscape optima. A statistical analysis comparing best and first improvement network models for a set of NK landscapes, is presented and discussed. Our results suggest structural differences between the two models with respect to both the network connectivity, and the nature of the basins of attraction. The impact of these differences in the behavior of search heuristics based on first and best improvement local search is thoroughly discussed.