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Journal articles on the topic 'Mathematical optimization. Dynamic programming'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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1

Cakir, Merve Nur, Mehwish Saleemi, and Karl-Heinz Zimmermann. "Dynamic Programming in Topological Spaces." WSEAS TRANSACTIONS ON COMPUTERS 20 (June 25, 2021): 88–91. http://dx.doi.org/10.37394/23205.2021.20.11.

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Dynamic programming is a mathematical optimization method and a computer programming method as well. In this paper, the notion of sheaf programming in topological spaces is introduced and it is demonstrated that it relates very well to the concept of dynamic programming.

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2

Zhang, Mei, Jing Hua Wen, and Wei Xiao. "Optimization Allocation Research of Enterprise Resources Based on Dynamic Programming." Applied Mechanics and Materials 55-57 (May 2011): 2157–62. http://dx.doi.org/10.4028/www.scientific.net/amm.55-57.2157.

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Dynamic programming algorithm is classical strategy to solve the optimization problem. The distributing of enterprise resource is a multistage decision problem, having the characteristic of dynamic programming algorithm. We establish distribution of mathematical model of planning target, using dynamic programming principle and method to divide enterprise resource allocation stage reasonably, and then we use the recursion method to structure dynamic programming equation from the bottom up. Using VC++6.0 development platform is to compute the optimal decision-making sequence and maximum of profit. Dynamic programming makes optimum resource allocation for an enterprise, and it is high application value in resource allocation.

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Chaari, Riadh, Moez Abennadher, Jamel Louati, and Mohamed Haddar. "Mathematical methodology for optimization of the clamping forces accounting for workpiece vibratory behaviour." International Journal for Simulation and Multidisciplinary Design Optimization 5 (2014): A13. http://dx.doi.org/10.1051/smdo/2013005.

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This paper addresses the problem of determining the minimum clamping forces that ensure the dynamic fixturing stability. The clamping force optimization problem is formulated as a bi-level nonlinear programming problem and solved using a computational intelligence technique called particle swarm optimization (PSO). Indeed, we present an innovative simulation methodology that is able to study the effects of fixture-workpiece system dynamics and the continuously change due to material removal on fixturing stability and the minimum required clamping forces during machining. The dynamic behaviour of the fixtured workpiece subjected to time-and space-varying machining loads is simulated using a forced vibration model based on the regenerative vibrations of the cutter and workpiece excited by the dynamic cutting forces. Indeed, Material removal significantly affects the fixture-workpiece system dynamics and subsequently the minimum clamping forces required for achieving fixturing dynamic stability.

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4

Mankowski, Michal, and Mikhail Moshkov. "Dynamic programming bi-criteria combinatorial optimization." Discrete Applied Mathematics 284 (September 2020): 513–33. http://dx.doi.org/10.1016/j.dam.2020.04.016.

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5

Gatter, Thomas, Robert Giegerich, and Cédric Saule. "Integrating Pareto Optimization into Dynamic Programming." Algorithms 9, no. 1 (January 27, 2016): 12. http://dx.doi.org/10.3390/a9010012.

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6

Coşgun, Özlem, Ufuk Kula, and Cengiz Kahraman. "Markdown Optimization via Approximate Dynamic Programming." International Journal of Computational Intelligence Systems 6, no. 1 (February 2013): 64–78. http://dx.doi.org/10.1080/18756891.2013.754181.

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7

Al-Sulami, Hamed H., Nawab Hussain, and Jamshaid Ahmad. "Some Generalized Fixed Point Results with Applications to Dynamic Programming." Journal of Function Spaces 2020 (September 26, 2020): 1–8. http://dx.doi.org/10.1155/2020/8130764.

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The aim of this paper is to introduce some generalized contractions and prove certain new fixed point results for self-mappings satisfying these contractions in the setting of F-metric space. As an application of our results, we investigate the problem of dynamic programming related to the multistage process which formulates the problems of computer programming and mathematical optimization. We also provide an example to support the validity of our main results.

