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Evolving combinatorial problem instances that are difficult to solve.

Jano I van Hemert1

  • 1National e-Science Centre, University of Edinburgh, United Kingdom. http://www.vanhemert.co.uk/

Evolutionary Computation
|November 18, 2006
PubMed
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This study uses evolutionary computation to create challenging combinatorial optimization problems. These evolved instances stress-test algorithms in constraint satisfaction, Boolean satisfiability, and the traveling salesman problem, revealing algorithmic weaknesses.

Area of Science:

  • Computational intelligence
  • Combinatorial optimization

Background:

  • Combinatorial optimization problems are crucial in computer science and operations research.
  • Existing benchmarks may not adequately stress-test algorithms for solving complex instances.
  • Evolutionary computation offers a novel approach to generate challenging problem instances.

Purpose of the Study:

  • To demonstrate the use of evolutionary computation for generating difficult combinatorial problem instances.
  • To stress-test algorithms by applying them to these novel, challenging instances.
  • To analyze the structural properties of evolved instances to understand algorithm weaknesses.

Main Methods:

  • Applying evolutionary computation to generate problem instances.
  • Utilizing the generated instances to stress-test algorithms.

Related Experiment Videos

  • Analyzing the structural properties of the evolved problem instances.
  • Focusing on domains including binary constraint satisfaction, Boolean satisfiability, and the traveling salesman problem.
  • Main Results:

    • Successfully generated problem instances that are more difficult than those in popular benchmarks.
    • Evolved instances effectively stress-tested algorithms across multiple combinatorial optimization domains.
    • Identified specific structural properties contributing to the difficulty of evolved instances.
    • Exposed weaknesses in existing algorithms when confronted with these challenging instances.

    Conclusions:

    • Evolutionary computation is an effective method for creating difficult combinatorial optimization problems.
    • The generated instances provide valuable benchmarks for rigorously evaluating algorithm performance.
    • Understanding the structural properties of problem instances is key to improving algorithm design and robustness.