The problem addressed in this paper is minimization of the number of linear functions in a linear decomposition. This paper proposes an exact minimization method based on dynamicprogramming for index generation funct...
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(纸本)9781728100920
The problem addressed in this paper is minimization of the number of linear functions in a linear decomposition. This paper proposes an exact minimization method based on dynamicprogramming for index generation functions. The proposed method searches for an optimum solution while recursively dividing an index set of a given index generation function. To use partial solutions efficiently in solution search, the proposed method represents partitions of an index set compactly and uniquely by zero-suppressed binary decision diagrams (ZDDs). Existing methods based on a branch-and-bound approach search for a solution sequentially in a depth first manner. On the other hand, the proposed method searches for multiple partial solutions in parallel in a breadth-first manner. Thus, once a solution is found, we can terminate the search process. This is because the depth of searches corresponds to the number of linear functions. Experimental results using benchmark index generation functions show the effectiveness of the proposed method.
This study employs the dynamicprogramming (DP) optimization approach to maximize the daily revenue of a concentrating solar power plant (CSP) equipped with a thermal energy storage system (TES). DP guarantees the opt...
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This study employs the dynamicprogramming (DP) optimization approach to maximize the daily revenue of a concentrating solar power plant (CSP) equipped with a thermal energy storage system (TES). DP guarantees the optimal solution and is easy from the computer coding point of view;therefore, it can be of great importance. Two real-life case studies are considered. The first case has a simple thermal model and is mainly chosen in order to verify the present optimization program. In this case, the present work achieves 1.3% (or US$480 /day) higher daily revenue in comparison with the literature. However, the simple thermal model of the first case study cannot appropriately simulate the actual operation of a CSP. Therefore, the optimization was applied to another case with a more detailed thermal model. The findings indicate that in order to maximize revenue, the charging and discharging of the TES should be managed such that the power block works under base load conditions (whenever it is active) and during periods of high electricity prices, regardless of the level of the daily solar radiation pattern. Furthermore, quantitative investigations show the substantial influence of the TES system on the daily revenue, especially for the case of low solar radiation pattern.
Building zoning is crucial for regional energy planning. Appropriate building zoning can effectively optimize the peak load, daily load rate and load standard deviation of buildings. However, a clear quantitative stan...
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Building zoning is crucial for regional energy planning. Appropriate building zoning can effectively optimize the peak load, daily load rate and load standard deviation of buildings. However, a clear quantitative standard for building zoning is currently lacking, and zoning methods based on minimum distance or load fluctuation are often employed, which often fail to achieve optimal zoning and energy-saving effects. To clarify building zoning in regional energy planning, this study proposes a dynamicprogramming approach and employs the analytic hierarchy process (AHP) to improve the zoning method. This is achieved by using the daily load rate, load standard deviation and building distance of each building group as the criterion layer, and assigns each peripheral building group to the appropriate building group. Taking a university campus as an example, this method reduces the peak heating load of 6136.61 kW and the peak cooling load of 15507.88 kW. The standard deviation of heating and cooling load of the building group has been reduced by 1272.53 kW and 2352.54 kW, respectively. Furthermore, the daily load rate of the building has been stabilized, and the staggered peak has been adjusted, resulting in a more uniform distribution frequency of the building load.
A dynamic programming method is used for the numerical solution of optimal control problems for forming structural elements under creep conditions. The method is implemented in a finite-element software package. The s...
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A dynamic programming method is used for the numerical solution of optimal control problems for forming structural elements under creep conditions. The method is implemented in a finite-element software package. The stability of the method is analyzed.
The Yellow River diversion project consists of three gates, two pumping stations, and one plain reservoir, with a total river length of 17.46 km in the Panzhuang Yellow River irrigation area, which provides the primar...
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The Yellow River diversion project consists of three gates, two pumping stations, and one plain reservoir, with a total river length of 17.46 km in the Panzhuang Yellow River irrigation area, which provides the primary water source for the Dezhou central city, Shandong Province, China. The project is subject to the constraints of the Yellow River diversion sluice diverting water time, reservoir diverting water time, and combinations of pumping stations with self -flowing gates. The opening and closing forms of the gates and pumps are complicated and irregular, and the switching of the gates and pumps mainly depends on the experience of the staff, which makes the water transfer cost high and the water transfer time long. Based on engineering compositions in the study area, an optimal mathematical model is constructed by the dynamic programming method. By combining the flow and water level, the objectives of the minimum operation cost, the shortest water transfer time and the combination of the two are established. A new optimization scheme of the switch between gates and pumps combined with water level and flow is proposed, which reduces the operation cost by 20% and the water transfer time by 8%, providing an efficient operation mode.
The influence of phase and other constraints on the method of searching for the trajectories of a civil supersonic aircraft that are optimal in terms of fuel consumption is considered. Based on the solutions found by ...
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The influence of phase and other constraints on the method of searching for the trajectories of a civil supersonic aircraft that are optimal in terms of fuel consumption is considered. Based on the solutions found by the dynamic programming method, which take into account the numerous conditions that must be satisfied by the flight altitude, pitch angle, normal overload, aircraft speed, engine thrust, etc., it is shown that almost all of these conditions can be ignored during the initial stage of calculations, since these constraints do not affect the optimal solutions. Therefore, one can first apply the maximum principle and use the dynamic programming method only in those cases where a sizeable part of the constraints turns out to be significant.
In this paper, optimal control models ruled by discrete and continuous stochastic descriptor systems are investigated in order. These descriptor systems are assumed to be regular and impulse-free. For settling discret...
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In this paper, optimal control models ruled by discrete and continuous stochastic descriptor systems are investigated in order. These descriptor systems are assumed to be regular and impulse-free. For settling discrete optimal control problems, a recurrence equation is proposed with the help of dynamic programming method. Then, optimal control problems for two types of discrete stochastic descriptor systems are considered and optimal solutions are presented by analytical expressions. To simplify continuous optimal control problems, an equation of optimality is derived according to the principle of optimality, and it reveals the essential connection between optimal value and optimal control. Two numerical examples and a factory management model are provided to illustrate the validness of above results.
Chance theory is a useful tool to deal with the analysis of indeterminacy, including both uncertainty and randomness. Based on chance theory, an optimal control for uncertain random continuous-time systems is introduc...
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Chance theory is a useful tool to deal with the analysis of indeterminacy, including both uncertainty and randomness. Based on chance theory, an optimal control for uncertain random continuous-time systems is introduced to design dynamic optimization problems. Applying the method of dynamicprogramming, the principle of optimality is presented and then the equation of optimality is provided to solve the proposed problem. Meanwhile, three special cases of optimal control problems are discussed by using the equation obtained. Finally, a numerical example and an optimal cash balance problem are given to show the effectiveness of the results achieved.
This paper investigates optimal control of a susceptible-infected-recovered (SIR) epidemic model using the dynamicprogramming approach. In fact, our study focuses on the modified model by incorporating it with a Bolz...
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Linear decomposition of index generation functions is a representation of index generation functions using two kinds of functions: linear functions and a function storing indices. Minimization of the number of linear ...
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Linear decomposition of index generation functions is a representation of index generation functions using two kinds of functions: linear functions and a function storing indices. Minimization of the number of linear functions in a linear decomposition is required for efficient implementation of index generation functions. This paper proposes a fast method to exactly minimize the number of linear functions, and shows its time and space complexities. The complexities are large because of the exact optimization method. But, experimental results show that actual computation time and memory size are quite small. This is because the proposed method searches for an optimum solution efficiently based on a dynamic programming method using zero-suppressed binary decision diagrams (ZDDs).
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