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8

She, Kun, Lian Zhe Ma, Jian Ru Wan, and Dong Hui Li. "Application of Dynamic Chaos PSO Algorithm in Elevator Configuration." Applied Mechanics and Materials 734 (February 2015): 548–53. http://dx.doi.org/10.4028/www.scientific.net/amm.734.548.

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A multi-objective optimized mathematical model of elevator configuration is established based on the analysis of the fact that elevator configuration is a problem of multi-objective optimization, and the weight coefficient of multi-objective function is set according to the characteristics of office building traffic flow. Dynamic Chaos Particle Swarm Optimization (DCPSO) algorithm, which is the improvement of the standard PSO algorithm, is used to optimize the multi-objective optimized mathematical model of elevator configuration. An application case illustrates that the DCPSO algorithm is reasonable and effective in elevator configuration through the application system of elevator configuration which is designed by the hybrid programming technology of VB and MATLAB.

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9

Senchukov, Viktor. "The solution of optimization problems in the economy by overlaying integer lattices: applied aspect." Economics of Development 18, no. 1 (June 10, 2019): 44–55. http://dx.doi.org/10.21511/ed.18(1).2019.05.

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The results of generalization of scientific approaches to the solution of modern economic optimization tasks have shown the need for a new vision of their solution based on the improvement of existing mathematical tools. It is established that the peculiarities of the practical use of existing mathematical tools for solving economic optimization problems are caused by the problems of enterprise management in the presence of nonlinear processes in the economy, which also require consideration of the corresponding characteristics of nonlinear dynamic processes. The approach to solving the problem of integer (discrete) programming associated with the difficulties that arise when applying precise methods (methods of separation and combinatorial methods) is proposed, namely: a fractional Gomorrhic algorithm – for solving entirely integer problems (by gradual "narrowing" areas of admissible solutions of the problem under consideration); the method of branches and borders - which involves replacing the complete overview of all plans by their partial directional over. Illustrative examples of schemes of geometric programming, fractional-linear programming, nonlinear programming with a non-convex region, fractional-nonlinear programming with a non-convex domain, and research on the optimum model of Cobb-Douglas model are given. The advanced mathematical tools on the basis of the method of overlaying integer grids (OIG), which will solve problems of purely discrete, and not only integer optimization, as an individual case, are presented in the context of solving optimization tasks of an applied nature and are more effective at the expense of reducing the complexity and duration of their solving. It is proved that appropriate analytical support should be used as an economic and mathematical tool at the stage of solving tasks of an economic nature, in particular optimization of the parameters of the processes of organization and preparation of production of new products of the enterprises of the real sector of the economy.

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10

van Otterlo, Martijn. "Intensional dynamic programming. A Rosetta stone for structured dynamic programming." Journal of Algorithms 64, no. 4 (October 2009): 169–91. http://dx.doi.org/10.1016/j.jalgor.2009.04.004.

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11

Bian, Tao, and Zhong-Ping Jiang. "Continuous-Time Robust Dynamic Programming." SIAM Journal on Control and Optimization 57, no. 6 (January 2019): 4150–74. http://dx.doi.org/10.1137/18m1214147.

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12

Gong, Yi, and Jilin Cheng. "Combinatorial Optimization Method for Operation of Pumping Station with Adjustable Blade and Variable Speed Based on Experimental Optimization of Subsystem." Advances in Mechanical Engineering 6 (January 1, 2014): 283520. http://dx.doi.org/10.1155/2014/283520.

