Paper:

# An Evolutionary Algorithm for Black-Box Chance-Constrained Function Optimization

## Kazuyuki Masutomi^{*}, Yuichi Nagata^{**}, and Isao Ono^{*}

^{*}Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology,

^{*}4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan

Education Academy of Computational Life Sciences, Tokyo Institute of Technology,

^{**}4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501, Japan

This paper presents an evolutionary algorithm for Black-Box Chance-Constrained Function Optimization (BBCCFO). BBCCFO is to minimize the expectation of the objective function under the constraints that the feasibility probability is higher than a userdefined constant in uncertain environments not given the mathematical expressions of objective functions and constraints explicitly. In BBCCFO, only objective function values of solutions and their feasibilities are available because the algebra expressions of objective functions and constraints cannot be used. In approaches to BBCCFO, a method based on an evolutionary algorithm proposed by Loughlin and Ranjithan shows relatively good performance in a realworld application, but this conventional method has a problem in that it requires many samples to obtain a good solution because it estimates the expectation of the objective function and the feasibility probability of an individual by sampling the individual plural times. In this paper, we propose a new evolutionary algorithm that estimates the expectation of the objective function and the feasibility probability of an individual by using the other individuals in the neighborhood of the individual. We show the effectiveness of the proposed method through experiments both in benchmark problems and in the problem of a inverted pendulum balancing with a neural network controller.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.17, No.2, pp. 272-282, 2013.

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