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Following the Dynamics of Structural Variants in Experimentally Evolved Populations
Published on: February 3, 2023
A new approach for analyzing average time complexity of population-based evolutionary algorithms on unimodal
Tianshi Chen1, Jun He, Guangzhong Sun
1Department of Computer Science and Technology, Nature Inspired Computation and Applications Laboratory, University of Science and Technology of China, Hefei, China.
Summary
This study introduces a general method for analyzing evolutionary algorithms (EAs) on unimodal problems by generalizing takeover time. This approach yields new theoretical time complexity bounds for EAs on specific unimodal benchmark functions.
Area of Science:
- Computer Science
- Artificial Intelligence
- Algorithm Analysis
Background:
- Theoretical analysis of evolutionary algorithms (EAs) has yielded many results on time complexity.
- A general, easy-to-apply analytical approach for population-based EAs on unimodal problems is lacking.
Purpose of the Study:
- To propose a general theoretical framework for analyzing population-based evolutionary algorithms on unimodal problems.
- To generalize the concept of takeover time for EAs incorporating mutation.
Main Methods:
- Generalized the concept of takeover time to include mutation in evolutionary algorithms.
- Utilized the generalized takeover time to derive the mean first hitting time for EAs.
- Proposed a general analytical approach for population-based EAs on unimodal problems.
Main Results:
- Derived new time complexity bounds for (N + N) EAs on the leadingones and onemax unimodal problems: O(n ln n + n(2)/N) and O(n ln ln n + n ln n/N) generations, respectively.
- Demonstrated the applicability of the proposed approach to other population-based EAs and unimodal problems.
- Discussed the conditions under which the general approach provides tight bounds and when problem-specific knowledge is needed.
Conclusions:
- The study presents the first general theoretical framework for analyzing population-based EAs on unimodal problems.
- The generalized takeover time provides a powerful tool for deriving mean first hitting times and complexity bounds.
- The proposed approach offers a versatile method for understanding EA performance on a class of optimization problems.
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