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Relevant bibliographies by topics / Mathematical optimization. Dynamic programming

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Academic literature on the topic 'Mathematical optimization. Dynamic programming'

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Published: 4 June 2021

Last updated: 8 February 2022

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

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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Mathematical optimization. Dynamic programming"

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Hearnes, Warren E. II. "Near-optimal intelligent control for continuous set-point regulator problems via approximate dynamic programming." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/24882.

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Angulo, Olivares Gustavo I. "Integer programming approaches for semicontinuous and stochastic optimization." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51862.

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This thesis concerns the application of mixed-integer programming techniques to solve special classes of network flow problems and stochastic integer programs. We draw tools from complexity and polyhedral theory to analyze these problems and propose improved solution methods. In the first part, we consider semi-continuous network flow problems, that is, a class of network flow problems where some of the variables are required to take values above a prespecified minimum threshold whenever they are not zero. These problems find applications in management and supply chain models where orders in small quantities are undesirable. We introduce the semi-continuous inflow set with variable upper bounds as a relaxation of general semi-continuous network flow problems. Two particular cases of this set are considered, for which we present complete descriptions of the convex hull in terms of linear inequalities and extended formulations. We also consider a class of semi-continuous transportation problems where inflow systems arise as substructures, for which we investigate complexity questions. Finally, we study the computational efficacy of the developed polyhedral results in solving randomly generated instances of semi-continuous transportation problems. In the second part, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of optimizing a linear function on the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear problem and finds applications in stochastic integer programming. We observe that the complexity of the problem depends on how P and X are specified. For instance, P can be explicitly given by its linear description, or implicitly by an oracle. Similarly, X can be explicitly given as a list of vectors, or implicitly as a face of P. While removing vertices turns to be hard in general, it is tractable for tractable 0-1 polytopes, and compact extended formulations can be obtained. Some extensions to integral polytopes are also presented. The third part is devoted to the integer L-shaped method for two-stage stochastic integer programs. A widely used model assumes that decisions are made in a two-step fashion, where first-stage decisions are followed by second-stage recourse actions after the uncertain parameters are observed, and we seek to minimize the expected overall cost. In the case of finitely many possible outcomes or scenarios, the integer L-shaped method proposes a decomposition scheme akin to Benders' decomposition for linear problems, but where a series of mixed-integer subproblems have to be solved at each iteration. To improve the performance of the method, we devise a simple modification that alternates between linear and mixed-integer subproblems, yielding significant time savings in instances from the literature. We also present a general framework to generate optimality cuts via a cut-generating problem. Using an extended formulation of the forbidden-vertices problem, we recast our cut-generating problem as a linear problem and embed it within the integer L-shaped method. Our numerical experiments suggest that this approach can prove beneficial when the first-stage set is relatively complicated.

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Doddapaneni, Srinivas P. "Automatic dynamic decomposition of programs on distributed memory machines." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/8158.

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Tosukhowong, Thidarat. "Dynamic Real-time Optimization and Control of an Integrated Plant." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/14087.

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Applications of the existing steady-state plant-wide optimization and the single-scale fast-rate dynamic optimization strategies to an integrated plant with material recycle have been impeded by several factors. While the steady-state optimization formulation is very simple, the very long transient dynamics of an integrated plant have limited the optimizers execution rate to be extremely low, yielding a suboptimal performance. In contrast, performing dynamic plant-wide optimization at the same rate as local controllers requires exorbitant on-line computational load and may increase the sensitivity to high-frequency dynamics that are irrelevant to the plant-level interactions, which are slow-scale in nature. This thesis proposes a novel multi-scale dynamic optimization and control strategy suitable for an integrated plant. The dynamic plant-wide optimizer in this framework executes at a slow rate to track the slow-scale plant-wide interactions and economics, while leaving the local controllers to handle fast changes related to the local units. Moreover, this slow execution rate demands less computational and modeling requirement than the fast-rate optimizer. An important issue of this method is obtaining a suitable dynamic model when first-principles are unavailable. The difficulties in the system identification process are designing proper input signal to excite this ill-conditioned system and handling the lack of slow-scale dynamic data when the plant experiment cannot be conducted for a long time compared to the settling time. This work presents a grey-box modeling method to incorporate steady-state information to improve the model prediction accuracy. A case study of an integrated plant example is presented to address limitations of the nonlinear model predictive control (NMPC) in terms of the on-line computation and its inability to handle stochastic uncertainties. Then, the approximate dynamic programming (ADP) framework is investigated. This method computes an optimal operating policy under uncertainties off-line. Then, the on-line multi-stage optimization can be transformed into a single-stage problem, thus reducing the real-time computational effort drastically. However, the existing ADP framework is not suitable for an integrated plant with high dimensional state and action space. In this study, we combine several techniques with ADP to apply nonlinear optimal control to the integrated plant example and show its efficacy over NMPC.

