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Journal articles on the topic 'Mathematical programming formulation'

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Published: 10 December 2022

Last updated: 19 February 2023

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1

Lee, Jae Sik, Christopher V. Jones, and Monique Guignard. "MAPNOS: Mathematical programming formulation normalization system." Expert Systems with Applications 1, no. 4 (January 1990): 367–81. http://dx.doi.org/10.1016/0957-4174(90)90046-w.

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2

Bonatsos, Nikolaos, Endrit Dheskali, Denise M. G. Freire, Aline Machado de Castro, Apostolis A. Koutinas, and Ioannis K. Kookos. "A mathematical programming formulation for biorefineries technology selection." Biochemical Engineering Journal 116 (December 2016): 135–45. http://dx.doi.org/10.1016/j.bej.2016.05.001.

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3

Adi, Vincentius Surya Kurnia, and Chuei-Tin Chang. "A mathematical programming formulation for temporal flexibility analysis." Computers & Chemical Engineering 57 (October 2013): 151–58. http://dx.doi.org/10.1016/j.compchemeng.2013.04.001.

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4

Gringauz, M. "On mathematical programming formulation for contact crack problems." International Journal of Fracture 60, no. 1 (March 1993): R3—R7. http://dx.doi.org/10.1007/bf00034516.

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5

Urahama, Kiichi. "Mathematical programming formulation for neural combinatorial optimization algorithms." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 78, no. 9 (September 1995): 67–75. http://dx.doi.org/10.1002/ecjc.4430780907.

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6

Chen, Zeng Hai, Bin Gang Xu, Zhe Ru Chi, and Da Gan Feng. "Mathematical formulation of knitted fabric spirality using genetic programming." Textile Research Journal 82, no. 7 (January 25, 2012): 667–76. http://dx.doi.org/10.1177/0040517511435011.

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This paper proposes the use of genetic programming for the mathematical formulation of knitted fabric spirality. Both dry relaxed and wash-and-dry relaxed states of fabric spirality are studied. In total, six parameters are investigated, in which three parameters are derived from yarn and fabric, and the other three parameters are from the knitted condition. The three yarn and fabric parameters used are yarn twist liveliness, tightness factor and dyeing method, and the three knitting parameters are the number of feeders, rotational direction and gauge. Genetic programming is adopted to formulize the mathematical relationships between above the six parameters and two states of fabric spirality, respectively. For a comparison, a multiple linear regression approach is studied as well. The formulas generated by genetic programming and multiple regression for two states of spirality are comprehensively investigated and compared. Experimental results show that genetic programming, which can model non-linear mathematical relationships, obtains more accurate expressions than multiple regression for both dry relaxed and wash-and-dry relaxed states of spirality, demonstrating that genetic programming is a promising alternative for the mathematical formulation of fabric spirality.

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Patil, Vishal, Radha Gupta, Rajendran D, and Ravinder Singh Kuntal. "COMPARATIVE STUDY ON FEED FORMULATION SOFTWARE- A SHORT REVIEW." International Journal of Research -GRANTHAALAYAH 5, no. 4RAST (April 30, 2017): 105–15. http://dx.doi.org/10.29121/granthaalayah.v5.i4rast.2017.3311.

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The paper highlightsthe different feed formulation software’s for least cost formulation of livestock and animals, where the comparison of techniques is donebased on different aspectslike data collection, software used, price, scope and limitations. Feed formulation requires large amount of data about the composition of feeds, environment conditions,and availability of feeds.Development of Software’sfor feed formulations is changing with change in computer. With advancement of technology, the feed formulation can be calculated for ‘n’ number of feed stuff but still Linear Programming is used as base for mathematical modelling, where uses of non-linear programming is very less. Maximum number of feed formulation software’s is developed to select the feeds for formulation within budget of the farmers or dairy industry.

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8

Zhao, LiJin, and Liang Huang. "A Mathematical Programming Formulation of Disjoint Dominating Sets Problem." Journal of Computational and Theoretical Nanoscience 13, no. 11 (November 1, 2016): 8760–64. http://dx.doi.org/10.1166/jctn.2016.6037.

