Simulated Annealing and the Generation of the Objective Function: A Model of Learning During Problem Solving

A computational model of problem solving based on significant aspects of human problem solving is introduced. It is observed that during problem solving humans often start searching more or less randomly, becoming more deterministic over time as they learn more about the problem. This two‐phase aspect of problem‐solving behavior and its relation to learning is one of the important features this model accounts for. The model uses an accelerated simulated annealing technique as a search mechanism within a real‐time dynamic programming‐like framework upon a connected graph of neighboring problem states. The objective value of each node is adjusted as the model moves between nodes, learning more accurate values for the nodes and also compensating for misleading heuristic information as it does so. In this manner the model is shown to learn to more effectively solve isomorphs of the Balls and Boxes and Tower of Hanoi problems. The major issues investigated with the model are (a) whether such a simulated annealing‐based model exhibits the kind of random‐to‐directed transition in behavior exhibited by people, and (b) whether the progressive discovery of the objective function, even when given very little or poor initial information, is a plausible method for representing the learning that occurs during problem solving and the knowledge that results from that learning.     

A Recursive Method for Solving a Climate–Economy Model: Value Function Iterations with Logarithmic Approximations

A recursive method for solving an integrated assessment model of climate and the economy is developed in this paper. The method approximates a value function with a logarithmic basis function and searches for solutions on a set satisfying optimality conditions. These features make the method suitable for a nonlinear model with many state variables and various constraints. The method produces exact solutions to a simple economic growth model and is useful for solving more demanding models such as the well-known DICE model (dynamic integrated model of climate and the economy).     

The use of an adaptive bandpass filter as an observer in the control loop of the international space station

For a parametrically uncertain model of the International Space Station (ISS), an algorithm using an adjustable model is proposed; on the basis of this algorithm, a self-tuning discrete bandpass filter is designed. The asymptotic stability of the proposed algorithm is ensured using the novel method for solving the matrix completion problem where the completed matrix is required to be stable. The use of the symbolic method for solving the matrix completion problem makes it possible to obtain a universal solution of the self-tuning bandpass filter design problem.     

一种用于汽车发动机故障诊断的贝叶斯网络模型

在汽车发动机故障诊断领域,由于设备内部的复杂性和导致故障的不确定因素,使得解决不确定性问题成为目前发动机故障诊断的首要问题;文章提出了一种用于解决不确定性问题的贝叶斯网络模型,该模型的网络结构学习采用了基于簇的搜索算法;为了获得更高准确率的故障诊断结果,模型加入了对当前信息集的采用,进行结构和参数的在线学习,改进了网络结构,网络通过概率传播算法,推理出产生故障的原因节点;在实例中表明,该模型能准确有效地解决发动机故障诊断中存在的不确定性问题,并与专家系统故障诊断模型做出比较,验证了基于该算法的贝叶斯网络模型在信息不确定性条件下能够提高诊断的准确率。     

基于多重马尔可夫Bayes网的软件失效预测模型

软件开发的复杂性决定了理想的软件可靠性模型既应具有包容众多复杂因素的能力,又要有构造灵活的功能。迄今为止,人们提出的众多模型,由于设定了很多近乎苛刻的条件,使它们难以具有普适性。Bayes网提供了解决这一问题的有力工具,论文就利用多重马尔可夫Bayes网建立起基于Bayes网的软件失效预测模型,并对此进行了详细的分析,给出了模型的求解步骤。最后,通过实例验证了该模型的有效性。     

基于Bayes网的软件失效预测模型

Owing to the complexity of software development,the software reliability model should not only have the capability of dealing with multiple complex factors,but also provide the furtction of flexibility in construction.So far,no software reliability model is universally applicable.The main reason for this is of too many conditions ,thus making software reliability models introvert.Bayesian network is a powerful tool for solving this problem,which exhibits strong adaptability in dealing with problems involving complex variant factors.In the paper,software failure predication model based oft Markov.Bayesian network is established and analyzed thoroughly.Then a method of solving the model is given.Finally,through an example the validity of the model is validated.     

