约束非线性l1问题的调节熵函数法

针对约束非线性l1问题不可微的特点,提出了一种光滑函数的近似逼近方法。该方法利用调节熵函数和罚函数技术将约束非线性l1问题转化为无约束可微优化问题,因而可利用光滑优化的经典算法求出原问题的近似最优解。给出了基于光滑优化问题的BFGS迭代,并介绍了约束非线性l1问题的调节熵函数的有关性质、算法的迭代步骤及其收敛性分析。最后通过数值实例表明了该算法的有效性。     

Distributed Algorithm for Robust Resource Allocation with Polyhedral Uncertain Allocation Parameters

This paper studies a distributed robust resource allocation problem with nonsmooth objective functions under polyhedral uncertain allocation parameters. In the considered distributed robust resource allocation problem, the (nonsmooth) objective function is a sum of local convex objective functions assigned to agents in a multi-agent network. Each agent has a private feasible set and decides a local variable, and all the local variables are coupled with a global affine inequality constraint, which is subject to polyhedral uncertain parameters. With the duality theory of convex optimization, the authors derive a robust counterpart of the robust resource allocation problem. Based on the robust counterpart, the authors propose a novel distributed continuous-time algorithm, in which each agent only knows its local objective function, local uncertainty parameter, local constraint set, and its neighbors’ information. Using the stability theory of differential inclusions, the authors show that the algorithm is able to find the optimal solution under some mild conditions. Finally, the authors give an example to illustrate the efficacy of the proposed algorithm.     

具有模糊关系约束的线性规划的解法

研究了具有模糊关系方程约束的线性规划问题.由于此类规划的非空可行集一般是一个非凸集,传统的求解线性规划的方法不适合求解此类规划问题,因此有必要提出一个求解此类规划问题的有效算法,本文首先刻画了该类规划可行集的结构,基于该可行集的结构,应用惩罚函数和遗传算法给出了该类规划问题的一个具体求解方法,得到了近似最优解.为了说明该方法的有效性,最后给出了具体的算例.     

基于TDOA/AOA混合的高精度室内可见光定位算法

为了提高室内三维空间的定位精度,提出了一种基于联合到达时间差与到达角度(time difference of arrival/angle of arrival,TDOA/AOA)信息的混合定位算法。由于构建的目标函数具有非凸性,采用传统定位算法在目标函数求解过程中会出现局部最优解的问题。因此,针对该问题,将目标函数转成二次约束二次规划问题,通过引入半定松弛(semi-definite relaxation,SDR)方法将目标函数转换为二阶锥规划(second order cone programming, SOCP)问题,寻找全局最优解。其次,针对SOCP无法对凸包外的目标进行有效定位的问题,在该算法的基础上引入了惩罚项,使松弛后的约束条件进一步逼近原始约束条件,解决了定位过程中的凸包问题。数值仿真结果表明:在10 m×10 m×3 m的三维定位空间内,选取40×40个测试点,平均定位误差为1.39 cm,可实现室内三维空间高精度定位。与传统的混合定位算法相比,均能够获得较高的定位精度。     

价格控制问题及其推广形式的罚函数法

价格控制问题是一类重要的二层规划问题。本文提出了求解这一问题及其推广形式的罚函数法,且在唯一解的假高条件下证明了方法的有限终止性数值结果表明算法是可行的、有效的。     

植物多向生长模拟算法

针对整数规划问题提出了一种以植物向光性为启发式准则的智能优化算法——植物多向生长模拟算法. 改进了植物生长激素的分配方式并将随机选择机制引入新枝生长方向的选择,更符合植物生长的自然机理. 利用马尔可夫链描述算法迭代过程,证明了算法的收敛性. 利用无约束和有约束两类具有多个全局最优解的非线性整数规划实例测试了植物多向生长模拟算法的性能,并与基本植物生长模拟算法、填充函数法、罚函数法以及基于遗传算法的混合算法进行了对比. 植物多向生长模拟算法不仅提高全局寻优能力,增加解的多样性和准确性而且提高收敛速度.     

A Superlinearly Convergent Combined PhaseⅠ-PhaseⅡ Subfeasible Method

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Bilevel programming model and solution method for mixed transportation network design problem

By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower-level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an all-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm. This research is supported by the National Basic Research Program of China under Grant No. 2006CB705500, the National Natural Science Foundation of China under Grant No. 0631001, the Program for Changjiang Scholars and Innovative Research Team in University, and Volvo Research and Educational Foundations.     

