带学习效应的两台平行机时间表长问题

研究机器带学习效应, 目标函数为时间表长的两台平行机排序问题, 问题是NP-难的. 首先建立了求解该问题最优解的整数规划模型. 其次, 基于模拟退火算法给出了该问题的近似算法SA, 并证明了该算法依概率1 全局收敛到最优解. 最后, 通过数值模拟对所提出的算法进行了性能分析. 数值模拟结果表明, 近似算法SA可以达到最优值的99%, 准确度高, 算法较有效.     

Parallelizing simulated annealing algorithms based on high-performance computer

We implemented five conversions of simulated annealing (SA) algorithm from sequential-to-parallel forms on high-performance computers and applied them to a set of standard function optimization problems in order to test their performances. According to the experimental results, we eventually found that the traditional approach to parallelizing simulated annealing, namely, parallelizing moves in sequential SA, difficultly handled very difficult problem instances. Divide-and-conquer decomposition strategy used in a search space sometimes might find the global optimum function value, but it frequently resulted in great time cost if the random search space was considerably expanded. The most effective way we found in identifying the global optimum solution is to introduce genetic algorithm (GA) and build a highly hybrid GA+SA algorithm. In this approach, GA has been applied to each cooling temperature stage. Additionally, the performance analyses of the best algorithm among the five implemented algorithms have been done on the IBM Beowulf PCs Cluster and some comparisons have been made with some recent global optimization algorithms in terms of the number of functional evaluations needed to obtain a global minimum, success rate and solution quality.     

变邻域模拟退火算法求解速度时变的VRPTW问题

本文在经典的带时间窗的车辆路径问题(VRPTW)的基础上,考虑不同时间段车辆行驶速度不同的情况,研究速度时变的带时间窗车辆路径问题(TDVRPTW),使问题更具实际意义。本文用分段函数表示不同时间段下的车辆行驶速度,并解决了速度时变条件下行驶时间计算的问题。针对模拟退火算法(SA)在求解VRPTW问题时易陷入局部最优解,变邻域搜索算法(VNS)在求解VRPTW问题时收敛速度慢的问题,本文将模拟退火算法以一定概率接受非最优解的思想和变邻域搜索算法系统地改变当前解的邻域结构以拓展搜索范围的思想结合起来,提出了一种改进的算法——变邻域模拟退火算法(SAVN),使算法在退火过程中一陷入局部最优解就改变邻域结构,更换搜索范围,以此提升算法跳出局部最优解的能力,加快收敛速度。通过在仿真实验中将SAVN算法的求解结果与VNS算法、SA算法进行对比,验证了SAVN算法确实能显著提升算法跳出局部最优解的能力。     

Combinatorial optimization by stochastic automata

The significance of combinatorial optimization for many important applications is well understood. The simulated annealing algorithm (which we will denote from here on as SA) has generated great interest and attention in the scientific community. Its authors derived it from analogies to the physical domain [15,10], and a myriad of publications followed (see references to the book on simulated annealing in [11]). The prevailing opinion expressed in these publications was that the SA algorithm represents a new, hitherto unknown class of algorithms and provides a breakthrough in the solution of NP-hard optimization problems. As might be expected, roots of the SA do exist, and one of the purposes of this paper is to trace these roots. We prove that SA, like many other randomized algorithms, belongs to the class of S-type GH-stochastic automata. We provide other representatives of this class together with algorithms from some other classes, and discuss the issue of convergence. Large computational experiemts were performed on a network of Apollo computers.     

Simulated annealing for the unconstrained quadratic pseudo-Boolean function

In this paper, we develop a simulated annealing (SA) based heuristic for the unconstrained quadratic pseudo-Boolean function. An algorithm that solves the problem in O(n²) at each temperature of the cooling schedule is given. The performance of SA based heuristic is compared with existing bounding algorithms for this problem. Computational results and comparisons on several hundred test problems demonstrate the efficiency of our heuristic in terms of solution quality and computational time. A new set of hard test problems with their best solution is provided to facilitate future comparison.     

Balancing stochastic two-sided assembly lines: A chance-constrained,piecewise-linear,mixed integer program and a simulated annealing algorithm

Two-sided assembly lines are often designed to produce large-sized products, such as automobiles, trucks and buses. In this type of a production line, both left-side and right-side of the line are used in parallel. In all studies on two-sided assembly lines, the task times are assumed to be deterministic. However, in real life applications, especially in manual assembly lines, the tasks may have varying execution times defined as a probability distribution. The task time variation may result from machine breakdowns, loss of motivation, lack of training, non-qualified operators, complex tasks, environment, etc. In this paper, the problem of balancing two-sided assembly lines with stochastic task times (STALBP) is considered. A chance-constrained, piecewise-linear, mixed integer program (CPMIP) is proposed to model and solve the problem. As a solution approach a simulated annealing (SA) algorithm is proposed. To assess the effectiveness of CPMIP and SA algorithm, a set of test problems are solved. Finally, computational results indicating the effectiveness of CPMIP and SA algorithm are reported.     

