求解一类凸优化问题的区间迭代算法

研究了一类非线性带约束的凸优化问题的求解.利用Kuhn-Tucker条件将凸优化问题等价地转化为多变元非线性方程组的求解问题.基于区间算术的包含原理及改进的Krawczyk区间迭代算法,提出一个求解凸优化问题的区间算法.对于目标函数和约束函数可微的凸优化,所提算法具有全局寻优的特性.在数值实验方面,与遗传算法、模式搜索法、模拟退火法及数学软件内置的求解器进行了比较,结果表明所提算法就此类凸优化问题能找到较多且误差较小的全局最优点.     

一种高效的函数可微的全局优化模拟退火算法

针对函数可微的全局优化问题,将最速下降法,Newton法和罚函数法引入模拟退火算法中,提出了一种高效的模拟退火算法.该算法可以求得可微函数优化问题的全局最优解,且具有计算量小,效率高的特点.利用罚函数将约束优化问题转化为无约束优化问题后,可以利用提出的算法进行求解.数值算例表明,提出的算法能够高效地求解无约束及带约束的函数可微的全局优化问题.     

同顺序（Flow—shop）排序问题的模拟退火求解

本文为Ｆｌｏｗ－ｓｈｐｏ问题的求解一般地构造一类随机方法－模拟退火算法，基于６种不同的随机抽样方式，分析表明求解算法渐近收敛于全局最优解集且具有多项式计算复杂特性，以不同实例规模的ＵＩＳ，ＦＩＳ和ＮＩＳ的Ｍａｋｅｓｐａｎ最小Ｆｌｏｗ－ｓｈｏｐ排序问题为例，计算结果表明模拟退火求解Ｆｌｏｗ－ｓｈｏｐ排序问题是有效的。     

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。     

高维复杂函数的混合模拟退火全局优化策略

对于高维复杂函数优化问题,经典的优化算法存在着初始点敏感、局部收敛等问题;而模拟退火算法等智能算法则有着计算成本高昂、算法早熟等缺陷。NFL定理犤1犦预示了混合优化策略是解决实际优化问题的最好途径。该文融合了模拟退火算法和经典算法的优点,设计了高维复杂函数混合模拟退火优化策略。混合优化策略具有模拟退火算法的全局收敛性,同时引入强局部收敛经典算法作为模拟退火算法的精英个体提高算子,提高了模拟退火算法局部开采能力,加快了收敛速度。数值仿真计算结果表明,混合模拟退火策略求解高维复杂函数的性能大大优于单一算法,具有强鲁棒性、高收敛速度和高精度等优点。该文的算法设计思想对于解决实际问题有较好的借鉴意义。     

一种移动机器人全局路径规划新型算法

针对模拟退火算法收敛速度慢这一缺陷，提出了一种基于共轭方向法和模拟退 火算法相结合的新型混合优化算法，并成功应用于机器人神经网络路径规划中．该算法可以 使优化解不陷入局部极值解而得到全局最优解．仿真实验研究表明：本文提出的这种新型混 合优化算法，计算简单，收敛速度快，显著提高了求解移动机器人全局最优化问题的计算效 率．     

运用模拟退火遗传算法估计地下水反演参数

在估计地下水数值模型参数时,常运用智能优化算法求解数学模型的近似解,以再现现实地下水流的运动。在传统的模拟退火算法基础上,结合遗传算法,提出了一种改进模拟退火遗传算法,它吸收了遗传算法的全局搜索性能和保护最优个体的策略,解决了遗传算法早熟的问题,加强了模拟退火的局部搜索能力。以非均质各向异性承压二维流为例,运用该算法对地下水流数值模型参数进行了反演计算。计算结果表明,该算法克服了传统全局搜索算法收敛速度慢、迭代次数多的缺点,具有计算精度高,可以并行计算等优点。     

引入模拟退火算子的差分进化算法性能研究

为了提高差分进化算法的优化性能,将模拟退火算子引入到差分进化算法中,利用模拟退火算子良好的全局搜索能力进一步提高差分进化算法对复杂问题的优化能力．通过对复杂函数优化的仿真结果表明,算法在求解复杂优化问题上具有更快的收敛速度和更好的全局收敛性．     

基于混合算法的带时间窗的车辆路径问题求解

建立了有时间窗车辆路径问题的数学模型，针对遗传算法在局部搜索能力方面的不足，提出将模拟退火算法与遗传算法相结合，从而构造了有时间窗车辆路径问题的混合遗传算法，并进行了实验计算。结果表明，用混合遗传算法求解该优化问题，可以在一定程度上克服遗传算法在局部搜索能力方面的不足和模拟退火算法在全局搜索能力方面的不足，从而得到了质量较高的解。     

基于变分的图像恢复算法及收敛性

提出了一种保持边缘的正则化图像恢复算法,该方法可有效地用于求解线性逆问题的 非凸优化过程.通过对正则化函数及相应泛函性质的理论分析,得出了使泛函达到最小的正则 化函数表达式;引入一个与原非凸泛函相应的二元泛函,将非凸优化问题转化为本质上的凸优 化问题,采用松弛迭代算法获得非凸优化问题的局部极小解;证明了所提出的算法是全局收敛 的.通过实验验证了算法的有效性.     

准时化生产计划的半无限规划模型与模拟退火方法

半无限规划模型是描述ＪＩＴ环境下，提前／拖期生产计划问题的一种数学模型。因为目标函数是非线性的、有无限多约束和约束的非凸性，所以求解比较困难。用模型退火结合启发式方法和最速下降法求解半无限规划模型，与遗传算法进行比较，计算结果表明用模拟退火方法求解更有效。     

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.     

求解SAT问题的拟人退火算法

该文利用一个简单的变换，将可满足性（SAT）问题转换为一个求相应目标函数最小值的优化问题，提出了一种用于跳出局部陷阱的拟人策略，基于模拟退火算法和拟人策略，为SAT问题的高效近注解得出了拟人退火算法（PA），该方法不仅具有模拟退火算法的全局收敛性质，而且具有一定的并行性，继承性。数值实验表明，对于本文随机产生的测试问题例，采用拟人策略的模拟退火算法的结果优于局部搜索算法，模拟退火算法以及近来国际上流行的WALKSAT算法，因此拟人退火算法是可行的和有效的。     

模拟退火算法中关键参数的研究

模拟退火算法是求解组合优化问题的一个有效方法,但算法中各个参数值的选择和设置对运行的结果和效果有较大影响。因此,本文主要是利用几个具体的TSP问题对算法中 的几个重要参数做比较研究,得出了一组比较有效的参数取值,为求解与TSP问题类似的其他问题奠定了有效的参数基础。     

多维多极值函数优化的和声退火算法

针对多极值实函数优化问题,本文结合和声搜索与模拟退火算法,提出了一种新的搜索算法,即和声退火算法。新算法保留了和声搜索的搜索机理,但对和声搜索中于和声记忆库外的搜索方法用超快速模拟退火算法作了改进,对和声记忆库内新解产生方法也作了相应的调整,从而提高了对多维问题的搜索效率。数值实验结果表明算法对和声搜索有明显的改进,收敛速度更快,跳出局部极值点的能力较强。新算法在解决多维多极值优化问题方面比遗传算法更具效率,值得进一步研究与推广应用。     

Improved orthogonal array based simulated annealing for design optimization

Recent research shows that simulated annealing with orthogonal array based neighbourhood functions can help in the search for a solution to a parametrical problem which is closer to an optimum when compared with conventional simulated annealing. Previous studies of simulated annealing analyzed only the main effects of variables of parametrical problems. In fact, both main effects of variables and interactions between variables should be considered, since interactions between variables exist in many parametrical problems. In this paper, an improved orthogonal array based neighbourhood function (IONF) for simulated annealing with the consideration of interaction effects between variables is described. After solving a set of parametrical benchmark function problems where interaction effects between variables exist, results of the benchmark tests show that the proposed simulated annealing algorithm with the IONF outperforms significantly both the simulated annealing algorithms with the existing orthogonal array based neighbourhood functions and the standard neighbourhood functions. Finally, the improved orthogonal array based simulated annealing was applied on the optimization of emulsified dynamite packing-machine design by which the applicability of the algorithm in real world problems can be evaluated and its effectiveness can be further validated.     

A dynamic convexized method for nonconvex mixed integer nonlinear programming

We consider in this paper the nonconvex mixed-integer nonlinear programming problem. We present a mixed local search method to find a local minimizer of an unconstrained nonconvex mixed-integer nonlinear programming problem. Then an auxiliary function which has the same global minimizers and the same global minimal value as the original problem is constructed. Minimization of the auxiliary function using our local search method can escape successfully from previously converged local minimizers by taking increasing values of parameters. For the constrained nonconvex mixed-integer nonlinear programming problem, we develop a penalty based method to convert the problem into an unconstrained one, and then use the above method to solve the later problem. Numerical experiments and comparisons on a set of MINLP benchmark problems show the effectiveness of the proposed algorithm.     

A new evolutionary approach to the degree-constrained minimumspanning tree problem

Finding the degree-constrained minimum spanning tree (d-MST) of a graph is a well-studied NP-hard problem of importance in communications network design and other network-related problems. In this paper we describe some previously proposed algorithms for solving the problem, and then introduce a novel tree construction algorithm called the randomized primal method (RPM) which builds degree-constrained trees of low cost from solution vectors taken as input. RPM is applied in three stochastic iterative search methods: simulated annealing, multistart hillclimbing, and a genetic algorithm. While other researchers have mainly concentrated on finding spanning trees in Euclidean graphs, we consider the more general case of random graph problems. We describe two random graph generators which produce particularly challenging d-MST problems. On these and other problems we find that the genetic algorithm employing RPM outperforms simulated annealing and multistart hillclimbing. Our experimental results provide strong evidence that the genetic algorithm employing RPM finds significantly lower-cost solutions to random graph d-MST problems than rival methods     

Simulation optimization using simulated annealing

The purpose of this study is to investigate the feasibility of using a simulated annealing algorithm in conjunction with a simulation model to find the optimal parameter levels at which to operate a system. In particular, we discuss an effort to use simulated annealing to find a combination of input parameter values for a model which optimizes a nonconvex, nonconcave objective function of the input parameters. In the absence on an optimal annealing schedule, we demonstrate that multiple runs of the simulated annealing algorithm can result in an optimal or near-optimal solution to the problem.