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A decomposition-dynamic programming aggregation method based on experimental optimization for subsystem was proposed to solve mathematical model of optimal operation for single pumping station with adjustable blade and variable speed. Taking minimal daily electric cost as objective function and water quantity pumped by units as coordinated variable, this model was decomposed into several submodels of daily optimal operation with adjustable blade and variable speed for single pump unit which was solved by experimental optimization. The constructed aggregation model took water quantity pumped by each pump unit as decision variable and discrete values of water quantity pumped by pumping station as state variable and was solved by one-dimensional dynamic programming. Taking operation of typical pumping station as a study case, optimal operation with adjustable blade and variable speed, respectively, had an average cost saving of 4.19%, 22.15%, and 29.86% compared with operation with fixed blade angle and constant speed under 100%, 80%, and 60% load, which also had a remarkable saving amplitude of 15.85% and 24.18%, respectively, corresponding to 80% load and 60% load compared with operation with adjustable blade and constant speed. Meanwhile, the proposed method has provided a new way for solving complex nonlinear mathematical models with 3 decision variables.

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Tang, Wen Xian, Jun Jie Sun, and Bin Wang. "Study on Dynamic Balance in Main Driving Mechanism of Cold Rolling Mill Based on the Particle Swarm Optimization Algorithm." Applied Mechanics and Materials 55-57 (May 2011): 633–38. http://dx.doi.org/10.4028/www.scientific.net/amm.55-57.633.

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A method for comprehensive dynamic balance of mechanism based on the particle swarm optimization is presented. This paper adopted nonlinear multi-objective programming method to carry out a study on three dynamic property indexes including inertia force, reaction of kinematic pair and input torque. Optimum solution for the parameters estimation problem based on the particle swarm optimization algorithm is obtained by constructing a fitness function of the mathematical optimization model, which consists of those property indexes. The simulation results indicate that the proposed method could eliminate the reluctant evaluations and interactions remarkably, thus improves the application's performance.

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Kazaryan, Ruben, Peraskovya Andreeva, and Natalya Galaeva. "Organization of planning in transport construction." E3S Web of Conferences 157 (2020): 04006. http://dx.doi.org/10.1051/e3sconf/202015704006.

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Purpose. Development of methods and models of economic efficiency of the integrated use of various modes of transport in the interests of ensuring national security of the state. Methods. System analysis, logical-mathematical modeling, systems theory, economic-visual modeling, research methods of operations, economic and mathematical methods. Results. The paper discusses the need for the application of economic and mathematical models in the design of transport construction (model of “moving the earth masses”, linear programming model, design of the “red line” on the longitudinal profile, dynamic programming model). Conclusion. The difficult stage of the transition of economic and mathematical analysis from the verbal description of the system process to the elemental base of the mathematical apparatus. Most research models of operations are designed for single criteria. Economic and mathematical modeling allows the effect of “private optimization”.

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15

Weiner, Dan. "A Dynamic Optimization for Operation of a Compressed Air Energy Storage System." Journal of Dynamic Systems, Measurement, and Control 111, no. 1 (March 1, 1989): 112–14. http://dx.doi.org/10.1115/1.3153008.

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A mathematical model is derived, simulating the dynamic behavior of a cavern-type (constant volume) compressed air energy storage system (CAES). With the aid of the model, optimal control of the system decision variables, namely: charging and discharging timing and duration as well as the fuel injection policy are determined by periodic dynamic programming method. The performance criterion is maximizing the net benefits over the operation cycle. An algorithm for numerical solution of the problem is presented and computational results for an example representing a real plant are given.

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16

Schnack, Eckart, and Uwe Spörl. "A mechanical dynamic programming algorithm for structure optimization." International Journal for Numerical Methods in Engineering 23, no. 11 (November 1986): 1985–2004. http://dx.doi.org/10.1002/nme.1620231103.

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17

Sun, Zhi-Yuan, Yue Li, Wen-Cong Qu, and Yan-Yan Chen. "Collaboration optimization model of dynamic traffic control and guidance based on Internet of Vehicles." Modern Physics Letters B 32, no. 22 (August 7, 2018): 1850253. http://dx.doi.org/10.1142/s0217984918502536.

