A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.     

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。     

A comparison of global optimization algorithms applied to a ride comfort optimization problem

This study presents a comparison of global optimization algorithms applied to an industrial engineering optimization problem. Three global stochastic optimization algorithms using continuous variables, i.e. the domain elimination method, the zooming method and controlled random search, have been applied to a previously studied ride comfort optimization problem. Each algorithm is executed three times and the total number of objective function evaluations needed to locate a global optimum is averaged and used as a measure of efficiency. The results show that the zooming method, with a proposed modification, is most efficient in terms of number of objective function evaluations and ability to locate the global optimum. Each design variable is thereafter given a set of discrete values and two optimization algorithms using discrete variables, i.e. a genetic algorithm and simulated annealing, are applied to the discrete ride comfort optimization problem. The results show that the genetic algorithm is more efficient than the simulated annealing algorithm for this particular optimization problem.     

超导MRI主磁体优化设计的模拟退火算法

在进行MRI(magneticresonanceimaging)超导主磁体的设计时常采用优化设计的方法,将各设计参数看作连续变量处理,但实际上很多参数是离散变量,为了更符合工程实际,将超导MRI主磁体的设计作为一个含有离散变量的全局优化问题。建立了适用于多种超导MRI主磁体结构的数学模型,包括设计变量、目标函数、约束条件等,选用了适用于MRI超导主磁体优化设计的含有离散变量的模拟退火算法进行设计。算例结果表明,本文选取的数学模型和优化算法是有效的,能够达到超导MRI主磁体设计的要求。     

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．     

Stochastic optimization over continuous and discrete variables withapplications to concept learning under noise

We consider optimization problems where the objective function is defined over some continuous and some discrete variables, and only noise corrupted values of the objective function are observable. Such optimization problems occur naturally in PAC learning with noisy samples. We propose a stochastic learning algorithm based on the model of a hybrid team of learning automata involved in a stochastic game with incomplete information to solve this optimization problem and establish its convergence properties. We then illustrate an application of this automata model in learning a class of conjunctive logic expressions over both nominal and linear attributes under noise     

Optimization of stochastic simulation models

An algorithm called SAMOPT is developed for optimizing the response function of simulation models that describe systems exhibiting stochastic behavior. Because of the stochastic nature of these simulated systems, the result of each evaluation of response by simulation is only a noisy (i.e., uncertain) observation of the true response. The SAMOPT algorithm uses these noisy responses to find a set of values for decision variables of the system such that the true response is optimized. Principles of the Stochastic Approximation Method have been used in developing this algorithm. The SAMOPT algorithm also allows for the case where the decision variables are subject to a set of linear constraints. Comparison of results between applications of SAMOPT and another well-known method are given for problems and a simulation model.     

An Introduction to Simulated Annealing Algorithms for the Computation of Economic Equilibrium

Economic equilibrium computation has raised the issue of global optimization algorithms since economic equilibrium problems can be cast as a global optimization problem. However, nearly all conventional algorithms stop when they find a local optimum. Over the last decade a number of new optimization algorithms have appeared, simulated annealing is one of them. It is a powerful stochastic search algorithm applicable to a wide range of problems for which little prior knowledge is available, and it asymptotically probabilistically converges to a global optimum. In this paper, we will give a brief introduction to simulated annealing and apply it to the computation of economic equilibrium. We also reported our computational experience in the paper. This early result shows that the application of simulated annealing to computation of economic equilibrium is encouraging and it deserves further research.     

A novel stochastic optimization algorithm

This paper presents a new stochastic approach SAGACIA based on proper integration of simulated annealing algorithm (SAA), genetic algorithm (GA), and chemotaxis algorithm (CA) for solving complex optimization problems. SAGACIA combines the advantages of SAA, GA, and CA together. It has the following features: (1) it is not the simple mix of SAA, GA, and CA; (2) it works from a population; (3) it can be easily used to solve optimization problems either with continuous variables or with discrete variables, and it does not need coding and decoding,; and (4) it can easily escape from local minima and converge quickly. Good solutions can be obtained in a very short time. The search process of SAGACIA can be explained with Markov chains. In this paper, it is proved that SAGACIA has the property of global asymptotical convergence. SAGACIA has been applied to solve such problems as scheduling, the training of artificial neural networks, and the optimizing of complex functions. In all the test cases, the performance of SAGACIA is better than that of SAA, GA, and CA.     

基于模拟退火高斯扰动的蝙蝠优化算法

蝙蝠算法（bat algorithm, BA）是一类新型的搜索全局最优解的随机优化技术。为了提高BA算法的搜索效果, 把模拟退火的思想引入到蝙蝠优化算法中, 并对蝙蝠算法的某些个体进行高斯扰动, 提出了一种基于模拟退火的高斯扰动蝙蝠优化算法（SAGBA）。分别将蝙蝠优化算法、模拟退火粒子群算法、SAGBA在20个典型的基准测试函数中进行仿真对比, 结果表明SAGBA不仅增加了全局收敛性, 而且在收敛速度和精度方面均优于其他两种算法。     

基于蜂群算法和新阈值函数的信号去噪算法

针对阈值和阈值函数的调节参数取值问题,提出一种基于人工蜂群优化算法的带参新阈值函数的信号去噪算法。首先,验证带参新阈值函数的连续性、高阶可微性、参数可调性;其次,根据最小均方误差（MSE）策略,利用人工蜂群优化算法优化各分解层的阈值和调整参数,得到最优去噪信号;最后,利用信噪比（SNR）、MSE指标验证信号的去噪效果。实验结果表明,人工蜂群优化算法选取的阈值参数和新小波阈值函数可以有效地对带噪信号去噪。     

Experiments with repeating weighted boosting search for optimization in signal processing applications.

