Variant Of Dynamic Programming Research Articles

Developing an integrated restoration model of multimodal transportation network

This paper presents a new optimisation model for restoring a multimodal transportation network disrupted by a catastrophic disaster. The model provides an integrated decision of restoration activities by considering the interdependencies of the road network and multimodal terminals for sending relief goods. A new particle swarm optimisation is proposed to determine the number of repair teams for the road network and restoration activities at the terminal. The problem of road restoration is addressed by presenting a new variant of dynamic programming and a greedy heuristic. The model was applied to a multimodal transportation network that was struck by the earthquake and tsunami. The optimal solution considering multimodal restoration decisions has been found to reduce the unsatisfied demand. The proposed particle swarm optimisation and greedy heuristic offer stability in searching for optimal solutions, whereas the proposed dynamic programming can provide an optimal solution with lower computational time.

Improved progressive optimality algorithm and its application to determination of optimal release trajectory of long-term power generation operation of cascade reservoirs

Dynamic programming (DP) is an effective method for solving multi-stage decision-making problems and has been extensively applied to the optimization of reservoir operations. However, the method is limited by the dimensionality problem; hence, it cannot be directly applied to optimizing the operations of a reservoir system with more than three reservoirs at current computing power. The progressive optimality algorithm (POA) is a classic variant of DP and has been widely used for optimizing multi-reservoir operations. Despite the use of a static variable decoupling strategy to ease DP's dimensionality problem, the POA's performance is reduced by an inherent drawback of the blind search of the static variable decoupling strategy and the dimensionality problem in two-stage solutions. To enhance the POA's performance, we propose an improved version of the POA known as the dipole optimization procedure (DOP) for optimizing cascade reservoir operations. In the improved algorithm, we use a dynamic variable decoupling strategy to obtain search directions that are more targeted than those of the POA so as to improve the quality of the solutions. The dynamic decoupling of variables was achieved by constructing and solving a dipole optimization problem using a DP model developed in this study. Moreover, a perturbation mechanism was introduced to address the POA's dimensionality problem so that the algorithm can be extended to larger reservoir systems. The results of the simulation of a hypothetical four-reservoir system and a real-world cascade reservoir system showed the superiority of the DOP over the POA and other five available alternatives. The comparison was based on the quality of solutions and solving efficiency. The results indicate that the DOP is rational and feasible and has the potential to be applied to optimizing the operation of large-scale multi-reservoir systems with numerous reservoirs.

Динамическое программирование в задаче маршрутизации: декомпозиционный вариант

The questions of applying the dynamic programming (DP) apparatus to the routing problem with constraints and cost functions with the tasks list dependence are investigated. It is supposed that binary partition of the task set is given; tasks of the first task group must be fulfilled before the fulfillment of the task of the second group begins. In each of the groups, precedence conditions may be present. This setting can be applied in the case of sheet cutting on CNC machines, where two above-mentioned groups form zones planned at the cutting stage. In general case, for the optimal solution construction, the two-stage variant of DP is used. Linking two versions of DP is realized by identification of the criterion terminal component for service problem of the first group with extremum function connected with the second group. The connection of optimal solutions for above-mentioned two problems allows to construct an optimal solution for the initial joint problem. Based on the theoretical constructions algorithm realized on personal computer is constructed; computing experiment is realized.

One task of routing jobs in high radiation conditions

The problem of sequential bypass of megalopolises is investigated, focused on the problem of dismantling a system of radiation hazardous objects under constraints in the form of precedence conditions. The radiation impact on the performers is assessed by the doses received during movements and during the performance of dismantling works. The route problem of minimizing the dose load of workers carrying out dismantling in one or another sequence of operations is considered. The procedure for constructing an optimal solution using a variant of dynamic programming is investigated. On this basis, an algorithm is built, implemented on a PC. Examples of the numerical solution of a model problem for the minimum dose load are given.

Multiple Object Tracking Using K-Shortest Paths Optimization

Multi-object tracking can be achieved by detecting objects in individual frames and then linking detections across frames. Such an approach can be made very robust to the occasional detection failure: If an object is not detected in a frame but is in previous and following ones, a correct trajectory will nevertheless be produced. By contrast, a false-positive detection in a few frames will be ignored. However, when dealing with a multiple target problem, the linking step results in a difficult optimization problem in the space of all possible families of trajectories. This is usually dealt with by sampling or greedy search based on variants of Dynamic Programming which can easily miss the global optimum. In this paper, we show that reformulating that step as a constrained flow optimization results in a convex problem. We take advantage of its particular structure to solve it using the k-shortest paths algorithm, which is very fast. This new approach is far simpler formally and algorithmically than existing techniques and lets us demonstrate excellent performance in two very different contexts.

FIXED PARAMETER ALGORITHMS FOR THE MINIMUM WEIGHT TRIANGULATION PROBLEM

We discuss and compare four fixed parameter algorithms for finding the minimum weight triangulation of a simple polygon with (n – k) vertices on the perimeter and k vertices in the interior (hole vertices), that is, for a total of n vertices. All four algorithms rely on the same abstract divide-and-conquer scheme, which is made efficient by a variant of dynamic programming. They are essentially based on two simple observations about triangulations, which give rise to triangle splits and paths splits. While each of the first two algorithms uses only one of these split types, the last two algorithms combine them in order to achieve certain improvements and thus to reduce the time complexity. By discussing this sequence of four algorithms we try to bring out the core ideas as clearly as possible and thus strive to achieve a deeper understanding as well as a simpler specification of these approaches. In addition, we implemented all four algorithms in Java and report results of experiments we carried out with this implementation.

