Genetic algorithm to optimize fitness function with sampling error and its application to financial optimization problem

In this paper we discuss the optimization problems with noisy fitness function. On financial optimization problems, Monte-Carlo method is commonly used to evaluate the optimization criteria such as value at risk. The evaluation model is often very complex which needs considerable computational overheads. In order to realize efficient optimization of financial problems, we propose a method to decide the number of samples used to estimate the optimization criteria. Selection efficiency proposed in this paper is a index that shows how close the population approaches to the convergence to a good solution. In general, it is difficult to calculate selection efficiency analytically. Thus we also employ bootstrap method to estimate selection efficiency. The resulting algorithm is applied to the optimization of the procurement plan optimization problem. The result shows that Value at Risk of the problem is optimized efficiently by the proposed method.