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Motif difficulty (MD): a predictive measure of problem difficulty for evolutionary algorithms using network motifs.

Jing Liu1, Hussein A Abbass, David G Green

  • 1School of Engineering and Information Technology, The University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia. jing.liu@adfa.edu.au

Evolutionary Computation
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Predicting evolutionary algorithm (EA) performance is challenging. This study introduces fitness landscape networks (FLNs) and motif difficulty (MD) to measure problem complexity for EAs, validated on knapsack problems.

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Computational Intelligence

Background:

  • Characterizing problem difficulty is a major challenge in evolutionary algorithms (EAs).
  • Predicting EA behavior across diverse problem domains is crucial for algorithm selection and design.
  • Existing methods lack comprehensive measures for evolutionary computation problem complexity.

Purpose of the Study:

  • To introduce fitness landscape networks (FLNs) as a novel framework for analyzing evolutionary algorithms.
  • To define a new predictive measure, motif difficulty (MD), for assessing problem complexity in comparison-based EAs.
  • To evaluate the efficacy of MD and its approximation on various problem instances, including multidimensional knapsack problems (MKPs).

Main Methods:

  • Construction of fitness landscape networks (FLNs) using operators with specific conditions.
  • Definition and calculation of motif difficulty (MD) as a predictive measure for EAs.
  • Development and application of a sampling technique for approximating MD on large networks.
  • Experimental validation using binary search spaces and multidimensional knapsack problems (MKPs).

Main Results:

  • Demonstration of the advantages and limitations of the MD measure through extensive experiments on binary search spaces.
  • Validation of approximate MD performance on FLNs with varying topologies using MKPs.
  • Analysis of the impact of binary and permutation representations on MKP difficulty.

Conclusions:

  • Motif difficulty (MD) offers a promising approach for predicting the performance of evolutionary algorithms.
  • The proposed sampling technique provides a practical method for estimating MD on complex fitness landscapes.
  • Understanding representation effects on problem difficulty is essential for optimizing EA performance on problems like MKPs.