Showing papers on "Dynamic programming published in 1981"

A comparative study of several dynamic time-warping algorithms for connected-word recognition

Abstract: Several different algorithms have been proposed for time registering a test pattern and a concatenated (isolated word) sequence of reference patterns for automatic connected-word recognition. These algorithms include the two-level, dynamic programming algorithm, the sampling approach and the level-building approach. In this paper, we discuss the theoretical differences and similarities among the various algorithms. An experimental comparison of these algorithms for a connected-digit recognition task is also given. The comparison shows that for typical applications, the level-building algorithm performs better than either the two-level DP matching or the sampling algorithm.

Optimal short-term scheduling of large-scale power systems

Abstract: This paper is concerned with the long-standing problem of optimal unit commitment in an electric power system. We follow the traditional formulation of this problem which gives rise to a large-scale, dynamic, mixed-integer programming problem. We describe a solution methodology based on duality, Lagrangian relaxation, and nondifferentiable optimization that has two unique features. First, computational requirements typically grow only linearly with the number of generating units. Second, the duality gap decreases in relative terms as the number of units increases, and as a result our algorithm tends to actually perform better for problems of large size. This allows for the first time consistently reliable solution of large practical problems involving several hundreds of units within realistic time constraints. Aside from the unit commitment problem, this methodology is applicable to a broad class of large-scale dynamic scheduling and resource allocation problems involving integer variables.

Surrogate Constraints Algorithm for Reliability Optimization Problems with Multiple Constraints

Abstract: This paper presents a surrogate constraints algorithm for solving nonlinear programming, nonlinear integer programming, and nonlinear mixed integer programming problems. The algorithm contains a new technique for generating a succession of vector values of surrogate multiplier (ie, surrogate problems). By using this technique, a computer can keep a polyhedron, which is a vector space of surrogate multipliers to be considered at a certain time, in its memory. Furthermore it can cut the polyhedron by a given hyperplane, and produce the remaining space as the next polyhedron. Simple examples are included.

Breaking paragraphs into lines

Abstract: This paper discusses a new approach to the problem of dividing the text of a paragraph into lines of approximately equal length. Instead of simply making decisions one line at a time, the method considers the paragraph as a whole, so that the final appearance of a given line might be influenced by the text on succeeding lines. A system based on three simple primitive concepts called ‘boxes’, ‘glue’, and ‘penalties’ provides the ability to deal satisfactorily with a wide variety of typesetting problems in a unified framework, using a single algorithm that determines optimum breakpoints. The algorithm avoids backtracking by a judicious use of the techniques of dynamic programming. Extensive computational experience confirms that the approach is both efficient and effective in producing high-quality output. The paper concludes with a brief history of line-breaking methods, and an appendix presents a simplified algorithm that requires comparatively few resources.

Distributed dynamic programming

Abstract: We consider distributed algorithms for solving dynamic programming problems whereby several processors participate simultaneously in the computation while maintaining coordination by information exchange via communication links. A model of asynchronous distributed computation is developed which requires very weak assumptions on the ordering of computations, the timing of information exchange, the amount of local information needed at each computation node, and the initial conditions for the algorithm. The class of problems considered is very broad and includes shortest path problems, and finite and infinite horizon stochastic optimal control problems. When specialized to a shortest path problem the algorithm reduces to the algorithm originally implemented for routing of messages in the ARPANET.

Stochastic dynamic programming: Caution and probing

Abstract: The purpose of this paper is to unify the concepts of caution and probing put forth by Feldbaum [14] with the mathematical technique of stochastic dynamic programming originated by Bellman [5]. The decomposition of the expected cost in a stochastic control problem, recently developed in [8], is used to assess quantitatively the caution and probing effects of the system uncertainties on the control. It is shown how in some problems, because of the uncertainties, the control becomes cautious (less aggressive) while in other problems it will probe (by becoming more aggressive) in order to enhance the estimation/identification while controlling the system. Following this a classification of stochastic control problems according to the dominant effect is discussed. This is then used to point out which are the stochastic control problems where substantial improvements can be expected from using a sophisticated algorithm versus a simple one.

