Evolving Reliable Differentiating Constraints for the Chance-constrained Maximum Coverage Problem

TL;DR

This paper develops an evolutionary approach to identify reliable chance constraints in stochastic maximum coverage problems, enabling better understanding and automatic selection of algorithms under uncertainty.

Contribution

It introduces a new measure for evolving reliable chance constraints and demonstrates its effectiveness in differentiating algorithm performance with high confidence.

Findings

Successfully evolves reliable chance constraints that distinguish algorithm performance

Addresses instability in performance ratios with a new variance-aware measure

Enhances understanding of algorithm behavior under different stochastic constraints

Abstract

Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search algorithms and study the classical maximum coverage problem in graphs with chance constraints. Our goal is to evolve reliable chance constraint settings for a given graph where the performance of algorithms differs significantly not just in expectation but with high confidence. This allows to better learn and understand how different types of algorithms can deal with different types of constraint settings and supports automatic algorithm selection. We develop an evolutionary algorithm that provides sets of chance constraints that differentiate the performance of two stochastic search algorithms with high confidence. We initially use traditional approximation ratio as the fitness function of (1+1)~EA to evolve instances, which shows inadequacy to generate reliable instances. To address this issue, we introduce a new measure to calculate the performance difference for two algorithms, which considers variances of performance ratios. Our experiments show that our approach is highly successful in solving the instability issue of the performance ratios and leads to evolving reliable sets of chance constraints with significantly different performance for various types of algorithms.