An enhanced sample average approximation method for stochastic optimization

Choosing the appropriate sample size in Sample Average Approximation (SAA) method is very challenging. Inappropriate sample size can lead to the generation of low quality solutions with high computational burden. To overcome this challenge, our study proposes an enhanced SAA algorithm that utilizes clustering techniques to dynamically update the sample sizes and offers high quality solutions in a reasonable amount of time. We evaluate this proposed algorithm in the context of a facility location problem [FLP]. A number of numerical experiments (e.g., impact of different clustering techniques, fixed vs. dynamic clusters) are performed for various problem instances to illustrate the effectiveness of the proposed method. Results indicate that on average, enhanced SAA with fixed clustering size and dynamic clustering size solves [FLP] almost 631% and 699% faster than the basic SAA algorithm, respectively. Furthermore, it is observed that there is no single winner among the clustering techniques to solve all the problem instances of enhanced SAA algorithm and the performance is highly impacted by the size of the problems.