Parallel Dynamic Programming Algorithm Research Articles

Multidimensional Parallel Dynamic Programming Algorithm Based on Spark for Large-Scale Hydropower Systems

The “curse of dimensionality” is a major problem in dynamic programming (DP) algorithms for large-scale hydropower systems. This study proposes a parallel DP algorithm based on Spark (PDPoS) to alleviate the “curse of dimensionality”. Parallel computing experiments are formulated by varying the number of reservoirs, the number of discrete water levels and the number of CPU cores to analyze the quality and efficiency of PDPoS. The methodologies were applied to a cascade reservoir system made up of eight reservoirs in the Yuanshui River Basin in China. The results are as follows. (1) The number of discrete water levels is the dominant factor in the solution quality, while the number of reservoirs is the dominant factor in the solving efficiency. (2) The runtime of PDPoS is markedly affected by the calculational scale (determined by the number of reservoirs and discrete water levels), and the relationship between the number of CPU cores and the runtime is triphasic with increasing calculational scale. (3) The larger the calculational scale is, the better the parallel performance (i.e., the parallel speedup and parallel efficiency). The proposed PDPoS method has strong generality, high parallel performance, and high practical value.

Multicore Parallel Dynamic Programming Algorithm for Short-Term Hydro-Unit Load Dispatching of Huge Hydropower Stations Serving Multiple Power Grids

Short-term hydro-unit load dispatching (SHULD) refers to the determination of the power output of each unit within a hydropower station over a planning horizon to minimize the operational cost or maximize the power-generation profit while satisfying hydraulic and electrical constraints. In China, huge hydropower stations, such as the Three Gorges (TG) and Xiluodu (XLD) stations, are composed of a large number of hydro units, which feature a high installed capacity and a high water head. SHULD models of these stations are more complex and difficult to solve compared with those of traditional stations, especially when the stations serve multiple power grids. This study develops a practical method for optimizing SHULD models by considering the XLD hydropower station as a case study. First, a SHULD model for huge hydropower stations with multiple vibration zones and multiple receiving power grids is presented. Second, classical and sophisticated dynamic programming (DP) is applied to the SHULD model, and a practical strategy is proposed to balance the available water in a reservoir’s left and right banks to satisfy their load demands. Finally, the Fork/Join framework is used to parallelize DP to reduce the computation time and fully utilize the computer resources. The wet and dry season results demonstrate that the approach is efficient and suitable for huge hydropower stations with a high water head and multiple receiving power grids, thereby demonstrating its potential practicability and validity for solving the SHULD problem.

Multi-product continuous plant scheduling: combination of decomposition, genetic algorithm, and constructive heuristic

We propose a polylithic method for medium-term scheduling of a large-scale industrial plant operating in a continuous mode. The method combines a decomposition approach, a genetic algorithm (GA) and a constructive MILP-based heuristic. In the decomposition, decisions are made at two levels, using the rolling horizon approach. At the upper level, a reduced set of products and the time period is chosen to be considered in the lower level. At the lower level, a short-term scheduling MILP-model with event-based representation is used. A heuristic solution to the lower level problem is found using a constructive Moving Window heuristic guided by a genetic algorithm. The GA is applied for finding efficient utilisation of critical units in the lower level problem. For solving the one unit scheduling problem, a parallel dynamic programming algorithm is proposed. Implementation of the dynamic programming algorithm for a graphics processing unit (GPU) is incorporated in the GA for improving its performance. The experimental study of the proposed method on a real case of a large-scale plant shows a significant improvement of the solution quality and the solving time comparing to the pure decomposition algorithm proposed in the earlier study, and confirmed suitability of the proposed approach for the real-life production scheduling. In particular, the reduction of the number of changeovers and their duration in the obtained solution as well as the CPU time of solving the problem was about 60% using the new approach.

A Pareto optimal multi-objective optimisation for parallel dynamic programming algorithm applied in cognitive radio ad hoc networks

In this paper, we present a Pareto optimal multi-objective optimisation for parallel dynamic programming algorithm applied in cognitive radio ad hoc networks. To measure the performance of our contribution, we have used a multi-core architecture. The parallel version of the dynamic programming is implemented with the concept of Pareto. To select the most compromising solution from the Pareto front, Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used in this paper. We have also implemented a meta-heuristic (cuckoo search) with the Pareto principle in order to validate our proposal. Our simulations approve the desired results, showing significant gain in terms of execution time. The main objective is to allow a cognitive engine to use an exact method and to have better results compared to the use of meta-heuristics while satisfying QoS parameters.

