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How to Specify a Reference Point in Hypervolume Calculation for Fair Performance Comparison.

Hisao Ishibuchi1, Ryo Imada2, Yu Setoguchi3

  • 1Shenzhen Key Laboratory of Computational Intelligence, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, 518005, China hisao@sustc.edu.cn.

Evolutionary Computation
|May 23, 2018
PubMed
Summary
This summary is machine-generated.

A new reference point method ensures fair comparison of evolutionary multi-objective optimization (EMO) algorithms. This approach optimizes hypervolume calculations, moving beyond the common practice of using points slightly worse than the nadir point.

Keywords:
Evolutionary multi-objective optimizationhypervolumeperformance comparison.reference point

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Area of Science:

  • Multi-objective Optimization
  • Computational Intelligence
  • Algorithm Performance Analysis

Background:

  • The hypervolume indicator is a standard metric for comparing evolutionary multi-objective optimization (EMO) algorithms.
  • Current EMO practices often use a reference point slightly worse than the nadir point for hypervolume calculations.
  • The specification of this reference point lacks detailed discussion regarding fair performance comparison.

Purpose of the Study:

  • To propose a novel reference point specification method for fair performance comparison of EMO algorithms.
  • To investigate the impact of reference point location on the optimal distribution of solutions for hypervolume maximization.
  • To ensure that well-distributed solutions achieve large hypervolumes with similar contributions.

Main Methods:

  • Theoretical analysis of the relationship between reference point specification and optimal solution distribution.
  • Development of a new reference point specification method based on optimal distribution principles.
  • Computational experiments on various test problems to validate the proposed method.

Main Results:

  • The optimal distribution of solutions is highly dependent on the reference point's location, especially for inverted triangular Pareto fronts.
  • The proposed method aims to set reference points that maximize hypervolume for well-distributed solutions.
  • Experimental results demonstrate that a point slightly worse than the nadir point is not universally appropriate for EMO algorithm comparison.

Conclusions:

  • The proposed reference point specification method offers a more theoretically sound approach for fair EMO algorithm performance comparison.
  • This method addresses the limitations of the commonly used reference point strategy.
  • The findings advocate for a re-evaluation of reference point selection in hypervolume-based EMO algorithm analysis.