Comma Selection Outperforms Plus Selection on OneMax with Randomly Planted Optima

Evolutionary algorithms (EAs) are general-purpose optimisation algorithms that maintain a population (multiset) of candidate solutions and apply variation operators to create new solutions called offspring. A new population is typically formed using one of two strategies: a  EA (plus selection) keep...

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Bibliographic Details
Published in:Algorithmica Vol. 87; no. 12; pp. 1804 - 1863
Main Authors: Jorritsma, Joost, Lengler, Johannes, Sudholt, Dirk
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2025
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Benchmarks
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Evolutionary algorithms
Mathematics of Computing
Parameters
Theory of Computation
Non-elitism
Drift analysis
Fixed-target running times
Multimodal optimisation
Runtime analysis
Comma strategies
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:Evolutionary algorithms (EAs) are general-purpose optimisation algorithms that maintain a population (multiset) of candidate solutions and apply variation operators to create new solutions called offspring. A new population is typically formed using one of two strategies: a  EA (plus selection) keeps the best search points out of the union of parents in the old population and offspring, whereas a  EA (comma selection) discards all parents and only keeps the best out of offspring. Comma selection may help to escape from local optima, however when and how it is beneficial is subject to an ongoing debate. We propose a new benchmark function to investigate the benefits of comma selection: the well known benchmark function OneMax with randomly planted local optima, generated by frozen noise. We show that comma selection (the  EA) is faster than plus selection (the  EA) on this benchmark, in a fixed-target scenario, and for offspring population sizes  for which both algorithms behave differently. For certain parameters, the  EAfinds the target in evaluations, with high probability (w.h.p.), while the  EAw.h.p. requires evaluations. We further show that the advantage of comma selection is not arbitrarily large: w.h.p. comma selection outperforms plus selection at most by a factor of for most reasonable parameter choices. We develop novel methods for analysing frozen noise and give powerful and general fixed-target results with tail bounds that are of independent interest.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-025-01330-y