Showing papers on "Dynamic programming published in 1983"

An Exact Algorithm for the Single Vehicle Many-to-Many Dial-A-Ride Problem with Time Windows

Abstract: This paper modifies the exact Dynamic Programming algorithm developed by the author for the single vehicle many-to-many immediate request Dial-A-Ride problem to solve the problem where each customer has specified upper and lower bounds for his pickup and delivery times and where the objective is to minimize the time needed to service all customers. The major difference between the two algorithms is the substitution of backward recursion with forward recursion. The new algorithm requires the same computational effort as the old one (0(N23N) for N customers) and is able to recognize infeasible problem instances.

Distributed asynchronous computation of fixed points

Abstract: We present an algorithmic model for distributed computation of fixed points whereby several processors participate simultaneously in the calculations while exchanging information via communication links. We place essentially no assumptions on the ordering of computation and communication between processors thereby allowing for completely uncoordinated execution. We provide a general convergence theorem for algorithms of this type, and demonstrate its applicability to several classes of problems including the calculation of fixed points of contraction and monotone mappings arising in linear and nonlinear systems of equations, optimization problems, shortest path problems, and dynamic programming.

Shape Optimization of Skeletal Structures: A Review

Abstract: This paper presents a state of the art review of mathematical programming methods used in the design of skeletal elastic structures in which the possibility of altering the shape, position or layout of the members is considered. Virtually every type of optimization procedure including linear, nonlinear, and dynamic programming has been applied to this design problem. These methods have been implemented using three main approaches. The first, referred to as the ground structure approach, is one in which members are removed from a highly connect structure to derive an optimum subset of bars. In the second approach the co‐ordinates of the joints of the structure are treated as design variables and moved during the optimization procedure to enable an optimum layout to be designed. The third type of method includes those which allow for topological considerations at certain points during the design process and generally keeps the design variables in two separate groups. The paper discusses the way in which eac...

On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming

Abstract: An approximation of the Hamilton-Jacobi-Bellman equation connected with the infinite horizon optimal control problem with discount is proposed. The approximate solutions are shown to converge uniformly to the viscosity solution, in the sense of Crandall-Lions, of the original problem. Moreover, the approximate solutions are interpreted as value functions of some discrete time control problem. This allows to construct by dynamic programming a minimizing sequence of piecewise constant controls.

Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions.

Abstract: This paper concerns control of partially observable diffusions. The problem is formulated as a control problem with full information, but for the Zakai equation of nonlinear filtering. A maximum principle is derived and a treatment of the problem from the point of view of nonlinear semigroup is given.

Myopic Heuristics for the Single Machine Weighted Tardiness Problem

Abstract: : It is well known that the single machine weighted tardiness problem is NP-complete Hence, it is unlikely that there exist polynomially bounded algorithms to solve this problem Further, the problem is of great practical significance We develop myopic heuristics for this problem; these heuristics have been tested against competing heuristics, against a tight lower bound, and where practical, against the optimum, with uniformly good results Also, these heuristics can be used as dispatching rules in practical situations In our efforts to seek optimum solutions we develop a hybrid dynamic programming procedure (a modified version of Baker's procedure) which provides lower and upper bounds when it becomes impractical to find the optimum solution Further, stopping rules are developed for identifying optimal first job/jobs (Author)

Sequence alignments in the neighborhood of the optimum with general application to dynamic programming.

Abstract: When applying dynamic programming techniques to obtain optimal sequence alignments, a set of weights must be assigned to mismatches, insertion/deletions, etc. These weights are not predetermined, although efforts are being made to deduce biologically meaningful values from data. In addition, there are sometimes unknown constraints on the sequences that cause the "true" alignment to disagree with the optimum (computer) solution. To assist in overcoming these difficulties, an algorithm has been developed to produce all alignments within a specified distance of the optimum. The distance can be chosen after the optimum is computed, and the algorithm can be repeated at will. Earlier algorithms to solve this problem were very complex and not practical for any case involving sequences with significant time or storage requirements. The algorithm presented here overcomes these difficulties and has application to general, discrete dynamic programming problems.