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Ng, Chi Kong. "Globally convergent and efficient methods for unconstrained discrete-time optimal control." HKBU Institutional Repository, 1998. http://repository.hkbu.edu.hk/etd_ra/149.

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Papageorgiou, Dimitri Jason. "Optimization in maritime inventory routing." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/50117.

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The primary aim of this thesis is to develop effective solution techniques for large-scale maritime inventory routing problems that possess a core substructure common in many real-world applications. We use the term “large-scale” to refer to problems whose standard mixed-integer linear programming (MIP) formulations involve tens of thousands of binary decision variables and tens of thousands of constraints and require days to solve on a personal computer. Although a large body of literature already exists for problems combining vehicle routing and inventory control for road-based applications, relatively little work has been published in the realm of maritime logistics. A major contribution of this research is in the advancement of novel methods for tackling problems orders of magnitude larger than most of those considered in the literature. Coordinating the movement of massive vessels all around the globe to deliver large quantities of high value products is a challenging and important problem within the maritime transportation industry. After introducing a core maritime inventory routing model to aid decision-makers with their coordination efforts, we make three main contributions. First, we present a two-stage algorithm that exploits aggregation and decomposition to produce provably good solutions to complex instances with a 60-period (two-month) planning horizon. Not only is our solution approach different from previous methods discussed in the maritime transportation literature, but computational experience shows that our approach is promising. Second, building on the recent successes of approximate dynamic programming (ADP) for road-based applications, we present an ADP procedure to quickly generate good solutions to maritime inventory routing problems with a long planning horizon of up to 365 periods. For instances with many ports (customers) and many vessels, leading MIP solvers often require hours to produce good solutions even when the planning horizon is limited to 90 periods. Our approach requires minutes. Our algorithm operates by solving many small subproblems and, in so doing, collecting and learning information about how to produce better solutions. Our final research contribution is a polyhedral study of an optimization problem that was motivated by maritime inventory routing, but is applicable to a more general class of problems. Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in a distribution network so that they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) that we study captures a core structure encountered in many of these environments. We model the FCTPwB as a mixed-integer linear program and derive two classes of facets, both exponential in size, for the convex hull of solutions for the problem with a single consumer and show that they can be separated in polynomial time. Finally, a computational study demonstrates that these classes of facets are effective in reducing the integrality gap and solution time for more general instances of the FCTPwB.

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Stellato, Bartolomeo. "Mixed-integer optimal control of fast dynamical systems." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:b8a7323c-e36e-45ec-ae8d-6c9eb4350629.

