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Sampling-based Pareto Optimization for Chance-constrained Monotone Submodular Problems

Xiankun Yan, Aneta Neumann, Frank Neumann

TL;DR

This work addresses maximizing a monotone submodular function under a chance constraint by introducing a direct sampling-based evaluation within a Pareto-optimized evolutionary framework. It presents ASW-GSEMO, an enhanced GSEMO with an adaptive sliding window, and demonstrates its superiority on a chance-constrained maximum coverage problem under IID and Uniform weight settings. The results show that the sampling-based approach can achieve performance comparable to, and sometimes better than, surrogate-based evaluations, while the adaptive window improves exploration and solution diversity. Overall, the study provides a practical alternative to surrogate evaluations for chance-constrained submodular optimization and highlights the value of adaptive windowing in evolutionary Pareto optimization.

Abstract

Recently surrogate functions based on the tail inequalities were developed to evaluate the chance constraints in the context of evolutionary computation and several Pareto optimization algorithms using these surrogates were successfully applied in optimizing chance-constrained monotone submodular problems. However, the difference in performance between algorithms using the surrogates and those employing the direct sampling-based evaluation remains unclear. Within the paper, a sampling-based method is proposed to directly evaluate the chance constraint. Furthermore, to address the problems with more challenging settings, an enhanced GSEMO algorithm integrated with an adaptive sliding window, called ASW-GSEMO, is introduced. In the experiments, the ASW-GSEMO employing the sampling-based approach is tested on the chance-constrained version of the maximum coverage problem with different settings. Its results are compared with those from other algorithms using different surrogate functions. The experimental findings indicate that the ASW-GSEMO with the sampling-based evaluation approach outperforms other algorithms, highlighting that the performances of algorithms using different evaluation methods are comparable. Additionally, the behaviors of ASW-GSEMO are visualized to explain the distinctions between it and the algorithms utilizing the surrogate functions.

Sampling-based Pareto Optimization for Chance-constrained Monotone Submodular Problems

TL;DR

This work addresses maximizing a monotone submodular function under a chance constraint by introducing a direct sampling-based evaluation within a Pareto-optimized evolutionary framework. It presents ASW-GSEMO, an enhanced GSEMO with an adaptive sliding window, and demonstrates its superiority on a chance-constrained maximum coverage problem under IID and Uniform weight settings. The results show that the sampling-based approach can achieve performance comparable to, and sometimes better than, surrogate-based evaluations, while the adaptive window improves exploration and solution diversity. Overall, the study provides a practical alternative to surrogate evaluations for chance-constrained submodular optimization and highlights the value of adaptive windowing in evolutionary Pareto optimization.

Abstract

Recently surrogate functions based on the tail inequalities were developed to evaluate the chance constraints in the context of evolutionary computation and several Pareto optimization algorithms using these surrogates were successfully applied in optimizing chance-constrained monotone submodular problems. However, the difference in performance between algorithms using the surrogates and those employing the direct sampling-based evaluation remains unclear. Within the paper, a sampling-based method is proposed to directly evaluate the chance constraint. Furthermore, to address the problems with more challenging settings, an enhanced GSEMO algorithm integrated with an adaptive sliding window, called ASW-GSEMO, is introduced. In the experiments, the ASW-GSEMO employing the sampling-based approach is tested on the chance-constrained version of the maximum coverage problem with different settings. Its results are compared with those from other algorithms using different surrogate functions. The experimental findings indicate that the ASW-GSEMO with the sampling-based evaluation approach outperforms other algorithms, highlighting that the performances of algorithms using different evaluation methods are comparable. Additionally, the behaviors of ASW-GSEMO are visualized to explain the distinctions between it and the algorithms utilizing the surrogate functions.
Paper Structure (13 sections, 6 equations, 4 figures, 6 tables, 5 algorithms)

This paper contains 13 sections, 6 equations, 4 figures, 6 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Problem Definition and Settings
  3. Related work
  4. Fast sampling-based Pareto Optimization
  5. Experiments
  6. Experimental Setup
  7. The Result on Uniform IID Weights
  8. Results comparison and Visualization of ASW-GSEMO
  9. Sampling VS. Surrogate
  10. The Result on Uniform Weights with Same Dispersion
  11. Results comparison and Visualization of ASW-GSWMO
  12. Sampling VS. Surrogate
  13. Conclusion

Figures (4)

  • Figure 1: Optimization process for ca-HepPh with IID weights using sampling-based evaluation
  • Figure 2: The weights obtained by ASW-GSEMO using different approaches in ca-HepPh with IID weights
  • Figure 3: Optimization process for ca-HepPh with uniform weights using sampling-based evaluation
  • Figure 4: The weights obtained by ASW-GSEMO using different evaluation approaches in ca-HepPh with uniform weights