A Pareto optimal multi-objective optimisation for parallel dynamic programming algorithm applied in cognitive radio ad hoc networks

A Pareto optimal multi-objective optimisation for parallel dynamic programming algorithm applied in cognitive radio ad hoc networks

A parallel dynamic programming algorithm for multi-reservoir system optimization

This paper develops a parallel dynamic programming algorithm to optimize the joint operation of a multi-reservoir system. First, a multi-dimensional dynamic programming (DP) model is formulated for a multi-reservoir system. Second, the DP algorithm is parallelized using a peer-to-peer parallel paradigm. The parallelization is based on the distributed memory architecture and the message passing interface (MPI) protocol. We consider both the distributed computing and distributed computer memory in the parallelization. The parallel paradigm aims at reducing the computation time as well as alleviating the computer memory requirement associated with running a multi-dimensional DP model. Next, we test the parallel DP algorithm on the classic, benchmark four-reservoir problem on a high-performance computing (HPC) system with up to 350 cores. Results indicate that the parallel DP algorithm exhibits good performance in parallel efficiency; the parallel DP algorithm is scalable and will not be restricted by the number of cores. Finally, the parallel DP algorithm is applied to a real-world, five-reservoir system in China. The results demonstrate the parallel efficiency and practical utility of the proposed methodology.

Use of parallel deterministic dynamic programming and hierarchical adaptive genetic algorithm for reservoir operation optimization

Reservoir operation optimization (ROO) is a complicated dynamically constrained nonlinear problem that is important in the context of reservoir system operation. In this study, parallel deterministic dynamic programming (PDDP) and a hierarchical adaptive genetic algorithm (HAGA) are proposed to solve the problem, which involves many conflicting objectives and constraints. In the PDDP method, multi-threads are found to exhibit better speed-up than single threads and to perform well for up to four threads. In the HAGA, an adaptive dynamic parameter control mechanism is applied to determine parameter settings, and an elite individual is preserved in the archive from the first hierarchy to the second hierarchy. Compared with other methods, the HAGA provides a better operational result with greater effectiveness and robustness because of the population diversity created by the archive operator. Comparison of the results of the HAGA and PDDP shows two contradictory objectives in the ROO problem-economy and reliability. The simulation results reveal that: compared with proposed PDDP, the proposed HAGA integrated with parallel model appears to be better in terms of power generation benefit and computational efficiency.

Dynamic programming for the quadratic assignment problem on trees

We consider the quadratic assignment problem in terms of graph theory. To solve it on a tree-like network, we present both sequential and parallel dynamic programming algorithms. We also present the results of numerical comparison of our algorithms with the IBM ILOG CPLEX suite.

Heuristics for work distribution of a homogeneous parallel dynamic programming scheme on heterogeneous systems

In this paper the possibility of including automatic optimization techniques in the design of parallel dynamic programming algorithms in heterogeneous systems is analyzed. The main idea is to automatically approach the optimum values of a number of algorithmic parameters (number of processes, number of processors, processes per processor), and thus obtain low execution times. Hence, users could be provided with routines which execute efficiently, and independently of the experience of the user in heterogeneous computing and dynamic programming, and which can adapt automatically to a new network of processors or a new network configuration.

Load balancing methods and parallel dynamic programming algorithm using dominance technique applied to the 0–1 knapsack problem

The parallelization on a supercomputer of a one list dynamic programming algorithm using dominance technique and processor cooperation for the 0–1 knapsack problem is presented. Such a technique generates irregular data structure, moreover the number of undominated states is unforeseeable. Original and efficient load balancing strategies are proposed. Finally, computational results obtained with an Origin 3800 supercomputer are displayed and analyzed. To the best of our knowledge, this is the first time for which computational experiments on a supercomputer are presented for a parallel dynamic programming algorithm using dominance technique.

Nondeterministic dynamic programming on a parallel coprocessing system

We describe how nondeterministic dynamic programming (DP) algorithms can be designed for a new class of parallel coprocessing systems using “functional memory”, an architecture based upon dataflow computer principles. We also show how Petri nets can be used to model and express such parallel DP algorithms. Finally, we discuss architectural improvements that would facilitate the processing of Petri net models of nondeterministic DP algorithms on functional memory computers (FMC).

Optimal operation of large hydrothermal systems applying parallelization techniques

Different alternatives to instrument parallelization techniques of long-term hydrothermal scheduling algorithms are given. First, a model for long-term operation planning is outlined, where uncertainties are handled with probabilistic and simulation techniques, and where hydrothermal optimization is carried out using dynamic programming (DP). Then, the application of parallelization to stochastic calculation is given, followed by four ways to solve DP in parallel. Finally, a cross-comparison is made regarding performance and code complexity using a test case, focusing on run-time characteristics of parallel DP algorithms.

