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Multiple comparison test, abbreviated as MCT, is a post hoc analysis generally performed after comparing multiple samples with one or more tests. An MCT will help identify a significantly different sample among multiple samples or a factor among multiple factors.
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Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites.

Dimo Brockhoff1, Anne Auger2, Nikolaus Hansen3

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Summary
This summary is machine-generated.

This study introduces the bbob-biobj and bbob-biobj-ext test suites, featuring 55 and 92 bi-objective functions respectively. These new suites address limitations in existing benchmarks for multiobjective optimization algorithms.

Keywords:
Black-box optimization benchmarkingalgorithm comparisonbenchmark suite generatormultiobjective optimization

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Area of Science:

  • Numerical Optimization
  • Computational Intelligence
  • Algorithm Benchmarking

Background:

  • Existing test functions for multiobjective optimization algorithms often lack real-world problem characteristics.
  • Common issues include separability, boundary optima, and distance-controlling variables, which are underrepresented.

Purpose of the Study:

  • Introduce the bbob-biobj and bbob-biobj-ext test suites for numerical benchmarking.
  • Provide a more realistic and diverse set of bi-objective functions for algorithm evaluation.
  • Facilitate better comparison of deterministic and stochastic solvers.

Main Methods:

  • Constructed new bi-objective test functions by combining existing single-objective problems.
  • Implemented the test suites within the COCO (Continuous Optimization: Black-Box Optimization) platform.
  • Visualized test functions to reveal their properties and characteristics.

Main Results:

  • Developed the bbob-biobj suite with 55 bi-objective functions and an extended version (bbob-biobj-ext) with 92 functions.
  • Demonstrated the implementation and properties of these functions within the COCO platform.
  • Grouped functions by similar properties, normalized objective spaces, and created problem instances for robust benchmarking.

Conclusions:

  • The bbob-biobj and bbob-biobj-ext suites offer improved realism for benchmarking multiobjective optimization algorithms.
  • The approach addresses limitations of current test functions, enhancing the evaluation of algorithm performance.
  • Standardized benchmarking facilitates more reliable comparisons between different optimization solvers.