Traditional Dynamic Programming Algorithm Research Articles

Intelligent Low-Consumption Optimization Strategies: Economic Operation of Hydropower Stations Based on Improved LSTM and Random Forest Machine Learning Algorithm

The economic operation of hydropower stations has the potential to increase water use efficiency. However, there are some challenges, such as the fixed and unchangeable flow characteristic curve of the hydraulic turbines, and the large number of variables in optimal load distribution, which limit the progress of research. In this paper, we propose a new optimal method of the economic operation of hydropower stations based on improved Long Short-Term Memory neural network (I-LSTM) and Random Forest (RF) algorithm. Firstly, in order to accurately estimate the water consumption, the LSTM model’s hyperparameters are optimized using improved particle swarm optimization, and the I-LSTM method is proposed to fit the flow characteristic curve of the hydraulic turbines. Secondly, the Random Forest machine learning algorithm is introduced to establish a load-distribution model with its powerful feature extraction and learning ability. To improve the accuracy of the load-distribution model, we use the K-means algorithm to cluster the historical data and optimize the parameters of the Random Forest model. A Hydropower Station in China is selected for a case study. It is shown that (1) the I-LSTM method fits the operating characteristics under various working conditions and actual operating characteristics of hydraulic turbines, ensuring that they are closest to the actual operating state; (2) the I-LSTM method is compared with Support Vector Machine (SVM), Extreme Learning Machine (ELM) and Long Short-Term Memory neural network (LSTM). The prediction results of SVM have a large error, but compared with ELM and LSTM, MSE is reduced by about 46% and 38% respectively. MAE is reduced by about 25% and 21%, respectively. RMSE is reduced by about 27% and 24%, respectively; (3) the RF algorithm performs better than the traditional dynamic programming algorithm in load distribution. With the passage of time and the increase in training samples, the prediction accuracy of the Random Forest model has steadily improved, which helps to achieve optimal operation of the units, reducing their average total water consumption by 1.24%. This study provides strong support for the application of intelligent low-consumption optimization strategies in hydropower fields, which can bring higher economic benefits and resource savings to renewable energy production.

An improved dynamic programming algorithm for security-constrained unit commitment under spatial-temporal decomposition framework

The security-constrained unit commitment with AC power flow constraints (AC-SCUC) is a typical NP-hard problem, which is difficult to be solved by traditional methods in a reasonable time. In this paper, it is decomposed into a number of tractable subproblems in both spatial and temporal dimensions, and then solved by an improved dynamic programming (IDP) algorithm. Different from traditional dynamic programming (DP) algorithms, which need to enumerate each unit status at each period, we just need to determine the start and end periods of each consecutive status. Such that the state space can be reduced greatly. Moreover, compared with traditional DP algorithms, which acquire the optimal cost of each decision by iteration, IDP directly obtains them through a closed-form solution technique without iteration, and thus has higher computational efficiency. Case studies on various test systems demonstrate the effectiveness of the proposed algorithm.

Research on Global Optimization Algorithm of Integrated Energy and Thermal Management for Plug-In Hybrid Electric Vehicles.

Power distribution and battery thermal management are important technologies for improving the energy efficiency of plug-in hybrid electric vehicles (PHEVs). In response to the global optimization of integrated energy thermal management strategy (IETMS) for PHEVs, a dynamic programming algorithm based on adaptive grid optimization (AGO-DP) is proposed in this paper to improve optimization performance by reducing the optimization range of SOC and battery temperature, and adaptively adjusting the grid distribution of state variables according to the actual feasible region. The simulation results indicate that through AGO-DP optimization, the reduction ratio of the state feasible region is more than 30% under different driving conditions. Meanwhile, the algorithm can obtain better global optimal driving costs more rapidly and accurately than traditional dynamic programming algorithms (DP). The computation time is reduced by 33.29-84.67%, and the accuracy of the global optimal solution is improved by 0.94-16.85% compared to DP. The optimal control of the engine and air conditioning system is also more efficient and reasonable. Furthermore, AGO-DP is applied to explore IETMS energy-saving potential for PHEVs. It is found that the IETMS energy-saving potential range is 3.68-23.74% under various driving conditions, which increases the energy-saving potential by 0.55-3.26% compared to just doing the energy management.

Link Analysis for Solving Multiple-Access MDPs With Large State Spaces

Wireless communication networks can be well-modeled by Markov Decision Processes (MDPs). While traditional dynamic programming algorithms such as value and policy iteration have lower complexity than brute force strategies, they still suffer from complexity issues for large state spaces. In this paper, the development of moderate complexity algorithms with high performance is sought for wireless network control. To this end, the approximate value function can be computed by projecting the original value function into a lower-dimensional subspace with the careful choice of basis vectors using tools from graph signal processing (GSP). Although GSP theory mainly focuses on undirected graphs, the transition graphs of MDPs for wireless networks are generally directed. For this reason, graph symmetrization based on the co-link method is considered due to its ability to preserve multi-hop dependencies in the graph. Given the multiple-access model under consideration, key properties of the transition probability matrix are exploited to determine the optimal subspace for the approximate value function with low complexity. The numerical results for a multiple-access channel show that the proposed algorithm can find the optimal basis vectors with high accuracy, and furthermore, the approach is robust to changes in system parameters. It is also shown that the projected equation method outperforms the state aggregation technique in producing higher accuracy with a lower runtime complexity.

Online Control Strategy for Plug-In Hybrid Electric Vehicles Based on an Improved Global Optimization Algorithm

Neural networks are widely used in the learning of offline global optimization rules to reduce the fuel consumption and real-time performance of hybrid electric vehicles. Considering that the torque and transmission ratio are direct control variables, online recognition by a neural network of these two parameters is insufficiently accurate. In the meanwhile, the dynamic program (DP) algorithm requires huge computing costs. Based on these problems, a fusion algorithm combining a dynamic programming algorithm and an approximate equivalent fuel consumption minimum control strategy (A-ECMS) is proposed in this paper. Taking the equivalent factor as the control variable, the global optimal sequence of the factor is obtained offline. The back propagation (BP) neural network is used to extract the sequence to form an online control strategy. The simulation results illustrate that, compared with the traditional dynamic programming algorithm, although the fuel consumption increases slightly, the computational cost of the fusion algorithm proposed in this paper is significantly reduced. Moreover, because the optimal sequence of the equivalent factors is within a particular range, the online control strategy based on DP-A-ECMS has a high robustness. Compared with an online control strategy based on the torque and transmission ratio, the fuel economy is improved by 2.46%.

Intelligent Test Paper Generation Based on Dynamic Programming Algorithm

This paper describes the problem of intelligent paper grouping and its mathematical model. By optimizing and improving the traditional dynamic programming algorithm, its space complexity is reduced from O(nb) to O(b). At the same time, the flexibility of dynamic programming algorithm is increased by using marker function and tracking algorithm, and the result composition is tracked to obtain the optimal solution. Finally, through several experiments, the improved dynamic programming algorithm is compared with the greedy algorithm and brute force algorithm, and it is found that the improved dynamic programming algorithm has a very good result and is with high efficiency when applied to the simple test paper. It is the most recommended algorithm among the two algorithms compared in this paper.

Fast gap-affine pairwise alignment using the wavefront algorithm.

MotivationPairwise alignment of sequences is a fundamental method in modern molecular biology, implemented within multiple bioinformatics tools and libraries. Current advances in sequencing technologies press for the development of faster pairwise alignment algorithms that can scale with increasing read lengths and production yields.ResultsIn this article, we present the wavefront alignment algorithm (WFA), an exact gap-affine algorithm that takes advantage of homologous regions between the sequences to accelerate the alignment process. As opposed to traditional dynamic programming algorithms that run in quadratic time, the WFA runs in time O(ns), proportional to the read length n and the alignment score s, using memory. Furthermore, our algorithm exhibits simple data dependencies that can be easily vectorized, even by the automatic features of modern compilers, for different architectures, without the need to adapt the code. We evaluate the performance of our algorithm, together with other state-of-the-art implementations. As a result, we demonstrate that the WFA runs 20–300× faster than other methods aligning short Illumina-like sequences, and 10–100× faster using long noisy reads like those produced by Oxford Nanopore Technologies.Availability and implementationThe WFA algorithm is implemented within the wavefront-aligner library, and it is publicly available at https://github.com/smarco/WFA.

EFFECTIVE DYNAMIC PROGRAMMING ALGORITHMS

This article is devoted to the analysis of the possibilities of increasing the speed of dynamic programming algorithms in solving applied problems of large dimension. Dynamic programming is considered rather than as an optimization method, but as a methodology that allows developing, from a single theoretical point of view, algorithms for solving problems that can be formalized in the form of multi-stage (multi-step) processes in which similar tasks are solved at all steps. It is shown that traditional dynamic programming algorithms based on preliminary setting of a regular grid of states are ineffective, especially if the parameters defining the states are not integer. The problems are considered, in the solution of which it is advisable to build a set of states in the process of counting, moving from one stage to another. Additional conditions are formulated that must be satisfied by the problem so that deliberately hopeless states do not fall into sets of states at each step. This ensures the rejection of not only the paths leading to each of the states, as in traditional dynamic programming algorithms, but also the unpromising states themselves, which greatly increases the efficiency of dynamic programming. Examples of applied problems are given, for the solution of which traditional dynamic programming algorithms were previously proposed, but which can be more efficiently solved by the proposed algorithm with state rejection. As applied to two-parameter problems, the concrete examples demonstrate the effectiveness of the algorithm with rejecting states in comparison with traditional algorithms, especially with increasing the dimension of the problem. An applied problem is considered, in the solution of which dynamic programming is used to construct recurrent formulas for calculating the optimal solution without enumerating options at all.

Lecturer, Department of Management, Sichuan Conservatory of Music, Chengdu, China.

At present, social media is developing rapidly, and the frequency of public crises is increasing, which has a certain impact on social stability. This paper studies the public crisis management measures based on dynamic programming algorithm. According to the knapsack problem of public crisis management, dynamic programming algorithm was designed, and the traditional dynamic programming algorithm came up, then 5 different types of data sets used for three dynamic programming algorithms were run 10 times in the 5 different types of experimental data sets. The test results show that the efficiency of the algorithm proposed in this paper is improved.

Development of Global Optimization Algorithm for Series-Parallel PHEV Energy Management Strategy Based on Radau Pseudospectral Knotting Method

The powertrain model of the series-parallel plug-in hybrid electric vehicles (PHEVs) is more complicated, compared with series PHEVs and parallel PHEVs. Using the traditional dynamic programming (DP) algorithm or Pontryagin minimum principle (PMP) algorithm to solve the global-optimization-based energy management strategies of the series-parallel PHEVs is not ideal, as the solution time is too long or even impossible to solve. Chief engineers of hybrid system urgently require a handy tool to quickly solve global-optimization-based energy management strategies. Therefore, this paper proposed to use the Radau pseudospectral knotting method (RPKM) to solve the global-optimization-based energy management strategy of the series-parallel PHEVs to improve computational efficiency. Simulation results showed that compared with the DP algorithm, the global-optimization-based energy management strategy based on the RPKM improves the computational efficiency by 1806 times with a relative error of only 0.12%. On this basis, a bi-level nested component-sizing method combining the genetic algorithm and RPKM was developed. By applying the global-optimization-based energy management strategy based on RPKM to the actual development, the feasibility and superiority of RPKM applied to the global-optimization-based energy management strategy of the series-parallel PHEVs were further verified.

Collaborative Data Scheduling With Joint Forward and Backward Induction in Small Satellite Networks

Small satellite networks (SSNs) have attracted intensive research interest recently and have been regarded as an emerging architecture to accommodate the ever-increasing space data transmission demand. However, the limited number of on-board transceivers restricts the number of feasible contacts (i.e., an opportunity to transmit data over a communication link), which can be established concurrently by a satellite for data scheduling. Furthermore, limited battery space, storage space, and stochastic data arrivals can further exacerbate the difficulty of the efficient data scheduling design to well match the limited network resources and random data demands, so as to the long-term payoff. Based on the above motivation and specific characteristics of SSNs, in this paper, we extend the traditional dynamic programming algorithms and propose a finite-embedded-infinite two-level dynamic programming framework for optimal data scheduling under a stochastic data arrival SSN environment with joint consideration of contact selection, battery management, and buffer management while taking into account the impact of current decisions on the infinite future. We further formulate this stochastic data scheduling optimization problem as an infinite-horizon discrete Markov decision process (MDP) and propose a joint forward and backward induction algorithm framework to achieve the optimal solution of the infinite MDP. Simulations have been conducted to demonstrate the significant gains of the proposed algorithms in the amount of downloaded data and to evaluate the impact of various network parameters on the algorithm performance.

Ascent trajectory tracking method using time-varying quadratic adaptive dynamic programming

Ascent trajectory tracking in the longitudinal plane is a class of nonaffine noncascade nonlinear system control problems with single input and multiple output, which is difficult to control by nonlinear method directly. Adaptive dynamic programming algorithm has the advantages of precise control and adaptability for general nonlinear control problem, and the time-varying quadratic adaptive dynamic programming algorithm proposed in this paper promotes the convergence and calculation speed of the traditional adaptive dynamic programming algorithm. To implement the algorithm effectively, the independent variables of ascent model are substituted in the launching coordinate, and then the model is treated as a discrete nominal trajectory tracking problem. Besides, the heuristic dynamic programming structure is used to train the processed model, and thus only the time-varying weight in the designed evaluation network needs to be updated. Simulation shows that the proposed algorithm can update the control variable online after predicting the cost function offline with the dynamic equations, which is faster than the general adaptive dynamic programming algorithm. In addition, the proposed algorithm can effectively and accurately track the nominal trajectory under the uncertainty of parameters compared with the linear quadratic regulators algorithm.

New Algorithm for Determining the Similarities of Nucleotide Sequences Based on Comparisons of Torsion of Discrete Curves

Discrete curves can be used to characterize sequences and the complete coding information of DNA in three-dimensional space. When the curve possesses properties that, in a mapping relationship, mirror those of DNA sequences, its characteristic values reveal the biological characteristics of a DNA sequence. By describing a DNA sequence using the recent Z curve model, we here propose a new method to judge the similarities of discrete DNA curves based on comparisons of the torsion of the curves. This comparative method was verified by quantitatively analyzing the similarities of cDNA sequences of 10 types of avian influenza viruses. Compared with a traditional dynamic programming algorithm, this new method takes full advantage of computer geometry for genetic comparative analyses by shifting from the traditional approach of a direct comparison of gene sequence characteristics to a comparison of the similarity of spatially discrete curves.

HEV power management control strategy for urban driving

The aim of this paper is to further improve the fuel efficiency and keep the balance of battery SOC simultaneously during urban driving. A dynamic programming (DP)-optimized HEV power management control strategy is proposed. The DP algorithm is applied to obtain the optimal engine/motor power distribution and utilized for the design of the fuzzy control strategy. The traditional DP algorithm is modified with the consideration of SOC balance for HEVs. In the analysis of DP simulation results, rules of torque slip behaviors have been found, which are directly utilized in the design of fuzzy control strategy. In order to improve the practicality of the control strategy to meet the diversities of city driving patterns, an urban driving pattern recognition method is presented. To evaluate the control performance, the proposed control strategy is also compared with the conventional rule-based strategy. The simulation results indicate that by adopting the proposed strategy the fuel efficiency of HEV is improved, and the SOC of the battery is kept in balance during different urban driving cycles.

Physical topology optimization of infrastructure health monitoring sensor network for high-speed rail

With the rapid development of high-speed rail (HSR) systems, the security and safety of these huge systems are becoming the primary concerns for passengers. HSR infrastructure plays an important role in HSR systems, making the maintenance of security and safety of the HSR infrastructure especially important. Meanwhile, sensor network technologies allow the realization of real-time and all-weather monitoring of HSR infrastructure. This paper analyzes the application requirements and characteristics of infrastructure health monitoring sensor network (IHMSN) through construction of a three-layer IHMSN which is composed of end devices, repeater points, and access points. The physical topology optimization goal of IHMSN is to set the optimal number of network nodes (namely, minimum cost) as well as the best physical connections. Given types and amount of the end devices, a multiple knapsack model is established which converts the physical topology optimization problems into multiple knapsack problems. Based on the different needs of practical application, three different cases (basis case, adding devices case and weight-based case) are proposed, and the corresponding models are built. Some artificial intelligence algorithms and a traditional dynamic programming algorithm are presented to solve the problems. In addition, a general algorithmic finite state machine is proposed to describe the solving process. After comparing these algorithms in execution time, memory, and optimal results, the genetic algorithm and particle swarm optimization algorithm stand out when used to solve the basic case as well as the extended cases. The numerical results show that these proposed models and algorithms can effectively solve the physical topology optimization problem of IHMSN for HSR systems. Moreover, these methods can effectively reduce network costs and provide a theoretical basis for network communication link optimization.

