一类非线性规划的模拟退火求解

本文针对一类非线性规划问题，提出并设计了模拟退火求解算法，分析证明了算法能够渐近敛于全局最优解且具有多项式计算复杂性，为研究非线性规划提供了新的有效的求解途径。实例计算也表明，模拟退火求解非线性规划确实是有效的。     

一种求解混合整数非线性规划问题的模拟退火算法

通过适当处理离散变量，将求解无约束非凸ＮＬＰ问题的高效模拟退火全局优化算法推广到求解一般非凸混合整数非线性规划问题。数值计算结果表明，文中模拟退火算法在适用性、解的质量和计算效率等方面优于其它方法，是求解一般非凸ＭＩＮＬＰ问题的一种有效的全局优化算法。     

一个通用的混合非线性规划问题的演化算法

提出了一种新的求解非线性规划问题的演化算法，它是在郭涛算法的基础上提出的，新算法的主要特点是引入了变维子空间，加入了子空间搜索过程和规范化约束条件以及增加了处理带等式约束的实数规划，整数规划，0－1规划和混合整数规划问题的功能，使之成为一种求解非线性规划（NLP）问题的通用算法，数值实验表明，新算法不仅是一种通用的算法，而且与已有算法的计算结果相比，其解的精确度也最好。     

改进的复合形算法在产品组合优化中的应用

针对混合约束非线性规划问题,本文提出了一种改进的复合形方法,并给出了相应的算法步骤.应用此改进复合形法求解一典型算例,经过23次迭代达到了收敛条件,其结果与MATLAB计算得到的最优解误差为0.002%,并应用于求解一产品组合边际贡献模型,其结果与MATLAB计算结果相近.     

进化算法的计算结果呈现方式

进化算法（Evolutionary Algorithms,EAs）作为求解非线性规划问题的有效求解工具已经越来越受到工程和优化领域的国内外专家和学者的重视,进化算法类的文章在世界上各种期刊中占据了大量比例。目前仍有很多刚刚从事进化算法理论与实践方面研究的国内学者对如何表现进化算法的计算结果比较迷茫。为此对于算法的计算结果展现方面进行了阐述。     

基于非线性规划协同进化遗传算法的防空导弹火力优化分配研究

为了进一步提高防空导弹目标分配问题的求解效率和解算能力,建立了防空导弹目标火力分配模型,提出了一种非线性规划协同进化遗传算法(NLPCGA).该算法是综合非线性规划算法(NLPA)局部搜索能力强和协同进化算法(CA)求解质量高的优点,并利用遗传理论提高算法的求解效率.通过结合实例,仿真结果表明NLPCGA算法在求解防空目标火力分配问题上要优于单独两种智能算法,可以有效快速地找到最优火力分配方案,为防空作战指挥决策提供支持.     

自适应主从式并行遗传算法在区间非线性规划问题求解中的应用

讨论了区间参数非线性规划问题．通过引入决策风险因子的概念，提出了一种不确定性非线性规划的一般命题形式．为求解该命题形式，提出一种自适应主从式并行遗传算法，该算法可以满足大规模优化问题的求解实时性要求，具有全局收敛性能．相对于常规主从式并行遗传算法，该算法通过动态调整从机的计算负荷，有效地解决了从机间计算负荷不均衡分布的问题．仿真结果表明了该自适应主从式并行遗传算法的可行性．     

无约束非线性规划的数值方法

在自动控制、科学管理和其它一些科学领域中，很多问题可以归结为线性规划。但是，还有另外一些问题，其目标函数和约束条件却很难用线性函数来表达。我们称这种数学规划为非线性规划。1951年，库恩（Kuhn）一塔克（Tucker）提出了处理非线性规划问题的完整理论，得到一组不等式约束最优化问题的必要条件，称为库恩一塔克定理，非线性规划到目前为止，还没有适用于各种问题的一般算法。各个方法都有自己特定的适用范围。优化包括数学规划的全部内容，最简单的优化问题是无约束最优化，对这类问题，已经研究出比较有效的求解方法，因而构成…     

一种采用规划方法的宏模块布局算法

提出一种基于非线性规划的宏模块布局算法。该算法将布局问题归纳为一个非线性规划问题，考虑了引脚的实际位置并使用取向向量来描述模块的取向,可以在确定模块位置的同时也确定模块的取向；同时使用交替求解的策略有效地简化了问题的求解。实验结果表明文中算法快速有效。     

一类特殊约束的规划问题Lingo求解

Lingo主要用来求解大型教学规划问题,针对一类特殊的约束规划同题,提出使用穿线法将该约束转化为一个等价的非线性约束,然后利用Lingo 8.0求解,取得了满意的结果.     

离散时间最优控制—–评论动态规划

阐述离散时间最优控制的特点.对比3种求解离散时间最优控制的解法,即:1)用非线性规划求解离散时间最优控制;2)用无约束优化求解离散时间最优控制;3)动态规划及其数值解.1)和2)都适用于多维静态优化,计算效率较高,是高级方法.在名义上,3)为动态优化.实际上,3)为一维分段无约束静态优化,计算效率较低,是初级方法.本文并用数字实例进一步阐明动态规划及其数值解在求解方面较差,故动态规划及其数值解已失去实用价值.在求解离散时间最优控制问题方面,无法与非线性规划求解相匹敌.     

