Showing papers on "Dynamic programming published in 1986"
TL;DR: In this article, the authors present a solution to the problem of minimizing the cost of moving a robotic manipulator along a specified geometric path subject to input torque/force constraints, taking the coupled, nonlinear dynamics of the manipulator into account.
Abstract: This paper presents a solution to the problem of minimizing the cost of moving a robotic manipulator along a specified geometric path subject to input torque/force constraints, taking the coupled, nonlinear dynamics of the manipulator into account. The proposed method uses dynamic programming (DP) to find the positions, velocities, accelerations, and torques that minimize cost. Since the use of parametric functions reduces the dimension of the state space from 2n for an n - jointed manipulator, to two, the DP method does not suffer from the "curse of dimensionality." While maintaining the elegance of our previous trajectory planning method, we have developed the DP method for the general case where 1) the actuator torque limits are dependent on one another, 2) the cost functions can have an arbitrary form, and 3) there are constraints on the jerk, or derivative of the acceleration. Also, we have shown that the DP solution converges as the grid size decreases. As numerical examples, the trajectory planning method is simulated for the first three joints of the PACS arm, which is a cylindrical arm manufactured by the Bendix Corporation.
367 citations
TL;DR: Both optimal and heuristic procedures are developed for this problem and are based on a dynamic programming formulation, which depends on the ability to solve the static problem efficiently.
Abstract: The problem of plant layout has generally been treated as a static one. In this paper, we deal with the dynamic nature of this problem. Both optimal and heuristic procedures are developed for this problem and are based on a dynamic programming formulation. The use of one of these approaches depends on the ability to solve the static problem efficiently. Finally, we briefly discuss the issue of extending the planning horizon, and how to resolve system nervousness when previously planned layouts need to be changed.
313 citations
TL;DR: The single-vehicle dial-a-ride problem with time window constraints for both pick-up and delivery locations, and precedence and capacity constraints, is solved using a forward dynamic programming algorithm.
Abstract: SYNOPTIC ABSTRACTThe single-vehicle dial-a-ride problem with time window constraints for both pick-up and delivery locations, and precedence and capacity constraints, is solved using a forward dynamic programming algorithm. The total distance is minimized. The development of criteria for the elimination of infeasible states results in solution times which increase linearly with problem size.
260 citations
TL;DR: A dynamic programming approach to select optimally among a given set of products and allocate integer shelf-space units to the selected products in supermarkets is proposed and a primary focus is on the development of a tractable model approach that can effectively be implemented on a microcomputer.
Abstract: A dynamic programming approach is proposed to select optimally among a given set of products and allocate integer shelf-space units to the selected products in supermarkets. The approach is designed to consider general objective-function specifications that account for space elasticity, costs of sales, and potential demand-related marketing variables. The optimization is subject to constraints due to product supply availability, 'block' product allocation and operational requirements. A primary focus is on the development of a tractable model approach that can effectively be implemented on a microcomputer. A discussion of applications and computational experience on a microcomputer is provided to support the practical applicability of the optimization approach.
151 citations
TL;DR: A dynamic programming approach is proposed to solve the complete set partitioning problem, which has time complexityO(3 m ), wheren=2 m −1 is the size of the problem space.
Abstract: The complete set partitioning (CSP) problem is a special case of the set partitioning problem where the coefficient matrix has 2
m
−1 columns, each column being a binary representation of a unique integer between 1 and 2
m
−1,m⩾1. It has wide applications in the area of corporate tax structuring in operations research. In this paper we propose a dynamic programming approach to solve the CSP problem, which has time complexityO(3
m
), wheren=2
m
−1 is the size of the problem space.
137 citations
TL;DR: New dynamic programming algorithms are presented which reduce the required computation and the first polynomial time algorithm is given for predicting general secondary structure.
111 citations
TL;DR: The optimal ordering policy for impulse control of a one-product inventory system subject to a demand modelised by a diffusion process is analyzed to minimize the expected discounted cost that includes a fixed set-up cost and linear costs of purchase, storage and shortage.
Abstract: We analyse the optimal ordering policy for impulse control of a one-product inventory system subject to a demand modelised by a diffusion process The purpose is to minimize the expected discounted cost that includes a fixed set-up cost and linear costs of purchase, storage and shortage The optimal cost is explicitly obtained as the smoothest solution of a Quasi-Variational Inequality derived from the optimal principle of Dynamic Programming The optimal s, S policy is determined as the unique solution of a system of algebraic equations
104 citations
Book•
01 Aug 1986
TL;DR: In this article, the authors present a dual of a dynamic inventory control model: the deterministic case and the stochastic case, and present a list of optimization problems for both cases.
