Abstract Stochastic bilevel programming is a bilevel program having some form of randomness in the problem definition. The main objective is to optimize the leader’s (upper level) stochastic programming problem, where the follower’s problem is assumed to be satisfied as part of the constraints. Due to the involvement of randomness property and the hierarchical nature of the optimization procedure, the problem is computationally expensive and challenging. In this paper, a new meta-heuristic type algorithm is proposed that can effectively solve stochastic bilevel programs. The algorithm is based on realizing the random space, systematic sampling technique to choose a representative action from the leader’s decision space and on a hybrid particle swarm optimization procedure for searching its corresponding follower’s reaction for each leader’s action until Stackelberg equilibrium is achieved. The algorithm is shown to be convergent and its performance is checked using test problems from literature. The simulation result of the algorithm is very much promising and can be used to solve complex stochastic bilevel programming problems.

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一种用于随机双层规划问题的系统抽样进化 (SSE) 方法

摘要 随机双层规划是在问题定义中具有某种形式随机性的双层规划。主要目标是优化领导者的（上层）随机规划问题，其中假设追随者的问题作为约束的一部分得到满足。由于涉及随机性和优化过程的分层性质，该问题在计算上是昂贵且具有挑战性的。在本文中，提出了一种新的元启发式算法，可以有效地解决随机双层程序。该算法基于随机空间的实现，系统采样技术从领导者的决策空间中选择一个有代表性的行动，并在混合粒子群优化过程中搜索其对应的追随者对每个领导者的行动的反应，直到达到 Stackelberg 平衡。该算法被证明是收敛的，并且使用文献中的测试问题来检查其性能。该算法的仿真结果很有前景，可用于解决复杂的随机双层规划问题。