Spatial branch-and-bound algorithm for MIQCPs featuring multiparametric disaggregation

Spatial branch-and-bound (B&B) is widely used for the global optimization of non-convex problems. It basically works by iteratively reducing the domain of the variables so that tighter relaxations can be achieved that ultimately converge to the global optimal solution. Recent developments for bilinear problems have brought us piecewise relaxation techniques that can prove optimality for a sufficiently large number of partitions and hence avoid spatial B&B altogether. Of these, normalized multiparametric disaggregation (NMDT) exhibits a good performance due to the logarithmic increase in the number of binary variables with the number of partitions. We now propose to integrate NMDT with spatial B&B for solving mixed-integer quadratically constrained minimization problems. Optimality-based bound tightening is also part of the algorithm so as to compute tight lower bounds in every step of the search and reduce the number of nodes to explore. Through the solution of a set of benchmark problems from the literature, it is shown that the new global optimization algorithm can potentially lead to orders of magnitude reduction in optimality gap when compared to commercial solvers BARON and GloMIQO.     

Dynamic PSO method for nonlinear constrained programming problems

A new approach is presented to solve the nonlinear constrained programming problems. Firstly, the nonlinear constrained programming problem is transformed into a bi-ohjective optimization problem. Based on the reasonable design of the searching operation and different parameters, a new dynamic particle swarm optimization algorithm （TS-MC） is proposed. The numerical experiments show that the proposed algorithm is effective in dealing with the nonlinear constrained programming problems.     

解非线性约束规划问题的新型多目标遗传算法

给出非线性约束规划问题的一种新解法。把带约束的非线性规划问题转化成为两个目标的多目标优化问题,并为转化后的多目标优化模型设计了一种新型多目标遗传算法,数据实验表明该算法对带约束的非线性规划问题求解是非常有效的。     

Solving Irregular Econometric and Mathematical Optimization Problems with a Genetic Hybrid Algorithm

In the present paper we apply a new Genetic Hybrid Algorithm (GHA) to globally minimize a representative set of ill-conditioned econometric/mathematical functions. The genetic algorithm was specifically designed for nonconvex mixed integer nonlinear programming problems and it can be successfully applied to both global and constrained optimization. In previous studies, we have demonstrated the efficiency of the GHA in solving complicated NLP, INLP and MINLP problems. The present study is a continuation of this research, now focusing on a set of highly irregular optimization problems. In this paper we discuss the genetic hybrid algorithm, the nonlinear problems to be solved and present the results of the empirical tests.     

解非线性规划的多目标遗传算法及其收敛性

给出非线性约束规划问题的一种新解法。它既不需用传统的惩罚函数,又不需区分可行解和不可行解,新方法把带约束的非线性规划问题转化成为两个目标函数优化问题,其中一个是原约束问题的目标函数,另一个是违反约束的度函数,并利用多目标优化中的Pareto优劣关系设计了一种新的选择算子,通过对搜索操作和参数的合理设计给出了一种新型遗传算法,且给出了算法的收敛性证明,最后数据实验表明该算法对带约束的非线性规划问题求解是非常有效的。     

Optimising multi-product multi-chance-constraint inventory control system with stochastic period lengths and total discount under fuzzy purchasing price and holding costs

While the usual assumptions in multi-periodic inventory control problems are that the orders are placed at the beginning of each period (periodic review) or depending on the inventory level they can happen at any time (continuous review), in this article, we relax these assumptions and assume that the periods between two replenishments of the products are independent and identically distributed random variables. Furthermore, assuming that the purchasing price are triangular fuzzy variables, the quantities of the orders are of integer-type and that there are space and service level constraints, total discount are considered to purchase products and a combination of back-order and lost-sales are taken into account for the shortages. We show that the model of this problem is a fuzzy mixed-integer nonlinear programming type and in order to solve it, a hybrid meta-heuristic intelligent algorithm is proposed. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology and to compare its performance with one of the existing algorithms in real world inventory control problems.     

A study of one class of NLP problems arising in parametric semi-infinite programming

The paper deals with a nonlinear programming (NLP) problem that depends on a finite number of integers (parameters). This problem has a special form, and arises as an auxiliary problem in study of solutions' properties of parametric semi-infinite programming (SIP) problems with finitely representable compact index sets. Therefore, it is important to provide a deep study of this NLP problem and its properties w.r.t. the values of the parameters. We are especially interested in the case when optimal solutions of the NLP problem satisfy certain properties due to some specific requirements arising in parametric SIP. We establish the values of the parameters for which optimal solutions of the corresponding NLP problem fulfil the needed properties, and suggest an algorithm that determines the right values of the parameters. An example is proposed to illustrate the application of the algorithm.     

A feasibility evaluation approach for time-evolving multi-item production–distribution networks

Time-dependent multi-item problems arise frequently in management applications, communication systems, and production–distribution systems. Our problem belongs to the last category, where we wish to address the feasibility of such systems when all network parameters change over time and product. The objective is to determine whether it is possible to have a dynamic production–shipment circuit within a finite planning horizon. And, if there is no such a flow, the goal is to determine where and when the infeasibility occurs and the approximate magnitude of the infeasibility. This information may help the decision maker in their efforts to resolve the infeasibility of the system. The problem in the discrete-time settings is investigated and a hybrid of scaling approach and penalty function method together with network optimality condition is utilized to develop a network-based algorithm. This algorithm is analysed from theoretical and practical perspectives by means of instances corresponding to some electricity transmission-distribution networks and many random instances. Computational results illustrate the performance of the algorithm.     

解非线性约束规划问题的分组粒子群算法

文章运用分组粒子群的方法来解决非线性约束规划问题,将粒子群分成几个小组分别进化,几个小组的参数各自随机产生。在一定的间隔时刻对各个小组的粒子进行重新分组和参数的调整,并根据收敛性检查的情况将劣质粒子淘汰重新初始化,这不仅有助于在不同环境进化出的粒子相互取长补短,而且可以有效的防止陷入局部最优。