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In order to improve the comprehensive effect of Urban Traffic Control System (UTCS) and Urban Traffic Flow Guidance System (UTFGS), this paper puts forward a collaboration optimization model of dynamic traffic control and guidance based on Internet of Vehicles (IOV). With consideration of dynamic constraints of UTCS and UTFGS, UTCS is taken as the fast variable, and UTFGS is taken as the slow variable in the collaboration optimization modeling. The conception of Variable Cycle Management (VCM) is presented to solve the mathematical modeling problem under the background of the two variables. A unified framework for VCM is proposed based on IOV. The delay and travel time are calculated based on lane-group-based cell transmission model (LGCTM). The collaboration optimization problem is abstracted into a tri-level programming model. The upper level model is a cycle length optimization model based on multi-objective programming. The middle level model is a dynamic signal control decision model based on fairness analysis. The lower level model is a user equilibrium model based on average travel time. A Heuristic Iterative Optimization Algorithm (HIOA) is set up to solve the tri-level programming model. The upper level model is solved by Non-dominated Sorting Genetic Algorithm II (NSGA II), the middle level model and the lower level model are solved by Method of Successive Averages (MSA). A case study shows the efficiency and applicability of the proposed model and algorithm.

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18

Yu, Furong, Wenxi Lu, Ping Li, Xin Xin, and Jun Li. "Dynamic optimal control for groundwater optimization management with covariates." Journal of Hydroinformatics 14, no. 2 (June 30, 2011): 386–94. http://dx.doi.org/10.2166/hydro.2011.076.

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It is well known that obtaining optimal solutions for groundwater management models with covariates is a challenging task, especially for dynamic planning and management. Here, a theory and method of dealing with mutual-feed joint variation in groundwater management models is described. Specifically, an equation expressing the inherent connection between covariates and groundwater level was developed. This equation was integrated into a mathematical simulation model of groundwater, after which a groundwater dynamic optimization management model with covariates was constructed using the state transition equation method and solved with differential dynamic programming algorithms. Finally, the above theory and method were applied to a hypothetical groundwater system. For the same groundwater system, a groundwater management model with covariates was developed and the results of the two optimization methods were found to be nearly identical, which validated the theory and methods put forth here.

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19

Metelski, Andrzej, Srecko Krile, Radoslaw W. Maruda, Stanislaw Legutko, and Grzegorz M. Krolczyk. "Taguchi Design of Experiment versus Dynamic Programming Approach in the Optimization of Turning Process." Applied Mechanics and Materials 808 (November 2015): 66–71. http://dx.doi.org/10.4028/www.scientific.net/amm.808.66.

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The paper examines the influence of cutting parameters, namely cutting speed and feed rate on the tool life in machining process of cylindrical billets made from a Duplex Stainless Steel (DSS). Two optimization methods is presents, one based on the Taguchi design of the experiment with orthogonal array L9 and signal-to-noise ratio (S/N) and the second based on the dynamic programming approach with modified Dijkstra's algorithm have been used to find optimal levels of the control parameters. ANOVA was performed to determine the significance of the input variables. A predictive mathematical model has been developed through a regression analysis to study the response. The results at optimum cutting conditions are predicted using estimated values. Finally, the features, the merits and the limitations of the presented optimization approaches were discussed.

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20

Bugrov, V. "Dynamic Quantization of Digital Filter Coefficients." Proceedings of Telecommunication Universities 7, no. 2 (June 30, 2021): 8–17. http://dx.doi.org/10.31854/1813-324x-2021-7-2-8-17.

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The possibility of quantizing the coefficients of a digital filter in the concept of dynamic mathematical programming, as a dynamic process of step-by-step quantization of coefficients with their discrete optimization at each step according to the objective function, common to the entire quantization process, is considered. Dynamic quantization can significantly reduce the functional error when implementing the required characteristics of a lowbit digital filter in comparison with classical quantization. An algorithm is presented for step-by-step dynamic quantization using integer nonlinear programming methods, taking into account the specified signal scaling and the radius of the poles of the filter transfer function. The effectiveness of this approach is illustrated by dynamically quantizing the coefficients of a cascaded high-order IIR bandpass filter with a minimum bit depth to represent integer coefficients. A comparative analysis of functional quantization errors is carried out, as well as a test of the quantized filter performance on test and real signals.