Heuristic Techniques for Simultaneous Scheduling of Production and Distribution in Multi-Echelon Structures: Theory and Empirical Comparisons

Abstract: Seven heuristic algorithms are discussed. Each can be used for production scheduling in an assembly network a network where each work station has at most one immediate successor work station, but may have any number of immediate predecessor work stations, distribution scheduling in an arborescence network a network where each warehouse or stocking point is supplied by at most one immediate predecessor stocking point, but may itself supply any number of immediate successor stocking points, and joint production-distribution scheduling in a conjoined assembly-arborescence network. The objective of each algorithm is to determine a production and/or product distribution schedule which satisfies final product demand and minimizes the sum of the average inventory holding costs and average fixed charges for processing ordering, delivery, or setup costs, per period, over an infinite planning horizon. Exogenous demand for product is assumed to be deterministic, at a constant rate, and to occur only at "retail" facilities of the networks. On the basis of their performance in 11,000 computer generated problems, the seven heuristic methods are compared with each other and with a dynamic programming algorithm. The results indicate that for most of the network structures considered, the best heuristic is the method of steepest descent; the second best is a simple extension of a method originally developed by Crowston, Wagner, and Henshaw. The improved myopic procedure of Graves and Schwarz performs very well for some particular types of structures. Surprisingly, two particularly naive heuristics also perform quite well in certain situations. In addition to the computer simulation experiments, we also discuss a simple computer-compatible algebraic notation scheme for identifying structure facility interrelationships within networks of the three types considered.

Arm-Acquiring Bandits

Abstract: We consider the problem of allocating effort between projects at different stages of development when new projects are also continually appearing. An expression (14) is derived for the expected reward yielded by the Gittins index policy. This is shown to satisfy the dynamic programming equation for the problem, so confirming optimality of the policy.

Optimal short-term hydro scheduling from the principle of progressive optimality

Abstract: This paper presents an algorithm based on the principle of progressive optimality for determining the optimal short-term scheduling of multireservoir power systems; the method takes into account water head variations, spilling, and time delays between upstream and downstream reservoirs. The method is computationally efficient and has minimal storage requirements. The convergence is monotonic and a global solution is reached. Contrary to dynamic programing, the state variables do not have to be discretized with this method. An example consisting of four hydroplants in series is solved, and the results are presented.

Surrogate Constraints Algorithm forReliability Optimization Problems withTwoConstraints

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On the One-Dimensional Space Allocation Problem

Abstract: The One-Dimensional Space Allocation Problem ODSAP arises when locating rooms along a corridor, when setting books on a shelf, when allocating information items among the "cylinders" of a magnetic disk, or when storing products in certain warehouses The rooms objects to be located have a known length or width and, for each pair of rooms, there is a given number of "trips" between them; the problem is to find a sequencing of the rooms which minimizes the total traveled distance This paper deals first with two particular cases In the rooted tree case, previous results obtained by Adolphson and T C Hu for the Linear Ordering Problem are extended and provide efficient solution methods In addition, it is shown that most of the assumptions made by Adolphson and Hu are necessary, since relaxing any of them leads to an NP-complete problem In the case of independent destinations solved by Bergmans and Pratt when all lengths are equal, a unimodality property is shown for an optimum solution, but this is not sufficient to lead to a "good" algorithm and the problem is shown to be NP-complete For the general problem, an exact algorithm using dynamic programming is described and computationally tested

Multicriteria integer programming: A (hybrid) dynamic programming recursive approach

Abstract: Dynamic programming recursive equations are used to develop a procedure to obtain the set of efficient solutions to the multicriteria integer linear programming problem. An alternate method is produced by combining this procedure with branch and bound rules. Computational results are reported.

Scheduling Jobs with Linear Delay Penalties and Sequence Dependent Setup Costs

Abstract: We discuss the problem of minimizing the sum of the setup costs and linear delay penalties when N jobs, arriving at time zero, are to be scheduled for sequential processing on a continuously available machine. The delay penalty for each job is a nondecreasing linear function of the sum of the various processing times for preceding jobs. The setup cost for each job is dependent only upon the job that immediately precedes it. The equivalence of the traveling salesman problem to the setup portion of this problem creates a special challenge. The application of several Branch-and-Bound algorithms using various branching rules is discussed. Since the problem has a highly attractive Dynamic Programming formulation, a hybrid algorithm analogous to Morin and Marsten's Dynamic Programming/Branch-and-Bound approach to the traveling salesman problem is also utilized. This technique, detailed in the paper, applies a fathoming criterion to the states of the Dynamic Program in order to drastically reduce memory and comp...

