NDLI: Investigating EA solutions for approximate KKT conditions in smooth problems

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Investigating EA solutions for approximate KKT conditions in smooth problems

Content Provider	ACM Digital Library
Author	Tulshyan, Rupesh Arora, Ramnik Dutta, Joydeep Deb, Kalyanmoy
Abstract	Evolutionary algorithms (EAs) are increasingly being applied to solve real-parameter optimization problems due to their flexibility in handling complexities such as non-convexity, non-differentiability, multi-modality and noise in problems. However, an EA's solution is never guaranteed to be optimal in generic problems, even for smooth problems, and importantly EAs still lack theoretically motivated termination criterion for stopping an EA run only when a near-optimal point is found. We address both these issues in this paper by integrating the Karush-Kuhn-Tucker (KKT) optimality conditions that involve first-order derivatives of objective and constraint functions with an EA. For this purpose, we define a KKT-proximity measure by relaxing the complimentary slackness condition associated with the KKT conditions. Results on a number of standard constrained test problems indicate that in spite of not using any gradient information and any theoretical optimality conditions, an EA's selection, recombination and mutation operation lead the search process to a point close to the KKT point. This suggests that the proposed KKT-proximity measure can be used termination criterion in an EA simulation.
Starting Page	689
Ending Page	696
Page Count	8
File Format	PDF
ISBN	9781450300728
DOI	10.1145/1830483.1830609
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-07-07
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Karush-kuhn-tucker conditions Nonlinear programming Termination condition Evolutionary optimization
Content Type	Text
Resource Type	Article

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