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21

Shapiro, Alexander. "A dynamic programming approach to adjustable robust optimization." Operations Research Letters 39, no. 2 (March 2011): 83–87. http://dx.doi.org/10.1016/j.orl.2011.01.001.

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22

Sangha, Pavan, Prudence W. H. Wong, and Michele Zito. "Dynamic programming optimization in line of sight networks." Information and Computation 270 (February 2020): 104460. http://dx.doi.org/10.1016/j.ic.2019.104460.

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23

Galewska, E., and A. Nowakowski. "Multidimensional Dual Dynamic Programming." Journal of Optimization Theory and Applications 124, no. 1 (January 2005): 175–86. http://dx.doi.org/10.1007/s10957-004-6471-z.

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24

Amin, Talha, Igor Chikalov, Mikhail Moshkov, and Beata Zielosko. "Dynamic Programming Approach for Partial Decision Rule Optimization." Fundamenta Informaticae 119, no. 3-4 (2012): 233–48. http://dx.doi.org/10.3233/fi-2012-735.

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25

Fulmański, Piotr, Andrzej Nowakowski, and Jan Pustelnik. "Dynamic programming approach to structural optimization problem - numerical algorithm." Opuscula Mathematica 34, no. 4 (2014): 699. http://dx.doi.org/10.7494/opmath.2014.34.4.699.

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26

Azhmyakov, Vadim, Vladimir Boltyanski, and Alexander Poznyak. "The dynamic programming approach to multi-model robust optimization." Nonlinear Analysis: Theory, Methods & Applications 72, no. 2 (January 2010): 1110–19. http://dx.doi.org/10.1016/j.na.2009.07.050.

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27

Jung, M., and E. S. Lee. "Numerical optimization of a queueing system by dynamic programming." Journal of Mathematical Analysis and Applications 141, no. 1 (July 1989): 84–93. http://dx.doi.org/10.1016/0022-247x(89)90207-2.

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28

Ito, K., R. Yokoyama, and T. Shiba. "Optimal Operation of a Diesel Engine Cogeneration Plant Including a Heat Storage Tank." Journal of Engineering for Gas Turbines and Power 114, no. 4 (October 1, 1992): 687–94. http://dx.doi.org/10.1115/1.2906643.

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The effect of heat storage on a cogeneration plant is investigated using a mathematical programming approach. For a diesel engine plant, an optimal planning method is presented by which the operational policy of constituent equipment is determined together with the charging history of a heat storage tank so as to minimize the daily operational cost. An algorithm is designed to solve this optimization problem efficiently by combining the dynamic programming method with the mixed-integer programming one. Through a case study, it is made clear how the volume of the heat storage tank influences the daily operational policy and the long-term economy of the total plant.

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29

Göçgün, Yasin. "Performance comparison of approximate dynamic programming techniques for dynamic stochastic scheduling." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 11, no. 2 (May 9, 2021): 178–85. http://dx.doi.org/10.11121/ijocta.01.2021.00987.

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This paper focuses on the performance comparison of several approximate dynamic programming (ADP) techniques. In particular, we evaluate three ADP techniques through a class of dynamic stochastic scheduling problems: Lagrangian-based ADP, linear programming-based ADP, and direct search-based ADP. We uniquely implement the direct search-based ADP through basis functions that differ from those used in the relevant literature. The class of scheduling problems has the property that jobs arriving dynamically and stochastically must be scheduled to days in advance. Numerical results reveal that the direct search-based ADP outperforms others in the majority of problem sets generated.

