Showing papers on "Dynamic programming published in 1992"
TL;DR: In this article, the authors present a greedy algorithm for the active contour model, which has performance comparable to the dynamic programming and variational calculus approaches, but is more than an order of magnitude faster than that approach, being O(nm).
Abstract: A model for representing image contours in a form that allows interaction with higher level processes has been proposed by Kass et al. (in Proceedings of First International Conference on Computer Vision, London, 1987, pp. 259–269). This active contour model is defined by an energy functional, and a solution is found using techniques of variational calculus. Amini et al. (in Proceedings, Second International Conference on Computer Vision, 1988, pp. 95–99) have pointed out some of the problems with this approach, including numerical instability and a tendency for points to bunch up on strong portions of an edge contour. They proposed an algorithm for the active contour model using dynamic programming. This approach is more stable and allows the inclusion of hard constraints in addition to the soft constraints inherent in the formulation of the functional; however, it is slow, having complexity O(nm3), where n is the number of points in the contour and m is the size of the neighborhood in which a point can move during a single iteration. In this paper we summarize the strengths and weaknesses of the previous approaches and present a greedy algorithm which has performance comparable to the dynamic programming and variational calculus approaches. It retains the improvements of stability, flexibility, and inclusion of hard constraints introduced by dynamic programming but is more than an order of magnitude faster than that approach, being O(nm). A different formulation is used for the continuity term than that of the previous authors so that points in the contour are more evenly spaced. The even spacing also makes the estimation of curvature more accurate. Because the concept of curvature is basic to the formulation of the contour functional, several curvature approximation methods for discrete curves are presented and evaluated as to efficiency of computation, accuracy of the estimation, and presence of anomalies.
1,111 citations
TL;DR: This paper presents a new optimization algorithm capable of optimally solving 100-customer problems of the vehicle routing problem with time windows VRPTW and indicates that this algorithm proved to be successful on a variety of practical sized benchmark VRPTw test problems.
Abstract: The vehicle routing problem with time windows VRPTW is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service. In this paper, we present the development of a new optimization algorithm for its solution. The LP relaxation of the set partitioning formulation of the VRPTW is solved by column generation. Feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming. The LP solution obtained generally provides an excellent lower bound that is used in a branch-and-bound algorithm to solve the integer set partitioning formulation. Our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark VRPTW test problems. The algorithm was capable of optimally solving 100-customer problems. This problem size is six times larger than any reported to date by other published research.
1,085 citations
01 Jan 1992
820 citations
TL;DR: In this article, an iterative dynamic programming method for solving the economic dispatch problems of a system of thermal generating units including transmission line losses is presented along with a clear explanation of modifying generator cost functions during each iteration.
Abstract: An iterative dynamic programming method for solving the economic dispatch problems of a system of thermal generating units including transmission line losses is presented along with a clear explanation of modifying generator cost functions during each iteration A zoom feature is applied during the iterative process in order to converge to the economic dispatch solution with low computer time and storage requirements, Dynamic programming including a short-term load forecast is briefly discussed A three-generator example is used to illustrate the method Computer memory and time requirements are presented, along with results for a 15-unit system >
405 citations
TL;DR: In this paper, an optimization-based method for unit commitment using the Lagrangian relaxation technique is presented, which includes nondiscretization of generation levels, a systematic method to handle ramp rate constraints, and a good initialization procedure.
228 citations
01 Jun 1992
TL;DR: This work extends dynamic programming and shows how optimization metrics which correctly predict response time may be designed and observes that the response time optimization metric violates a fundamental assumption in the dynamic programming algorithm that is the linchpin in the optimizers of most commercial DBMSs.
Abstract: The decreasing cost of computing makes it economically viable to reduce the response time of decision support queries by using parallel execution to exploit inexpensive resources. This goal poses the following query optimization problem: Minimize response time subject to constraints on throughput, which we motivate as the dual of the traditional DBMS problem. We address this novel problem in the context of Select-Project-Join queries by extending the execution space, cost model and search algorithm that are widely used in commercial DBMSs. We incorporate the sources and deterrents of parallelism in the traditional execution space. We show that a cost model can predict response time while accounting for the new aspects due to parallelism. We observe that the response time optimization metric violates a fundamental assumption in the dynamic programming algorithm that is the linchpin in the optimizers of most commercial DBMSs. We extend dynamic programming and show how optimization metrics which correctly predict response time may be designed.
219 citations
TL;DR: In this article, a model for the optimization of machining conditions in a multi-pass turning operation is presented, where both rough cutting and finishing cutting are considered in the model and dual optimization of cost functions for each subproblem is pursued.