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9

Olhoff, N. "Multicriterion structural optimization via bound formulation and mathematical programming." Structural Optimization 1, no. 1 (March 1989): 11–17. http://dx.doi.org/10.1007/bf01743805.

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10

Chwatal, Andreas M., and Günther R. Raidl. "Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques." Advances in Operations Research 2011 (2011): 1–38. http://dx.doi.org/10.1155/2011/143732.

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We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further, we show how to use odd-hole inequalities and additional inequalities to strengthen the formulation. Label variables can be added dynamically to the model in the pricing step. Primal heuristics are incorporated into the framework to speed up the overall solution process. After a polyhedral comparison of the involved formulations, comprehensive computational experiments are presented in order to compare and evaluate the underlying formulations and the particular algorithmic building blocks of the overall branch-and-cut- (and-price) framework.

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Briec, Walter, Laurent Cavaignac, and Kristiaan Kerstens. "Input Efficiency Measures: A Generalized, Encompassing Formulation." Operations Research 68, no. 6 (November 2020): 1836–49. http://dx.doi.org/10.1287/opre.2019.1963.

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In the article “Input Efficiency Measures: A Generalized, Encompassing Formulation” we develop a generalized, encompassing formulation unifying four traditional input efficiency measures: radial, Färe-Lovell, asymmetric Färe, and multiplicative Färe-Lovell. This is basically motivated by the fact that observations on production need not be situated near the efficient subset, but could also be positioned close to the isoquant or even the boundary of the technology. This new generalized Färe-Lovell input efficiency measure shares its axiomatic properties with the original Färe-Lovell input efficiency measure. In addition, we can derive new dual interpretations for this generalized Färe-Lovell input efficiency measure. Finally, we derive mathematical programming formulations, with a special focus on cases where linear programming applies.

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12

Verwer, Sicco, and Yingqian Zhang. "Learning Optimal Classification Trees Using a Binary Linear Program Formulation." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1625–32. http://dx.doi.org/10.1609/aaai.v33i01.33011624.

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We provide a new formulation for the problem of learning the optimal classification tree of a given depth as a binary linear program. A limitation of previously proposed Mathematical Optimization formulations is that they create constraints and variables for every row in the training data. As a result, the running time of the existing Integer Linear programming (ILP) formulations increases dramatically with the size of data. In our new binary formulation, we aim to circumvent this problem by making the formulation size largely independent from the training data size. We show experimentally that our formulation achieves better performance than existing formulations on both small and large problem instances within shorter running time.

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13

Shen, Pingning. "Mathematical Programming Formulation of Combined Transportation and Land Use Model." Transportation Research Record: Journal of the Transportation Research Board 1607, no. 1 (January 1997): 62–68. http://dx.doi.org/10.3141/1607-09.

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A mathematical programming model of combined trip distribution, equilibrium network assignment, and residential location choice is presented. The model is developed on the basis of Wardrop’s user equilibrium principle and the random utility theory. A traveler’s route choice behavior is assumed to follow the user-optimized principle, whereas the residential location choice behavior is captured by the random utility theory. The simultaneous choice of travel routes and residential location is based on the assumption that each individual tries to minimize his or her travel cost and maximize his or her living utility. On the basis of this assumption the choice of travel routes is determined by using a user equilibrium assignment model and the choice of residential location is quantified by using a multinomial logit model. After defining the system equations of the combined model, the model is reformulated as a mathematical programming problem so that the characteristics of the combined model can be explored clearly and the model can be solved efficiently. After the properties of the model are analyzed the process of using the gradient search technique with a maximum-likelihood criterion to calibrate the model and by using the Evans algorithm to solve the optimization problem is presented. Furthermore, the model application procedure is also clearly defined.

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14

Panning, Thomas D., Layne T. Watson, Clifford A. Shaffer, and John J. Tyson. "A Mathematical Programming Formulation for the Budding Yeast Cell Cycle." SIMULATION 83, no. 7 (July 2007): 497–514. http://dx.doi.org/10.1177/0037549707085075.