Assignment of phonemes to the graphemes producing them

The assignment of phonemes to graphemes producing them in a lexicon having words (grapheme sequences) and their associated phonetic transcription (phoneme sequences) for the preparation of patterns for training neural networks for the purpose of grapheme-phoneme conversion is carried out with the aid of a variant of dynamic programming which is known as dynamic time warping (DTW).

A hierarchical non-parametric method for capturing non-rigid deformations

We present a novel approach for measuring image similarity based on the composition of parts. The measure identifies common sub-regions between the images at multiple sizes, and evaluates the amount of deformation required to align the common regions. The scheme allows complex, non-rigid deformation of the images, and penalizes irregular deformations more than coherent shifts of larger sub-parts. The measure is implemented by an algorithm which is a variant of dynamic programming, extended to multi-dimensions, and is using scores measured on a relative scale. The similarity measure is shown to be robust to non-rigid deformations of parts at various positions and scales, and to capture basic characteristics of human similarity judgments.

DETERMINATION OF THE FUEL-OPTIMAL TRAJECTORY FOR A VEHICLE ALONG A KNOWN ROUTE

Integration of topology data of the entire road ahead into the powertrain control unit in combination with hybrid electric powertrains offers a huge potential for optimising the control strategy. The intension of the present paper is to show a methodology for computing the maximum potential of fuel saving over a specified route. For this offline calculation a non-linear state-space model of the longitudinal dynamics is used to find the fuel optimal trajectory using Bellman's Dynamic Programming (DP). As the model is of third order with three control inputs and DP can only be applied to systems with a maximum sum of inputs and states of four, the iterative variant of DP is used. This special method described in this paper allows the solution of optimisation problems with a number of states and inputs up to six, without leading to insufferable computing times.

User Dependent Control of Dynamic Routing

The paper considers a user dependent control applied in dynamic routing tasks. These tasks are considered as multi-criteria optimization problem. Five fuzzy defined parameters, namely: time delay, waiting queue, cost of routing, link capacity, and priority, form theoptimization set. Hierarchical fuzzy decision system, which optimizes user choices among great number of perspective and affordable paths, has been created. Another system selects the set of perspective paths. It is based on a variant of dynamic programming. Both systems are realized on C++ executive code for better compatibility and real time applications. Simulations on MATLAB SIMULINK shellhave been performed.

A systematic approach to dynamic programming in bioinformatics.

Dynamic programming is probably the most popular programming method in bioinformatics. Sequence comparison, gene recognition, RNA structure prediction and hundreds of other problems are solved by ever new variants of dynamic programming. Currently, the development of a successful dynamic programming algorithm is a matter of experience, talent and luck. The typical matrix recurrence relations that make up a dynamic programming algorithm are intricate to construct, and difficult to implement reliably. No general problem independent guidance is available. This article introduces a systematic method for constructing dynamic programming solutions to problems in biosequence analysis. By a conceptual splitting of the algorithm into a recognition and an evaluation phase, algorithm development is simplified considerably, and correct recurrences can be derived systematically. Without additional effort, the method produces an early, executable prototype expressed in a functional programming language. The method is quite generally applicable, and, while programming effort decreases, no overhead in terms of ultimate program efficiency is incurred.

A dynamic programming successive approximations technique with convergence proofs

Dynamic programming (DP) is an effective method for solving multi-stage decision-making problems and has been extensively applied to the optimization of reservoir operations. However, the method is limited by the dimensionality problem; hence, it cannot be directly applied to optimizing the operations of a reservoir system with more than three reservoirs at current computing power. The progressive optimality algorithm (POA) is a classic variant of DP and has been widely used for optimizing multi-reservoir operations. Despite the use of a static variable decoupling strategy to ease DP's dimensionality problem, the POA's performance is reduced by an inherent drawback of the blind search of the static variable decoupling strategy and the dimensionality problem in two-stage solutions. To enhance the POA's performance, we propose an improved version of the POA known as the dipole optimization procedure (DOP) for optimizing cascade reservoir operations. In the improved algorithm, we use a dynamic variable decoupling strategy to obtain search directions that are more targeted than those of the POA so as to improve the quality of the solutions. The dynamic decoupling of variables was achieved by constructing and solving a dipole optimization problem using a DP model developed in this study. Moreover, a perturbation mechanism was introduced to address the POA's dimensionality problem so that the algorithm can be extended to larger reservoir systems. The results of the simulation of a hypothetical four-reservoir system and a real-world cascade reservoir system showed the superiority of the DOP over the POA and other five available alternatives. The comparison was based on the quality of solutions and solving efficiency. The results indicate that the DOP is rational and feasible and has the potential to be applied to optimizing the operation of large-scale multi-reservoir systems with numerous reservoirs.