Abstract: This paper presents a model for the optimization of machining conditions in a multi-pass turning operation. Both rough cutting and finishing cutting are considered in the model and dual optimization of cost functions for each subproblem is pursued. The preventive tool replacement strategy used in practice is incorporated. Machining idle time is also regarded as a variable. After practical constraints are established, optimization is carried out using the dynamic programming method. An example illustrates the formulation of the problem and the optimization procedure
198 citations
TL;DR: Dynamic programming solutions to a number of different recurrence equations for sequence comparison and for RNA secondary structure prediction are considered, when the weight functions used in the recurrences are taken to be linear.
Abstract: Dynamic programming solutions to a number of different recurrence equations for sequence comparison and for RNA secondary structure prediction are considered. These recurrences are defined over a number of points that is quadratic in the input size; however only a sparse set matters for the result. Efficient algorithms for these problems are given, when the weight functions used in the recurrences are taken to be linear. The time complexity of the algorithms depends almost linearly on the number of points that need to be considered; when the problems are sparse this results in a substantial speed-up over known algorithms.
175 citations
11 Oct 1992
TL;DR: An adaptive boundary detection algorithm that uses two-dimensional dynamic programming (DP) is presented and accurately detects the boundaries of low contrast objects, which occur with intravenous injections, as well as those found in noisy, low SNR images.
Abstract: An adaptive boundary detection algorithm that uses two-dimensional dynamic programming (DP) is presented. The algorithm is less constrained than previous one-dimensional dynamic programming algorithms and allows the user to interactively determine the mathematically optimal boundary between a user-selected seed point and any other dynamically selected free point in the image. Interactive movement of the free point by the cursor causes the boundary to behave like a live wire as it adapts to the new minimum cost path between the seed point and the currently selected free point. The algorithm can also be adapted or customized to learn boundary-defining features for a particular class of images. Adaptive 2-D DP performs well on a variety of images. It accurately detects the boundaries of low contrast objects, which occur with intravenous injections, as well as those found in noisy, low SNR images. >
163 citations
TL;DR: It is shown that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time and a fully polynomial approximation scheme is proposed.
Abstract: We discuss a single-machine scheduling problem where the objective is to minimize the variance of job completion times. To date, the problem has not been solved in polynomial time. This paper presents a dynamic programming algorithm that is pseudopolynomial in complexity. We also propose a fully polynomial approximation scheme and derive a lower bound that is useful in its implementation. Furthermore, we show that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time.
122 citations
TL;DR: The experimental results indicate that the proposed algorithm can significantly reduce the execution time of the traditional dynamic programming approach without degrading the quality of the generation schedule.
Abstract: A hybrid dynamic programming-artificial neural network algorithm is studied. The proposed two-step process uses an artificial neural network to generate a preschedule according to the input load profile. A dynamic search is then performed at those stages where the commitment states of some of the units are not certain. The experimental results indicate that the proposed algorithm can significantly reduce the execution time of the traditional dynamic programming approach without degrading the quality of the generation schedule. >
TL;DR: Methods for calculating similarity scores and distances that use gap penalties of the form g = rk are discussed, which are much slower than the heuristic approach used by the RDF2 program and should take less than 1 hr to complete.
Abstract: Efficient dynamic programming algorithms are available for a broad class of protein and DNA sequence comparison problems. These algorithms require computer time proportional to the product of the lengths of the two sequences being compared [O(N2)] but require memory space proportional only to the sum of these lengths [O(N)]. Although the requirement for O(N2) time limits use of the algorithms to the largest computers when searching protein and DNA sequence databases, many other applications of these algorithms, such as calculation of distances for evolutionary trees and comparison of a new sequence to a library of sequence profiles, are well within the capabilities of desktop computers. In particular, the results of library searches with rapid searching programs, such as FASTA or BLAST, should be confirmed by performing a rigorous optimal alignment. Whereas rapid methods do not overlook significant sequence similarities, FASTA limits the number of gaps that can be inserted into an alignment, so that a rigorous alignment may extend the alignment substantially in some cases. BLAST does not allow gaps in the local regions that it reports; a calculation that allows gaps is very likely to extend the alignment substantially. Although a Monte Carlo evaluation of the statistical significance of a similarity score with a rigorous algorithm is much slower than the heuristic approach used by the RDF2 program, the dynamic programming approach should take less than 1 hr on a 386-based PC or desktop Unix workstation. For descriptive purposes, we have limited our discussion to methods for calculating similarity scores and distances that use gap penalties of the form g = rk. Nevertheless, programs for the more general case (g = q+rk) are readily available. Versions of these programs that run either on Unix workstations, IBM-PC class computers, or the Macintosh can be obtained from either of the authors.
TL;DR: Dynamic programming solutions to two recurrence equations, used to compute a sequence alignment from a set of matching fragments between two strings, and to predict RNA secondary structure, are considered.