Assembly line balancing algorithms: computation comparisons

Abstract: A comparative investigation is performed on the (optimizing) algorithms which have appeared in the literature to solve the basic assembly line balancing problem. Each algorithm is subjected to a series of test problems, and the computation times are noted It was observed that problems of 20 tasks were within the capabilities of most algorithms studied. Solutions could he found for 40-task problems if the average number of tasks per station was no more than four. For the 20-task problems, branch and bound algorithms performed the best for problems with four or more tasks per station, while a particular dynamic programming formulation performed best on problems with an average of two tasks per station Details of a newest node search branch and bound algorithm, where arcs represent stations is presented. This algorithm performed successfully in the investigation.

Aspects of dynamic programming in signal and image processing

Abstract: The techniques peculiar to dynamic programming have found a variety of successful applications in the theory and practice of modern control. Successes in the theory and practice of signal and image processing are less numerous and prominent, but they do exist. In this paper, we sound a call for renewed attention to the potential of dynamic programming for solving knotty, nonlinear filtering problems in signal and image processing, and outline successes we have recently enjoyed in nonlinear frequency tracking and random boundary estimation in noisy black and white images. Two classical results, the fast Fourier transform and Levinson's recursion for determining autoregressive parameters, are treated in the context of dynamic programming simply to reinforce the point that many of the algorithms we take for granted, and which were derived without recourse to dynamic programming, can be nicely interpreted as dynamic programming algorithms.

Dynamic Programming and the Calculus of Variations

Abstract: This chapter focuses an optimization problem, where a set X will consist of a set of functions. It presents the definition of a functional on Ζ as a function J (·) such that to each function in X , it associates a single real number. It is the optimization of functional that constitutes the class of problems that is analyzed and solved by the calculus of variations. The chapter discusses computational solution of variational problems by dynamic programming. It describes the use of the Euler–Lagrange equation. The chapter also discusses the way in which a variation differs from a differential.

Scheduling of Generation and Reserve Margin Using Dynamic and Linear Programming

Abstract: It has become common practice to schedule generation over time by using dynamic programming techniques that compare the economic dispatch of different combinations of generating units at one hour intervals. Recently, a linear programming technique for economic dispatch has been developed that optimally dispatches generation such that reserve margins and ramp rate constraints are also met at minimum cost. This paper presents a method that combines these dynamic and linear programming techniques such that the real operational constraints of reserve margins and ramp rates are optimally met by the resulting generation schedules. A major advantage of this method is that it can be used to determine the minimum cost of providing a particular level of reserves or operating with a particular set of ramp rate capabilities. Such a costing method makes it feasible to make economic decisions on whether to buy or sell regulation or spinning margin, or whether to install new ramping capability. The algorithm, program design, and the results for a large midwestern utility are presented.

Optimal Hydrothermal Scheduling with Cascaded Plants Using Progressive Optimality Algorithm

Abstract: This paper presents an application of the 'Progressive Optimality Algorithm' (POA) to the problem of short range optimal hydrothermal scheduling in a power system consisting of ca. caded plants with time delay. Head variation and constraints imposed due to equipment ratings and operating conditions on hydro as well as thermal-electric subsystems have been considered. Electrical subsystem has been represented in detail through ac power flows. Resulbs for a sample 5 bus system consisting of two hydro (cascaded) and two thermal stations clearly reveal the simplicity, effectiveness and distinct superiority of the progressive optamility algorithm over many of the existing techniques. The algorithm requires minimal storage and is extremely fast. It is envisaged thst POA technique would greatly appeal to the utility engineers for practical application.

Segmenting speech using dynamic programming

Abstract: Speech is modeled as a Markov chain. Scoring is developed to convert observations of the speech signal into estimated probabilities of the locations of segment boundaries. Dynamic programming is then used to compute a most‐probable segmentation for the speech. The process automatically adjusts to speakers and incorporates a priori information in a probabilistic and systematic fashion. The performance of the algorithm appears to be state‐of‐the‐art, independent of speaker.

