Symmetry Breaking for Voting Mechanisms

Preethi Sankineni, Andrew M. Sutton

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recently, Rowe and Aishwaryaprajna [FOGA 2019] introduced a simple majority vote technique that efficiently solves Jump with large gaps, OneMax with large noise, and any monotone function with a polynomial-size image. In this paper, we identify a pathological condition for this algorithm: the presence of spin-flip symmetry. Spin-flip symmetry is the invariance of a pseudo-Boolean function to complementation. Many important combinatorial optimization problems admit objective functions that exhibit this pathology, such as graph problems, Ising models, and variants of propositional satisfiability. We prove that no population size exists that allows the majority vote technique to solve spin-flip symmetric functions with reasonable probability. To remedy this, we introduce a symmetry-breaking technique that allows the majority vote algorithm to overcome this issue for many landscapes. We prove a sufficient condition for a spin-flip symmetric function to possess in order for the symmetry-breaking voting algorithm to succeed, and prove its efficiency on generalized TwoMax and families of constructed 3-NAE-SAT and 2-XOR-SAT formulas. We also prove that it fails on the one-dimensional Ising model, and suggest different techniques for overcoming this. Finally, we present empirical results that explore the tightness of the runtime bounds and the performance of the technique on randomized satisfiability variants.

Original languageEnglish (US)
Title of host publicationEvolutionary Computation in Combinatorial Optimization - 21st European Conference, EvoCOP 2021, Held as Part of EvoStar 2021, Proceedings
EditorsChristine Zarges, Sébastien Verel
PublisherSpringer Science and Business Media Deutschland GmbH
Pages185-201
Number of pages17
ISBN (Print)9783030729035
DOIs
StatePublished - 2021
Externally publishedYes
Event21st European Conference on Evolutionary Computation in Combinatorial Optimization, EvoCOP 2021 Held as Part of EvoStar 2021 - Virtual, Online
Duration: Apr 7 2021Apr 9 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12692 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st European Conference on Evolutionary Computation in Combinatorial Optimization, EvoCOP 2021 Held as Part of EvoStar 2021
CityVirtual, Online
Period4/7/214/9/21

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Fingerprint

Dive into the research topics of 'Symmetry Breaking for Voting Mechanisms'. Together they form a unique fingerprint.

Cite this