Abstract: 1 Introduction and Summary.- 2 Mathematical Programming and Duality Theory.- 3 Stochastic Linear Programming Models.- 4 Some Linear Programs in Probabilities and Their Duals.- 5 On Integrated Chance Constraints.- 6 On The Behaviour of the Optimal Value Operator of Dynamic Programming.- 7 Robustness against Dependence in Pert.- 8 A Dual of a Dynamic Inventory Control Model: The Deterministic and the Stochastic Case.- List of Optimization Problems.
99 citations
TL;DR: This paper describes a dynamic programming algorithm for aligning three sequences at a time that uses an effective technique for memory management, which is applicable to a wide range of sequence-matching methods.
95 citations
TL;DR: A dynamic programming algorithm is presented that can determine optimal and suboptimal secondary structures for an RNA and is demonstrated in the folding of the intervening sequence of the rRNA of Tetrahymena.
Abstract: Dynamic programming algorithms that predict RNA secondary structure by minimizing the free energy have had one important limitation. They were able to predict only one optimal structure. Given the uncertainties of the thermodynamic data and the effects of proteins and other environmental factors on structure, the optimal structure predicted by these methods may not have biological significance. We present a dynamic programming algorithm that can determine optimal and suboptimal secondary structures for an RNA. The power and utility of the method is demonstrated in the folding of the intervening sequence of the rRNA of Tetrahymena. By first identifying the major secondary structures corresponding to the lowest free energy minima, a secondary structure of possible biological significance is derived.
78 citations
TL;DR: The present paper gives conditions under which convergence to the stationary policy is assured, and hinges upon a notion which it is referred to as the "stagewise" Kuhn-Tucker condition.
Abstract: The intention of this work is to describe and examine a differential dynamic programming (DDP) algorithm for constrained, discrete-time optimal control. This algorithm has performed successfully on a large-scale reservoir control problem [11]. The present paper gives conditions under which convergence to the stationary policy is assured. The convergence demonstration hinges upon a notion which we refer to as the "stagewise" Kuhn-Tucker condition. Strategies generated to satisfy this condition determine policies which satisfy the conventional Kuhn-Tucker condition. This observation may be of wider importance in discrete optimal control theory, for the stagewise condition might be a convenient criterion for constructing strategies.
TL;DR: In this article, a general dynamic programming algorithm for the solution of optimal stochastic control problems concerning a class of discrete event systems is presented, where the emphasis is put on the numerical technique used for the approximation of the dynamic programming equation.
Abstract: This paper presents a general dynamic programming algorithm for the solution of optimal stochastic control problems concerning a class of discrete event systems. The emphasis is put on the numerical technique used for the approximation of the solution of the dynamic programming equation. This approach can be efficiently used for the solution of optimal control problems concerning Markov renewal processes. This is illustrated on a group preventive replacement model generalizing an earlier work of the authors.
TL;DR: A state transition model for the optimization of query processing in a distributed database system that permits significant reductions of the necessary computations by taking advantage of simple additivity and site-uniformity properties of a cost model and of clever strategies that improve on the basic dynamic programming algorithm.
Abstract: A state transition model for the optimization of query processing in a distributed database system is presented. The problem is parameterized by means of a state describing the amount of processing that has been performed at each site where the database is located. A state transition occurs each time a new join or semijoin is executed. Dynamic programming is used to compute recursively the costs of the states and the globally optimal solution, taking into account communication and local processing costs. The state transition model is general enough to account for the possibility of parallel processing among the various sites, as well as for redundancy in the database. The model also permits significant reductions of the necessary computations by taking advantage of simple additivity and site-uniformity properties of a cost model, and of clever strategies that improve on the basic dynamic programming algorithm.
TL;DR: In this paper, a 2-phase solution method is presented for solving a class of reliability optimization problems with multiple-choice constraints, where at least one design alternative can be chosen as redundancy for each subsystem.
Abstract: This paper presents a class of reliability optimization problems with multiple-choice constraints. We assume that at least one design alternative can be chosen as redundancy for each subsystem. A 2-phase solution method is presented for solving these problems. In phase I, we decompose a problem into n subproblems. These subproblems can be solved by dynamic programming, independently. That is, these subproblems can be solved by parallelism. In phase II, we solve a 0-1 multiple-choice knapsack problem which is generated from phase I. We use a combinatorial tree which always satisfies the multiple-choice constraints. The 2-phase solution method is illustrated with a numerical example.
