NK landscapes difficulty and Negative Slope Coefficient: How Sampling Influences the Results

TL;DR

This paper investigates how sampling affects the Negative Slope Coefficient, an indicator of problem difficulty, revealing its sensitivity to bin sampling and discussing its advantages and limitations.

Contribution

It is the first study to analyze the influence of sampling on the Negative Slope Coefficient in NK-landscapes, providing formal justification and critical discussion.

Findings

Negative Slope Coefficient is highly influenced by the minimum number of points in a bin.

Sampling variability significantly impacts the measure's reliability.

The paper discusses the strengths and weaknesses of using this indicator.

Abstract

Negative Slope Coefficient is an indicator of problem hardness that has been introduced in 2004 and that has returned promising results on a large set of problems. It is based on the concept of fitness cloud and works by partitioning the cloud into a number of bins representing as many different regions of the fitness landscape. The measure is calculated by joining the bins centroids by segments and summing all their negative slopes. In this paper, for the first time, we point out a potential problem of the Negative Slope Coefficient: we study its value for different instances of the well known NK-landscapes and we show how this indicator is dramatically influenced by the minimum number of points contained into a bin. Successively, we formally justify this behavior of the Negative Slope Coefficient and we discuss pros and cons of this measure.