Showing papers on "Dynamic programming published in 1996"

A genetic algorithm solution to the unit commitment problem

Abstract: This paper presents a genetic algorithm (GA) solution to the unit commitment problem. GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as natural selection, genetic recombination and survival of the fittest. A simple GA algorithm implementation using the standard crossover and mutation operators could locate near optimal solutions but in most cases failed to converge to the optimal solution. However, using the varying quality function technique and adding problem specific operators, satisfactory solutions to the unit commitment problem were obtained. Test results for power systems of up to 100 units and comparisons with results obtained using Lagrangian relaxation and dynamic programming are also reported.

Reliability optimization of series-parallel systems using a genetic algorithm

Abstract: A problem-specific genetic algorithm (GA) is developed and demonstrated to analyze series-parallel systems and to determine the optimal design configuration when there are multiple component choices available for each of several k-out-of-n:G subsystems. The problem is to select components and redundancy-levels to optimize some objective function, given system-level constraints on reliability, cost, and/or weight. Previous formulations of the problem have implicit restrictions concerning the type of redundancy allowed, the number of available component choices, and whether mixing of components is allowed. GA is a robust evolutionary optimization search technique with very few restrictions concerning the type or size of the design problem. The solution approach was to solve the dual of a nonlinear optimization problem by using a dynamic penalty function. GA performs very well on two types of problems: (1) redundancy allocation originally proposed by Fyffe, Hines, Lee, and (2) randomly generated problem with more complex k-out-of-n:G configurations.

Dynamic Programming and Optimal Control. Volume 1

Abstract: (1996). Dynamic Programming and Optimal Control. Volume 1. Journal of the Operational Research Society: Vol. 47, No. 6, pp. 833-834.

A stochastic model for the unit commitment problem

Abstract: The authors develop a model and a solution technique for the problem of generating electric power when demands are not certain. They also provide techniques for improving the current methods used in solving the traditional unit commitment problem. The solution strategy can be run in parallel due to the separable nature of the relaxation used. Numerical results indicate significant savings in the cost of operating power generating systems when the stochastic model is used instead of the deterministic model.

Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions

Abstract: This paper develops an efficient, general economic dispatch (ED) algorithm for generating units with nonsmooth fuel cost functions. Based on the evolutionary programming (EP) technique, the new algorithm is capable of determining the global or near global optimal dispatch solutions in the cases where the classical Lagrangian based algorithms cease to be applicable. Effectiveness of the new algorithm is demonstrated on two example power systems and compared to that of the dynamic programming, simulated annealing, and genetic algorithms. Practical application of the developed algorithm is additionally verified on the Taiwan power (Taipower) system. Numerical results show that the proposed EP based ED algorithm can provide accurate dispatch solutions within reasonable time for any type of fuel cost functions.

Feature-based methods for large scale dynamic programming

Abstract: We develop a methodological framework and present a few different ways in which dynamic programming and compact representations can be combined to solve large scale stochastic control problems. In particular, we develop algorithms that employ two types of feature-based compact representations; that is, representations that involve feature extraction and a relatively simple approximation architecture. We prove the convergence of these algorithms and provide bounds on the approximation error. As an example, one of these algorithms is used to generate a strategy for the game of Tetris. Furthermore, we provide a counter-example illustrating the difficulties of integrating compact representations with dynamic programming, which exemplifies the shortcomings of certain simple approaches.

A First Course in Optimization Theory

Abstract: This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

Stochastic shortest path problems with recourse

Abstract: We consider shortest path problems defined on graphs with random arc costs We assume that information on arc cost values is accumulated as the graph is being traversed The objective is to devise a policy that leads from an origin to a destination node with minimal expected cost We provide dynamic programming algorithms, estimates for their complexity, negative complexity results, and analysis of some possible heuristic algorithms