Matrix reorganization and dynamic programming: Applications to paired comparisons and unidimensional seriation

Abstract: A recursive dynamic programming strategy is discussed for optimally reorganizing the rows and simultaneously the columns of ann ×n proximity matrix when the objective function measuring the adequacy of a reorganization has a fairly simple additive structure. A number of possible objective functions are mentioned along with several numerical examples using Thurstone's paired comparison data on the relative seriousness of crime. Finally, the optimization tasks we propose to attack with dynamic programming are placed in a broader theoretical context of what is typically referred to as the quadratic assignment problem and its extension to cubic assignment.

A multiobjective dynamic programming method for capacity expansion

Abstract: This paper integrates two existing methodologies-a single-objective dynamic programming method for capacity expansion and the surrogate worth tradeoff (SWT) method for optimizing multiple objectives -into a unified schema. In particular it shows 1) how a multiobjective mixed integer programming formulation representing the multiobjective capacity expansion problem can be translated into a multiobjective dynamic programming formulation, 2) how such DP formulation can be used to generate noninferior solutions, and 3) how tradeoff information can be obtained from solutions in 2). The necessary theoretical machinery for 3) is developed. To demonstrate the computational viability of the proposed schema, an example problem is formulated and solved.

A dynamic programming technique for nonlinear smoothing

Abstract: This paper describes an optimization approach to the nonlinear smoothing problem. Linear techniques of smoothing do not yield satisfactory results for curves which exhibit both sharp discontinuities to be preserved and incorrect samples to be filtered out. The presented nonlinear approach employs the concept of a cost function which penalizes for large variations between two consecutive samples and rewards for close vicinity between them. The overall cost is used as a criterion of optimality. The optimization is carried out by a dynamic programming strategy. The resulting algorithm requires only very moderate computational costs. Examples of the application of the non-linear smoothing to pitch period contours are presented.

Analysis of a Preference Order Assembly Line Problem

Abstract: An analysis is made of a preference order dynamic programming procedure proposed in the literature for stochastic assembly line balancing problems. It is shown that in general the procedure does not satisfy the monotonicity condition and that therefore there is no guarantee that the solutions will be optimal. It is also shown that for a certain class of problems for which the procedure does yield optimal solutions, the proposed preference order model can be reformulated as a regular dynamic programming model.

A Dynamic Programming Approach to Machine Requirements Planning

Abstract: This paper presents an approach to determining the optimum number of machines, and their operating rates, for each machine center in a serial-flow production system. Computational comparisons are given to solve this problem using dynamic programming and a standard mixed-integer programming package.

Optimal Exploration and Consumption of a Natural Resource Deterministic Case

Abstract: An exploration and consumption model for exhaustible natural resources is used to formulate a deterministic optimal control problem over an infinite time horizon. A dynamic programming approach is employed throughout. The non-linear partial differential equation which results from an application of the necessary conditions is solved analytically by the method of characteristics. Several properties of the solution are discussed.

The dynamic linear exponential Gaussian team problem

Abstract: The dynamic team problem for a linear system with Gaussian noise, exponential of a quadratic performance index, and one-step delayed sharing information pattern is considered. It is shown, via dynamic programming, that the multistage problem can be decomposed into a series of static team problems. Moreover, the optimal policy of the i th team member at time k is an affine function of both the one-step predicted Kalman filter estimate and the i th team member's observation at time k . Efficient algorithms are available for determining the gains of this affine controller. This model and solution are applied to an approximate resource allocation problem associated with a defense network, and a numerical example is discussed.

Optimal control of a class of nonlinear stochastic systems

Abstract: Bellman's principle of optimality and dynamic programming are shown to be the basis for solution of a physically significant class of nonlinear stochastic control problems. Various previous results are integrated into a survey here, and a new result which extends the separation principle is presented. Certain bilinear and linear-in-control systems are included in the analysis.

A Probabilistic Production Costing Methodology for Systems with Storage

Abstract: Using the concept of an Expected Incremental Generation Cost Curve (EIGC), a new probabilistic production cost methodology is presented. This method, somewhat related to the Baleriaux-Booth equivalent load concept, is useful for production costing in both traditional systems and those involving storage. In fact, the probabilistic storage-thermal scheduling problem is shown to reduce to a deterministic scheduling problem easily solved using a linear programming approach.