research-article

Evolutionary Diversity Optimisation in Constructing Satisfying Assignments

Authors:

Adel Nikfarjam,

Ralf Rothenberger,

Tobias FriedrichAuthors Info & Claims

GECCO '23: Proceedings of the Genetic and Evolutionary Computation Conference

Pages 938 - 945

https://doi.org/10.1145/3583131.3590517

Published: 12 July 2023 Publication History

Abstract

Computing diverse solutions for a given problem, in particular evolutionary diversity optimisation (EDO), is a hot research topic in the evolutionary computation community. This paper studies the Boolean satisfiability problem (SAT) in the context of EDO. SAT is of great importance in computer science and differs from the other problems studied in EDO literature, such as KP and TSP. SAT is heavily constrained, and the conventional evolutionary operators are inefficient in generating SAT solutions. Our approach avails of the following characteristics of SAT: 1) the possibility of adding more constraints (clauses) to the problem to forbid solutions or to fix variables, and 2) powerful solvers in the literature, such as minisat. We utilise such a solver to construct a diverse set of solutions.

Moreover, maximising diversity provides us with invaluable information about the solution space of a given SAT problem, such as how large the feasible region is. In this study, we introduce evolutionary algorithms (EAs) employing a well-known SAT solver to maximise diversity among a set of SAT solutions explicitly. The experimental investigations indicate the introduced algorithms' capability to maximise diversity among the SAT solutions.

References

[1]

Bradley Alexander, James Kortman, and Aneta Neumann. 2017. Evolution of artistic image variants through feature based diversity optimisation. In GECCO. ACM, 171--178.

[2]

Maxime Allard, Simón C. Smith, Konstantinos I. Chatzilygeroudis, and Antoine Cully. 2022. Hierarchical quality-diversity for online damage recovery. In GECCO. ACM, 58--67.

[3]

Carlos Ansótegui, Maria Luisa Bonet, and Jordi Levy. 2009. Towards IndustrialLike Random SAT Instances. In IJCAI. 387--392.

[4]

Jakob Bossek, Pascal Kerschke, Aneta Neumann, Markus Wagner, Frank Neumann, and Heike Trautmann. 2019. Evolving diverse TSP instances by means of novel and creative mutation operators. In Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms. 58--71.

Digital Library

[5]

Jakob Bossek, Aneta Neumann, and Frank Neumann. 2021. Breeding diverse packings for the knapsack problem by means of diversity-tailored evolutionary algorithms. In GECCO. ACM, 556--564.

[6]

Jakob Bossek and Frank Neumann. 2021. Evolutionary diversity optimization and the minimum spanning tree problem. In GECCO. ACM, 198--206.

[7]

Jakob Bossek and Frank Neumann. 2022. Exploring the feature space of TSP instances using quality diversity. In GECCO. ACM, 186--194.

[8]

Supratik Chakraborty, Daniel J. Fremont, Kuldeep S. Meel, Sanjit A. Seshia, and Moshe Y. Vardi. 2015. On Parallel Scalable Uniform SAT Witness Generation. In TACAS (Lecture Notes in Computer Science, Vol. 9035). Springer, 304--319.

[9]

Stephen A. Cook. 1971. The Complexity of Theorem-Proving Procedures. In STOC. ACM, 151--158.

[10]

Martin Davis, George Logemann, and Donald W. Loveland. 1962. A machine program for theorem-proving. Commun. ACM 5, 7 (1962), 394--397.

Digital Library

[11]

Anh Viet Do, Jakob Bossek, Aneta Neumann, and Frank Neumann. 2020. Evolving diverse sets of tours for the travelling salesperson problem. In GECCO. ACM, 681--689.

[12]

Anh Viet Do, Mingyu Guo, Aneta Neumann, and Frank Neumann. 2022. Analysis of Evolutionary Diversity Optimization for Permutation Problems. ACM Trans. Evol. Learn. Optim. 2, 3 (2022), 11:1--11:27.

Digital Library

[13]

Rafael Dutra, Kevin Laeufer, Jonathan Bachrach, and Koushik Sen. 2018. Efficient sampling of SAT solutions for testing. In ICSE. ACM, 549--559.

[14]

Niklas Eén and Niklas Sörensson. 2003. An Extensible SAT-solver. In SAT (Lecture Notes in Computer Science, Vol. 2919). Springer, 502--518.

[15]

Matthew C. Fontaine, Ruilin Liu, Ahmed Khalifa, Jignesh Modi, Julian Togelius, Amy K. Hoover, and Stefanos Nikolaidis. 2021. Illuminating Mario Scenes in the Latent Space of a Generative Adversarial Network. In AAAI. AAAI Press, 5922--5930.

