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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.

Stochastic bilevel programming with multiple followers: a solution approach using the systematic sampling evolutionary method