Genetic Algorithms for Product Design

Abstract: Product design is increasingly recognized as a critical activity that has a significant impact on the performance of firms. Consequently, when firms undertake a new existing product design redesign activity, it is important to employ techniques that will generate optimal solutions. As optimal product design using conjoint analysis data is an NP-hard problem, heuristic techniques for its solution have been proposed. This research proposes the use of and evaluates the performance of Genetic Algorithms GA, which is based on the principles of natural selection, as an alternative procedure for generating "good" i.e., close to optimal solutions for the product design problem. The paper focuses on 1 how GA can be applied to the product design problems, 2 determining the comparative performance of GA vis-i-vis the dynamic programming DP heuristic Kohli and Krishnamurti [Kohli, R., R. Krishnamurti. 1987. A heuristic approach to product design. Management Sci.3312 1523-1533.], [Kohli, R., R. Krishnamurti. 1989. Optimal product design using conjoint analysis: Computational complexity and algorithms. Eur. J. Oper. Res.40 186-195.] in generating solutions to the product design problems, 3 the sensitivity of the GA solutions to variations in parameter choices, and 4 generalizing the results of the dynamic programming heuristic to product designs involving attributes with varying number of levels and studying the impact of alternate attribute sequencing rules.

New prospects in line detection by dynamic programming

Abstract: The detection of lines in satellite images has drawn a lot of attention within the last 15 years. Problems of resolution, noise, and image understanding are involved, and one of the best methods developed so far is the F* algorithm of Fischler, which achieves robustness, rightness, and rapidity. Like other methods of dynamic programming, it consists of defining a cost which depends on local information; then a summation-minimization process in the image is performed. The authors present herein a mathematical formalization of the F* algorithm, which allows them to extend the cost both to cliques of more than two points (to deal with the contrast), and to neighborhoods of size larger than one (to take into account the curvature). Thus, all the needed information (contrast, grey-level, curvature) is synthesized in a unique cost function defined on the digital original image. This cost is used to detect roads and valleys in satellite images (SPOT).

Deriving a General Operating Policy for Reservoirs Using Neural Network

Abstract: Reservoir operating policies are derived to improve the operation and efficient management of available water for the Aliyar Dam in Tamil Nadu, India, using a dynamic programming (DP) model, a stochastic dynamic programming (SDP) model, and a standard operating policy (SOP). The objective function for this case study is to minimize the squared deficit of the release from the irrigation demand. From the DP algorithm, general operating policies are derived using a neural network procedure (DPN model), and using a multiple linear regression procedure (DPR model). The DP functional equation is solved for 20 years of fortnightly historic data. The field irrigation demand is computed for this study by the modified Penman method with daily meteorological data. The performance of the DPR, DPN, SDP, and SOP models are compared for three years of historic data, using the proposed objective function. The neural network procedure based on the dynamic programming algorithm provided better performance than the other mo...

Control of Systems with Aftereffect

Abstract: Elements of the theory of systems with aftereffect The dynamic programming method Optimality conditions for deterministic systems with aftereffect Investigation of self-adjusting systems with reference model Optimal control of stochastic systems Optimal control of systems defined by stochastic integro-functional equations Optimal estimation Optimal control with incomplete data Bibliography.

Energy minimization using multiple supply voltages

Abstract: We present a dynamic programming technique for solving the multiple supply voltage scheduling problem in both non-pipelined and functionally pipelined data-paths. The scheduling problem refers to the assignment of a supply voltage level to each operation in a data flow graph so as to minimize the average energy consumption for given computation time or throughput constraints or both. The energy model is accurate and accounts for the input pattern dependencies, re-convergent fanout induced dependencies, and the energy cost of level shifters. Experimental results show that using four supply voltage levels on a number of standard benchmarks, an average energy saving of 53% (with a computation time constraint of 1.5 times the critical path delay) can be obtained compared to using one fixed supply voltage level.

Optimization on Low Rank Nonconvex Structures

Abstract: Preface. Part I: Foundations. 1. Scope of Global Optimization. 2. Quasi-Convexity. 3. D.C. Functions and D.C. Sets. 4. Duality. 5. Low-Rank Nonconvex Structures. 6. Global Search Methods and Basic D.C. Optimization Algorithms. Part II: Methods and Algorithms. 7. Parametric Approaches in Global Optimization. 8. Multiplicative Programming Problems. 9. Monotonic Problems. 10. Decomposition Methods by Prices. 11. Dynamic Programming Algorithms in Global Optimization. Part III: Selected Applications. 12. Low Rank Nonconvex Quadratic Programming. 13. Continuous Location. 14. Design Centering and Related Geometric Problems. 15. Multiobjective and Bilevel Programming. References. Index.