[16]

Matthew C. Fontaine, Julian Togelius, Stefanos Nikolaidis, and Amy K. Hoover. 2020. Covariance matrix adaptation for the rapid illumination of behavior space. In GECCO. ACM, 94--102.

[17]

Tobias Friedrich, Anton Krohmer, Ralf Rothenberger, Thomas Sauerwald, and Andrew M. Sutton. 2017. Bounds on the Satisfiability Threshold for Power Law Distributed Random SAT. In ESA (LIPIcs, Vol. 87). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 37:1--37:15.

[18]

Tobias Friedrich, Anton Krohmer, Ralf Rothenberger, and Andrew M. Sutton. 2017. Phase Transitions for Scale-Free SAT Formulas. In AAAI. AAAI Press, 3893--3899.

[19]

Wanru Gao, Samadhi Nallaperuma, and Frank Neumann. 2021. Feature-Based Diversity Optimization for Problem Instance Classification. Evol. Comput. 29, 1 (2021), 107--128.

[20]

Xiaodong Li, Michael G. Epitropakis, Kalyanmoy Deb, and Andries P. Engelbrecht. 2017. Seeking Multiple Solutions: An Updated Survey on Niching Methods and Their Applications. IEEE Trans. Evol. Comput. 21, 4 (2017), 518--538.

Digital Library

[21]

Matthew W. Moskewicz, Conor F. Madigan, Ying Zhao, Lintao Zhang, and Sharad Malik. 2001. Chaff: Engineering an Efficient SAT Solver. In Proceedings of the 38th Design Automation Conference DAC. ACM, 530--535.

Digital Library

[22]

Alexander Nadel. 2011. Generating Diverse Solutions in SAT. In SAT (Lecture Notes in Computer Science, Vol. 6695). Springer, 287--301.

[23]

Aneta Neumann, Denis Antipov, and Frank Neumann. 2022. Coevolutionary Pareto diversity optimization. In GECCO. ACM, 832--839.

[24]

Aneta Neumann, Jakob Bossek, and Frank Neumann. 2021. Diversifying greedy sampling and evolutionary diversity optimisation for constrained monotone submodular functions. In GECCO. ACM, 261--269.

[25]

Aneta Neumann, Wanru Gao, Carola Doerr, Frank Neumann, and Markus Wagner. 2018. Discrepancy-based evolutionary diversity optimization. In GECCO. ACM, 991--998.

[26]

Aneta Neumann, Wanru Gao, Markus Wagner, and Frank Neumann. 2019. Evolutionary diversity optimization using multi-objective indicators. In GECCO. ACM, 837--845.

[27]

Adel Nikfarjam, Jakob Bossek, Aneta Neumann, and Frank Neumann. 2021. Computing diverse sets of high quality TSP tours by EAX-based evolutionary diversity optimisation. In FOGA. ACM, 9:1--9:11.

[28]

Adel Nikfarjam, Jakob Bossek, Aneta Neumann, and Frank Neumann. 2021. Entropy-based evolutionary diversity optimisation for the traveling salesperson problem. In GECCO. ACM, 600--608.

[29]

Adel Nikfarjam, Anh Viet Do, and Frank Neumann. 2022. Analysis of Quality Diversity Algorithms for the Knapsack Problem. In PPSN (2) (Lecture Notes in Computer Science, Vol. 13399). Springer, 413--427.

[30]

Adel Nikfarjam, Amirhossein Moosavi, Aneta Neumann, and Frank Neumann. 2022. Computing High-Quality Solutions for the Patient Admission Scheduling Problem Using Evolutionary Diversity Optimisation. In PPSN (1) (Lecture Notes in Computer Science, Vol. 13398). Springer, 250--264.

[31]

Adel Nikfarjam, Aneta Neumann, Jakob Bossek, and Frank Neumann. 2022. Co-evolutionary Diversity Optimisation for the Traveling Thief Problem. In PPSN (1) (Lecture Notes in Computer Science, Vol. 13398). Springer, 237--249.

[32]

Adel Nikfarjam, Aneta Neumann, and Frank Neumann. 2022. Evolutionary diversity optimisation for the traveling thief problem. In GECCO. ACM, 749--756.

[33]

Adel Nikfarjam, Aneta Neumann, and Frank Neumann. 2022. On the use of quality diversity algorithms for the traveling thief problem. In GECCO. ACM, 260--268.

[34]

Nemanja Rakicevic, Antoine Cully, and Petar Kormushev. 2021. Policy manifold search: exploring the manifold hypothesis for diversity-based neuroevolution. In GECCO. ACM, 901--909.

[35]

João P. Marques Silva and Karem A. Sakallah. 1999. GRASP: A Search Algorithm for Propositional Satisfiability. IEEE Trans. Computers 48, 5 (1999), 506--521.

