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Greedy Hypervolume Subset Selection in Low Dimensions.

Andreia P Guerreiro1, Carlos M Fonseca2, Luís Paquete3

  • 1CISUC, Department of Informatics Engineering, University of Coimbra, Pólo II, P-3030 290 Coimbra, Portugal apg@dei.uc.pt.

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Summary
This summary is machine-generated.

This study introduces efficient greedy algorithms for the Hypervolume Subset Selection Problem (HSSP). These algorithms improve approximation performance in 2 and 3 dimensions, enhancing Pareto front approximation.

Keywords:
Hypervolume indicatorgreedy algorithmmonotone submodular functionmultiobjective optimizationsubset selection

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Area of Science:

  • Multi-objective optimization
  • Computational geometry
  • Algorithm design

Background:

  • The Hypervolume Subset Selection Problem (HSSP) aims to find a subset of nondominated points that maximizes the hypervolume indicator.
  • This problem is crucial for multiobjective selection, archiving strategies, and Pareto-front approximation for visualization and decision-making.
  • Existing efficient algorithms for HSSP are limited to the 2-dimensional case with a time complexity of O(n^2).

Purpose of the Study:

  • To develop efficient greedy algorithms for the HSSP in 2 and 3 dimensions.
  • To improve the time complexity of solving the HSSP, particularly for higher dimensions.
  • To enhance the approximation performance of the hypervolume indicator.

Main Methods:

  • The study proposes greedy algorithms leveraging the monotone submodular property of the hypervolume indicator.
  • The algorithms are designed for both 2 and 3-dimensional HSSP.
  • Time complexity analysis is performed for the proposed algorithms.

Main Results:

  • New greedy algorithms for HSSP in 2 and 3 dimensions are presented.
  • The proposed 2D algorithm achieves a time complexity of O(n^2), matching existing exact algorithms.
  • The algorithms offer improved approximation factors for the HSSP, outperforming previous results.

Conclusions:

  • The developed greedy algorithms provide efficient solutions for the HSSP in 2 and 3 dimensions.
  • These algorithms significantly advance the state-of-the-art in Pareto-front approximation and multi-objective optimization.
  • The findings contribute to more effective visualization and decision-making in complex multi-objective scenarios.