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Many applications in engineering, computer science and economics involve mixed-integer optimal control problems. Solving these problems in real-time is a challenging task because of the explosion of integer combinations to evaluate. This thesis focuses on the development of new algorithms for mixed-integer programming with an emphasis on optimal control problems of fast dynamical systems with discrete controls. The first part proposes two reformulations to reduce the computational complexity. The first reformulation avoids integer variables altogether. By considering a sequence of switched dynamics, we analyze the switching time optimization problem. Even though it is a continuous smooth problem, it is non-convex and the cost function and derivatives are hard to compute. We develop a new efficient method to compute the cost function and its derivatives. Our technique brings up to two orders of magnitude speedups with respect to state-of-the-art tools. The second approach reduces the number of integer decisions. In hybrid model predictive control (MPC) the computational complexity grows exponentially with the horizon length. Using approximate dynamic programming (ADP) we reduce the horizon length while maintaining good control performance by approximating the tail cost offline. This approach allows, for the first time, the application of such control techniques to fast dynamical systems with sampling times of only a few microseconds. The second part investigates embedded branch-and-bound algorithms for mixed-integer quadratic programs (MIQPs). A core component of these methods is the solution of continuous quadratic programs (QPs). We develop OSQP, a new robust and efficient general-purpose QP solver based on the alternating direction method of multipliers (ADMM) and able, for the first time, to detect infeasible problems. We include OSQP into a custom branch-and-bound algorithm suitable for embedded systems. Our extension requires only a single matrix factorization and exploits warm-starting, thereby greatly reducing the number of ADMM iterations required. Numerical examples show that our algorithm solves small to medium scale MIQPs more quickly than commercial solvers.

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Toriello, Alejandro. "Time decomposition of multi-period supply chain models." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/42704.

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Many supply chain problems involve discrete decisions in a dynamic environment. The inventory routing problem is an example that combines the dynamic control of inventory at various facilities in a supply chain with the discrete routing decisions of a fleet of vehicles that moves product between the facilities. We study these problems modeled as mixed-integer programs and propose a time decomposition based on approximate inventory valuation. We generate the approximate value function with an algorithm that combines data fitting, discrete optimization and dynamic programming methodology. Our framework allows the user to specify a class of piecewise linear, concave functions from which the algorithm chooses the value function. The use of piecewise linear concave functions is motivated by intuition, theory and practice. Intuitively, concavity reflects the notion that inventory is marginally more valuable the closer one is to a stock-out. Theoretically, piecewise linear concave functions have certain structural properties that also hold for finite mixed-integer program value functions. (Whether the same properties hold in the infinite case is an open question, to our knowledge.) Practically, piecewise linear concave functions are easily embedded in the objective function of a maximization mixed-integer or linear program, with only a few additional auxiliary continuous variables. We evaluate the solutions generated by our value functions in a case study using maritime inventory routing instances inspired by the petrochemical industry. The thesis also includes two other contributions. First, we review various data fitting optimization models related to piecewise linear concave functions, and introduce new mixed-integer programming formulations for some cases. The formulations may be of independent interest, with applications in engineering, mixed-integer non-linear programming, and other areas. Second, we study a discounted, infinite-horizon version of the canonical single-item lot-sizing problem and characterize its value function, proving that it inherits all properties of interest from its finite counterpart. We then compare its optimal policies to our algorithm's solutions as a proof of concept.

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Samuelsson, Björn. "Heuristic Mathematical Programming Methods for Lot-sizing, Inventory Control, and Distribution Cost Estimation in the Supply Chain." Doctoral thesis, Luleå tekniska universitet, Industriell Ekonomi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-66246.

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The supply function has an important role to support the business to create a customer value. Two important parts of this process is to have the warehouses and production sites in the right location and to have the right items stocked at the right level. This thesis is concerned with those two parts of the supply chain management. Three different areas of inventory control are dealt with. In the first part we consider the classical dynamic lot size problem without backlogging. The second part deals with estimation of holding and shortage costs in two-level distribution inventory systems. In the third part of the thesis we consider the localisation problem in a multi-level supply network system where items are consolidated at a warehouse and distributed to customers on routes. Within the area of inventory control we have evaluated a method earlier suggested by Axsäter (1988), the method is evaluated using a set of test problems and compared other heuristic methods, including the well-known Silver-Meal’s method (Silver and Meal, 1973). The result shows that the method suggested by Axsäter does perform better than the other methods. In the latest contribution we point to the important differences between Least Period Cost and Silver-Meal when several periods have zero demand. In the area of inventory control we have also studied a two-echelon inventory system where we present methods for estimating the shortage- and stockholding costs in such inventory systems. The second part subject of the thesis concerns supply network optimization. We present a MIP formulation of the problem and evaluate in detail the approximation of the distribution cost when customers are delivered on multi-stop routes. An improved method for estimating the distribution is presented. Besides this introductory overview five research papers are included in the thesis. The first and the last paper consider evaluation of dynamic lot sizing heuristics. The second and third paper deals with cost evaluation of a stochastic two-echelon inventory system and the forth paper with evaluation of methods for estimating distribution costs in a supply network.

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Schöllig, Angela. "Optimal Control of Hybrid Systems with Regional Dynamics." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19874.

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In this work, hybrid systems with regional dynamics are considered. These are systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, the attention is focused on the optimal control problem associated with such systems. More precisely, given a specific cost function, the goal is to determine the optimal path of going from a given starting point to a fixed final state during an a priori specified time horizon. The key characteristic of the approach presented in this thesis is a hierarchical decomposition of the hybrid optimal control problem, yielding to a framework which allows a solution on different levels of control. On the highest level of abstraction, the regional structure of the state space is taken into account and a discrete representation of the connections between the different regions provides global accessibility relations between regions. These are used on a lower level of control to formulate the main theorem of this work, namely, the Hybrid Bellman Equation for multimodal systems, which, in fact, provides a characterization of global optimality, given an upper bound on the number of transitions along a hybrid trajectory. Not surprisingly, the optimal solution is hybrid in nature, in that it depends on not only the continuous control signals, but also on discrete decisions as to what domains the system's continuous state should go through in the first place. The main benefit with the proposed approach lies in the fact that a hierarchical Dynamic Programming algorithm can be used to representing both a theoretical characterization of the hybrid solution's structural composition and, from a more application-driven point of view, a numerically implementable calculation rule yielding to globally optimal solutions in a regional dynamics framework. The operation of the recursive algorithm is highlighted by the consideration of numerous examples, among them, a heterogeneous multi-agent problem.

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Books on the topic "Mathematical optimization. Dynamic programming"

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author, Muler Nora, ed. Stochastic optimization in insurance: A dynamic programming approach. New York, NY: Springer, 2014.

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N, Tsitsiklis John, ed. Neuro-dynamic programming. Belmont, Mass: Athena Scientific, 1996.

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White, William Alexander. Dynamic programming applications to stand level optimization. Victoria, B.C: Pacific Forestry Centre, 1989.

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Branke, Jürgen. Evolutionary optimization in dynamic environments. Boston: Kluwer Academic Publishers, 2002.

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Barbu, V. Mathematical methods in optimization of differential systems. Dordrecht: Kluwer Academic, 1994.

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Mathematical methods in optimization of differential systems. Dordrecht: Kluwer Academic, 1994.

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Agrawal, Sunil Kumar. Optimization of dynamic systems. Dordrecht: Kluwer Academic Publishers, 1999.

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Fabella, Raul V. A class of reducible dynamic control problems. [Quezon?]: University of the Philippines, School of Economics, 1985.

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Zhang, Huaguang. Adaptive Dynamic Programming for Control: Algorithms and Stability. London: Springer London, 2013.

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Barbu, Viorel. Metode matematice în optimizarea sistemelor diferențiale. București: Editura Academiei Republicii Socialiste România, 1989.

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Book chapters on the topic "Mathematical optimization. Dynamic programming"

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Andreatta, Giovanni, and Wolfgang J. Runggaldier. "An approximation scheme for stochastic dynamic optimization problems." In Mathematical Programming Studies, 118–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0121116.

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Barbu, Viorel. "The Dynamic Programming Method." In Mathematical Methods in Optimization of Differential Systems, 104–67. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0760-0_3.

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Hartley, Roger. "Vector Optimal Routing by Dynamic Programming." In Mathematics of Multi Objective Optimization, 215–24. Vienna: Springer Vienna, 1985. http://dx.doi.org/10.1007/978-3-7091-2822-0_10.

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Papi, Marco, Luca Pontecorvi, Roberto Setola, and Fabrizio Clemente. "Stochastic Dynamic Programming in Hospital Resource Optimization." In Springer Proceedings in Mathematics & Statistics, 139–47. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67308-0_15.