TL;DR: It is argued that a failure to recognize the special features of the model in the context of which the principle was stated has resulted in the latter being misconstrued in the dynamic programming literature.
Abstract: New light is shed on Bellman's principle of optimality and the role it plays in Bellman's conception of dynamic programming. It is argued that a failure to recognize the special features of the model in the context of which the principle was stated has resulted in the latter being misconstrued in the dynamic programming literature.
TL;DR: It is shown that when the state space is finite the computation of the dynamic allocation indices can be handled by linear programming methods.
Abstract: We consider the multi-armed bandit problem. We show that when the state space is finite the computation of the dynamic allocation indices can be handled by linear programming methods.
TL;DR: The combination of dynamic programming with partial-order decomposition algorithms enables us to solve sequencing problems in polynomial time for substantially larger classes of precedence constraints than previously realized.
Abstract: We show that the combination of dynamic programming with partial-order decomposition algorithms enables us to solve sequencing problems in polynomial time for substantially larger classes of precedence constraints than previously realized. The algorithm's efficiency depends on the maximum number of jobs that are not related by the precedence constraints in certain subsets of the jobs. We also demonstrate how to modify this general algorithm lo take advantage of special problem characteristics.
TL;DR: The optimal paths selected by the branch‐and‐bound search algorithm augmented with dynamic programming are investigated in detail with respect to what information about the dynamics they may contain.
Abstract: A new, systematic method for selecting the most important basis functions by using an artificial intelligence tree pruning algorithm is introduced. The technique can be applied to any physical problem which gives rise to coupled equations but is applicable in general to any problem which could benefit from an orderly exploration of linked alternatives in a decision tree. The method is applied here to select the most important states for modeling the multiphoton dynamics of a general vibrating–rotating spherical top molecule. The optimal paths selected by the branch‐and‐bound search algorithm augmented with dynamic programming are investigated in detail with respect to what information about the dynamics they may contain.
TL;DR: In this article, sampling is introduced as a way to study control and estimation questions for the linear hereditary (delay) systems, and the formulation of the quadratic cost (discrete-time version) and the possibility of computer implementation of the control algorithm are discussed.
Abstract: Sampling is introduced as a way to study control and estimation questions for the linear hereditary (delay) systems. Special emphasis is given to the formulation of the quadratic cost (discrete-time version) and the possibility of computer implementation of the control algorithm. The simplifying assumption for computer implementation is that the control value is to remain constant between the sampling times. The techniques of optimization associated with dynamic programming then provide the recurrence relationships from which the feedback gains of the controller can be determined.
01 Jan 1986
TL;DR: This paper describes a new instruction selection algorithm, and its prototype implementation, based on bottom-up tree pattern-matching, which is capable of doing optimal instruction selection for the DEC VAX-11 with its rich set of addressing modes.
Abstract: High-quality local code generation is one of the most difficult tasks the compiler-writer faces. Even if register allocation decisions are postponed and common subexpressions are ignored, instruction selection on machines with complex addressing can be quite difficult. Efficient and general algorithms have been developed to do instruction selection, but these algorithms fail to always find optimal solutions. Instruction selection algorithms based on dynamic programming or complete enumeration always find optimal solutions, but seem to be too costly to be practical. This paper describes a new instruction selection algorithm, and its prototype implementation, based on bottom-up tree pattern-matching. This algorithm is both time and space efficient, and is capable of doing optimal instruction selection for the DEC VAX-11 with its rich set of addressing modes.
TL;DR: The dynamic programming method which minimizes the number of stations for a given cycle time is extended here to solve two variants of the assembly-line balancing problem.
TL;DR: Inference of Markov networks from finite sets of sample strings is formulated using dynamic programming and the method is illustrated with artificial data and with data representing banded human chromosomes.
Abstract: Inference of Markov networks from finite sets of sample strings is formulated using dynamic programming. Strings are installed in a network sequentially via optimal string-to-network alignments computed with a dynamic programming matrix, the cost function of which uses relative frequency estimates of transition probabilities to emphasize landmark substrings common to the sample set. Properties of an inferred network are described and the method is illustrated with artificial data and with data representing banded human chromosomes.