An O (T 3 ) algorithm for the economic lot-sizing problem with constant capacities

Abstract: We develop an algorithm that solves the constant capacities economic lot-sizing problem with concave production costs and linear holding in OT3 time. The algorithm is based on the standard dynamic programming approach which requires the computation of the minimal costs for all possible subplans of the production plan. Instead of computing these costs in a straightforward manner, we use structural properties of optimal subplans to arrive at a more efficient implementation. Our algorithm improves upon the OT4 running time of an earlier algorithm.

Computational optimality theory

Abstract: In Optimality Theory, a linguistic input is assigned a grammatical structural description by selecting, from an infinite set of candidate structural descriptions, the description which best satisfies a ranked set of the same universal constraints. Cross-linguistic variation is explained as different rankings of the same universal constraints. Two questions are of primary interest concerning the computational tractibility of Optimality Theory. The first concerns the ability to compute optimal structural descriptions. The second concerns the learnability of the constraint rankings. Parsing algorithms are presented for the computation of optimal forms, using dynamic programming. These algorithms work for grammars in Optimality Theory employing universal constraints which may be evaluated on the basis of information local within the structural description. This approach exploits optimal substructure to construct the optimal description, rather than searching for the solution by moving from one entire description to another. A class of learning algorithms, the Constraint Demotion algorithms, are presented, which solve the problem of learning constraint rankings based upon hypothesized structural descriptions (an important subproblem of the general problem of language learning). Constraint Demotion exploits the implicit negative evidence available in the form of the competing (suboptimal) structural descriptions of the input. The data complexity of this algorithm is quadratic in the number of constraints.

Learning by doing and the value of optimal experimentation

Abstract: Research on learning-by-doing has typically been restricted to cases where estimation and control can be treated separately. Recent work has provided convergence results for more general learning problems where experimentation is an important aspect of optimal control. However the associated optimal policy cannot be derived analytically because Bayesian learning introduces a nonlinearity in the dynamic programming problem. This paper characterizes the optimal policy numerically and shows that it incorporates a substantial degree of experimentation. Dynamic simulations indicate that optimal experimentation dramatically improves the speed of learning, while separating control and estimation frequently induces a long-lasting bias in the control and target variables.

A parallel genetic algorithm for generation expansion planning

Abstract: This paper presents an application of parallel genetic algorithm to optimal long-range generation expansion planning. The problem is formulated as a combinatorial optimization problem that determines the number of newly introduced generation units of each technology during different time intervals. A new string representation method for the problem is presented. Binary and decimal coding for the string representation method are compared. The method is implemented on transputers, one of the practical multi-processors. The effectiveness of the proposed method is demonstrated on a typical generation expansion problem with four technologies, five intervals, and a various number of generation units. It is compared favorably with dynamic programming and conventional genetic algorithm. The results reveal the speed and effectiveness of the proposed method for solving this problem.

Iterative dynamic programming: an approach to minimum energy trajectory planning for robotic manipulators

Abstract: This paper proposes a technique of iterative dynamic programming to plan minimum energy consumption trajectories for robotic manipulators. The dynamic programming method is modified to perform a series of dynamic programming passes over a small reconfigurable grid covering only a portion of the solution space at any one pass. Although strictly no longer a global optimization process, this iterative approach retains the ability to avoid some poor local minima while avoiding the curse of dimensionality associated with a pure dynamic programming approach. The algorithm has an inherent parallel structure, allowing for reduced computation time on parallel architecture computers. No limiting assumptions are made about the performance index, or function to be optimized. As such, extremely complex functions and constraints are easily handled. Joint actuator and time constraints are considered in this work. The modified dynamic programming approach is verified experimentally by planning and executing a minimum energy consumption path for a Reis V15 industrial manipulator.