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30

Azadeh, Ali, and Hamed Vafa Arani. "Biodiesel supply chain optimization via a hybrid system dynamics-mathematical programming approach." Renewable Energy 93 (August 2016): 383–403. http://dx.doi.org/10.1016/j.renene.2016.02.070.

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31

Kim, Se, and Moo Kim. "Fuel-Optimal Thrust-Allocation Algorithm Using Penalty Optimization Programing for Dynamic-Positioning-Controlled Offshore Platforms." Energies 11, no. 8 (August 15, 2018): 2128. http://dx.doi.org/10.3390/en11082128.

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This research, a new thrust-allocation algorithm based on penalty programming is developed to minimize the fuel consumption of offshore vessels/platforms with dynamic positioning system. The role of thrust allocation is to produce thruster commands satisfying required forces and moments for position-keeping, while fulfilling mechanical constraints of the control system. The developed thrust-allocation algorithm is mathematically formulated as an optimization problem for the given objects and constraints of a dynamic positioning system. Penalty programming can solve the optimization problems that have nonlinear object functions and constraints. The developed penalty-programming thrust-allocation method is implemented in the fully-coupled vessel–riser–mooring time-domain simulation code with dynamic positioning control. Its position-keeping and fuel-saving performance is evaluated by comparing with other conventional methods, such as pseudo-inverse, quadratic-programming, and genetic-algorithm methods. In this regard, the fully-coupled time-domain simulation method is applied to a turret-moored dynamic positioning assisted FPSO (floating production storage offloading). The optimal performance of the penalty programming in minimizing fuel consumption in both 100-year and 1-year storm conditions is demonstrated compared to pseudo-inverse and quadratic-programming methods.

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32

Ghassemi Tari, Farhad. "A Hybrid Dynamic Programming for Solving Fixed Cost Transportation with Discounted Mechanism." Journal of Optimization 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/8518921.

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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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33

Haussmann, Ulrich G., and Wulin Suo. "Singular Optimal Stochastic Controls II: Dynamic programming." SIAM Journal on Control and Optimization 33, no. 3 (May 1995): 937–59. http://dx.doi.org/10.1137/s0363012993250529.

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34

Verdu, Sergio, and H. Vincent Poor. "Abstract Dynamic Programming Models under Commutativity Conditions." SIAM Journal on Control and Optimization 25, no. 4 (July 1987): 990–1006. http://dx.doi.org/10.1137/0325054.

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35

Bertsekas, Dimitri P. "Stable Optimal Control and Semicontractive Dynamic Programming." SIAM Journal on Control and Optimization 56, no. 1 (January 2018): 231–52. http://dx.doi.org/10.1137/17m1122815.

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36

Karatzas, Ioannis, and William D. Sudderth. "Two Characterizations of Optimality in Dynamic Programming." Applied Mathematics and Optimization 61, no. 3 (November 19, 2009): 421–34. http://dx.doi.org/10.1007/s00245-009-9093-x.

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37

Lai, Hang-Chin, and Kensuke Tanaka. "On continuous-time discounted stochastic dynamic programming." Applied Mathematics & Optimization 23, no. 1 (January 1991): 155–69. http://dx.doi.org/10.1007/bf01442395.

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38

Tataru, Daniel. "Viscosity solutions for the dynamic programming equations." Applied Mathematics & Optimization 25, no. 2 (March 1992): 109–26. http://dx.doi.org/10.1007/bf01182476.

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39

Janová, Jitka. "The dynamic programming approach to long term production planning in agriculture." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 59, no. 2 (2011): 129–36. http://dx.doi.org/10.11118/actaun201159020129.