Digital Library

[36]

Kirby Steckel and Jacob Schrum. 2021. Illuminating the space of beatable lode runner levels produced by various generative adversarial networks. In GECCO Companion. ACM, 111--112.

[37]

Tamara Ulrich and Lothar Thiele. 2011. Maximizing population diversity in single-objective optimization. In GECCO. ACM, 641--648.

[38]

Enrico Zardini, Davide Zappetti, Davide Zambrano, Giovanni Iacca, and Dario Floreano. 2021. Seeking quality diversity in evolutionary co-design of morphology and control of soft tensegrity modular robots. In GECCO. ACM, 189--197.

Cited By

Schmidbauer MOpris ABossek JNeumann FSudholt DLi XHandl J(2024)Guiding Quality Diversity on Monotone Submodular Functions: Customising the Feature Space by Adding Boolean ConjunctionsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654160(1614-1622)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654160
Goel DMoore KGuo MWang DKim MCamtepe S(2024)Optimizing Cyber Defense in Dynamic Active Directories Through Reinforcement LearningComputer Security – ESORICS 202410.1007/978-3-031-70879-4_17(332-352)Online publication date: 5-Sep-2024
https://doi.org/10.1007/978-3-031-70879-4_17
Antipov DNeumann ANeumann FSutton A(2024)Runtime Analysis of Evolutionary Diversity Optimization on a Tri-Objective Version of the (LeadingOnes, TrailingZeros) ProblemParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70071-2_2(19-35)Online publication date: 7-Sep-2024
https://doi.org/10.1007/978-3-031-70071-2_2
Show More Cited By

Index Terms

Evolutionary Diversity Optimisation in Constructing Satisfying Assignments
1. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
      1. Discrete optimization
        Optimization with randomized search heuristics
        Evolutionary algorithms

Recommendations

Evolutionary diversity optimisation for the traveling thief problem
GECCO '22: Proceedings of the Genetic and Evolutionary Computation Conference

There has been a growing interest in the evolutionary computation community to compute a diverse set of high-quality solutions for a given optimisation problem. This can provide the practitioners with invaluable information about the solution space and ...
Co-evolutionary Diversity Optimisation for the Traveling Thief Problem
Parallel Problem Solving from Nature – PPSN XVII
Abstract
Recently different evolutionary computation approaches have been developed that generate sets of high quality diverse solutions for a given optimisation problem. Many studies have considered diversity 1) as a mean to explore niches in behavioural ...
Prime clauses for fast enumeration of satisfying assignments to boolean circuits
DAC '05: Proceedings of the 42nd annual Design Automation Conference

Finding all satisfying assignments of a propositional formula has many applications in the design of hardware and software. An approach to this problem augments a clause-recording propositional satisfiability solver with the ability to add blocking ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

GECCO '23: Proceedings of the Genetic and Evolutionary Computation Conference

July 2023

1667 pages

ISBN:9798400701191

DOI:10.1145/3583131

Chair:
Sara Silva,
Program Chair:
Luís Paquete

Copyright © 2023 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Sponsors

SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 July 2023

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

Australian Research Council

Conference

GECCO '23

Sponsor:

SIGEVO

GECCO '23: Genetic and Evolutionary Computation Conference

July 15 - 19, 2023

Lisbon, Portugal

Acceptance Rates

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
94
Total Downloads

Downloads (Last 12 months)47
Downloads (Last 6 weeks)1

Reflects downloads up to 16 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Schmidbauer MOpris ABossek JNeumann FSudholt DLi XHandl J(2024)Guiding Quality Diversity on Monotone Submodular Functions: Customising the Feature Space by Adding Boolean ConjunctionsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654160(1614-1622)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654160
Goel DMoore KGuo MWang DKim MCamtepe S(2024)Optimizing Cyber Defense in Dynamic Active Directories Through Reinforcement LearningComputer Security – ESORICS 202410.1007/978-3-031-70879-4_17(332-352)Online publication date: 5-Sep-2024
https://doi.org/10.1007/978-3-031-70879-4_17
Antipov DNeumann ANeumann FSutton A(2024)Runtime Analysis of Evolutionary Diversity Optimization on a Tri-Objective Version of the (LeadingOnes, TrailingZeros) ProblemParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70071-2_2(19-35)Online publication date: 7-Sep-2024
https://doi.org/10.1007/978-3-031-70071-2_2
Antipov DNeumann ANeumann F(2024)Local Optima in Diversity Optimization: Non-trivial Offspring Population is EssentialParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70071-2_12(181-196)Online publication date: 7-Sep-2024
https://doi.org/10.1007/978-3-031-70071-2_12

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten