Investigating EA solutions for approximate KKT conditions in smooth problems

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 a 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&#...

• Type: Conference
• Year: 2010
• Where: GECCO
• Authors: Rupesh Tulshyan, Ramnik Arora, Kalyanmoy Deb, Joydeep Dutta
• Keywords: GECCO 2010, Optimality Conditions, Optimization, Real-parameter Optimization Problems, Termination Criterion