On the Hamilton-Jacobi-Bellman equations

Abstract: We consider general problems of optimal stochastic control and the associated Hamilton-Jacobi-Bellman equations. We recall first the usual derivation of the Hamilton-Jacobi-Bellman equations from the Dynamic Programming Principle. We then show and explain various results, including (i) continuity results for the optimal cost function, (ii) characterizations of the optimal cost function as the maximum subsolution, (iii) regularity results, and (iv) uniqueness results. We also develop the recent notion of viscosity solutions of Hamilton-Jacobi-Bellman equations.

Vector-Valued Dynamic Programming

Abstract: Dynamic programming models with vector-valued returns are investigated. The sets of (Pareto) maximal returns and (Pareto) maximal policies are defined. Monotonicity conditions are shown to be sufficient for the set of maximal policies to include a stationary policy, and for the set of maximal returns to be in the convex hull of returns of stationary policies. In particular, it is shown that these results hold for Markov decision processes.

Dynamic programming algorithm for optimal estimation of speech parameter contours

Abstract: A method for incorporating the requirement of smoothness into the estimation procedure for speech parameters is described. The traditional method of estimating a speech parameter, such as the fundamental period or a formant, is to determine the speech parameter separately for each time frame, usually by optimizing a suitable function of the speech signal. However, it is known a priori that adjacent speech parameters are strongly correlated, and that the overall contour of the parameter versus time must be a relatively smooth curve. An overall criterion of optimality for the contour of the speech parameter is introduced; the optimization problem is solved by means of dynamic programming. A recursive algorithm is obtained which does without statistical assumptions and is purely deterministic. The algorithm, although computationally expensive, can easily be implemented and has a tracking capability for on-line estimation.

The design of optimal DFT algorithms using dynamic programming

Abstract: A broad class of efficient discrete Fourier transform algorithms is developed by partitioning short DFT algorithms into factors. The factored short DFT's are combined into longer DFT's using multi-dimensional index maps. By exploiting a property which allows some of the factors to commute, a large set of possible DFT algorithms is generated which contains both the prime factor algorithm (PFA) and the Winograd Fourier transform algorithm (WFTA) as special cases. The problem of finding an algorithm from this class which is optimal with respect to the specific add, multiply, and data transfer characteristics of a particular implementation is posed, and a highly effective dynamic programming algorithm is presented as a solution.

Controlled Markov Chains and Stochastic Networks

Abstract: Controlled Markov chains with average cost criterion and with special cost and transition structures are studied. Existence of optimal stationary strategies is established for the average cost criterion. Corresponding dynamic programming equations are derived. A stochastic network problem that includes interconnected queues as a special case is described and studied within this framework.

Gravity wastewater collection systems optimization

Abstract: A computer algorithm for the selection of optimal depth‐diameter combinations for all links of a complete gravity wastewater collection system has been developed using dynamic programming. The algorithm incorporates two subprocesses P1 and P2. The subprocesses P1 generates all feasible designs of inflowing lines at a junction manhole whereas P1 uses these feasible designs to provide the upstream invert level of the outflow line, simultaneously solving the matching problem encountered at each junction manhole. The problem of dimensionality has been minimized by exploiting the characteristic features of wastewater collection system. The optimal design for a 10.7 km long collection system at Indian Institute of Technology, Bombay with 52 lines, 245 links, 224 ordinary manholes and 21 junction manholes has been compared with conventional design to bring out that the algorithm requires small computer memory, small execution time and leads to optimal solution of a complete gravity wastewater collection system.

Column Generation Based Heuristic Algorithm for Multi-Item Scheduling

Abstract: The column generation algorithm for the multi-item lot-size scheduling problem under resource constraints is examined and improved upon by augmenting simpler heuristic routines in place of the time-consuming Wagner-Whitin dynamic programming routine. The heuristic algorithms thus developed are tested by controlling problem size, setup time, demand variability, and capacity change costs in test problems. The empirical results indicate that the proposed heuristic algorithms reduce CPU time as well as the number of iterations with only a slight loss in optimality.

Hybrid algorithm for sequencing with bicriteria

Abstract: This paper presents a solution algorithm for a single machine scheduling problem with two criteria: total tardiness and total flow time. Theoretical results of precedence properties which are respected by all nondominated schedules are first derived. These precedence properties are then incorporated into a multiple-criteria dynamic programming framework to improve the computational efficiency. Results of the computational experiment and the average behavior (computation time and efficiency) of the algorithm are reported.