Abstract: Dynamic programming solutions to two recurrence equations, used to compute a sequence alignment from a set of matching fragments between two strings, and to predict RNA secondary structure, are considered. These recurrences are defined over a number of points that is quadratic in the input size; however, only a sparse set matters for the result. Efficient algorithms are given for solving these problems, when the cost of a gap in the alignment or a loop in the secondary structure is taken as a convex or concave function of the gap or loop length. The time complexity of our algorithms depends almost linearly on the number of points that need to be considered; when the problems are sparse, this results in a substantial speed-up over known algorithms.
TL;DR: The test showed that dual dynamic programming has reasonable computing times and can be a useful tool in stochastic scheduling in a hydro-dominated system.
Abstract: The aim is to show an application of stochastic dual dynamic programming to seasonal planning in a part of the Norwegian hydro-dominated power system. The subsystem under study has 35 reservoirs on 28 watercourses. It is found that for the study system the new procedure is entirely feasible and gives good results. Two implementation details are studied more closely: use of relaxation in the solution of the subproblems, and a starting technique, called pre-segment, to save iterations in the overall problem. Both are found to have a significant effect on computer time. The test showed that dual dynamic programming has reasonable computing times and can be a useful tool in stochastic scheduling in a hydro-dominated system. >
TL;DR: In this paper, the authors investigated the facility layout problem under the two assumptions of changing demand and a constraint on the layout rearrangement funds, and proposed a new algorithm to solve the problem and compared to an extension of the old algorithm.
TL;DR: The parallel method provides rapid, high-resolution alignments for users of the software toolkit for pairwise sequence comparison, as illustrated here by a comparison of the chloroplast genomes of tobacco and liverwort.
Abstract: The local similarity problem is to determine the similar regions within two given sequences. We recently developed a dynamic programming algorithm for the local similarity problem that requires only space proportional to the sum of the two sequence lengths, whereas earlier methods use space proportional to the product of the lengths. In this paper, we describe how to parallelize the new algorithm and present results of experimental studies on an Intel hypercube. The parallel method provides rapid, high-resolution alignments for users of our software toolkit for pairwise sequence comparison, as illustrated here by a comparison of the chloroplast genomes of tobacco and liverwort.
06 Jan 1992
TL;DR: This paper presents a classification of dynamic programming problems and surveys efficient algorithms based on the three conditions: convexity, concavity and sparsity.
Abstract: Dynamic programming is a general problem-solving technique that has been widely used in various fields such as control theory, operations research, biology and computer science. In many applications dynamic programming problems satisfy additional conditions of convexity, concavity and sparsity. This paper presents a classification of dynamic programming problems and surveys efficient algorithms based on the three conditions.
TL;DR: It is demonstrated that bounds for optimal multiple alignment of k sequences can be derived from a solution of the maximum weighted matching problem in a k-vertex graph.
Abstract: Multiple sequence alignment is an important problem in computational molecular biology. Dynamic programming for optimal multiple alignment requires too much time to be practical. Although many algorithms for suboptimal alignment have been suggested, no “performance guarantees” algorithms have been known until recently. A computationally efficient approximation multiple alignment algorithm with guaranteed error bounds equal to the normalized communication cost of a corresponding graph is given in this paper. Recently, Altschul and Lipman [SIAM J. Appl. Math., 49 (1989), pp. 197–209] used suboptimal alignments for reducing the computational complexity of the optimal alignment algorithm. This paper develops the Altschul–Lipman approach and demonstrates that bounds for optimal multiple alignment of k sequences can be derived from a solution of the maximum weighted matching problem in a k-vertex graph. Fast maximum matching algorithms allow efficient implementation of dynamic bounds for the multiple alignment ...
01 Jan 1992
TL;DR: This paper considers the three-dimensional problem of optimal packing of a container with rectangular pieces and proposes an approximation algorithm based on the “forward state strategy” of dynamic programming.
Abstract: In this paper we consider the three-dimensional problem of optimal packing of a container with rectangular pieces. We propose an approximation algorithm based on the “forward state strategy” of dynamic programming. A suitable description of packings is developed for the implementation of the approximation algorithm, and some computational experience is reported.
01 Jan 1992
TL;DR: In this article, the authors presented an algorithm which combines the linear prograining with the dynamic programing to solve the problem of fleet planning, which has not only the merits that the linear model for fleet planning has, but also the merit of saving computing time.
Abstract: By analyzing the merits and shortcomings of the linear model for fleet planning, the paper presents an algorithm which combines the linear prograining with the dynamic programing to solve the problem of fleet planning. This approach has not only the merits that the linear model for fleet planning has, but also the merit of saving computing time. And the number of any kind of ships newly added into the fleet in every year are always integers in the last optimal results. This feature of the results directly meets the demand of practical application.The mathematic model of the dynamic fleet planning and its algorithm are both put forward in the paper. A calculating example is also given in the paper.