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Henig, Mordechai I. "Applicability of the Functional Equation in Multi Criteria Dynamic Programming." In Mathematics of Multi Objective Optimization, 189–213. Vienna: Springer Vienna, 1985. http://dx.doi.org/10.1007/978-3-7091-2822-0_9.

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Dash, Gordon H., and Nina Kajiji. "Combinatorial Nonlinear Goal Programming for ESG Portfolio Optimization and Dynamic Hedge Management." In Mathematical and Statistical Methods for Actuarial Sciences and Finance, 77–80. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05014-0_18.

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Belenky, Alexander S. "Mathematical Programming." In Applied Optimization, 13–90. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6075-0_2.

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Zabczyk, Jerzy. "Dynamic programming." In Mathematical Control Theory, 127–41. Boston, MA: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4733-9_9.

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Escoffier, Bruno, and Olivier Spanjaard. "Dynamic Programming." In Concepts of Combinatorial Optimization, 71–99. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2013. http://dx.doi.org/10.1002/9781118600245.ch4.

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Escoffier, Bruno, and Olivier Spanjaard. "Dynamic Programming." In Concepts of Combinatorial Optimization, 71–99. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781119005216.ch4.

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Conference papers on the topic "Mathematical optimization. Dynamic programming"

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Tytler, Charles, Jian Wei, Inseok Hwang, and William Hall. "Mathematical Programming Based Algorithm for Dynamic Terminal Airspace Configuration." In 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-5541.

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Zavalishchin, Dmitry. "Dynamic programming in applied optimization problems." In 41ST INTERNATIONAL CONFERENCE “APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS” AMEE ’15. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4936687.

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Risco-Martín, José L., J. Ignacio Hidalgo, David Atienza, Juan Lanchares, and Oscar Garnica. "Mixed heuristic and mathematical programming using reference points for dynamic data types optimization in multimedia embedded systems." In the 11th Annual conference. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1569901.1570115.

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Radmanesh, Mohammadreza, and Manish Kumar. "UAV Path Planning in the Framework of MILP-Tropical Optimization." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5231.

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This paper proposes a fast method for obtaining mathematically optimal trajectories for UAVs while avoiding collisions. A comparison of the proposed method with previously used Mixed Integer Linear Programming (MILP) to find the optimal collision-free path UAVs, aircraft, and spacecraft show the effectiveness and performance of this method. Here, the UAV path planning problem is formulated in the new framework named MILP-Tropical optimization that exploits tropical mathematics for obtaining solution and then casted in a novel branch-and-bound method. Various constraints including UAV dynamics are incorporated in the proposed Tropical framework and a solution methodology is presented. An extensive numerical study shows that the proposed method provides faster solution. The proposed technique can be extended to distributed control for multiple vehicles and multiple way-points.

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Bin, Y., A. Reama, A. Cela, R. Natowicz, H. Abderrahmane, and Y. Li. "On Fast Dynamic Programming for Power Splitting Control of Plug-In Hybrid Electric Vehicles." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2716.

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A Fast Dynamic Programming (FDP) algorithm is proposed to optimize the fuel consumption of the Plug-in Hybrid Electronic Vehicles (PHEV) over a prescribed driving cycle. Firstly, an innovative DP mathematical model for PHEV with reduced dimension is created. It composes of a linear state transfer equation and a quadratic cost function with 1×1 dimension. Based on this model, two algorithms expressed as the simple analytic forms are derived. One is the control algorithm for the optimal power splitting ratio (PSR) between the internal combustion engine (ICE) power and demand power. Another is the recursive algorithm to calculate the optimization value of the fuel consumption. Then, the optimal output power of ICE (or electronic motor (EM)) and the optimal speed ratio of the gear position can be calculated rapidly as the consequence of using the algorithms with analytic forms. Finally, the simulation results confirm that the computational efficiency of the FDP control algorithm has been improved with a geometric ratio, while its control performance maintains in an acceptable range in contrast with conventional DP control algorithm.