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15

Jha, Nand K., and Jha Prabhudutt. "Mathematical programming formulation and optimum design of robot control system." Applied Mathematical Modelling 20, no. 11 (November 1996): 853–65. http://dx.doi.org/10.1016/s0307-904x(96)00093-5.

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16

Gan, Li Ping, and Will Recker. "A mathematical programming formulation of the household activity rescheduling problem." Transportation Research Part B: Methodological 42, no. 6 (July 2008): 571–606. http://dx.doi.org/10.1016/j.trb.2007.11.004.

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17

Chan, Wai Kin Victor. "Linear Programming Formulation of Idle Times for Single-Server Discrete-Event Simulation Models." Asia-Pacific Journal of Operational Research 33, no. 05 (October 2016): 1650038. http://dx.doi.org/10.1142/s021759591650038x.

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Mathematical programming representations (MPRs) are discrete-event simulation models represented using math programming. In this paper, we first introduce an MPR formulation for single-server queueing systems based on idle times. We use this formulation to conduct a perturbation analysis to study the effect of imposing a constraint on idle times. We apply the formulation to obtain a linear programming-based gradient estimator for idle times. We demonstrate the integration of optimization into MRP and identify properties of the optimal solution to facilitate finding the optimal solution.

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18

Carrión, Miguel, Rafael Zárate-Miñano, and Ruth Domínguez. "A Practical Formulation for Ex-Ante Scheduling of Energy and Reserve in Renewable-Dominated Power Systems: Case Study of the Iberian Peninsula." Energies 11, no. 8 (July 25, 2018): 1939. http://dx.doi.org/10.3390/en11081939.

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Scheduling energy and reserve in power systems with a large number of intermittent units is a challenging problem. Traditionally, the reserve requirements are assigned after clearing the day-ahead energy market using ad hoc rules or solving computationally intense mathematical programming problems to co-optimize energy and reserve. While the former approach often leads to costly oversized reserve provisions, the computational time required by the latter makes it generally incompatible with the daily power system operational practices. This paper proposes an alternative deterministic formulation for computing the energy and reserve scheduling, considering the uncertainty of the demand and the intermittent power production in such a way that the resulting problem requires a lower number of constraints and variables than stochastic programming-based formulations. The performance of the proposed formulation has been compared with respect to two standard stochastic programming formulations in a small-size power system. Finally, a realistic case study based on the Iberian Peninsula power system has been solved and discussed.

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19

Wakefield, Ron R., and Francis Tin-Loi. "Elastoplastic Analysis of Flat Grids Using Mathematical Programming." International Journal of Space Structures 4, no. 4 (December 1989): 228–34. http://dx.doi.org/10.1177/026635118900400404.

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This paper presents a method of analysing elastoplastic grids using a mathematical programming based formulation. The elastoplastic analysis is cast as a linear complementarity problem which can be efficiently solved by means of a scheme proposed by Kaneko. A computer program based on this scheme has been developed and can be used to analyse skeletal structures including grillages. The program's application is illustrated in this paper by performing the historical elastoplastic analysis of one of the grids tested at the University of Surrey.

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20

Gagliardo, R., F. P. A. Portioli, L. Cascini, and R. Landolfo. "Rocking Response of the Rigid Block Under Rectangular Pulse Excitation: A Comparison between ODE and Optimization-Based Solvers." Journal of Advances in Applied & Computational Mathematics 8 (March 1, 2022): 109–16. http://dx.doi.org/10.15377/2409-5761.2021.08.8.

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In this paper, the response of the rigid block under rectangular pulse excitation is investigated using two different modeling approaches and solvers. The first approach relies on the numerical integration of the differential equation of motion. The second approach is based on the formulation of the dynamic problem in terms of a special class of mathematical programming problem that is the linear complementarity problem. A validation study is carried out comparing the solutions given by the proposed formulation with the ones given by the numerical integration of the differential equation of motion obtained from ODE solvers available in MATLAB®. Potentialities and limitations of the mathematical programming formulation are discussed in terms of energy dissipation and restitution coefficient at impacts and in terms of solution times.

