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中文摘要：
结合粒子群优化方法和单纯形法为二层线性规划构造了一个混合粒子群优化算法。算法具有两层结构，其中粒子群算法用以求解上层规划问题，单纯形法用以求解下层规划问题。设计的粒子群在上层决策变量的可行域内搜索最优解，同时通过单纯形法求解下层规划问题得到每个粒子相应的下层规划问题的解。算法通过初始种群可行化，以及步长控制、不可行粒子淘汰等技巧避免了使用罚函数处理约束带来的困难，提高了粒子群优化算法的计算性能。最后，我们给出算法的数值例子并对该算法的计算性能加以分析。
英文摘要：
This paper proposes a hybrid particle swarm optimization algorithm for the linear bilevel programming problem by combining the method of particle swarm optimization （PSO） with simplex algorithm. The particle swarm optimization algorithm was designed to operate in the up-level problems of BLP and the simplex algorithm was employed to solving the lower-level problems. The particle swarm was designed to search in the solution space of up-level problem, and the solutions of the lower-level problem corresponding to each particle can be obtained by the simplex algorithm. With testing the solvability of the lower-level problems by the simplex algorithm and taking measures of step controlling, the infeasible particles can be screened out and the difficulty of using penalty functions to deal with the constraints is avoided. Finally, we give numerical examples and the performance analyses show that the algorithm is effective and practical.
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