On Evolutionary Optimization with Approximate Fitness Functions.

The evaluation of the quality of solutions is usually very time-consuming in design optimization. Therefore, time-efficient approximate models can be particularly beneficial for the evaluation when evolutionary algorithms are applied. In this paper, the convergence property of an evolution strategy (ES) with neural network based fitness evaluations is investigated. It is found that the evolutionary algorithm will converge incorrectly if the approximate model has false optima. To address this problem, two strategies to control the evolution process are introduced. In addition, methods to eliminate false minima in neural network training are proposed. The effectiveness of the methods are shown with simulation studies on the Ackley function and the Rosenbrock function.