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21

Oladokun, V., and A. Johnson. "Feed formulation problem in Nigerian poultry farms: a mathematical programming approach." American Journal of Scientific and Industrial Research 3, no. 1 (February 2012): 14–20. http://dx.doi.org/10.5251/ajsir.2012.3.1.14.20.

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22

Scholz, André, Sebastian Henn, Meike Stuhlmann, and Gerhard Wäscher. "A new mathematical programming formulation for the Single-Picker Routing Problem." European Journal of Operational Research 253, no. 1 (August 2016): 68–84. http://dx.doi.org/10.1016/j.ejor.2016.02.018.

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23

Zhang, Lei, Stefano Cignitti, and Rafiqul Gani. "Generic mathematical programming formulation and solution for computer-aided molecular design." Computers & Chemical Engineering 78 (July 2015): 79–84. http://dx.doi.org/10.1016/j.compchemeng.2015.04.022.

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24

Chen, Anthony, Panatda Kasikitwiwat, and Zhaowang Ji. "Solving the Overlapping Problem in Route Choice with Paired Combinatorial Logit Model." Transportation Research Record: Journal of the Transportation Research Board 1857, no. 1 (January 2003): 65–73. http://dx.doi.org/10.3141/1857-08.

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Recently, there has been renewed interest in improving the logit-based route choice model because of the importance of the route choice model in intelligent transportation systems applications, particularly the applications of advanced traveler information systems. The paired combinatorial logit (PCL) model and its equivalent mathematical programming formulation for the route choice problem have been studied. An algorithm based on the partial linearization method is presented for solving the PCL stochastic user equilibrium problem. Detailed examples are provided to explain how this hierarchical logit model resolves the overlapping problem through the similarity index while still accounting for both congestion and stochastic effects in the mathematical programming formulation.

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25

ZGAJNAR, J., E. ERJAVEC, and S. KAVCIC. "Multi-step beef ration optimisation: application of linear and weighted goal programming with a penalty function." Agricultural and Food Science 19, no. 3 (December 4, 2008): 193. http://dx.doi.org/10.2137/145960610792912611.

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The aim of this paper is to present the method and tool for optimisation of beef-fattening diets. Changes in policy environment and changes in costs of feed pose challenges for farm efficiency. We construct a spreadsheet from two modules based on mathematical deterministic programming techniques. In order to obtain an estimate of the magnitude of costs that may be incurred, the first module utilizes a linear program for least-cost ration formulation. The resulting value is then targeted as a cost goal in the second module. This is supported by weighted goal programming with a penalty function system. The approach presented here is an example of how a combination of mathematical programming techniques might be applied to prepare a user-friendly tool for optimal ration formulations. We report results that confirm this approach as useful, since one is able to formulate a least-cost ration without risking a decrease in the rations nutritive value or affecting the balance between nutrients.;

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26

Aras, R., and A. Dutech. "An Investigation into Mathematical Programming for Finite Horizon Decentralized POMDPs." Journal of Artificial Intelligence Research 37 (March 26, 2010): 329–96. http://dx.doi.org/10.1613/jair.2915.

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Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs). Although DEC-POMDPS are a general and powerful modeling tool, solving them is a task with an overwhelming complexity that can be doubly exponential. In this paper, we study an alternate formulation of DEC-POMDPs relying on a sequence-form representation of policies. From this formulation, we show how to derive Mixed Integer Linear Programming (MILP) problems that, once solved, give exact optimal solutions to the DEC-POMDPs. We show that these MILPs can be derived either by using some combinatorial characteristics of the optimal solutions of the DEC-POMDPs or by using concepts borrowed from game theory. Through an experimental validation on classical test problems from the DEC-POMDP literature, we compare our approach to existing algorithms. Results show that mathematical programming outperforms dynamic programming but is less efficient than forward search, except for some particular problems. The main contributions of this work are the use of mathematical programming for DEC-POMDPs and a better understanding of DEC-POMDPs and of their solutions. Besides, we argue that our alternate representation of DEC-POMDPs could be helpful for designing novel algorithms looking for approximate solutions to DEC-POMDPs.