随机线性规划的α可靠度线性规划

在约束条件的右端和目标函数的系数为四种重要随机变量的情况下，利用对偶规划，将随机线性规划化成一定可靠度下的确定性线性规划模型，从而可以利用单纯形方法讨论并求出随机线性规划在一度可靠度下的可行解和最优解。     

A penalty function method for solving ill-posed bilevel programming problem via weighted summation

For ill-posed bilevel programming problem, the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model＇s satisfactory degree in application. To acquire a more satisfying solution than the optimistic one to realize the two levels＇ most profits, this paper considers both levels＇ satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation. Then, using the duality gap of the lower level as the penalty function, the authors transfer these two levels problem to a single one and propose a corresponding algorithm. Finally, the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.     

CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C     

小卫星星务规划的Hopfield神经网算法

小卫星的任务规划是为确定飞行任务目标并根据飞行任务目标制定控制小卫星运行的指令序列，小卫星的任务可以归结为在资源一定的情况下的规划与调度问题，对于0－1整性和二次型规划（0－1ILQP）问题，本文提出了Hopfield神经网的解法。即将0－1ILQP的目标函数和约束条件用函数的方法写成能量函数形式，然后利用Hopfield神经网求解出该能量函数的全局最小点，从而求解出原0－1ILQP的最优解，最后，作为一个算例，给出了用此方法成功的在优化卫星任务规划中的应用。     

A quadratic objective penalty function for bilevel programming

The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to find an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at lower level problems, a quadratic objective penalty function without lower level problems is defined and is proved equal to the original bilevel programming.     

基于限价订单簿的最优高频做市商策略研究

建立具有成交风险和存货风险的价差过程模型,在引入存货惩罚函数的同时将策略的目标确定为效用最大化.将策略求解的过程看成是随机最优控制问题,并通过动态规划求解,离散模型框架下采用有限差分的方法对每个时间点不同存货及市场价差下的下单策略进行求解.该策略满足了模型定义之初对于成交强度,市场价差及存货量对下单行为影响的假设,而策略的实证及可靠性检验进一步表明了该策略具有较为稳定的收益.     

一种区间数线性规划的满意解

针对目标函数和约束条件均为区间数的线性规划问题，提出了一种基于模糊约束满意度的求解方法，把区间数线性规划卖座经为确定型的一般参数规划问题来求解，决策者可以根据自己的主观判断和客观情况，对目标函数优化水平和约束条件满意水平作出不同的估计，从而得到在相应情况下的满意解，使决策过程更具柔性。     

0-1整型规划的Hopfield神经网算法分析

提出了0-1整型线性和二次型规划(0-1ILQP)的Hopfield神经网的解法.即将0-1ILQP的目标函数和约束条件用罚函数的方法写成能量函数形式,然后利用Hopfield神经网求解出该能量函数的全局最小点,从而求解出原0-1ILQP的最优解.最后,作为一个算例,给出了此方法在优化卫星任务规划中的成功应用.     

一种随机微粒群混合算法求解约束优化问题

将微粒群算法（Particle Swarm Optimization,PSO）与随机优化方法-Alopex算法相结合,提出一种随机微粒群混合算法（APSO）求解约束优化问题。该算法使PSO算法中微粒的飞行速度无记忆性,结合Alopex算法重新生成停止进化微粒的位置;采用双群体搜索机制,一个群体保存具有可行解的微粒,用APSO算法使微粒逐步搜索到最优解,另一个群体保存具有不可行解的微粒,并且可行解群体以一定的概率接受性能较优的不可行解微粒,这种简单的群体多样性机制使微粒能够快速、准确地找到位于约束边界上或附近的最优解。结果表明该算法寻优性能优良且具有较好的稳定性。     

含直觉模糊弹性约束的模糊线性规划求解

本文基于模糊结构元方法构建并讨论了一类含有直觉模糊弹性约束的新型模糊线性规划问题. 通过引入模糊数的加权特征数, 定义了一种序关系并拓展了Verdegay的模糊线性规划方法, 将新型模糊线性规划问题转化成两个等价的含参数约束条件的清晰线性规划模型, 给出了此类线性规划模型对比最优可行解的求法. 最后通过一个数值实例来说明此类问题的一般求解方法.     

一类非线性两级规划问题的模拟退火求解

提出一种基于模拟退火算法求解一类非线性两级规划问题的方法。为了提高模拟退火算法处理上级约束的能力，在模拟退火算法中引入一个辅助优化问题，通过求解该辅助优化问题产生满足上级约束的试探点，避免了使用罚函数处理上级约束。数值计算结果表明，与使用罚函数处理上级约束的模拟退火算法相比，本文提出的方法不仅可以提高求得全局最优解的可靠性，而且可以减少模拟退火算法的迭代次数，提高计算效率.     

基于模糊比例指标的模糊线性规划求解方法

定义了一种模糊数之间的模糊比例指标，并利用模糊比例指标提出了约束条件中含有三角模糊数的模糊线性规划转化为经典的线性规划的方法。实例表明，与其他方法相比，该方法得到的解优于其它解，且约束条件个数保存不变。因此，本文方法是可行和有效的。