线性规划的原始松弛——对偶MBU单纯形算法

线性最优化广泛应用于经济与管理的各个领域.对于含有等式约束的线性规划问题,单纯形算法需要构造辅助的第一阶段问题求得问题的一个可行基.本文提出了一种原始松弛—对偶MBU单纯形算法(来求解第一阶段问题).首先,忽略不等式约束构造一个原始可行的松弛子问题,再用原始单纯形法求解该子问题;然后用对偶MBU单纯形法求解第一阶段问题.通过大规模数值试验对这种算法进行计算检验,数值结果表明,与经典单纯形算法相比,本文所提出的算法简便可行且具有更高的计算效率.     

Smoothing Newton algorithm for linear programming over symmetric cones

By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones (SCLP).The algorithm is globally convergent under suitable assumptions.     

整数规划中精确罚函数的一般形式

In this paper, the general exact penalty functions in integer programming were studied. The conditions which ensure the exact penalty property for the general penalty function with one penalty parameter were given and a general penalty function with two parameters was proposed.     

多约束非线性背包问题的一种有效算法

1IntroductionWe consider the following multi-di mensional nonlin-ear knapsack problem(MNKP)maxf(x)=∑nj=1fj(xj)s.t.gi(x)=∑nj=1gij(xj)≤bi,i=1,…,m,x∈X={x|lj≤xj≤uj,xjinteger,j=1,…,n},where allfjand allgijare nondecreasing functions ofxjon[lj,uj]forj=1,…,n,i=1,…,m,andljandujare integer lower and upper bounds forxj,re-spectively,j=1,…,n.It has been proved that0-1linear knapsack problemis NP-hard[1].Nonlinear knapsack problems have numerous appli-cations in various fields,for example,ca…     

Two-parameters quasi-filled function algorithm for nonlinear integer programming

INTRODUCTION Considering the following nonlinear integer programming problem: (PI) min f(x), s.t. x∈XI, (1) where XI?In is a bounded and closed box set con- taining more than one point, In is the set of integer points in n . If we suppose that f(x) satisfies the following conditions: if x∈XI, then f(x)=f(x), otherwise f(x)= ∞, then Problem PI is equal to the following nonlinear integer programming problem (UPI) min f(x), s.t. x∈In. (2) The formulation in PI allows the set XI t…     

凹资源配置问题的混合动态规划方法

Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems are encountered in optimization models involving economies of scale. In this paper, a new hybrid dynamic programming method was proposed for solving concave resource allocation problems. A convex underestimating function was used to approximate the objective function and the resulting convex subproblem was solved with dynamic programming technique after transforming it into a 0-1 linear knapsack problem. To ensure the convergence, monotonicity and domain cut technique was employed to remove certain integer boxes and partition the revised domain into a union of integer boxes. Computational results were given to show the efficiency of the algorithm.     

One-parameter quasi-filled function algorithm for nonlinear integer programming

INTRODUCTION We consider the following nonlinear integerprogramming problem (PI) minf(x), s.t. x∈XI (1)where XI?In is a bounded and closed box set con-taining more than one point; In is the set of integerpoints in Rn. Notice that the formulation in (PI) allows the setXI to be defined by equality constraints as well asinequality constraints. Furthermore, when f(x) is co-ercive, i.e., f(x) → ∞ as ||x||→∞, there always exists abo…     

基于粒子群算法求解整数规划的改进方法

标准粒子群算法主要用于优化连续性,而对粒子群算法求解非线性整数规划,算法的粒子位置必须解决取整问题。基此,文章提出一种粒子位置最终取整的方法,以改进粒子群算法解决整数规划的具体过程。基准函数的仿真结果表明,改进后的取整方法的搜索成功率优于直接取整和随机取整,综合搜索效率更佳。     

线性对称锥规划的一步光滑牛顿法

基于光滑Fischer-Burmeister函数,给出求解线性对称锥规划的一步光滑牛顿法．该算法在每一步迭代只需求解一个线性方程组,并进行一次线性搜索．不必满足严格互补,算法具有全局收敛性．     

