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Bilevel linear programming,which consists of the objective functions of the upper level and lower level,is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem.Of all the algorithms,the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming.In this paper,we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation.In addition,some techniques are adopted not only to deal with the difficulty that most of the chromosomes may be infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm.The performance of this proposed algorithm is illustrated by the examples from references. 相似文献
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对于具有非线性等式约束且变量有界的非线性规划问题,提出了一个由三阶段组成的广度既约梯度变位算法,即线性近似、既约梯度求极小和可行变位阶段.同时我们证明了该算法所具有的收敛性. 相似文献
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圆锥规划是一类重要的非对称锥优化问题.基于一个光滑函数,将圆锥规划的最优性条件转化成一个非线性方程组,然后给出求解圆锥规划的光滑牛顿法.该算法只需求解一个线性方程组和进行一次线搜索.运用欧几里得约当代数理论,证明该算法具有全局和局部二阶收敛性.最后数值结果表明算法的有效性. 相似文献
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The penalty function method, presented many years ago, is an important numerical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach. 相似文献