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27

McCarl, Bruce A., and Jeffrey Apland. "Validation of Linear Programming Models." Journal of Agricultural and Applied Economics 18, no. 2 (December 1986): 155–64. http://dx.doi.org/10.1017/s0081305200006208.

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AbstractSystematic approaches to validation of linear programming models are discussed for prescriptive and predictive applications to economic problems. Specific references are made to a general linear programming formulation, however, the approaches are applicable to mathematical programming applications in general. Detailed procedures are outlined for validating various aspects of model performance given complete or partial sets of observed, real world values of variables. Alternative evaluation criteria are presented along with procedures for correcting validation problems.

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Mandal, Manoj Kumar, Arun Prasad Burnwal, Neelam Dubey, and Om Prakash Dubey. "USE OF FUZZY MATHEMATICAL QUADRATIC PROGRAMMING APPROACH IN JOB EVALUATION." International Journal of Students' Research in Technology & Management 9, no. 2 (May 15, 2021): 25–29. http://dx.doi.org/10.18510/ijsrtm.2021.925.

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Purpose of study: The current paper is the based on mathematical model of the job evolution system. Methodology: The proposed method is the fusion of quadratic programming and fuzzy logic where quadratic programming is used to optimize objective function with related constraints in the form of non-linear formulation. Fuzzy logic is used to control uncertainty related information by estimating imprecise parameters Main Finding: The optimal solution of the job evaluation based on fuzzy environment where goal is imprecise. Application of this study: It is used in the areas where information is not exact. The originality of this study: The novelty of the method is the fusion of quadratic programming and fuzzy logic.

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29

KECECI, Baris, Tusan DERYA, Esra DINLER, and Yusuf Tansel IC. "A COMPARATIVE STUDY OF THE CAPABILITY OF ALTERNATIVE MIXED INTEGER PROGRAMMING FORMULATIONS." Technological and Economic Development of Economy 24, no. 2 (May 9, 2017): 561–84. http://dx.doi.org/10.3846/20294913.2016.1213202.

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In selecting the best mixed integer linear programming (MILP) formulation the important issue is to figure out how to evaluate the performance of each candidate formulation in terms of selected criteria. The main objective of this study is to propose a systematic approach to guide the selection of the best MILP formulation among the alternatives according to the needs of the decision maker. For this reason we consider the problem of “selecting the most appropriate MILP formulation for a certain type of decision maker” as a multi-criteria decision making problem and present an integrated AHP-TOPSIS decision making methodology to select the most appropriate formulation. As an example the proposed decision making methodology is implemented on the selection of the MILP formulations of the Capacitated Vehicle Routing Problem (CVRP). A numerical example is provided for illustrative purposes. As a result, the proposed decision model can be a tool for the decision makers (here they are the scientists, engineers and practitioners) who intend to choose the appropriate mathematical model(s) among the alternatives according to their needs on their studies. The integrated AHP-TOPSIS approach can simply be incorporated into a computer-based decision support system since it has simplicity in both computation and application.

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30

Herer, Y. T., and M. Masin. "Mathematical programming formulation of CONWIP based production lines; and relationships to MRP." International Journal of Production Research 35, no. 4 (April 1997): 1067–76. http://dx.doi.org/10.1080/002075497195542.

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31

Kumar, Soumojit, and Ashis Kumar Chatterjee. "An improved mathematical programming formulation and application of multi-attribute choice behaviour." International Journal of Operational Research 25, no. 1 (2016): 100. http://dx.doi.org/10.1504/ijor.2016.073253.

