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Feature-based Evolutionary Diversity Optimization of Discriminating Instances for Chance-constrained Optimization Problems

Saba Sadeghi Ahouei, Denis Antipov, Aneta Neumann, Frank Neumann

TL;DR

The paper tackles algorithm selection in optimization by evolving discriminating instances for chance-constrained problems using a feature-based diversity framework. It introduces a $(\mu+1)\mathrm{EA}_D$ that optimizes four instance features derived from stochastic costs and employs two mutation operators to broaden feature diversity, enabling instance sets that differentiate algorithm pairs. Focusing on a chance-constrained maximum coverage problem, the authors demonstrate that independent-feature mutations expand averages of costs and their variances, while dependent-feature mutations broaden standard deviations, yielding more diverse and discriminating benchmark sets. The results highlight improved feature-space coverage and increased discriminatory power, offering a solid foundation for feature-based algorithm selection in CC settings and beyond.

Abstract

Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a detailed analysis of the problem's features. To do so, it is important to have a diverse set of benchmarking instances highlighting the difference in algorithms' performance. In this paper, we evolve diverse benchmarking instances for chance-constrained optimization problems that contain stochastic components characterized by their expected values and variances. These instances clearly differentiate the performance of two given algorithms, meaning they are easy to solve by one algorithm and hard to solve by the other. We introduce a $(μ+1)~EA$ for feature-based diversity optimization to evolve such differentiating instances. We study the chance-constrained maximum coverage problem with stochastic weights on the vertices as an example of chance-constrained optimization problems. The experimental results demonstrate that our method successfully generates diverse instances based on different features while effectively distinguishing the performance between a pair of algorithms.

Feature-based Evolutionary Diversity Optimization of Discriminating Instances for Chance-constrained Optimization Problems

TL;DR

The paper tackles algorithm selection in optimization by evolving discriminating instances for chance-constrained problems using a feature-based diversity framework. It introduces a that optimizes four instance features derived from stochastic costs and employs two mutation operators to broaden feature diversity, enabling instance sets that differentiate algorithm pairs. Focusing on a chance-constrained maximum coverage problem, the authors demonstrate that independent-feature mutations expand averages of costs and their variances, while dependent-feature mutations broaden standard deviations, yielding more diverse and discriminating benchmark sets. The results highlight improved feature-space coverage and increased discriminatory power, offering a solid foundation for feature-based algorithm selection in CC settings and beyond.

Abstract

Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a detailed analysis of the problem's features. To do so, it is important to have a diverse set of benchmarking instances highlighting the difference in algorithms' performance. In this paper, we evolve diverse benchmarking instances for chance-constrained optimization problems that contain stochastic components characterized by their expected values and variances. These instances clearly differentiate the performance of two given algorithms, meaning they are easy to solve by one algorithm and hard to solve by the other. We introduce a for feature-based diversity optimization to evolve such differentiating instances. We study the chance-constrained maximum coverage problem with stochastic weights on the vertices as an example of chance-constrained optimization problems. The experimental results demonstrate that our method successfully generates diverse instances based on different features while effectively distinguishing the performance between a pair of algorithms.
Paper Structure (12 sections, 9 equations, 4 figures, 3 tables, 3 algorithms)

This paper contains 12 sections, 9 equations, 4 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contribution
  4. Preliminaries
  5. Approach
  6. Evolving Discriminating Instances for Chance Constrained Problems with Diverse Features
  7. Experimental Setting
  8. Experimental Results
  9. Evolving Discriminating Chance Constraints with Diverse Dependent Features
  10. Experimental Setting
  11. Experimental Results
  12. Conclusions

Figures (4)

  • Figure 1: Distribution of average of weights ($ft_1$) for 20 instances. The left box plots show the features of the initial population and the right ones show them after using feature-based diversity optimization.
  • Figure 2: Distribution of average of variances ($ft_2$) for 20 instances. The left box plots show the features of the initial population and the right ones show them after using feature-based diversity optimization.
  • Figure 3: Distribution of standard deviation of weights ($ft_3$) for 20 instances. The left box plots show the features of the initial population and the right ones show them after using feature-based diversity optimization.
  • Figure 4: Distribution of standard deviation of variances ($ft_4$) for 20 instances. The left box plots show the features of the initial population and the right ones show them after using feature-based diversity optimization .