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

Genetic and Evolutionary Computation Conference (GECCO), pp. 1036–1044

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.

Authors 5

1. Saba Sadeghi Ahouei

   The University of Adelaide

   Affiliation as printed

   School of Computer and Mathematical Sciences, The University of Adelaide, Adelaide, Australia

2. Jacob de Nobel Aachen

   Leiden University

   Affiliation as printed

   LIACS, Leiden University, Leiden, Netherlands

3. Aneta Neumann

   The University of Adelaide

   Affiliation as printed

   School of Computer and Mathematical Sciences, The University of Adelaide, adelaide, Australia

4. Thomas Bäck Aachen

   Leiden University

   Affiliation as printed

   LIACS, Leiden University, leiden, Netherlands

5. Frank Neumann

   The University of Adelaide

   Affiliation as printed

   School of Computer and Mathematical Sciences, The University of Adelaide, adelaide, Australia