非线性整数规划的一个近似算法

利用连续总体优化填充函数法的思想，本文设计了非线性整数规划的一个近似算法．首先，给出了非线性整数规划问题离散局部极小解的定义，设计了找离散局部极小解的局部搜索算法；其次，用所设计的局部搜索算法极小化填充函数来找比当前离散局部极小解好的解．本文的近似算法是直接法，且与连续总体优化的填充函数法相比，本文填充函数中的参数易于选取．数值试验表明，本文的近似算法是有效的．     

总体优化一类双参数填充函数算法的改进

求解无约束总体优化问题的一类双参数填充函数算法需要假设该问题的局部极小解的个数只有有限个，而且填充函数中参数的选取与局部极小解的谷域的半径有关．该文对其填充函数作了适当改进，使得新的填充函数算法不仅无需对问题的局部极小解的个数作假设，而且填充函数中参数的选取与局部极小解的谷域的半径无关．数值试验表明算法是有效的．     

一个新的非线性整数规划问题的单参数填充函数算法

非线性整数规划问题是一类复杂的优化问题,填充函数算法是求解整数规划问题的一类有效方法.构造一个新的单参数填充函数,分析并证明了其填充性质;然后,基于该填充函数并结合离散最速下降法提出了一种新的填充函数算法;最后,采用新算法对6个测试函数进行数值实验,结果表明该算法具有良好的计算效果,是有效可行的.     

整数规划的广义填充函数算法

文[9,10]设计了直接求整数规划问题近似解的填充函数算法,但其所利用的文[2,3]的填充函数均带有参数,需要在算法过程中逐步调节。本文建立整数规划的广义填充函数的定义,说明了文[9,10]所利用的填充函数是整数规划问题的广义填充函数,并构造了一类不带参数的广义填充函数。进而本文设计了整数规划的一类不带参数的广义填充函数算法,数值试验表明算法是有效的。     

整数规划问题的滤子填充函数算法

全局优化是最优化的一个分支,非线性整数规划问题的全局优化在各个方面都有广泛的应用.填充函数是解决全局优化问题的方法之一,它可以帮助目标函数跳出当前的局部极小点找到下一个更好的极小点.滤子方法的引入可以使得目标函数和填充函数共同下降,省却了以往算法要设置两个循环的麻烦,提高了算法的效率.本文提出了一个求解无约束非线性整数规划问题的无参数填充函数,并分析了其性质.同时引进了滤子方法,在此基础上设计了整数规划的无参数滤子填充函数算法.数值实验证明该算法是有效的.     

一类不依赖于局部极小解个数的填充函数

求解无约束总体优化问题的一类单参数填充函数需要假设问题的局部极小解的个数只有有限个,而且填充函数中参数的选取与局部极小解的谷域的半径有关.本文对填充函数的定义作适当改进,而且对已有的这一类填充函数作改进,构造了一类双参数填充函数.新的填充函数不仅无须对问题的局部极小解的个数作假设,而且其中参数的选取与局部极小解的谷域的半径无关.     

0-1非线性混合整数规划的罚函数解法

本文中我们对一类0-1非线性混合整数规划的解法进行了探讨,通过罚函数把有约束问题化为相应的无约束问题,我们证明了可通过求解一个无约束非线性规划问题得到原问题的ε近似极小解,数值试验表明算法是有效的.     

约束全局整数规划问题的填充函数法

本文给出了一类新的求解箱约束全局整数规划问题的填充函数，并讨论了其填充性质．基于提出的填充函数，设计了一个求解带等式约束、不等式约束、及箱约束的全局整数规划问题的算法．初步的数值试验结果表明提出的算法是可行的。     

一个基于离散填充函数的整数线性规划方法

本文提出了一个有效的解决整数线性规划的新算法.如果离散化的局部搜索过程陷入局部最优解,则构造相应的离散填充函数,引导搜索过程跳出局部最优解并得到更好的解.该方法是在离散空间中进行优化的,无需增加新的约束,且一直保持整数可行性,收敛的速度非常快.该方法也为一般整数规划提出了一种新的途径.数值实例表明,与现有的方法相比,该算法能够较快的找到最优解.     