Asynchronous analysis of parallel dynamic programming algorithms

We examine a very simple asynchronous model of parallel computation that assumes the time to compute a task is random, following some probability distribution. The goal of this model is to capture the effects of unpredictable delays on processors, due to communication delays or cache misses, for example. Using techniques from queueing theory and occupancy problems, we use this model to analyze two parallel dynamic programming algorithms. We show that this model is simple to analyze and correctly predicts which algorithm will perform better in practice. The algorithms we consider are a pipeline algorithm, where each processor i computes in order the entries of rows i, i+p, and so on, where p is the number of processors; and a diagonal algorithm, where entries along each diagonal extending from the left to the top of the table are computed in turn. It is likely that the techniques used here can be useful in the analysis of other algorithms that use barriers or pipelining techniques.

An efficient parallel dynamic programming algorithm

Antonio, Tsai, and Huang proposed a scheme in 1991 to parallelize the standard dynamic programming approach to solve combinatorial multistage problems. However, their dynamic programming approach is restricted to those multistage problems where the decision made at each stage depends only on decisions made in the stage immediately preceding it. For many interesting problems the decision at each stage depends on the decisions made at all the previous stages, and therefore their approach doesn't apply. The Matrix Chain Multiplication problem, Longest Common Subsequence problem, and Optimal Polygon Triangulation problem are some examples of such problems. We also present techniques for parallelizing the dynamic programming solution to such problems. The parallel algorithm we develop for a PRAM has complexity θ( n) employing θ( n 2) processors. Since the traditional sequential algorithm for such problems is θ( n 3), our parallel algorithm is an optimal parallel algorithm based on this traditional algorithm. We also describe the results of our experiments that are in conformity with our theoretical complexity results. We also compare and contrast our result with results obtained by earlier researchers and show that our parallel algorithm has optimal efficiency of 100% with respect to the traditional Dynamic Programming Algorithm.

Optimization and Performance Analysis of a Massively Parallel Dynamic Programming Algorithm for Rna Secondary Structure Prediction

An optimized and parallelized form of a dynamic pro gramming algorithm capable of generating optimal and suboptimal RNA secondary structures is pre sented. Implementation of this algorithm on a MasPar MP-2 with 16K processors is shown to perform ex tremely well for very large nucleic acid sequences such as HIV (AIDS) and Rhinovirus (common cold). These sequences are, respectively, 9,128 and 7,208 nu cleotides in length. By taking advantage of the parallel nature of MasPar and also optimizing the communica tion requirements the implementation essentially re duced the algorithm from order O(n3) to 0(n2). This reduction in complexity enables us to fold large RNA sequences in reasonable amounts of time. This capa bility has proven to be a valuable tool in studying the molecular structure and biological function of mole cules this large.

Parallel dynamic programming and ship voyage management

AbstractThe paper is concerned with the design and implementation of a parallel dynamic programming algorithm for use in ship voyage management The basic concepts are presented in terms of a simple model for weather routing. Other factors involved in voyage management, and their inclusion in a more comprehensive algorithm, are also discussed. The algorithms have been developed and implemented using a transputer‐based distributed‐memory parallel machine using the high‐level communication harness CS Tools. Trial calculations over grids of up to 282 nodes have been carried out and the results are presented. Good speed‐ups for the calculations have been attained, and the factors affecting the efficiency of the parallel computations are reviewed. These trial calculations indicate that a ship voyage management system based on parallel dynamic programming is likely to be beneficial.

Vectorization and multitasking of dynamic programming in control: Experiments on a CRAY-2

Parallelism in dynamic programming is considered within the specificity of optimal control. We present the program PDVP developed for solving a general deterministic discrete-time optimization problem by means of a parallel dynamic programming algorithm on the state variables. Multitasking and vectorization are considered from the viewpoint to implement PDVP on a CRAY-2. The performances are analysed through a significant application to the optimization of satellite trajectories. Promising results are obtained.

A VLSI Algorithm for the optimal detection of a curve

This paper presents a parallel dynamic programming algorithm for the extraction of a smooth curve from a digitized image. The algorithm can be implemented on a systolic architecture with a limited number of processors, independent of the image size. The machine can be upgraded easily to detect arbitrarily irregular curves.

A parallel variable-metric dynamic programming algorithm

This paper presents a potentially parallel iterative algorithm for the solution of the unconstrainedN-stage decision problem of dynamic programming. The basis of the algorithm is the use of variable-metric minimization techniques to develop a quadratic approximation to the cost function at each stage. The algorithm is applied to various problems, and comparisons with other algorithms are made.