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32

Kaya, C. Yal�?n, Stephen K. Lucas, and Sergey T. Simakov. "Computations for bang-bang constrained optimal control using a mathematical programming formulation." Optimal Control Applications and Methods 25, no. 6 (November 2004): 295–308. http://dx.doi.org/10.1002/oca.749.

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33

Jarmolajeva, Ela, and Juozas Atkočiūnas. "SHAKEDOWN LOADING OPTIMIZATION UNDER CONSTRAINED RESIDUAL DISPLACEMENTS—FORMULATION AND SOLUTION FOR CIRCULAR PLATES." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 8, no. 1 (March 31, 2002): 54–67. http://dx.doi.org/10.3846/13923730.2002.10531250.

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The adapted plate load optimization problem is formulated applying the non-linear mathematical programming methods. The load variation bounds satisfying the optimality criterion in concert with the strength and stiffness requirements are to be identified. The stiffness constraints are realized via residual displacements. The dual mathematical programming problems cannot be applied directly when determining actual stress and strain fields of plate: the strained state depends upon the loading history. Thus the load optimization problem at shakedown is to be stated as a couple of problems solved in parallel: the shakedown state analysis problem and the verification of residual deflections bounds. The Rozen project gradient method is applied to solve the cyclically loaded non-linear shakedown plate stress and strain evaluation and that of the load optimization problems. The mechanical interpretation of Rozen optimality criterions allows to simplify the shakedown plate optimization mathematical model and solution algorithm formulations.

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34

Hou, Yan-Ting, Jia-Zhen Huo, and Feng Chu. "An Integrated Problem of p-Hub Location and Revenue Management with Multiple Capacity Levels under Disruptions." Journal of Advanced Transportation 2019 (April 1, 2019): 1–14. http://dx.doi.org/10.1155/2019/1812543.

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This paper considers an integrated hub location and revenue management problem in which a set of capacities is available from which one can be chosen for each hub and the disruption is considered in a star-star shaped airline network. We propose a two-stage stochastic programming model to maximize the profit of the network in which the cost of installing the hubs at different levels of capacities, the transportation cost, and the revenue obtained by selling airline tickets are considered. To provide flexible solutions, a hybrid two-stage stochastic programming-robust optimization model is developed by putting relative emphasis on a weighted sum of profit maximization. Furthermore, a sample average approximation approach is used for solving the stochastic programming formulation and a genetic algorithm approach is applied for both formulations. Numerical experiments are conducted to verify the mathematical formulations and compare the performance of the used approaches.

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35

Duarte, Belmiro P. M. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming." Mathematics 11, no. 4 (February 7, 2023): 854. http://dx.doi.org/10.3390/math11040854.

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The systematic design of exact optimal designs of experiments is typically challenging, as it results in nonconvex optimization problems. The literature on the computation of model-based exact optimal designs of experiments via mathematical programming, when the covariates are categorical variables, is still scarce. We propose mixed-integer semidefinite programming formulations, to find exact D-, A- and I-optimal designs for linear models, and locally optimal designs for nonlinear models when the design domain is a finite set of points. The strategy requires: (i) the generation of a set of candidate treatments; (ii) the formulation of the optimal design problem as a mixed-integer semidefinite program; and (iii) its solution, employing appropriate solvers. For comparison, we use semidefinite programming-based formulations to find equivalent approximate optimal designs. We demonstrate the application of the algorithm with various models, considering both unconstrained and constrained setups. Equivalent approximate optimal designs are used for comparison.

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36

Kalanta, Stanislovas. "DUAL MATHEMATICAL MODELS OF LIMIT LOAD ANALYSIS PROBLEMS OF STRUCTURES BY MIXED FINITE ELEMENTS." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 3, no. 10 (June 30, 1997): 43–51. http://dx.doi.org/10.3846/13921525.1997.10531683.