一种针对动态部分可重构SoC软硬件划分的高效MILP模型

异构片上系统(System-on-Chip,SoC)在同一芯片上集成了多种类型的处理器,在处理能力、尺寸、重量、功耗等各方面有较大优势,因此在很多领域得到了应用。具有动态部分可重构特性的SoC(Dynamic Partial Reconfigurability SoC,DPR-SoC)是异构SoC的一种重要类型,这种系统兼具了软件的灵活性和硬件的高效性。此类系统的设计通常涉及到软硬件协同问题,其中如何进行应用的软硬件划分是保证系统实时性的关键技术。DPR-SoC中的软硬件划分问题可归类为组合优化问题,问题目标是获得调度长度最短的调度方案,包括任务映射、排序和定时。混合整数线性规划(Mixed Integer Linear Programming,MILP)是求解组合优化问题的一种有效方法;然而,将具体问题建模为MILP模型是求解问题的关键一环,不同建模方式对问题求解时间有重要影响。已有针对DPR-SoC软硬件划分问题的MILP模型存在大量变量和约束方程,对问题求解时间产生了不利影响;此外,其假设条件过多,使得求解结果与实际应用不符。针对这些问题,提出了一种新颖的MILP模型,其极大地降低了模型复杂度,提高了求解结果与实际应用的符合度。将应用建模成DAG图,并使用整数线性规划求解工具对问题进行求解。大量求解结果表明,新的模型能够有效地降低模型复杂度,缩短求解时间;并且随着问题规模的增大,所提模型在求解时间上的优势表现得更加显著。     

A Constrained Multiple Raw Materials Manufacturing Batch Sizing Problem

The purpose of this research is to determine an optimal batch size for a product, and the purchasing policy of associated raw materials, for a manufacturing firm. Like any other practical situation, this manufacturing firm has a limited storage space, and transportation fleet of known capacity. The mathematical formulation of the problem indicates that the model is a constrained nonlinear integer program. Considering the complexity of solving such a model, we investigate the use of genetic algorithms (GAs) for solving this model. We develop both binary and real coded genetic algorithms with six different penalty functions. In addition, we develop a new procedure to solve constrained optimization models using penalty function based GAs. The real coded genetic algorithms work well for the batch sizing problems. The detailed computational experiences are presented.     

一个基于模拟退火的多主体模型及其应用

近些年,多主体系统的理论及应用得到了人们的广泛关注,并得以迅速发展.研究者提出了很多基于多主体系统理论的模型,用于求解各种问题.AER(Agent-environment-rules)模型正是一个用于求解约束满足问题较为成功的例子.但是,主体的静态策略选择在一定程度上限制了模型的求解性能.将模拟退火算法与多主体系统思想相结合,并赋予主体更为高效的动态策略选择的能力,提出了SAAER模型(simulated annealing based AER model).基于约束满足问题经典实例--N-Queen问题和染色问题的实验表明,改进后的模型较之原模型获得了更高的效率和稳定性.对于N=10000的大规模N-Queen问题,能在200s左右的时间求得精确解.     

基于多Agent的复合模型求解自适应QoS机制

在基于网络的分布式系统应用基础上,分析了大型复杂问题复合模型协作求解的过程特征描述,提出基于多Agent 的领域问题协作求解的主动控制策略,探讨了用户交互Agent、系统主控Agent、协作Agent以及模型Agent和数据Agent等复合模型协作求解的4种Agent类型。应用多Agent层次结构,提出一种复合模型协作求解的自适应QoS体系结构,通过实现复合模型协作求解的主动调度规划算法对其进行了验证,支持分布式网络环境下实现模型资源和数据资源的共享,以提高协同计算环境分布式问题协作求解的运行效率和服务质量。     

并行型Ramsey数DNA计算模型

求解Ramsey数的困难在于需要搜索的解空间太大,而传统的电子计算机无法在有效的时间和存储空间上进行求解.由于DNA计算具有巨大的并行性和高密度存储能力等优点,文中研究了Ramsey数的DNA计算模型.针对传统的Ramsey数DNA计算模型存在的DNA序列量过多和序列过长的不足,利用DNA分子的特性以及生物操作将非解尽可能较早地消除,提出了并行型Ramsey数DNA计算模型,并以R(3,10)为例,给出了具体的求解步骤.     

Multi-criteria human resource allocation for solving multistage combinatorial optimization problems using multiobjective hybrid genetic algorithm

Multi-criteria human resource allocation involves deciding how to divide human resource of limited availability among multiple demands in a way that optimizes current objectives. In this paper, we focus on multi-criteria human resource allocation for solving multistage combinatorial optimization problem. Hence we tackle this problem via a multistage decision-making model. A multistage decision-making model is similar to a complex problem solving, in which a suitable sequence of decisions is to be found. The task can be interpreted as a series of interactions between a decision maker and an outside world, at each stage of which some decisions are available and their immediate effect can be easily computed. Eventually, goals would be reached due to the found of optimized variables. In order to obtain a set of Pareto solutions efficiently, we propose a multiobjective hybrid genetic algorithm (mohGA) approach based on the multistage decision-making model for solving combinatorial optimization problems. According to the proposed method, we apply the mohGA to seek feasible solutions for all stages. The effectiveness of the proposed algorithm was validated by its application to an illustrative example dealing with multiobjective resource allocation problem.     

结束时间不确定的投资组合选择问题建模与模型求解方法

针对结束时间具有不确定性的投资问题,建立以区间风险值(PVaR)度量市场风险的收益最大化投资组合选择模型.PVaR计算的复杂性使得模型难以运用一般优化方法求解,因此提出并证明可以通过求解等效的混合整数规划模型来得到原模型的最优解.利用实际股价数据进行数值实验分析,结果表明,求解混合整数规划模型针对小规模短期投资问题可以快速给出最优投资决策方案.     

基于改进合同网协议的多Agent协作模型

合同网是用于分布式问题求解环境下各Agent进行通信和协作的一种协议,各个Agent内部的知识、能力和策略在问题求解过程中总是动态变化的。为了能够得到实用性强且易于实现的协作模型,分析了传统经典合同网的缺点并进行了改进,利用熟人模型对投标者进行了合理的筛选。采用Agent的主动感知特性,改进了任务Agent接受任务的被动性。在投标过程中引人信任度、感知系数和活跃度等智能参数,防止了投标者在投标过程中的自私性,平衡了各个合同承担者的负载。通过实验证明,改进的合同网降低了网络通信量,提高了多Agent系统协作的效率。     

线性离散时滞重复过程的H∞控制

首先给出了线性离散时滞重复过程的2D(两维)Roesser模型, 采用线性矩阵不等式方法导出了过程稳定并具有H_∞扰动抑制度的一个充分条件. 通过求一个线性矩阵不等式的可行解来构造系统的一个状态反馈H_∞控制器. 进一步, 通过求解一个线性矩阵不等式凸优化问题得到该过程的最优状态反馈H_∞控制器.     

Perspectives on problem solving and instruction

Most educators claim that problem solving is important, but they take very different perspective on it and there is little agreement on how it should be taught. This article aims to sort out the different perspectives and discusses problem solving as a goal, a method, and a skill. As a goal, problem solving should not be limited to well-structured problem solving but be extended to real-life problem solving. As a method, problem solving has clear limitations for novice learners; providing ample support to learners is of utmost importance for helping them to develop problem-solving skills. As a skill, problem solving should not be seen as something that only occurs in the early phases of a process of expertise development but as a process that develops in parallel in System 1 and System 2. The four-component instructional design model (4C/ID) is briefly discussed as an approach that is fully consistent with the conceptualization described in this article and as a preliminary answer to the question how problem solving is best taught.     

The multi-fuzzy N-soft set and its applications to decision-making

Neural Computing and Applications - The goal of this paper is to introduce a novel hybrid model called multi-fuzzy N-soft set, and to design an adjustable decision-making methodology for solving...     

Evolutionary design of Evolutionary Algorithms

Manual design of Evolutionary Algorithms (EAs) capable of performing very well on a wide range of problems is a difficult task. This is why we have to find other manners to construct algorithms that perform very well on some problems. One possibility (which is explored in this paper) is to let the evolution discover the optimal structure and parameters of the EA used for solving a specific problem. To this end a new model for automatic generation of EAs by evolutionary means is proposed here. The model is based on a simple Genetic Algorithm (GA). Every GA chromosome encodes an EA, which is used for solving a particular problem. Several Evolutionary Algorithms for function optimization are generated by using the considered model. Numerical experiments show that the EAs perform similarly and sometimes even better than standard approaches for several well-known benchmarking problems.     

Dantzig-Wolfe decomposition and branch-and-price solving in G12

The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a high-level model of the problem to an efficient combination of solving methods. Model annotations are used to control this process. In this paper we explain the mapping to branch-and-price solving. Dantzig-Wolfe decomposition is automatically performed using the additional information given by the model annotations. The models obtained can then be solved using column generation and branch-and-price. G12 supports the selection of specialised subproblem solvers, the aggregation of identical subproblems to reduce symmetries, automatic disaggregation when required by branch-and-bound, the use of specialised subproblem constraint-branching rules, and different master problem solvers including a hybrid solver based on the volume algorithm. We demonstrate the benefits of the G12 framework on three examples: a trucking problem, cutting stock, and two-dimensional bin packing.