An efficient algorithm for large scale global optimization of continuous functions

A fast descent algorithm, resorting to a “stretching” function technique and built on one hybrid method (GRSA) which combines simulated annealing (SA) algorithm and gradient based methods for large scale global optimizations, is proposed. Unlike the previously proposed method in which the original objective functions remain unchanged during the whole course of optimization, the new method firstly constructs an auxiliary function on one local minimizer obtained by gradient based methods and then SA is executed on this constructed auxiliary function instead of on the original objective function in order that we can improve the jumping ability of SA algorithm to escape from the currently discovered local minimum to a better one from which the gradient based methods restart a new local search. The above procedure is repeated until a global minimum is detected. In addition, corresponding to the adopted “stretching” technique, a new next trial point generating scheme is designed. It is verified by simulation especially on large scale problems that the convergence speed is greatly accelerated, which is its main difference from many other reported methods that mostly cope with functions with less than 50 variables and does not apply to large scale optimization problems. Furthermore, the new algorithm functions as a global optimization procedure with a high success probability and high solution precision.     

Application of the simulated annealing algorithm to the combinatorial optimisation problem with permutation property: An investigation of generation mechanism

Focusing on the generation mechanism of random permutation solutions, this paper investigates the application of the Simulated Annealing (SA) algorithm to the combinatorial optimisation problems with permutation property. Six types of perturbation scheme for generating random permutation solutions are introduced. They are proved to satisfy the asymptotical convergence requirements. The results of experimental evaluations on Traveling Salesman Problem (TSP), Flow-shop Scheduling Problem (FSP), and Quadratic Assignment Problem (QAP) reveal that the efficiencies of the perturbation schemes are different in searching a solution space. By adopting a proper perturbation scheme, the SA algorithm has shown to produce very efficient solutions to different combinatorial optimisation problems with permutation property.     

Simulated annealing for discrete optimization with estimation

We extend the basic convergence results for the Simulated Annealing (SA) algorithm to a stochastic optimization problem where the objective function is stochastic and can be evaluated only through Monte Carlo simulation (hence, disturbed with random error). This extension is important when either the objective function cannot be evaluated exactly or such an evaluation is computationally expensive. We present a modified SA algorithm and show that under suitable conditions on the random error, the modified SA algorithm converges in probability to a global optimizer. Computational results and comparisons with other approaches are given to demonstrate the performance of the proposed modified SA algorithm.     

Solving a dynamic cell formation problem using metaheuristics

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed by using some traditional metaheuristic methods such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Most of previous researches were done under the static condition. Due to the fact that CF is a NP-hard problem, then solving the model using classical optimization methods needs a long computational time. In this research, a nonlinear integer model of CF is first given and then solved by GA, SA and TS. Then, the results are compared with the optimal solution and the efficiency of the proposed algorithms is discussed.     

Rescaled Simulated Annealing—Accelerating Convergence of Simulated Annealing by Rescaling the States Energies

This paper presents a new metaheuristic, called rescaled simulated annealing (RSA) which is particularly adapted to combinatorial problems where the available computational effort to solve it is limited. Asymptotic convergence on optimal solutions is established and the results are favorably compared to the famous ones due to Mitra, Romeo, and Sangiovanni-Vincentelli (Mitra, Romeo, and Sangiovanni-Vincentelli. (1986). Adv. Appl. Prob. 18, 747–771.) for simulated annealing (SA). It is based on a generalization of the Metropolis procedure used by the SA algorithm. This generalization consists in rescaling the energies of the states candidate for a transition, before applying the Metropolis criterion. The direct consequence is an acceleration of convergence, by avoiding dives and escapes from high energy local minima. Thus, practically speaking, less transitions need to be tested with RSA to obtain a good quality solution. As a corollary, within a limited computational effort, RSA provides better quality solutions than SA and the gain of performance of RSA versus SA is all the more important since the available computational effort is reduced. An illustrative example is detailed on an instance of the Traveling Salesman Problem.     

Multi-mode resource availability cost problem with recruitment and release dates for resources

This paper investigates the multi-mode resource availability cost problem with recruitment and release dates for resources. This problem is a more realistic model and extended case of the resource availability cost problem. The project contains activities interrelated by finish–start precedence relations with zero time lags, which require a set of renewable resources. First, a mixed integer programming formulation is proposed for the problem. Then, simulated annealing (SA) algorithm is proposed to obtain a satisfying solution for this NP-hard problem. The effectiveness of the proposed algorithm is demonstrated through comprehensive experimentation based on 300 test problems. The results are analyzed and discussed.     