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The production planning in agriculture is one of the most important decision problems of the farmer. Although some decision support tools based mainly on linear programming and addressed to agriculture authorities were presented, their direct application by a farmer is not possible. This is mainly due to the local character of the models developed for particular agricultural conditions and also due to the complexness of underlying mathematical programming models.This paper aims to develop dynamic programming model for the long run crop plan optimization covering the typical conditions of Czech farms, which could serve as a platform for further enlargements and changes according to needs and conditions of particular farm. The dynamic programming algorithm is developed in detail for model case of four areas to be planted by four crops each year. The possibility of covering different constraints by generating the state space is discussed, and the generating procedure for crop rotation rules is shown. The goal function reflects the farmers objective of profit maximization and it is defined with respect to harvests’ randomness. The case study is solved for the data from South Moravian agriculture cooperative and the optimal solution is presented and discussed.

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40

Plesu, Gheorghe, and Stelian Cazan. "Contribution on the Optimization of the Spur Gears Design Process Using Software Application." Applied Mechanics and Materials 658 (October 2014): 117–22. http://dx.doi.org/10.4028/www.scientific.net/amm.658.117.

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This paper illustrates a method, in conformity with Standards [10 - 14], regarding gear design. The optimization process using this method consists in reducing the number of design steps and also in its accuracy. This method takes into consideration the functionality of gears. This method, called also the operational method [1], involves 10 kinematic and dynamic restrictions, that provide a direct calculus of gears, without any iterations. The standard methods require successive iterations, until the appropriate result is obtained. The comparison between these methods is presented below. The kinematic and dynamic restrictions, being defined as mathematical functions, could easily be implemented in a programming language.

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Gao, Li, Ke Lin Xu, Wei Zhu, and Na Na Yang. "A Two-Stage Hybrid Algorithm for Flexible Job-Shop Scheduling." Advanced Materials Research 268-270 (July 2011): 476–81. http://dx.doi.org/10.4028/www.scientific.net/amr.268-270.476.

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A mathematical model was constructed with two objectives. A two-stage hybrid algorithm was developed for solving this problem. At first, the man-hour optimization based on genetic algorithm and dynamic programming method, the model decomposes the flow shop into two layers: sub-layer and patrilineal layer. On the basis of the man-hour optimization，A simulated annealing genetic algorithm was proposed to optimize the sequence of operations. A new selection procedure was proposed and hybrid crossover operators and mutation operators were adopted. A benchmark problem solving result indicates that the proposed algorithm is effective.

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Pal, B. B., and I. Basu. "A Goal Programming Method for Solving Fractional Programming Problems via Dynamic Programming." Optimization 35, no. 2 (January 1995): 145–57. http://dx.doi.org/10.1080/02331939508844136.

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Qin, Yun Mei, Hai Jun Mao, and Yu Hui Li. "Optimizing Method of Express Delivery Network and Vehicle Routes Based on Automatic Parcel Machine." Applied Mechanics and Materials 496-500 (January 2014): 2912–16. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.2912.

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An express delivery mode based on automatic parcel machine (APM) is put forward and the delivery system is optimized in this paper. The optimization problem is described as a mathematical programming model, and the improved twice dynamic clustering algorithm and the C-W saving algorithm are developed for solving it. Obtained results show that the mode and the express delivery system have great practical application value and popularized significance.

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Parvez, Iram, JianJian Shen, Mehran Khan, and Chuntian Cheng. "Modeling and Solution Techniques Used for Hydro Generation Scheduling." Water 11, no. 7 (July 6, 2019): 1392. http://dx.doi.org/10.3390/w11071392.

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The hydro generation scheduling problem has a unit commitment sub-problem which deals with start-up/shut-down costs related hydropower units. Hydro power is the only renewable energy source for many countries, so there is a need to find better methods which give optimal hydro scheduling. In this paper, the different optimization techniques like lagrange relaxation, augmented lagrange relaxation, mixed integer programming methods, heuristic methods like genetic algorithm, fuzzy logics, nonlinear approach, stochastic programming and dynamic programming techniques are discussed. The lagrange relaxation approach deals with constraints of pumped storage hydro plants and gives efficient results. Dynamic programming handles simple constraints and it is easily adaptable but its major drawback is curse of dimensionality. However, the mixed integer nonlinear programming, mixed integer linear programming, sequential lagrange and non-linear approach deals with network constraints and head sensitive cascaded hydropower plants. The stochastic programming, fuzzy logics and simulated annealing is helpful in satisfying the ramping rate, spinning reserve and power balance constraints. Genetic algorithm has the ability to obtain the results in a short interval. Fuzzy logic never needs a mathematical formulation but it is very complex. Future work is also suggested.