基于遗传算法的二维排样问题求解新策略

针对采用自然编码的遗传算法在排样问题（CSP）过程中初始群体设置和交叉变异操作过于复杂的缺点,采用了顺序编码（Grefenstette编码）作为遗传算法编码方案,并对排样问题进行求解。采用这种遗传算法策略对CSP试算的结果表明,该策略利于排样问题的求解,算法操作简单,可推广应用到制造业及其他规划领域的排样规划中。     

线性规划非单调一阶段算法

为了获取计算的高效率，有必要修正单纯形算法的原则．本提出了一个新的单纯形一阶段算法．与传统单纯形算法不同的是，新算法不仅不要求目标函数值单调变化，且在一阶段的迭代过程中也不必保持变量的可行性，而是采用纯组合的方法去达到可行．这样摆脱了迭代时的比值检验，减少了每次迭代的计算工组量．理论分析及数值计算结果表明新算法的前景令人鼓舞．     

非线性凸半定规划的割平面算法

先把一般的非线性凸半定规划转化成目标函数是线性函数的非线性凸半定规划,然后用割平面算法求解转化后的半定规划．最后证明了割平面算法的收敛性．     

基于MATLAB的一类线性矩阵不等式正定解的通用算法分析

本文就控制理论中广泛应用的一类线性矩阵不等式的正定可行解问题进行了理论和算法上的研究。首先对一般线性矩阵不等式进行理论描述,进一步探讨了Lyapunov不等式稳定性的判定及其转换算法,建立了基于MATLAB的线性矩阵不等式可行解问题的模型,最后归纳出Riccati不等式正定可行解的通用算法,并进行了实变量运算。     

Primal-dual interior-point algorithms with dynamic step-size based on kernel functions for linear programming

In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming (LP) problems. The algorithms are based on a few kernel functions, including both self-regular functions and non-self-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynamic step size are more efficient than those with fixed step size. Project supported by Dutch Organization for Scientific Research (Grant No.613.000.010)     

一种求解多目标无约束0—1二次规划问题的文化基因算法

针对多目标无约束0—1二次规划问题,提出一种文化基因算法。该算法采用基于分解的多目标演化算法框架,能够获得分布均匀的非占优解;同时,采用一种简单、有效的禁忌搜索,能够利用更多问题相关的信息,获得质量更优的非占优解。该算法在优化的过程中能够动态地平衡多样性与收敛性。实验结果证明该算法能够很好地求解多目标无约束0-1二次规划问题,并且性能优于目前求解该问题较先进的算法。     

求解整数规划的割平面法的研究

在使用割平面法求解整数规划时,寻找Gomory约束是其中最为关键的一步.一般地,选取非整数解变量中分数部分最大的一个基变量,写下相应行的约束,由此推导出Gomory约束.本文主要讨论当非整数解变量中分数部分最大的基变量有两个以上时,如何通过比较选取切割条件较强的Gomory约束,以减少切割次数和运算量,较快地找到最优解.     

Interior-point algorithm based on general kernel function for monotone linear complementarity problem

A polynomial interior-point algorithm is presented for monotone linear complementarity problem (MLCP) based on:a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.     

求非线性整数规划的逐次下降方法

In this paper, a new method named as the gradually descent method was proposed to solve the discrete global optimization problem. With the aid of an auxiliary function, this method enables to convert the problem of finding one discrete minimizer of the objective function f to that of finding another at each cycle. The auxiliary function can ensure that a point, except a prescribed point, is not its integer stationary point if the value of objective function at the point is greater than the scalar which is chosen properly. This property leads to a better minimizer of f found more easily by some classical local search methods. The computational results show that this algorithm is quite efficient and reliable for solving nonlinear integer programming problems.     

DISCUSSION ON KARMARKAR''''S METHOD FOR SOLVING UNSTANDARD MODEL.

In this paper,a discussion on the new polynomial-time algorithm for linearprogramming as proposed by Karmarkar.N.is presented.The problem is solved when aninitial feasible solution is unknown.For the case where the optimum value of the objectivefunction is unknown,the reasonableness and feasibility of the sliding objective functionmethod are proved.And a method of modifying the parameters is put forward.     

两个加工时间恶化的半线性平行机排序问题的启发式MBLS 算法

The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∈[0, α], where 0 〈α≤ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, b = max1≤j≤n {bj }. For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list （LS） algorithm is investigated and it is proved that all the ratios are tight.