A stochastic bilevel programming problem with multiple followers is presented in this article. Such kinds of problem are computationally difficult and efficient algorithms are lacking thanks to the randomness properties in the problem setting, its hierarchical structure and the expected simultaneous decision at the followers' level for each strategy of the leader. This article proposes a systematic sampling evolutionary algorithm that is established on a sample average approximation, a systematic sampling technique and particle swarm optimization integrated with an iterated method. The solution procedure is implemented and its effectiveness is tested on a variety of illustrative examples from the literature and on carefully constructed problems. The simulation results show that the proposed method is promising and can be used to solve a variety of complex stochastic bilevel programming problems with multiple followers.

本文介绍了一个具有多个跟随者的随机双层规划问题。由于问题设置中的随机性，其层次结构以及领导者的每个策略在追随者级别的预期同时决策，此类问题在计算上是困难的，并且缺乏有效的算法。本文提出了一种基于样本平均逼近的系统采样进化算法、系统采样技术和粒子群优化与迭代法相结合。解决程序已实施，其有效性已在文献中的各种说明性示例和精心构建的问题上进行测试。