TL;DR: In this paper, the problem of scheduling the construction of a bridge due to Selinger is solved using a Continuous Optimal Control formulation of a hypothetical cut-and-fill job on a section of a highway.
Abstract: Construction planning and control literature reveal much effort in the recent past in the development of managerial control systems involving classical optimization techniques such as simulation, queuing theory, linear, dynamic programming, etc. Construction managers typically reach decisions in a perspective of time and in light of temporal criteria. The aforementioned techniques deal with the theoretical and computational aspects of time by static methods: Effects of one or more actions in a given interval are aggregated over time. Optimal Control Theory, a new branch of optimization, makes it possible to view the construction-production process as a dynamic system that evolves over time. This paper presents a Continuous Optimal Control formulation of a hypothetical cut-and-fill job on a section of a highway. It is shown that Discrete Optimal Control framework is adequate for construction. The problem of scheduling the construction of a bridge due to Selinger is solved using this approach.
TL;DR: A stereo matching algorithm based on dynamic programming that produces a set of candidate matches for each row separately and uses continuity constraints to choose the best matches.
Proceedings Article•
01 Jan 1986
TL;DR: A method to derive systolic designs with non-uniform data flow based on a subset of data dependencies eXITacted from the original problem specification to identify chains of dependem computations which are then convened into recurrence equations.
Abstract: In this paper we propose a method to derive systolic designs with non-uniform data flow. One of the major difficulties in systematic design is in transforming the original sequential specification of a problem into a Conn suitable [0 VLSI implementation. Our approach [Q auromatically restructuring a problem is based on a subset of me data dependencies eXITacted from the original problem specification. By using such dependencies we are able to identify chains of dependem computations which are then convened into recurrence equations. The mapping of the new specification imo hardware is also based on data dependencies. We illusrrate the methodology by applying it [0 algorithms using dynamic programming.
TL;DR: A complete derivation, based on transformational programming, of two linear-time algorithms for the problem of breaking paragraphs into lines is presented, reflecting different assumptions about the algebraic properties of waste functions.
TL;DR: A dynamic programming formulation for structure optimization is presented and mechanical theorems fix an iterative solution process for solid mechanics structure optimization.
Abstract: Structure optimization for problems of solid mechanics is gaining in importance. Of special interest to the ship and aeroplane designer is optimizing changes in sections and hols in such a way that the largest value of the von Mises stress becomes as small as possible, to optimize the use of material. Also, the temporal beginning of crack propagation should be delayed as long as possible. A dynamic programming formulation for structure optimization is presented and mechanical theorems fix an iterative solution process.
01 Jan 1986
TL;DR: A dynamic programming method based on a dynamic programming optimal path algorithm for the detection of edges in noisy images shows much better performance than the best parallel schemes for low values of SNR, but requires the definition of a region of interest.
Abstract: A method is described for the detection of edges in noisy images, which is based on a dynamic programming optimal path algorithm. The performance has been evaluated with ROC analysis and Pratt's Figure of Merit for edge detectors. The dynamic programming method shows much better performance than the best parallel schemes for low values of SNR, but requires the definition of a region of interest.
TL;DR: An efficient design procedure for designing FIR filters whose general structure consists of a transversal filter with tap coefficients restricted to -1, 0, or + 1 and cascaded with simple recursive sections.
Abstract: In this paper, we describe an efficient design procedure for designing FIR filters whose general structure consists of a transversal filter with tap coefficients restricted to -1, 0, or + 1 and cascaded with simple recursive sections. Due to the multiplication-free nature of this transversal filter, the configuration is particularly attractive from the standpoint of implementation with very simple hardware. Dynamic programming methods in conjunction with a mean-square error functional are presented to select the set of coefficient values for the taps. The approach is based on the assumption that the approximation sequence can be described as the output of a sequential machine whose state corresponds to the state-space representation of the sections in cascade with the transveral filter.
07 Apr 1986
TL;DR: A new algorithm of minimum time motion planning is proposed for robots operating in the obstacle strewn environment and enabled a merger between two kindred algorithms: A* search algorithm, and dynamic programming.
Abstract: A new algorithm of minimum time motion planning is proposed for robots operating in the obstacle strewn environment. Structure of the topological passageways is analyzed and represented using a model of slalom situations for which a number of rules is determined. Dynamical system of robot is described in a form of sequential machine. This enabled a merger between two kindred algorithms: A* search algorithm, and dynamic programming. An experimental analysis of the simulated mobile robot has confirmed the applicability of results.