Paper:

# AEGA: A New Real-Coded Genetic AlgorithmTaking Account of Extrapolation

## Kento Uemura and Isao Ono

Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology

4259 Nagatsuta, Midori-ku, Yokohama, 226-8502 Kanagawa, Japan

This study proposes a new real-coded genetic algorithm (RCGA) taking account of extrapolation, which we call adaptive extrapolation RCGA (AEGA). Real-world problems are often formulated as black-box function optimization problems and sometimes have ridge structures and implicit active constraints. mAREX/JGG is one of the most powerful RCGAs that performs well against these problems. However, mAREX/JGG has a problem of search inefficiency. To overcome this problem, we propose AEGA that generates offspring outside the current population in a more stable manner than mAREX/JGG. Moreover, AEGA adapts the width of the offspring distribution automatically to improve its search efficiency. We evaluate the performance of AEGA using benchmark problems and show that AEGA finds the optimum with fewer evaluations than mAREX/JGG with a maximum reduction ratio of 45%. Furthermore, we apply AEGA to a lens design problem that is known as a difficult real-world problem and show that AEGA reaches the known best solution with approximately 25% fewer evaluations than mAREX/JGG.

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