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.     

面向问题分析与决策的专家系统

专家系统的根本目标在于为实际应用问题提供强有力的分析与决策能力。以人类通过长期实践活动总结的复杂问题分析与决策方法为指导思想,建立了以问题对象为核心、相关对象为问题主体、问题现象为表现形式、因果关系为问题变化驱动力、过程知识和原理知识为参考对象的面向问题分析与决策的专家系统。这种专家系统围绕应用领域中的问题构建知识库,而不是使用规则,所以得到的知识系统比较合理、清晰,不容易产生知识矛盾与冲突,有利于大型知识库的构建;同时,采用基于问题的推理,与人类的思维习惯相符合,可以大大提高推理效率;此外,开发这种专家     

Optimization method for solving bang-bang and singular control problems

In this paper we study optimal control problems with the control variable appearing linearly.A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented.This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem.The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc.A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming(NLP) problem.The control profiles and stage lengths act as decision variables.Based on the Pontryagin maximal principle,a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers.Two examples are studied to demonstrate the effectiveness of this strategy.     

Dominant pole and eigenstructure assignment for positive systems with state feedback

In this paper, the dominant pole assignment problem, the dominant eigenstructure assignment problem and the robust dominant pole assignment problem for linear time-invariant positive systems with state feedback are considered. The dominant pole assignment problem is formulated as a linear programming problem, and the dominant eigenstructure problem is formulated as a quasiconvex optimisation problem with linear constraints. The robust dominant pole assignment problem is formulated as a non-convex optimisation problem with non-linear constraints which is solved using particle swarm optimisation (PSO) with an efficient scheme which employs the dominant eigenstructure assignment technique to accelerate the convergence of the PSO procedure. Each of the three problems can be further constrained by requiring that the controller has a pre-specified structure, or the gain matrix have both elementwise upper and lower bounds. These constraints can be incorporated into the proposed scheme without increasing the complexity of the algorithms. Both the continuous-time case and the discrete-time case are treated in the paper.     

Efficient constructive and composite heuristics for the Permutation Flowshop to minimise total earliness and tardiness

In this paper we address the problem of scheduling jobs in a permutation flowshop with a just-in-time objective, i.e. the minimisation of the sum of total tardiness and total earliness. Since the problem is NP-hard, there are several approximate procedures available for the problem, although their performance largely depends on the due dates of the specific instance to be solved. After an in-depth analysis of the problem, different cases or sub-problems are identified and, by incorporating this knowledge, four heuristics are proposed: a fast constructive heuristic, and three different local search procedures that use the proposed constructive heuristic as initial solution.The proposed Prod. Type: FLPheuristics have been compared on an extensive set of instances with the best-so-far heuristic for the problem, as well as with adaptations of efficient heuristics for similar scheduling problems. The computational results show the excellent performance of the proposed algorithms. Finally, the positive impact of the efficient heuristics is evaluated by including them as seed sequences for one of the best metaheuristic for the problem.     

Multiple- and single-objective approaches to laminate optimization with genetic algorithms

In this paper an application of a genetic algorithm to a material- and sizing-optimization problem of a plate is described. This approach has obvious advantages: it does not require any derivative information and it does not impose any restriction, in terms of convexity, on the solution space. The plate optimization problem is firstly formulated as a constrained mixed-integer programming problem with a single objective function. An alternative multiobjective formulation of the problem in which some constraints are included as additional objectives is also presented. Some numerical results are included that show the appropriateness of the algorithm and of the mathematical model for the solution of this optimization problem, as well as the superiority of the multiobjective approach.     

二维立体匹配模型及其数值解法

针对传统立体匹配模型中忽视的极线校准不精确的情况,提出一种二维立体匹配模型及其数值解法。该模型是在一维立体匹配模型的基础上,加入另一维度的视差估计函数得到的。首先利用笛卡尔理论,将提出的非凸模型表示为更高维空间中的变分问题,然后利用双共轭函数（共轭函数的共轭函数）将高维空间的变分问题凸松弛为鞍点问题,最后使用可以快速有效解决鞍点问题的一阶原始对偶算法进行求解。实验结果表明,二维模型可以解决极线校准不精确问题并获取更高精度的视差图像,采用的数值算法可以有效地收敛。     

Linear Problems and Linear Algorithms

Using predicate logic, the concept of a linear problem is formalized. The class of linear problems is huge, diverse, complex, and important. Linear and randomized linear algorithms are formalized. For each linear problem, a linear algorithm is constructed that solves the problem and a randomized linear algorithm is constructed that completely solves it, that is, for any data of the problem, the output set of the randomized linear algorithm is identical to the solution set of the problem. We obtain a single machine, referred to as the Universal (Randomized) Linear Machine, which (completely) solves every instance of every linear problem. Conversely, for each randomized linear algorithm, a linear problem is constructed that the algorithm completely solves. These constructions establish a one-to-one and onto correspondence from equivalence classes of linear problems to equivalence classes of randomized linear algorithms.Our construction of (randomized) linear algorithms to (completely) solve linear problems as well as the algorithms themselves are based on Fourier Elimination and have superexponential complexity. However, there is no evidence that the inefficiency of our methods is unavoidable relative to the difficulty of the problem.     

Targeting and scheduling problem for field artillery

We consider the targeting and the fire sequencing problem for field artillery. We show that the targeting problem, which can be modeled as a problem with nonlinear constraints, can be transformed into a set of independent bounded variable knapsack problems. We also propose a mathematical model for the fire sequencing problem which is NP-hard and developed a heuristic to solve the problem. Computational results using randomly generated data are presented.     

EPnL:一种高效且精确的PnL问题求解算法EI北大核心CSCD

现有Perspective-n-line (PnL)问题求解算法无法在获得高求解精度的同时保证高求解效率.为解决这个缺点,提出了同时兼具求解效率和求解精度算法EPnL.该方法首先将PnL问题转换为求二次曲面方程组交点的问题,然后利用单位四元数中变量不同时为零的特性,分类参数化PnL问题中的旋转矩阵.最后,为克服常规优化方法可靠性和效率较低的问题,同时兼具求解效率和求解精度算法利用二次曲面方程组自身的结构信息,采用低次项参数化高次项的方式将二次曲面方程组的求解问题转换为单变量多项式的求解问题.实验表明,相比于现有算法,该算法在具有高求解精度的同时也兼具有高求解效率.     

Agent coordination and communication in sociotechnological systems: Design and measurement issues

This article is concerned with enhancing agent coordination in modern sociotechnological systems. To this end, sociotechnological systems are conceptualized as problem solving systems that comprise human and technological agents engaged in dynamic collaboration. Following this, there is a discussion of the challenge of achieving agent coordination in problem solving systems as technological agents become increasingly autonomous. A key assertion is that agent coordination in problem solving systems might be enhanced through the study of competent coordination in living systems such as human and animal groups. Based on a review of research on competent coordination in human and animal groups, design principles for problem solving systems are then presented. Finally, methods are proposed for measuring the extent to which a given agent operates in accordance with these principles.     

Contingency evaluation and monitorization using artificial neural networks

In this paper, different neural network-based solutions to the contingency analysis problem are presented. Contingency analysis is examined from two perspectives: as a functional approximation problem obtaining a numerical evaluation and ranking contingencies; and as a graphical monitoring problem, obtaining an easy visualization system of the relative severity of the contingencies. For the functional evaluation problem, we analyze the use of different supervised feed-forward artificial neural networks (multilayer perceptron and radial basis function networks). The proposed systems produce a very accurate evaluation and ranking, and so present a high applicability. For the graphical monitoring problem, unsupervised artificial neural networks such as self-organizing maps by Kohonen have been used. This solution allows both a rapid, easy and simultaneous visualization of the severity level of the complete contingency set. The proposed solutions avoid the main drawbacks of previous neural network approaches to this problem, which are explicitly analyzed here.     

Rent-or-Buy Network Design Problem and the Sample-Augment Algorithm: A Survey

The Rent-or-Buy Network Design problem is a fundamental connectivity-related network design problem. The problem captures the "economies of scale" property, which says that the per-unit cost of installing capacity on edges of the network decreases as more capacity is installed. The Sample-Augment algorithm is a simple but powerful randomized approximation algorithm that effectively deals with the Rent-or-Buy and related problems. In this paper we systematically survey the Rent-or-Buy problem and the Sample-Augment algorithm, as well as its two analysis techniques, i.e., the cost-sharing method and the core-detouring scheme.     

Multi-period technician scheduling with experience-based service times and stochastic customers

This paper introduces the multi-period technician scheduling problem with experience-based service times and stochastic customers. In the problem, a manager must assign tasks of different types that are revealed at the start of each day to technicians who must complete the tasks that same day. As a technician gains experience with a type of task, the time that it takes to serve future tasks of that type is reduced (often referred to as experiential learning). As such, while the problem could be modeled as a single-period problem (i.e. focusing solely on the current day’s tasks), we instead choose to model it as a multi-period problem and thus capture that daily decisions should recognize the long-term effects of learning. Specifically, we model the problem as a Markov decision process and introduce an approximate dynamic programming-based solution approach. The model can be adapted to handle cases of worker attrition and new task types. The solution approach relies on an approximation of the cost-to-go that uses forecasts of the next day’s assignments for each technician and the resulting estimated time it will take to service those assignments given current period decisions. Using an extensive computational study, we demonstrate the value of our approach versus a myopic solution approach that views the problem as a single-period problem.     

Optimal Portfolio Hedging with Nonlinear Derivatives and Transaction Costs

We consider the problem of dynamically hedging a fixed portfolio of assets in the presence of non-linear instruments and transaction costs, as well as constraints on feasible hedging positions. We assume an investor maximizing the expected utility of his terminal wealth over a finite holding period, and analyse the dynamic portfolio optimization problem when the trading interval is fixed. An approximate solution is obtained from a two-stage numerical procedure. The problem is first transformed into a nonlinear programming problem which utilizes simulated coefficient matrices. The nonlinear programming problem is then solved numerically using standard constrained optimization techniques.     

Stereo Matching with Transparency and Matting

This paper formulates and solves a new variant of the stereo correspondence problem: simultaneously recovering the disparities, true colors, and opacities of visible surface elements. This problem arises in newer applications of stereo reconstruction, such as view interpolation and the layering of real imagery with synthetic graphics for special effects and virtual studio applications. While this problem is intrinsically more difficult than traditional stereo correspondence, where only the disparities are being recovered, it provides a principled way of dealing with commonly occurring problems such as occlusions and the handling of mixed (foreground/background) pixels near depth discontinuities. It also provides a novel means for separating foreground and background objects (matting), without the use of a special blue screen. We formulate the problem as the recovery of colors and opacities in a generalized 3D (x, y, d) disparity space, and solve the problem using a combination of initial evidence aggregation followed by iterative energy minimization.     

Cyclicity and conversion to cyclicity

Various equivalent definitions of cyclicity are given. The problem of converting a non-cyclic system to a cyclic one, by means of constant output feedback, is considered, This problem arises as an intermediate problem in many state or output feedback pole-assignment algorithms. It is shown that the problem has an infinite number of solutions.     

Lagrangian duality between constrained estimation and control

We show that the Lagrangian dual of a constrained linear estimation problem is a particular nonlinear optimal control problem. The result has an elegant symmetry, which is revealed when the constrained estimation problem is expressed as an equivalent nonlinear optimisation problem. The results extend and enhance known connections between the linear quadratic regulator and linear quadratic state estimation problems.     

Algorithms for the car sequencing and the level scheduling problem

This paper deals with two most important problems arising in sequencing mixed-model assembly lines. One problem is to keep the line's workstations loads as constant as possible (the 'car sequencing problem') while the other is to keep the usage rate of all parts fed into the final assembly as constant as possible (the 'level scheduling problem'). The first problem is a difficult constraint-satisfaction problem while the second requires to optimize a nonlinear objective function. The contribution of this paper is twofold: First, we describe a branching scheme and bounding algorithms for the computation of feasible sequences for the car sequencing problem. Second, we present an algorithm which can optimize a level scheduling objective while taking care of the car sequencing constraints. Computational results are presented which show that feasible sequences can be obtained quickly for large problem instances.     

Optimal lot size for a perishable good under conditions of finite production and partial backordering and lost sale

Perishable products constitute a sizable component of inventories. A common question in a reselling situation involving a perishable (or a non-perishable) product is: what should be the size of the replenishment? When a product is highly perishable, the demand may need to be backlogged to contain costs due to deterioration. In this sense, perishability and backlogging are complementary conditions. In this paper we consider the problem of determining the lot size for a perishable good under finite production, exponential decay and partial backordering and lost sale. The problem is complex because it involves exponential and logarithmic expressions. We offer some new insights to this important managerial problem in inventory control. We show that as a constrained non-linear problem, it does have the convexity characteristics that make the problem easy to solve. Practitioners can solve this problem without resorting to Taylor's series approximation. They can solve the original problem using common non-linear programming software such as the Solver in Excel and be confident that the solution returned is the global minimum.