TL;DR: The use of iterative dynamic programming employing systematic region contraction and accessible grid points is investigated for the optimal control of time-delay systems and the results compare very favourably with those reported in the literature using other computational procedures.
Abstract: The use of iterative dynamic programming employing systematic region contraction and accessible grid points is investigated for the optimal control of time-delay systems. At the time of generating the grid points for the state variables, the corresponding delayed variables at each time stage are also generated and stored in memory. Then, when applying dynamic programming, a linear approximation is used to obtain the initial profile for the delayed variables during integration. This procedure was tested with four problems of different complexity. In each case the optimal control policy is easily obtained and the results compare very favourably with those reported in the literature using other computational procedures.
TL;DR: In this article, the convergence properties of an iterative dynamic programming algorithm are examined by considering a singular optimal control problem involving five differential equations, and it is shown that even with a relatively coarse grid, convergence to the optimal control policy is rapid.
Abstract: The convergence properties of an iterative dynamic programming algorithm are examined by considering a singular optimal control problem involving five differential equations. Even with a relatively coarse grid, convergence to the optimal control policy is rapid. The procedure is easy to program, and the computations can be easily done on a personal computer. >
TL;DR: An interactive optimization system for multiperiod exhaust relief planning in the local loop of a public telephone network is described, which decomposes the optimization problem into a single-period dynamic programming problem, and a multiperiod greedy heuristic.
Abstract: We describe an interactive optimization system for multiperiod exhaust relief planning in the local loop of a public telephone network. In exhaust relief planning in the local loop one seeks the minimum cost capacity expansion plan that meets projected demand over a given planning horizon. The problem can be modeled as an integer programming problem. However, due to cost structures and varying transmission technologies, the single-period exhaust relief planning problem is NP-complete. The size of the problem precludes the use of general purpose integer programming. Based on the mathematical structure and complexity of the problem, we decompose the optimization problem into a single-period dynamic programming problem, and a multiperiod greedy heuristic. A software system surrounds the optimization algorithm and provides interactive planning capabilities, before and after creation of the optimized plan. Important aspects of the system are the model assumptions made to keep the problem tractable, and their effect on the standardization of input data and methodology. The system is in use by several hundred outside plant planners in a major U.S. telephone company. An overview of major elements of the package is given as well as a summary of important implementation issues that arose during the first three years of the on-going project.
01 Apr 1992
TL;DR: In this article, the dual approach to dynamic programming for the generalized problem of Bolza is described, and a suitable verification theorem is proved and a dual optimal feedback control is introduced, which is used in our work.
Abstract: The dual approach to dynamic programming for the generalized problem of Bolza is described. A suitable verification theorem is proved and a dual optimal feedback control is introduced
01 Jan 1992
TL;DR: A particular neural architecture is presented, which is based on what has been called the “Linear-Structure Preserving Principle” (the LISP principle), and backpropagation is applied to derive the optimal values of the synaptic weights.
Abstract: This paper deals with the problem of designing closed-loop feed-forward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods (e.g., dynamic programming, maximum principle, etc.) are difficult to apply. Then, an approximate solution is sought by constraining control strategies to take on the structure of multi-layer feed-forward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the “Linear-Structure Preserving Principle” (the LISP principle). The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to non-LQ problems show the effectiveness of the proposed method.
10 May 1992
TL;DR: A heuristic algorithm based on Lagrangian optimization and using an operational rate-distortion framework that, with much-reduced computing complexity, approaches the optimally achievable SNR is provided.
Abstract: The description of the buffer-constrained quantization problem is formalized. For a given set of admissible quantizers for coding a discrete nonstationary signal sequence in a buffer-constrained environment, and for any global distortion minimization criterion that is additive over the individual elements of the sequence, the optimal solution and slightly suboptimal but much faster approximations are formulated. The problem is first defined as one of constrained, discrete optimization, and its equivalence to some problems in integer programming is established. Dynamic programming using the Viterbi algorithm is shown to provide a way of computing the optimal solution. A heuristic algorithm based on Lagrangian optimization and using an operational rate-distortion framework that, with much-reduced computing complexity, approaches the optimally achievable SNR is provided. >
TL;DR: This work presents an alternative dynamic programming algorithm with pseudopolynomial complexity for the problem of minimizing total weighted completion time on parallel identical machines that is polynomial in the sum of all job weights.
TL;DR: A comparison of two search strategies for finding the optimal path, dynamic programming and heuristic search, is presented, based on theoretical considerations and experimental tests on a digit string task.
Abstract: A most successful approach to recognizing continuous speech is to model the recognition problem as one of finding an optimal path through a finite state network. A comparison of two search strategies for finding the optimal path, dynamic programming and heuristic search, is presented. The comparison is based on theoretical considerations and experimental tests on a digit string task. >