Development of a hybrid dynamic programming approach for solving discrete nonlinear knapsack problems

Ghassemi-Tari, Farhad; Jahangiri, Eshagh

doi:10.1016/j.amc.2006.10.067

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…Low-head large-discharge pumps are generally used in open-channel water transfer systems, among which the axial-discharge pump is the most common choice. Ghassemi-Tari et al [27] transformed the discharge optimization problem of the pumping station into a discrete non-linear knapsack problem and proposed a new hybrid algorithm to improve the computational efficiency of the dynamic programming in solving this problem. Feng et al [28] studied the optimal operation of parallel pumping stations in an open-channel water transfer system and the influence of the source water level on the discharge.…”

Section: Introductionmentioning

confidence: 99%

Economic Operation of Variable Speed and Blade Angle-Adjustable Pumping Stations of an Open-Channel Water Transfer Project

Du,

Zhang,

Chen

et al. 2023

Water

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A large amount of energy would be consumed for open-channel water transfer projects due to the low efficiency of pumping stations. One measure to improve the efficiency of a pumping station is to install variable-frequency drives (VFDs). In this paper, a discharge optimization model is proposed for a single pumping station equipped with different numbers of variable speed and blade angle-adjustable pump (VSBAP) units, and then a head optimization model is proposed for cascade pumping stations. The study on the Miyun Reservoir Regulation and Storage Project in China shows that the installation of VFDs can increase the number of operable conditions of a single BAP unit by changing the blade angle and speed and ensure the high efficiency of the pumping unit under most operating conditions, thus reducing the energy consumption of the pumping station. It is desirable to install two VFDs in the Tuancheng Lake–Huairou Reservoir section to ensure the long-term operation of the cascade pumping stations in an economically profitable way. In conclusion, the installation of VFDs can effectively reduce the operation cost of cascade pumping stations.

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Section: Introductionmentioning

confidence: 99%

Economic Operation of Variable Speed and Blade Angle-Adjustable Pumping Stations of an Open-Channel Water Transfer Project

Du,

Zhang,

Chen

et al. 2023

Water

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“…Latter attempt provides a powerful solution procedure for solving a general class of the dynamic programming models. Since then a set of research works have been devoted to the reduction of state space solution [33], Righini and Salani [34], Fang et al [35], Russo et al [36], and Chebil and Khemakhem [37].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Dynamic Programming for Solving Fixed Cost Transportation with Discounted Mechanism

Tari

2016

Journal of Optimization

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The problem of allocating different types of vehicles for transporting a set of products from a manufacturer to its depots/cross docks, in an existing transportation network, to minimize the total transportation costs, is considered. The distribution network involves a heterogeneous fleet of vehicles, with a variable transportation cost and a fixed cost in which a discount mechanism is applied on the fixed part of the transportation costs. It is assumed that the number of available vehicles is limited for some types. A mathematical programming model in the form of the discrete nonlinear optimization model is proposed. A hybrid dynamic programming algorithm is developed for finding the optimal solution. To increase the computational efficiency of the solution algorithm, several concepts and routines, such as the imbedded state routine, surrogate constraint concept, and bounding schemes, are incorporated in the dynamic programming algorithm. A real world case problem is selected and solved by the proposed solution algorithm, and the optimal solution is obtained.

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Study of Optimal Operation for Huai’an Parallel Pumping Stations with Adjustable-Blade Units Based on Two Stages Decomposition-Dynamic Programming Aggregation Method

Gong

Cheng

Zhang

et al. 2011

Computer and Computing Technologies in Agriculture IV

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Two-stage decomposition-dynamic programming aggregation method has been first proposed and introduced to solve the mathematical model of daily optimal operation for parallel pumping stations with adjustable-blade units. Taking minimal daily electricity cost of single pump station as objective function, the water quantity pumped by each station as coordinated variable, by means of the type of the pump units this model is decomposed into several first-stage sub-model of daily optimal operation with adjustable-blade for single pump station. Then taking minimal daily electricity cost of single pump unit as objective function, the water quantity pumped by each unit as coordinated variable, the first-stage sub-model is decomposed into several second-stage sub-model of daily optimal operation with adjustable-blade for single pump unit which takes the blade angle as decision variable, the discrete values of water quantity pumped by each unit as state variable, and is solved by means of dynamic programming method. The constructed aggregation model takes daily water quantity pumped by each pump unit as decision variable, the discrete values of water quantity pumped by parallel station group as state variable, and is also solved by dynamic programming method. The aggregation process replaces the traditional method of constructing equations. This method has first solved the optimal operation issues for multi-units of parallel stations with various operation modes, time period division and daily average head of each station, and also provided theoretical support for the study on optimal operation of multi-stage pumping stations. Taking Huai'an No.1, No.2, and No.4 parallel pumping stations as a study case, a series of optimization results have been obtained.

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Development of a hybrid dynamic programming approach for solving discrete nonlinear knapsack problems

Cited by 5 publications

References 17 publications

Economic Operation of Variable Speed and Blade Angle-Adjustable Pumping Stations of an Open-Channel Water Transfer Project

Economic Operation of Variable Speed and Blade Angle-Adjustable Pumping Stations of an Open-Channel Water Transfer Project

A Hybrid Dynamic Programming for Solving Fixed Cost Transportation with Discounted Mechanism

Study of Optimal Operation for Huai’an Parallel Pumping Stations with Adjustable-Blade Units Based on Two Stages Decomposition-Dynamic Programming Aggregation Method

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