选择决策的整数规划模型

在中国，决策者常常须在满足一定的均衡条件下从许多替代方案中选出一个最佳方案。本文提出了一个整数规划模型来描述这类问题，同时也给出了该模型的算法．     

整数规划的布谷鸟算法

布谷鸟搜索算法是一种新型的智能优化算法．本文采用截断取整的方法将基本布谷鸟搜索算法用于求解整数规划问题．通过对标准测试函数进行仿真实验并与粒子群算法进行比较,结果表明本文所提算法比粒子群算法拥有更好的性能和更强的全局寻优能力,可以作为一种实用方法用于求解整数规划问题．     

改进的非线性整数规划算法

通过对LUUS随机搜索算法的分析，本文首次提出了一种改进的随机定向搜索法（MRDISA）通过实例计算，说明该算法的优点是最优解的可靠性不受初始值X^(0)和初始搜索范围R^(0)的影响，并可用于求解高维约束非线性整数规划问题。     

我国民航企业飞行员转升规划方法研究

飞行员是民航企业发展的主要保障,其转升规划具有路径复杂、升级资格影响因素多等特点,是一项复杂的工作。如何制定合理的飞行员转升规划,是目前亟待解决的问题。本文构建以费用最小为目标的非线性整数规划模型,用以描述飞行员规划问题,并将其转换为一类带约束的网络优化问题。针对问题特点设计了流量调整算法并证明了该算法的解为原问题的最优解。最后通过实例分析验证了方法的有效性。该研究为我国民航企业飞行员发展规划提供了理论依据。     

求解整数规划代理对偶的一个新方法

考虑如下的整数线性规划问题: (P)min Cx, s.tAx≥b, x≥0,且为整数向量,其中c,b是具有适当维数的行向量或列向量,A是已知的矩阵,c的分量均为正数,且假定(P)是可行的,x是n维变量。 用V(·)表示优化问题(·)的最优值。如果对x放弃整数限制要求,问题(P)的线     

用0—1整数规划方法选择煤炭行业最优规划方案

文章基于采矿技术原理，运用０－１整数规划的数学方法，通过考察区域煤炭行业生产建设的总投资、总产量、总效益、安全程度这四者的相互制约关系，以求在有限投资条件下尽可能满足总产量和安全程度要求而需资金最少，产出投入比最大的最优规划方案。     

凸整数规划最优点的判定条件

本文得到判别已知可行整值点为凸整数规划最优解的一个充分条件,此条件只涉及目标函数在该整值点为中心的边长为2的超立方体上的性态.     

纠正一道不等式整数解问题的错误解法

不等式的整数解问题曾在2015年高考全国Ⅰ卷中出现,此后网络上出现了不少类似的改编题,在利用导数思想、数学结合思想来处理其中一些试题时,由于所画图形的区域限制,导致所提供的答案出现错误,本文结合函数的凹凸性、曲线的切线给出了试题的正确解法,使得计算出的结果没有遗漏.     

Cover and Pack Inequalities for (Mixed) Integer Programming

We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 0-1 knapsack set, the mixed 0-1 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a unified presentation of the inequalities based on covers and packs and highlight the connections among them. The focus of the paper is on recent research on the use of superadditive functions for the analysis of knapsack polyhedra. We also present some new results on integer knapsacks. In particular, we give an integer version of the cover inequalities and describe a necessary and sufficient facet condition for them. This condition generalizes the well-known facet condition of minimality of covers for 0-1 knapsacks. The author is supported, in part, by NSF Grants 0070127 and 0218265.     

Integer Programming Duality in Multiple Objective Programming

The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria integer programming. However, in this case one may apply the more general e-constraint approach, resulting in particular single-criteria integer programming problems to generate efficient solutions. We show how this approach implies a more general, composite utility function of the criteria yielding a unified treatment of multiple criteria optimization with and without integrality constraints. Moreover, any efficient solution can be found using appropriate composite functions. The functions may be generated by the classical solution methods such as cutting plane and branch and bound algorithms.     

邻域整点搜索法求解整数规划

从剖析线性规划的优化机理入手,将纯整数规划分为标准型和非标型两类.首先以标准型纯整数规划为突破口,提出一种新的解法,并在理论上加以证明,然后将其拓广延伸,用于求解非标准型纯整数规划和混合整数规划.这种新解法命名为松驰最优解邻域整点搜索法,属于常规解法,但在简捷高效方面,远胜过现有的两种常规解法—分枝定界法和割平面法.     

非线性整规划的连续化

本文讨论了非线性整规划问题的连续化途径．结论是可以将无约束和有约束的非线性整规划全局解问题化为非线性连续规划问题求解．     

Generalized Nonlinear Lagrangian Formulation for Bounded Integer Programming

Several nonlinear Lagrangian formulations have been recently proposed for bounded integer programming problems. While possessing an asymptotic strong duality property, these formulations offer a success guarantee for the identification of an optimal primal solution via a dual search. Investigating common features of nonlinear Lagrangian formulations in constructing a nonlinear support for nonconvex piecewise constant perturbation function, this paper proposes a generalized nonlinear Lagrangian formulation of which many existing nonlinear Lagrangian formulations become special cases.     

Global Optimization Techniques for Solving the General Quadratic Integer Programming Problem

We consider the problem of minimizing a general quadratic function over a polytope in the n-dimensional space with integrality restrictions on all of the variables. (This class of problems contains, e.g., the quadratic 0-1 program as a special case.) A finite branch and bound algorithm is established, in which the branching procedure is the so-called integral rectangular partition, and the bound estimation is performed by solving a concave programming problem with a special structure. Three methods for solving this special concave program are proposed.     

Sequence Independent Lifting for Mixed Integer Programs with Variable Upper Bounds

We investigate the convex hull of the set defined by a single inequality with continuous and binary variables with variable upper bound constraints. We extend the traditional flow cover inequality, and show that it is valid for a restriction of the set in which some variables are fixed. We also give conditions under which this inequality is facet-defining and, when it is not, we show how it can be lifted to obtain valid inequalities for the entire set using sequence independent lifting. In general, computing the lifting function is NP-hard, but under an additional restriction on the cover we obtain a closed form. Finally, we show how these results imply and extend known results about the single node fixed charge flow polyhedron. This material is based upon work supported by the National Science Foundation under Grant No. 0084826. Received: April 2004     

Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming

This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems.In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver.A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of up to 3 improvement over branch-and-bound is observed.     

FATCOP 2.0: Advanced Features in an Opportunistic Mixed Integer Programming Solver

We describe FATCOP 2.0, a new parallel mixed integer program solver that works in an opportunistic computing environment provided by the Condor resource management system. We outline changes to the search strategy of FATCOP 1.0 that are necessary to improve resource utilization, together with new techniques to exploit heterogeneous resources. We detail several advanced features in the code that are necessary for successful solution of a variety of mixed integer test problems, along with the different usage schemes that are pertinent to our particular computing environment. Computational results demonstrating the effects of the changes are provided and used to generate effective default strategies for the FATCOP solver.