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Phuong, Phan Thi Thu, Hoang Van Lai, and Bui Dinh Tri. "Reservoir optimization with differential evolution." Vietnam Journal of Mechanics 38, no. 1 (March 15, 2016): 39–48. http://dx.doi.org/10.15625/0866-7136/38/1/6490.

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Reservoir optimization, is one of recent problems, which has been researched by several methods such as Linear Programming (LP), Non-linear Programming (NLP), Genetic Algorithm (GA), and Dynamic Programming (DP). Differential Evolution (DE), a method in GA group, is recently applied in many fields, especially water management. This method is an improved variant of GA to converge and reach to the optimal solution faster than the traditional GA. It is also capable to apply for a wide range space, to a problem with complex, discontinuous, undifferential optimal function. Furthermore, this method does not requirethe gradient information of the space but easily find the global solution by asimple algorithm. In this paper, we introduce DE, compare to LP which was considered mathematically decades ago to prove DE's accuracy, then apply DE to Pleikrong, a reservoir in Vietnam, then discuss about the results.

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Itiki, C. "Dynamic Programming and Diagnostic Classification." Journal of Optimization Theory and Applications 127, no. 3 (December 2005): 579–86. http://dx.doi.org/10.1007/s10957-005-7504-y.

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Liu, Jing-yu, and Jiu-ju Cai. "An Optimization Model Based on Electric Power Generation in Steel Industry." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/924960.

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Electric power is an important energy in steel industry. Electricity accounts for roughly 20% to 30% of the gross energy consumption and costs about 10% of the gross cost of energy. In this paper, under the premise of ensuring the stability of energy supply and the normal production safety, the mathematical programming method and the dynamic mathematical optimization model were used to set up the surplus gas in the optimal allocation among the buffer users and steam production dispatching for the production equipment. The application of this optimization model can effectively improve the energy efficiency and the accuracy of power generation, making full use of secondary energy and residual heat. It also can realize the rationalization of the electricity production structure optimization which can effectively reduce the flare of the gas and steam on one hand, and save energy and decrease production cost on the other.

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Cervellera, Cristiano, and Marco Muselli. "Efficient sampling in approximate dynamic programming algorithms." Computational Optimization and Applications 38, no. 3 (June 23, 2007): 417–43. http://dx.doi.org/10.1007/s10589-007-9054-8.

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Li, D. "Iterative Parametric Dynamic Programming and Its Application in Reliability Optimization." Journal of Mathematical Analysis and Applications 191, no. 3 (May 1995): 589–607. http://dx.doi.org/10.1006/jmaa.1995.1150.

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Chen, Zhang, Liyuan Liu, Li Li, and Hui Li. "A Two-Stage Model for Project Optimization in Transportation Infrastructure Management System." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/914515.

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Mathematical optimization is very important for project decision in the Transportation Infrastructure Management System (TIMS). However, it has not been widely employed in TIMS due to poor performance of conventional optimization models in calculation speed and practical application. Therefore, it is necessary to improve the performance of optimization models. According to the process of decision-making in transportation management, a novel two-stage project optimization model, including budget allocation and project distribution, was proposed in this paper. Moreover, the methods of dynamic programming (DP) and genetic algorithm (GA) were applied to obtain an effective solution. The findings indicate that the new optimization method can provide a satisfactory and reasonable maintenance schedule for transportation infrastructure maintenance agencies whose routine management will benefit from the newly proposed model.

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