Algorithms for the Solution of Multiparametric Mixed-Integer Nonlinear Optimization Problems
Algorithms for the Solution of Multiparametric Mixed-Integer Nonlinear Optimization Problems
复制标题
多参数混合整数非线性优化问题的求解算法
DOI：
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发表时间：
1999
期刊：
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通讯作者：
E. Pistikopoulos
中科院分区：
文献类型：
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作者：
V. Dua;E. Pistikopoulos
在本文中，我们提出了新的理论和算法的发展，解决涉及不确定性的混合整数优化问题，这可以构成多参数混合整数优化模型，其中不确定性是由一组参数之间的下限和上限。特别是，我们解决凸非线性公式，涉及（i）0−1个整数变量和（ii）线性和单独出现的不确定参数，并出现在约束的右侧。在这项工作中报告的发展是基于分解原则，其中的问题被分解成两个迭代收敛的子问题：（i）一个主要的和（ii）主子问题，代表有效的参数上限和下限的最终解决方案，分别。原始子问题通过固定整数变量而形成多参数非线性规划（mp-NLP）问题，该问题通过外逼近非线性函数来求解。
In this paper we present novel theoretical and algorithmic developments for the solution of mixed-integer optimization problems involving uncertainty, which can be posed as multiparametric mixed-integer optimization models, where uncertainty is described by a set of parameters bounded between lower and upper bounds. In particular, we address convex nonlinear formulations involving (i) 0−1 integer variables and (ii) uncertain parameters appearing linearly and separately and present on the right-hand side of the constraints. The developments reported in this work are based upon decomposition principles where the problem is decomposed into two iteratively converging subproblems: (i) a primal and (ii) a master subproblem, representing valid parametric upper and lower bounds on the final solution, respectively. The primal subproblem is formulated by fixing the integer variables which results in a multiparametric nonlinear programming (mp-NLP) problem, which is solved by outer-approximating the nonlinear funct...