Exploiting Model Uncertainty Estimates for Safe Dynamic Control Learning

Abstract: Model learning combined with dynamic programming has been shown to be effective for learning control of continuous state dynamic systems. The simplest method assumes the learned model is correct and applies dynamic programming to it, but many approximators provide uncertainty estimates on the fit. How can they be exploited? This paper addresses the case where the system must be prevented from having catastrophic failures during learning. We propose a new algorithm adapted from the dual control literature and use Bayesian locally weighted regression models with dynamic programming. A common reinforcement learning assumption is that aggressive exploration should be encouraged. This paper addresses the converse case in which the system has to reign in exploration. The algorithm is illustrated on a 4 dimensional simulated control problem.

PACE: a dynamic programming algorithm for hardware/software partitioning

Abstract: This paper presents the PACE partitioning algorithm which is used in the LYCOS co-synthesis system for partitioning control/dataflow graphs into hardware and software parts. The algorithm is a dynamic programming algorithm which solves both the problem of minimizing system execution time with a hardware area constraint and the problem of minimizing hardware area with a system execution time constraint. The target architecture consists of a single microprocessor and a single hardware chip (ASIC, FPGA, etc.) which are connected by a communication channel. The algorithm incorporates a realistic communication model and thus attempts to minimize communication overhead. The time-complexity of the algorithm is O(n/sup 2//spl middot//spl Ascr/) and the space-complexity is O(n/spl middot//spl Ascr/) where /spl Ascr/ is the total area of the hardware chip and n the number of code fragments which may be placed in either hardware or software.

Scheduling Parallel Manufacturing Cells with Resource Flexibility

Abstract: This paper investigates the improvements in manufacturing performance that can be realized by broadening the scope of the production scheduling function to include both job sequencing and processing-time control through the deployment of a flexible resource. We consider an environment in which a set of jobs must be scheduled over a set of parallel manufacturing cells, each consisting of a single machine, where the processing time of each job depends on the amount of resource allocated to the associated cell. Two versions of the problem are introduced: a static problem in which a single resource-allocation decision is made and maintained throughout the production horizon, and a dynamic problem in which resource can be reassigned among the production cells as local bottlenecks shift. We provide mathematical formulations for each version of the problem, establish problem complexity, identify important characteristics of optimal solutions, develop optimal and heuristic solution approaches, and report the results of a set of computational experiments. The computational results demonstrate that substantial improvements in operational performance can be achieved through effective utilization of resource flexibility.

Dispatching, routing, and scheduling of two automated guided vehicles in a flexible manufacturing system

Abstract: This article presents a new approach for planning the dispatching, conflict-free routing, and scheduling of automated guided vehicles in a flexible manufacturing system. The problem is solved optimally in an integrated manner, contrary to the traditional approach in which the problem is decomposed in three steps that are solved sequentially. The algorithm is based on dynamic programming and is solved on a rolling time horizon. Three dominance criteria are used to limit the size of the state space. The method finds the transportation plan minimizing the makespan (the completion time for all the tasks). Various results are discussed. A heuristic version of the algorithm is also proposed for an extension of the method to many vehicles.

Mean Flow Time Minimization in Reentrant Job Shops with a Hub

Abstract: This paper considers a reentrant job shop with one hub machine which a job enters K times. Between any two consecutive entries into the hub, the job is processed on other machines. The objective is to minimize the total flow time. Under two key assumptions, the bottleneck assumption and the hereditary order (HO) assumption on the processing times of the entries, it is proved that there is an optimal schedule with the shortest processing time (SPT) job order and a dynamic programming algorithm is derived to find such a schedule. An approximation algorithm based on the shortest path algorithm and the SPT job order is also proposed to solve the problem. The approximation algorithm finds an optimal clustered schedule. In clustered schedules, jobs are scheduled in disjoint clusters; they resemble batch processing and seem to be of practical importance. Worst-case bounds for clustered schedules are proved with the HO assumption relaxed. Two special cases with the restriction that there are only two entries to t...

Optimal bit allocation under multiple rate constraints

Abstract: We present a new Lagrangian-based iterative technique for rate-distortion optimization under multiple rate constraints. We show how for sets of "linear" constraints this technique can be proven to be optimal up to a convex hull approximation. As an application we consider the problem of optimal buffer-constrained bit allocation. Our technique can be used to find an excellent approximation to the solutions achieved using dynamic programming. In cases where the buffer size is relatively large our approach shows a significant reduction in complexity as compared to dynamic programming.