非线性整数规划的一个新的无参数填充函数算法

离散填充函数是一种用于求解多极值优化问题最优解的一种行之有效的方法.已被证明对于求解大规模离散优化问题是有效的.本文基于改进的离散填充函数定义,构造了一个新的无参数填充函数,并在理论上给出了证明,提出了一个新的填充函数算法.该填充函数无需调节参数,而且只需极小化一次目标函数.数值结果表明,该算法是高效的、可行的.     

一种求解非线性整数规划问题的填充函数算法(英文)

在本文中,对于求解非线性整数规划的问题,提出了一个新的填充函数和相应的算法,该函数只有一个参数,具有较好的可操作性.数值试验显示,该算法是有效和可靠的.     

A filled function method for finding a global minimizer on global integer optimization

The paper gives a definition of the filled function for nonlinear integer programming. This definition is modified from that of the global convexized filled function for continuous global optimization. A filled function with only one parameter which satisfies this definition is presented. We also discuss the properties of the proposed function and give a filled function method to solve the nonlinear integer programming problem. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.     

A discrete dynamic convexized method for nonlinear integer programming

In this paper, we consider the box constrained nonlinear integer programming problem. We present an auxiliary function, which has the same discrete global minimizers as the problem. The minimization of the function using a discrete local search method can escape successfully from previously converged discrete local minimizers by taking increasing values of a parameter. We propose an algorithm to find a global minimizer of the box constrained nonlinear integer programming problem. The algorithm minimizes the auxiliary function from random initial points. We prove that the algorithm can converge asymptotically with probability one. Numerical experiments on a set of test problems show that the algorithm is efficient and robust.     

A discrete filled function algorithm embedded with continuous approximation for solving max-cut problems

In this paper, a discrete filled function algorithm embedded with continuous approximation is proposed to solve max-cut problems. A new discrete filled function is defined for max-cut problems, and properties of the function are studied. In the process of finding an approximation to the global solution of a max-cut problem, a continuation optimization algorithm is employed to find local solutions of a continuous relaxation of the max-cut problem, and then global searches are performed by minimizing the proposed filled function. Unlike general filled function methods, characteristics of max-cut problems are used. The parameters in the proposed filled function need not to be adjusted and are exactly the same for all max-cut problems that greatly increases the efficiency of the filled function method. Numerical results and comparisons on some well known max-cut test problems show that the proposed algorithm is efficient to get approximate global solutions of max-cut problems.     

A NEW FILLED FUNCTION METHOD FOR INTEGER PROGRAMMING

The Filled Function Method is a class of effective algorithms for continuous globaloptimization.In this paper,a new filled function method is introduced and used to solveinteger programming.Firstly,some basic definitions of discrete optimization are given.Then an algorithm and the implementation of this algorithm on several test problems areshowed.The computational results show the algorithm is effective.     

Finding discrete global minima with a filled function for integer programming

The filled function method is an approach to find the global minimum of multidimensional functions. This paper proposes a new definition of the filled function for integer programming problem. A filled function which satisfies this definition is presented. Furthermore, we discuss the properties of the filled function and design a new filled function algorithm. Numerical experiments on several test problems with up to 50 integer variables have demonstrated the applicability and efficiency of the proposed method.     

A partitioning algorithm for the network loading problem

This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The approach is an iterative method in which the integer programming solver is not used to produce the best integer point in the polyhedral relaxation of the set of feasible capacities. Rather, it selects an integer solution that is closest to the best known integer solution. Contrary to previous approaches, the method does not exploit the original mixed integer programming formulation of the problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The method is compared to alternative approaches proposed in the literature and appears to be efficient for computing good upper bounds.