Analysis and comparison of optimal power management strategies for a series plug-in hybrid school bus via dynamic programming

This paper examines two optimal power management strategies, i.e., blending (BL) strategy and charge-depleting/charge-sustaining (CD/CS) strategy, for a series plug-in school bus. The minimum fuel consumption results of these two strategies are compared and the pattern of the globally optimal battery state of charge (SoC) trajectories is analysed. Dynamic programming (DP) approach which is able to achieve global optimisation is applied in this study to guarantee a fair comparison. More specifically, to overcome interpolation leakage in traditional DP algorithms, a level-set algorithm is utilised. Simulation results show that: 1) The globally optimal way to control is to linearly deplete the battery SoC to its minimum allowable value when the vehicle reaches to the end of the journey; 2) The difference between the optimal fuel economy that can be achieved by the BL and CD/CS strategies is very marginal for a series plug-in powertrain, which is in the order of 1-2%.

Cycle-based optimal NOx emission control of selective catalytic reduction systems with dynamic programming algorithm

In this work, we investigate the cycle-based optimal NOx emission control for Diesel engine selective catalytic reduction (SCR) systems. The optimization is carried out based on the SCR model and the SCR is assumed to be a continuous stirred tank reactor during the modeling. Considering the main chemical reactions inside an SCR cell, a three-state nonlinear model is obtained and the system parameters are determined by using the experimental data. The states of the nonlinear model consist of the NOx concentration, the ammonia concentration, and the ammonia coverage ratio. Though there are considerable works on the SCR dosing control in the literature, the optimal control strategy applied to the SCR systems has been rarely studied. The global optimality in the SCR dosing control can be used as a benchmark and evaluate the performance of other designed controllers. Moreover, it can be employed to find the limit of NOx conversion efficiency of a specific SCR aftertreatment system and select the minimal volume of the SCR catalyst cell. Therefore, it is quite meaningful to study the optimal NOx emission control of SCR systems via the dynamic programming approach. For the optimization, the challenges arise from the following aspects: (1) Due to the system stiffness, we cannot find an equivalent discrete-time model for the traditional dynamic programming, that is, the traditional dynamic programming algorithm is not applicable. (2) The computational load is relatively too heavy and a personal PC is not affordable. To deal with the existing challenges, we propose the dynamic programming algorithm based on the continuous-time SCR model. The computational load is adjustable in terms of the accuracy. The proposed algorithm is then applied to the SCR system for the NOx emission reduction. And the algorithm validation is carried out based on the US06 test cycle. It infers from the optimization results and the comparison, the prescribed ammonia slip constraint is satisfied and the tailpipe NOx emission is optimized.

Dynamic programming algorithms for the bi-objective integer knapsack problem

This paper presents two new dynamic programming (DP) algorithms to find the exact Pareto frontier for the bi-objective integer knapsack problem. First, a property of the traditional DP algorithm for the multi-objective integer knapsack problem is identified. The first algorithm is developed by directly using the property. The second algorithm is a hybrid DP approach using the concept of the bound sets. The property is used in conjunction with the bound sets. Next, the numerical experiments showed that a promising partial solution can be sometimes discarded if the solutions of the linear relaxation for the subproblem associated with the partial solution are directly used to estimate an upper bound set. It means that the upper bound set is underestimated. Then, an extended upper bound set is proposed on the basis of the set of linear relaxation solutions. The efficiency of the hybrid algorithm is improved by tightening the proposed upper bound set. The numerical results obtained from different types of bi-objective instances show the effectiveness of the proposed approach.

Parallel Evaluation of a Spatial Traversability Cost Function on GPU for Efficient Path Planning

A parallel version of the traditional grid based cost-to-go function generation algorithm used in robot path planning is introduced. The process takes advantage of the spatial layout of an occupancy grid by concurrently calculating the next wave front of grid cells usually evaluated sequentially in traditional dynamic programming algorithms. The algorithm offers an order of magnitude increase in run time for highly obstacle dense worst-case environments. Efficient path planning of real world agents can greatly increase their accuracy and responsiveness. The process and theoretical analysis are covered before the results of practical testing are discussed.

General space-efficient sampling algorithm for suboptimal alignment

Suboptimal alignments always reveal additional interesting biological features and have been successfully used to informally estimate the significance of an optimal alignment. Besides, traditional dynamic programming algorithms for sequence comparison require quadratic space, and hence are infeasible for long protein or DNA sequences. In this paper, a space-efficient sampling algorithm for computing suboptimal alignments is described. The algorithm uses a general gap model, where the cost associated with gaps is given by an affine score, and randomly selects an alignment according to the distribution of weights of all potential alignments. If x and y are two sequences with lengths n and m, respectively, then the space requirement of this algorithm is linear to the sum of n and m. Finally, an example illustrates the utility of the algorithm.