Many signal processing applications pose optimization problems with multimodal and nonsmooth cost functions. Gradient methods are ineffective in these situations, and optimization methods that require no gradient and can achieve a global optimal solution are highly desired to tackle these difficult problems. The paper proposes a guided global search optimization technique, referred to as the repeated weighted boosting search. The proposed optimization algorithm is extremely simple and easy to implement, involving a minimum programming effort. Heuristic explanation is given for the global search capability of this technique. Comparison is made with the two better known and widely used guided global search techniques, known as the genetic algorithm and adaptive simulated annealing, in terms of the requirements for algorithmic parameter tuning. The effectiveness of the proposed algorithm as a global optimizer are investigated through several application examples.     

Experiments with repeating weighted boosting search for optimization signal processing applications

Many signal processing applications pose optimization problems with multimodal and nonsmooth cost functions. Gradient methods are ineffective in these situations, and optimization methods that require no gradient and can achieve a global optimal solution are highly desired to tackle these difficult problems. The paper proposes a guided global search optimization technique, referred to as the repeated weighted boosting search. The proposed optimization algorithm is extremely simple and easy to implement, involving a minimum programming effort. Heuristic explanation is given for the global search capability of this technique. Comparison is made with the two better known and widely used guided global search techniques, known as the genetic algorithm and adaptive simulated annealing, in terms of the requirements for algorithmic parameter tuning. The effectiveness of the proposed algorithm as a global optimizer are investigated through several application examples.     

模拟退火法用于连续变量问题全局优化初探

针对过程系统连续变量优化问题中普遍存在的多峰现象，初步字应用模拟退火法求解全局最优解的问题，针对变量只有上下限下等式约束的问题，根据连续变量问题的特性，提出了一种用相状态的产生函数，并分析了模拟退火过程的起始温度，终止温度以及降温速度对优化计算的影响，给出了这些参数的适宜区域，通过三个例题的计算，将模拟退火法与传统优化方法－基于梯度的方法进行了对比分析，结果表明该法能够有效地解决传统的确定型优化方     

OPTIMIZING COMPLEX FUNCTIONS BY CHAOS SEARCH

During past decades, the role of optimization has steadily increased in many fields. It is a hot problem in research on control theory. In practice, optimization problems become more and more complex. Traditional algorithms cannot solve them satisfactorily. Either they are trapped to local minima or they need much more search time. Chaos often exists in nonlinear systems. It has many good properties such as ergodicity, stochastic properties, and ''regularity.'' A chaotic motion can go nonrepeatedly through every state in a certain domain. By use of these properties of chaos, an effective optimization method is proposed: the chaos optimization algorithm COA . With chaos search, some complex optimization problems are solved very well. The test results illustrate that the efficiency of COA is much higher than that of some stochastic algorithms such as the simulated annealing algorithm SAA and chemotaxis algorithm CA , which are often used to optimize complex problems. The chaos optimization method provides a new and efficient way to optimize kinds of complex problems with continuous variables.     

Simulated annealing for the design of structures with time-varying constraints

The optimal design of structural systems with conventional members or systems with conventional as well as passive or active members is presented. The optimal sizes of the conventional members of structural systems are obtained for dynamic loads. A modified simulated annealing algorithm is presented which is used to solve the optimization problem with dynamic constraints. The present algorithm differs from existing simulated annealing algorithms in two respects; first, an automatic reduction of the search range is performed, and second, a sensitivity analysis of the design variables is utilized. The present method converges to the minimum in less iterations when compared to existing simulated annealing algorithms. The algorithm is advantageous over classical methods for optimization of structural systems with constraints arising from dynamic loads. For certain initial values of the design variables, classical optimization methods either fail to converge or produce designs which are local minima; the present algorithm seems to be successful in yielding the global minimum design.     

Simulated annealing: An initial application in econometrics

A new global optimization algorithm simulated annealing, is tested on a difficult econometric problem. We find that simulated annealing performs better than conventional algorithms.     

解决多维全局最优问题的一种新方法

对一种新的全局优化方法(称为APSAM方法)进行了研究，将模拟退火方法的随机搜索策略与局部寻优算法POWELL相结合，使得求解过程可以跳出局部最优值的区域，最终获得全局最优解。最后通过对一些典型的多极值方程进行优化，比较了APSAM方法与模拟退火法、POWELL法和PSAM方法的优化结果，仿真结果说明提出的算法优化能力较强，效果稳定可靠。     

基于幂函数载波的混沌退火搜素算法

提出了一种用于求解组合优化问题的混沌优化策略.在寻优过程中,利用混沌搜索的方法确定解矩阵的变化位置,使得解矩阵在合法解空间内不断遍历寻优.为提高混沌搜索的充分性和遍历性,混沌载波采用幂函数载波的方式,并结合模拟退火的思想来确保算法具有跳出局部极小到达全局最优的遍历寻优能力.该算法可用于多种实际工程问题的求解中.仿真结果验证了该算法的有效性.     

模拟退火算法在全局查询优化中的应用

在分布式环境下,全局查询的代价函数空间形状包含了很多局部最小状态,需要多次局部最优化才可以找到全局最小状态。模拟退火算法是目前发展较快的智能优化算法,是一种以概率l收敛于全局最优解的全局优化算法。文中讨论了全局查询优化的过程以及模拟退火算法在全局查询优化中的应用,并对算法进行了一些改进。