NK Landscapes Difficulty and Negative Slope Coefficient: How Sampling Influences the Results

Authors:
Leonardo Vanneschi;Sébastien Verel;Marco Tomassini;Philippe Collard
Affiliations:
Dipartimento di Informatica, Sistemistica e Comunicazione (D.I.S.Co.), University of Milano-Bicocca, Milan, Italy;I3S Laboratory, University of Nice---Sophia Antipolis, France;Information Systems Department, HEC, University of Lausanne, Lausanne, Switzerland;I3S Laboratory, University of Nice---Sophia Antipolis, France
Venue:
EvoWorkshops '09 Proceedings of the EvoWorkshops 2009 on Applications of Evolutionary Computing: EvoCOMNET, EvoENVIRONMENT, EvoFIN, EvoGAMES, EvoHOT, EvoIASP, EvoINTERACTION, EvoMUSART, EvoNUM, EvoSTOC, EvoTRANSLOG
Year:
2009

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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 in a bin. Successively, we formally justify this behavior of the Negative Slope Coefficient and we discuss pros and cons of this measure.