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Willkomm, Johannes, Matthias Wahler, and Jürgen Weber. "Quadratic Programming to Optimize Energy Efficiency of Speed- and Displacement-Variable Pumps." In 8th FPNI Ph.D Symposium on Fluid Power. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fpni2014-7802.

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Within the last years, speed-variable pump drives were investigated in numerous applications. In combination with a variable displacement pump, the volume flow and the drive speed can be decoupled. In this paper the resulting degree of freedom will be used to minimize the energy consumption of hydraulic processes by means of a novel model predictive control concept. A dynamic loss model of all drive components will be transformed to a mathematical quadratic optimization problem. The optimum use of the two control variables can achieve energy savings of up to 25% in comparison to known control strategies of speed-variable variable-displacement pumps. Especially in highly dynamic process cycles the proposed optimization guarantees optimum energy efficiency while known approaches become inefficient.

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Zakhariev, Evtim V. "A General Method of Multibody System Motion Optimization." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4195.

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Abstract The present paper suggests a general off-line numerical algorithm for optimization of motion of multibody systems. The nonlinear dynamics model is numerically derived as Ordinary Differential Equations for the minimal set of the generalized coordinates. The trajectory is discretized of small intervals (nodes) where the robot motion is assumed to be with constant general coordinate accelerations. The mathematical description of the problem for optimal motion planning is presented as nonlinear programming problem. The characteristics of motion and discretized generalized forces in every node are parameters of the optimization problem. The convergence of the algorithm is tested in case of a five degrees of freedom redundant robot achieving point-to-point time optimal motion.

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Alfonso, Edgar, Xiaolan Xie, and Vincent Augusto. "A simulation-optimization approach for capacity planning and appointment scheduling of blood donors based on mathematical programming representation of event dynamics." In 2015 IEEE International Conference on Automation Science and Engineering (CASE). IEEE, 2015. http://dx.doi.org/10.1109/coase.2015.7294167.

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Dhingra, A. K., and S. S. Rao. "Integrated Optimal Design of Planar Mechanisms Using Fuzzy Theories." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0086.

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Abstract A new integrated approach to the design of high speed planar mechanisms is presented. The resulting nonlinear programming formulation combines both the kinematic and dynamic synthesis aspects of mechanism design. The multiobjective optimization techniques presented in this work facilitate the design of a linkage to meet several kinematic and dynamic design criteria. The method can be used for motion, path, and function generation problems. The nonlinear programming formulation also permits the imposition of constraints to eliminate solutions which possess undesirable kinematic and motion characteristics. To model the vague and imprecise information in the problem formulation, the tools of fuzzy set theory have been used. A method of solving the resulting fuzzy multiobjective problem using mathematical programming techniques is presented. The outlined procedure is expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.

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Shamieh, Hadi, and Ramin Sedaghati. "Design Optimization of a Magneto-Rheological Fluid Brake for Vehicle Applications." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9084.

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The magnetorheological Brake (MRB) is an electromechanical brake in which smart magnetorheological (MR) fluids have been utilized to generate the required braking torque. The purpose of this study is to design optimize a real-size MRB for automobile applications considering geometrical, material and magnetic circuit parameters. The mathematical equations governing the system’s braking torques are derived. The dynamic range of a disk-type MRB expressing the ratio of generated toque at on and off states has been formulated as a function of the rotational speed, geometrical and material properties, and applied electrical current. The magnetic circuit analysis of the proposed MRB is performed to find the relation between magnetic field intensity and the applied electrical current as a function of the MRB geometrical and material properties. Finally, a multidisciplinary design optimization problem has been formulated to identify the optimal brake geometrical parameters to maximize the dynamic range of the MRB under weight, size and magnetic flux density constraints. The optimization problem has been solved using combined Genetic Algorithm and Sequential Quadratic Programming techniques. The optimal design is then compared with those available in the literature.

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Reports on the topic "Mathematical optimization. Dynamic programming"

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Groer, Christopher S., Blair D. Sullivan, and Dinesh P. Weerapurage. INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization. Office of Scientific and Technical Information (OSTI), October 2012. http://dx.doi.org/10.2172/1055043.

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