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Abstract
Co-evolutionary algorithms have a wide range of applications, such as in hardware design, evolution of strategies for board games, and patching software bugs. However, these algorithms are poorly understood and applications are often limited by pathological behaviour, such as loss of gradient, relative over-generalisation, and mediocre objective stasis. It is an open challenge to develop a theory that can predict when co-evolutionary algorithms find solutions efficiently and reliable.
This paper provides a first step in developing runtime analysis for population-based competitive co-evolutionary algorithms. We provide a mathematical framework for describing and reasoning about the performance of co-evolutionary processes. To illustrate the framework, we introduce a population-based co-evolutionary algorithm called \pdcoea, and prove that it obtains a solution to a bilinear maximin optimisation problem in expected polynomial time. Finally, we describe settings where \pdcoea needs exponential time with overwhelmingly high probability to obtain a solution.
This paper provides a first step in developing runtime analysis for population-based competitive co-evolutionary algorithms. We provide a mathematical framework for describing and reasoning about the performance of co-evolutionary processes. To illustrate the framework, we introduce a population-based co-evolutionary algorithm called \pdcoea, and prove that it obtains a solution to a bilinear maximin optimisation problem in expected polynomial time. Finally, we describe settings where \pdcoea needs exponential time with overwhelmingly high probability to obtain a solution.
Original language | English |
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Journal | Algorithmica |
Publication status | Accepted/In press - 23 Feb 2024 |
Bibliographical note
Not yet published as of 22/04/2024.Funding:
Lehre was supported by a Turing AI Acceleration Fellowship (EPSRC grant ref EP/V025562/1).
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Turing AI Fellowship: Rigorous time-complexity analysis of co-evolutionary algorithms
Engineering & Physical Science Research Council
1/01/21 → 31/12/25
Project: Research Councils