An Inspection Policy Model for Production Facilities

Abstract: Inspection policy models describe stochastically failing systems in which failures are detected by inspections only. We develop such an inspection model for a production facility. The model generalizes the recent work of Munford as well as the classical work of Barlow et al. Revenues are accrued for each time unit in which the facility is known to be in good operating condition. The costs considered include inspection, operating and repair costs. We present a dynamic programming algorithm that maximizes the expected profit between two successive repairs. This algorithm is then imbedded within an iterative procedure that maximizes the expected profit per time unit and the expected profit per time unit of good operating condition.

A multifacility capacity expansion model with joint expansion set‐up costs

Abstract: This article describes a multifacility capacity expansion model in which the different facility types represent different quality levels. These facility types are used to satisfy a variety of deterministic demands over a finite number of discrete time periods. Applications for the model can be found in cable sizing problems associated with the planning of communication networks. It is assumed that the cost function associated with expanding the capacity of any facility type is concave, and that a joint set-up cost is incurred in any period in which one or more facilities are expanded. The model is formulated as a network flow problem from which properties associated with optimal solutions are derived. Using these properties, we develop a dynamic programming algorithm that finds optimal solutions for problems with a few facilities, and a heuristic algorithm that finds near-optimal solutions for larger problems. Numerical examples for both algorithms are discussed.

A pareto optimization problem formulation for building performance and design

Abstract: A Pareto optimization problem formulation is described for the classic building design problem of choosing a building form, enclosure and siting given several different and conflicting performance requirements. The problem is defined as the determination of the fenestration, insulation, shape, massing and orientation of an air-conditioned parallelepiped office building for thermal, daylight, cost and spatial efficiency demands. The problem formulation uses a form of Pareto optimal dynamic programming optimization. It is shown that computational feasibility depends on the ordering of stages in the formulation to minimize the dimension of Pareto sets in the output states as well as the standard dynamic programming conditions of monotonicity and separability.

Preventive Replacement for Multicomponent Systems: An Opportunistic Discrete-Time Dynamic Programming Model

Abstract: We propose a dynamic programming (DP) model for the optimal preventive replacement of elements in a multicomponent system. The model generalizes previous work on the subject by: i) allowing for non identical components, ii) permitting the computation of an ?-optimal strategy for a medium size system (4 to 5 components), iii) showing that the control-limit rule does not extend to most of the multicomponent systems, and iv) proposing a class of suboptimal strategies to be used when the system is too large for directly implementing the DP algorithm. These features of the model are illustrated in a separately available Supplement via a numerical example inspired from the modular structure of a modern fighter aircraft's engine.

Pareto optimal serial dynamic programming

Abstract: A method for generating the Pareto optimal set, or an approximation to it for multi-criteria (multi-objective) problems capable of being formulated as serial stage-state discrete dynamic programs, is presented. It is shown that this set may be produced by using Pareto optimality as the optimization selection mechanism in dynamic programming, Worked examples are presented.

Circuit partitioning with size and connection constraints

Abstract: The problem of partitioning a circuit into subcomponents with constraints on the size of each subcomponent and the number of external connections is examined. While this problem is shown to be NP-complete even for very restricted cases, a pseudo-polynomial dynamic programming algorithm is given for the case where the circuit has a tree structure.

ZIP: A dynamic programming algorithm for time-aligning two indefinitely long utterances

Abstract: In automatic speech recognition (ASR) using whole-word templates, dynamic programming (DP) is frequently used to determine the similarity of two patterns (derived from spoken words) using the optimal way of aligning their timescales. In ASR the actual timescale alignment is of secondary interest to the degree of similarity and is not normally computed. We present ZIP, a modified DP algorithm designed to compute the time alignment of two utterances of the same text of any length. By using a window and partial traceback the amount of computation and storage is kept to a modest level, although the optimality of the final path is no longer absolutely guaranteed. Uses of ZIP are given.

An Algorithm for the Single-Machine Sequencing Problem to Minimize Total Tardiness

Abstract: This paper considers the basic single-machine sequencing problem to minimize total tardiness of all jobs. Using Emmons' well-known theoretical results, certain precedence relations among the jobs are established and used to describe an implicit enumeration scheme which requires only O(n2 ) computer storage. Computational experience indicates that the proposed algorithm is more suitable for microcomputers with limited storage capacity than Schrage and Baker's dynamic programming algorithm.