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The general and discrete dual mathematical models of the limit load analysis and optimization problems of rigid-plastic body are created in the article. The discrete models are formulated by mixed finite elements and presented in terms of kinematic and static formulation. In these models the velocity of the energy dissipation is estimated not only within the volume of finite elements, but also at the plastic surfaces between elements, where the discontinuities of displacement velocities functions appear. The theory of plastic flow, the theory of duality and mathematical programming are applied. The mixed energy functional (1) and (3) of both problems are formulated using the general static formulations of these problems, presented in the article [10], and Lagrangian multipliers method. The mixed finite elements are used for their discretization. The discrete expressions (8), (9) and (13) of mixed functionals are given choosing the interpolation functions (7) for the stress, displacement velocities, plastic multipliers and external load. Stationary conditions are created by static variables (stress and load vectors) of theses functionals. The discrete expressions of the geometric compatibility equations and constraint of load power are received from them. Using them as preliminary conditions for the functionals (8) and (9), the mathematical models (14), (15) and (17) of kinematic formulation of limit load analysis and optimization problems are formulated. The model (20) with a smaller number of unknowns is formed by elimination the displacement velocities. Using Lagrangian multipliers method, the mathematical models (21)-(23) of static formulation for the limit load parameter analysis problem and the models (24)-(26) for the load optimization problem are derived. All of them are the problems of mathematical programming. The mathematical models of static formulation for engineering purposes are more important and fit better. They are easier solved (a smaller quantity of unknowns), besides, they allow to determine the optimum distribution of the load. The formulated mathematical models allow to determine upper values of limit load, stresses, displacement and plastic multipliers velocities. Together with equilibrium models of these problems, presented in the article [10], they allow to determine the lower and upper values of aforementioned parameters. So, a good possibility is created to check reliability and exactness of numerical calculation results and to establish, if the computing net density of finite elements is sufficient.

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37

Kulian, V. R., and O. O. Yunkova. "Mathetical problem of banking assets diversification." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2021): 85–88. http://dx.doi.org/10.17721/1812-5409.2021/1.11.

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In article we consider a problem of optimal investment strategy by a commercial bank building. This task is actual and the development of a procedure to solve it can help in making investment banking decisions. The general formulation of the problem consists of two criteria. The first one is to maximize the expected return, and the second is to minimize the risk of the investment transaction. Mathematical formulation of the problem is considered as a problem of nonlinear programming under constraints. The procedure for solving such a two-criteria optimization problem allows to obtain many solutions, which requires further steps to make a single optimal solution. According to the algorithm proposed in the work, the problem is divided into two separate problems of single-criteria optimization. Each of these tasks allows to obtain the optimal values of the investment vector both in terms of its expected return and in terms of investment risk. Additional constraints in the mathematical formulation of the problem, make it possible to take into account factors that, from the point of view of the investor, may influence decision-making. The procedures presented in this work allow to obtain analytical representations of formulas that describe the optimal values of the investment distribution vector for both mathematical formulations of the problem.

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38

Dhingra, A. K., and S. S. Rao. "An Integrated Kinematic-Kinetostatic Approach to Optimal Design of Planar Mechanisms Using Fuzzy Theories." Journal of Mechanical Design 113, no. 3 (September 1, 1991): 306–11. http://dx.doi.org/10.1115/1.2912783.

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A new integrated approach to the design of high speed planar mechanisms is presented. The resulting nonlinear programming formulation combines both the kinematic and kinetostatic 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 an 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 novel 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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39

Esmaeili, Maryam, and Habibe Sadeghi. "An Investigation of the Optimistic Solution to the Linear Trilevel Programming Problem." Mathematics 6, no. 10 (September 27, 2018): 179. http://dx.doi.org/10.3390/math6100179.

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In this paper, we consider a general version of a linear trilevel programming problem. Three different types of optimistic optimal solutions for a special trilevel programming problem have formerly been suggested. This paper presents the mathematical formulation of all of the three types of optimistic optimal solutions for the given linear trilevel programming problem. Moreover, some properties of the inducible region (the feasible region for the trilevel programming problem) corresponding to each optimistic optimal solution are investigated. Finally, a numerical example is presented to compare the different types of optimistic optimal solutions.

