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

TL;DR

This work tackles the need for reliable benchmark instances to guide algorithm selection under uncertainty, focusing on the chance-constrained maximum coverage problem. It first demonstrates that using a traditional approximation-ratio fitness to evolve discriminating instances yields highly variable, unreliable results. By introducing a variability-aware discounting fitness that subtracts a multiple of the observed run std dev from the expected performance gap, the authors achieve high-confidence discrimination between algorithms with substantially reduced variance. The proposed approach enables more trustworthy benchmarking and automatic algorithm selection for chance-constrained submodular problems, with practical implications for designing robust stochastic optimization pipelines.

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.