混合启发式算法求解多配送人员车辆路径问题

为解决带时间窗和多配送人员的车辆路径问题,本文采用混合启发式算法对其进行求解。该算法主要由整数规划重组、局部搜索算法和模拟退火算法三部分组成。在算法中,整数规划重组有效提高了解的质量,局部搜索算法和模拟退火算法保证了算法搜索的深入性和广泛性。通过与CPLEX和禁忌搜索算法进行对比,证实了混合启发式算法实用价值更高,求解效果更好。     

Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography

The simulated annealing (SA) algorithm is a well-established optimization technique which has found applications in many research areas. However, the SA algorithm is limited in its application due to the high computational cost and the difficulties in determining the annealing schedule. This paper demonstrates that the temperature parallel simulated annealing (TPSA) algorithm, a parallel implementation of the SA algorithm, shows great promise to overcome these limitations when applied to continuous functions. The TPSA algorithm greatly reduces the computational time due to its parallel nature, and avoids the determination of the annealing schedule by fixing the temperatures during the annealing process. The main contributions of this paper are threefold. First, this paper explains a simple and effective way to determine the temperatures by applying the concept of critical temperature (T_C). Second, this paper presents systematic tests of the TPSA algorithm on various continuous functions, demonstrating comparable performance as well-established sequential SA algorithms. Third, this paper demonstrates the application of the TPSA algorithm on a difficult practical inverse problem, namely the hyperspectral tomography problem. The results and conclusions presented in this work provide are expected to be useful for the further development and expanded applications of the TPSA algorithm.     

A simulated annealing approach for reliability‐based chance‐constrained programming

The chance‐constrained programming (CCP) is a well‐known and widely used stochastic programming approach. In the CCP approach, determining the confidence levels of the constraints at the beginning of solution process is a critical issue for optimality. On one hand, it is possible to obtain better solutions at different confidence levels. On the other hand, the decision makers prefer to simplify their choices instead of grappling with the details such as determining confidence levels for all chance constraints. Reliability is an effective tool that enables the decision maker to look over the system integrity. In this paper, the CCP is considered as a reliability‐based nonlinear multiobjective model, and a simulated annealing (SA) algorithm is developed to solve the model. The SA represents different solution alternatives at the different reliability degrees to the decision makers by performing different confidence levels. Thus, the decision makers have the opportunity to make more effective decisions. Copyright © 2013 John Wiley & Sons, Ltd.     

Improving the Efficiency of Tabu Search for Machine Sequencing Problems

Tabu search (TS) is becoming increasingly recognized as an efficient way of finding high-quality solutions to hard combinatorial problems. It may be described as an intelligent meta-heuristic for controlling simpler local search procedures. However, reported applications have often used a ‘brute-force’ approach without considering the most effective use of the computing effort available. This paper intends firstly to give a basic introduction to the ideas of TS, and then it will report some computational experiments on TS in the context of machine sequencing. These have shown that it is important to define the balance between exploration of the solution space and exploitation of the information obtained. The results will be compared with those obtained from a proven Simulated Annealing (SA) algorithm, which tends to confirm the general opinion that when implemented efficiently, TS is a more effective search paradigm than SA.     

一种类微粒群算法及其在混流装配线调度问题中的应用

混流装配生产线的调度问题是准时化生产系统中最重要的问题之一.基于微粒群算法的原理,提出了一种类微粒群算法——PPSO(Pseudo Particle Swarm Optimization),可应用于解决准时化生产方式下的混流装配线调度问题.数值试验表明,采用PPSO方法比采用目标追随法、遗传算法和模拟退火算法的求解质量有很大提高.     

Spectral analytic comparisons for data augmentation

The sandwich algorithm (SA) is an alternative to the data augmentation (DA) algorithm that uses an extra simulation step at each iteration. In this paper, we show that the sandwich algorithm always converges at least as fast as the DA algorithm, in the Markov operator norm sense. We also establish conditions under which the spectrum of SA dominates that of DA. An example illustrates the results.     

A simulated annealing approach to mine production scheduling

Increasing global competition, quality standards, environmental awareness and decreasing ore prices impose new challenges to mineral industries. Therefore, the extraction of mineral resources requires careful design and scheduling. In this research, simulated annealing (SA) is recommended to solve a mine production scheduling problem. First of all, in situ mineral characteristics of a deposit are simulated by sequential Gaussian simulation, and averaging the simulated characteristics within specified block volumes creates a three-dimensional block model. This model is used to determine optimal pit limits. A linear programming (LP) scheme is used to identify all blocks that can be included in the blend without violating the content requirements. The Lerchs–Grosmann algorithm using the blocks identified by the LP program determines optimal pit limits. All blocks that lie outside of the optimal pit limit are removed from the system and the blocks within the optimal pit are submitted to the production scheduling algorithm. Production scheduling optimization is carried out in two stages: Lagrangean parameterization, resulting in an initial sub-optimal solution, and multi-objective SA, improving the sub-optimal schedule further. The approach is demonstrated on a Western Australian iron ore body.     

关于随机优化算法的几点讨论

关于随机优化算法的几点讨论李晓莉，雷功炎（河南驻马店师专，北京大学数学系）ＳＯＭＥＤＩＳＣＵＳＳＩＯＮＳＡＢＯＵＴＳＴＯＣＨＡＳＴＩＣＯＰＴＩＭＩＺＡＴＩＯＮＡＬＧＯＲＩＴＨＭＳ￥ＬｉＸｉａｏ－ｌｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｚ...