Describes a Lotus 1-2-3 spreadsheet developed to resolve the stagecoach problem by dynamic programming. Solution for general network models with multiple initial and final states using the same approach; Optimal route...
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Describes a Lotus 1-2-3 spreadsheet developed to resolve the stagecoach problem by dynamic programming. Solution for general network models with multiple initial and final states using the same approach; Optimal routes found from the information generated in the spreadsheet.
This research is about the development of a dynamic programming model for solving fuzzy linear programming problems. Initially, fuzzy dynamic linear programming model FDLP is developed. This research revises the estab...
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This research is about the development of a dynamic programming model for solving fuzzy linear programming problems. Initially, fuzzy dynamic linear programming model FDLP is developed. This research revises the established dynamic programming model for solving linear programming problems in a crisp environment. The mentioned approach is upgraded to address the problem in an uncertain environment. dynamic programming model can either be passing forward or backward. In the proposed approach backward dynamic programming approach is adopted to address the problem. It is then followed by implementing the proposed method on the education system of Pakistan. The education system of Pakistan comprises of the Primary, Middle, Secondary, and Tertiary education stages. The problem is to maximize the efficiency of the education system while achieving the targets with minimum usage of the constrained resources. Likewise the model tries to maximize the enrollment in the Primary, Middle, Secondary and Tertiary educational categories, subject to the total available resources in a fuzzy uncertain environment. The solution proposes that the enrollment can be increased by an amount 9997130, by increasing the enrollment in the Middle and Tertiary educational categories. Thus the proposed method contributes to increase the objective function value by 30%. Moreover, the proposed solutions violate none of the constraints. In other words, the problem of resources allocation in education system is efficiently managed to increase efficiency while remaining in the available constrained resources. The motivation behind using the dynamic programming methodology is that it always possesses a numerical solution, unlike the other approaches having no solution at certain times. The proposed fuzzy model takes into account uncertainty in the linear programming modeling process and is more robust, flexible and practicable.
In this paper, dynamic programming (DP) algorithm is applied to automatically segment multivariate time series. The definition and recursive formulation of segment errors of univariate time series are extended to mult...
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In this paper, dynamic programming (DP) algorithm is applied to automatically segment multivariate time series. The definition and recursive formulation of segment errors of univariate time series are extended to multivariate time series, so that DP algorithm is computationally viable for multivariate time series. The order of autoregression and segmentation are simultaneously determined by Schwarz's Bayesian information criterion. The segmentation procedure is evaluated with artificially synthesized and hydrometeorological multivariate time series. Synthetic multivariate time series are generated by threshold autoregressive model, and in real-world multivariate time series experiment we propose that besides the regression by constant, autoregression should be taken into account. The experimental studies show that the proposed algorithm performs well.
The concept of a super value node is developed to extend the theory of influence diagrams to allow dynamic programming to be performed within this graphical modeling framework. The operations necessary to exploit the ...
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The concept of a super value node is developed to extend the theory of influence diagrams to allow dynamic programming to be performed within this graphical modeling framework. The operations necessary to exploit the presence of these nodes and efficiently analyze the models are developed. The key result is that by representing value function separability in the structure of the graph of the influence diagram, formulation is simplified and operations on the model can take advantage of the separability. From the decision analysis perspective, this allows simple exploitation of separability in the value function of a decision problem. This allows algorithms to be designed to solve influence diagrams that automatically recognize the opportunity for applying dynamic programming. From the decision processes perspective, influence diagrams with super value nodes allow efficient formulation and solution of nonstandard decision process structures. They also allow the exploitation of conditional independence between state variables.
The paper presents a dynamic, discrete optimization model with returns in ordered structures. It generalizes multiobjective methods used in vector optimization in two ways: from real vector spaces to ordered structure...
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The paper presents a dynamic, discrete optimization model with returns in ordered structures. It generalizes multiobjective methods used in vector optimization in two ways: from real vector spaces to ordered structures and from the static model to the dynamic model. The proposed methods are based on isotone homomorphisms. These methods can be applied in dynamic programming with returns in ordered structures. The provided numerical example shows an application of fuzzy numbers and random variables with stochastic dominance in dynamic programming. The paper also proposes applications in the following problems: a problem of allocations in the market model, a location problem, a railway routing problem, and a single-machine scheduling problem. (C) 2010 Elsevier B.V. All rights reserved.
In this paper, the shortest path problem with forbidden paths is addressed. The problem under consideration is formulated as a particular instance of the resource-constrained shortest path problem. Different versions ...
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In this paper, the shortest path problem with forbidden paths is addressed. The problem under consideration is formulated as a particular instance of the resource-constrained shortest path problem. Different versions of a dynamic programming-based solution approach are defined and implemented. The proposed algorithms can be viewed as an extension of the node selection approach proposed by Desrochers in 1988. An extensive computational test is carried out on a meaningful number of random instances with the purpose of assessing the behaviour of the developed solution approaches. A comparison with the state-of-the-art method proposed to address the problem under study is also made. The computational results are very encouraging and highlight that the proposed algorithms are very efficient.
Least squares problems occur widely in regression analysis, parameterestimation, analytical mechanics, and in many other areas. In [1], we introduced a new dynamicprogramming approach to least squares problems. The al...
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Least squares problems occur widely in regression analysis, parameterestimation, analytical mechanics, and in many other areas. In [1], we introduced a new dynamicprogramming approach to least squares problems. The algorithm of that paper relied heavily onknowing the rank of the given matrix and knowing columns which are linearly independent. This paperextends the previous one by removing these restrictions. We develop a new algorithm which we callthe aQβR algorithm. This formulation introduces two cost functions, which is new to dynamicprogramming literature. The first cost function is the square of the length of the currentdiscrepancy vector, and the second is the square of the length of the current solution vector. Thetwo cost functions are to be minimized simultaneously by optimally selecting the minimum lengthvector solution. Finally, a connection with Greville's formula for generalized inverses isindicated.
This paper is devoted to the study of an extension of dynamic programming approach which allows sequential optimization of approximate decision rules relative to the length and coverage. We introduce an uncertainty me...
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This paper is devoted to the study of an extension of dynamic programming approach which allows sequential optimization of approximate decision rules relative to the length and coverage. We introduce an uncertainty measure R(T) which is the number of unordered pairs of rows with different decisions in the decision table T. For a nonnegative real number beta, we consider beta-decision rules that localize rows in subtables of T with uncertainty at most beta. Our algorithm constructs a directed acyclic graph Delta(beta)(T) which nodes are subtables of the decision table T given by systems of equations of the kind "attribute = value". This algorithm finishes the partitioning of a subtable when its uncertainty is at most beta. The graph Delta(beta)(T) allows us to describe the whole set of so-called irredundant beta-decision rules. We can describe all irredundant beta-decision rules with minimum length, and after that among these rules describe all rules with maximum coverage. We can also change the order of optimization. The consideration of irredundant rules only does not change the results of optimization. This paper contains also results of experiments with decision tables from UCI Machine Learning Repository. (C) 2012 Elsevier Inc. All rights reserved.
In power production problems maximum power and minimum entropy production and inherently connected by the Gouy-Stodola law. In this paper various mathematical tools are applied in dynamic optimization of power-maximiz...
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In power production problems maximum power and minimum entropy production and inherently connected by the Gouy-Stodola law. In this paper various mathematical tools are applied in dynamic optimization of power-maximizing paths, with special attention paid to nonlinear systems. Maximum power and/or minimum entropy production are governed by Hamilton-Jacobi-Bellman (HJB) equations which describe the value function of the problem and associated controls. Yet, in many cases optimal relaxation curve is non-exponential, governing HJB equations do not admit classical solutions and one has to work with viscosity solutions. Systems with nonlinear kinetics (e.g. radiation engines) are particularly difficult, thus, discrete counterparts of continuous HJB equations and numerical approaches arc recommended. Discrete algorithms of dynamic programming (DP), which lead to power limits and associated availabilities, are effective. We consider convergence of discrete algorithms to viscosity solutions of HJB equations, discrete approximations, and the role of Lagrange multiplier lambda associated with the duration constraint. In analytical discrete schemes, the Legendre transformation is a significant tool leading to original work function. We also describe numerical algorithms of dynamic programming and consider dimensionality reduction in these algorithms. Indications showing the method potential for other systems, in particular chemical energy systems, are given. (C) 2008 Elsevier Inc. All rights reserved.
This paper presents a nonserial dynamic programming formulation for the scheduling of linear projects with nonsequential activities. One of the major advantages of the approach presented is its ability to handle both ...
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This paper presents a nonserial dynamic programming formulation for the scheduling of linear projects with nonsequential activities. One of the major advantages of the approach presented is its ability to handle both serial and nonserial linear projects with activities performed with variable crew formations. The presented formulation determines the optimum crew size for production activities that lead to the minimum project total cost. An example project is provided in order to illustrate the computational steps, validate the calculation algorithm, and show the capabilities of the proposed method.
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