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Erromdhani, Ridha, Bassem Jarboui, Mansour Eddaly, Abdelwaheb Rebai, and Nenad Mladenovic. "Variable neighborhood formulation search approach for the multi-item capacitated lot-sizing problem with time windows and setup times." Yugoslav Journal of Operations Research 27, no. 3 (2017): 301–22. http://dx.doi.org/10.2298/yjor160417017e.

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In this paper we suggest a new variant of Variable neighborhood search designed for solving Mixed integer programming problems. We call it Variable neighborhood formulation search (VNFS), since both neighborhoods and formulations are changed during the search. VNS deals with integer variables, while an available (commercial) solver is responsible for continues variables and the objective function value. We address the multi-item capacitated lotsizing problem with production time windows and setup times, under the non-customer specific case. This problem is known to be NP-hard and can be formulated as a mixed 0-1 program. Neighborhoods are induced from the Hamming distance in 0-1 variables, while the objective function values in the corresponding neighborhoods are evaluated using different mathematical programming formulations of the problem. The computational experiments show that our approach is more effective and efficient when compared with the existing methods from the literature.

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Kim, Hu Gon. "A Mathematical Structure and Formulation of Bottom-up Model based on Linear Programming." Journal of Energy Engineering 23, no. 4 (December 31, 2014): 150–59. http://dx.doi.org/10.5855/energy.2014.23.4.150.

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Doudoumis, I. N. "A Mathematical Programming Incremental Formulation for Unilateral Frictional Contact Problems of Linear Elasticity." Applicable Analysis 82, no. 6 (June 2003): 503–15. http://dx.doi.org/10.1080/0003681031000112149.

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Mockus, L., and G. V. Reklaitis. "Mathematical programming formulation for scheduling of batch operations based on nonuniform time discretization." Computers & Chemical Engineering 21, no. 10 (July 1997): 1147–56. http://dx.doi.org/10.1016/s0098-1354(96)00325-0.

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Roshani, Abdolreza, and Davide Giglio. "A Mathematical Programming Formulation for Cost-oriented Multi-manned Assembly Line Balancing Problem." IFAC-PapersOnLine 48, no. 3 (2015): 2293–98. http://dx.doi.org/10.1016/j.ifacol.2015.06.429.

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Liberti, Leo, Carlile Lavor, and Nelson Maculan. "A mathematical programming formulation for the Hartree–Fock problem on open-shell systems." Optimization Letters 13, no. 2 (January 8, 2019): 429–37. http://dx.doi.org/10.1007/s11590-019-01386-0.

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Atkočiūnas, Juozas. "KUHN-TUCKER CONDITIONS IN SHAKEDOWN PROBLEMS." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 2, no. 5 (March 31, 1996): 14–28. http://dx.doi.org/10.3846/13921525.1996.10531545.

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An elastic perfectly plastic structure at shakedown to given cyclić loading is under consideration. The stress-strain field of dissipative system in general is related to the history of loading. And only in a particular case, i.e. at the moment prior to the failure of an elastic perfectly plastic structure the distribution of the actual residual forces is unique for each prescribed history of loading (the safety factor of shakedown approaches unity). Nevertheless, there exist some domains where the plastic strains are equal to zero. The residual forces in the statically indeterminate parts of the structure may be non-unique: the stress field is only determined by the equilibrium equations. The extremum energy principle of minimum complementary energy allows to derive the actual residual forces out of all statically admissible residual forces at the moment prior to cyclic plastic failure. Then the stress-strain field analysis problem at the moment prior to the cyclic plastic failure is formulated as a problem of non-linear mathematical programming. Formulating the dual pair of non-linear programming problem (statical and kinematic formulation of analysis problem) the differential constraints are neglected or replaced by algebraic conditions. When the safety factor is approching a unity, the degeneracy of the statical formulation of the analysis problem often can occur. In this case a mathematical model is proposed for obtaining an upper bounds for the displacement at shakedown. It is pointed out that the known Kuhn-Tucker conditions of mathematical programming theory (i.e. compatibility equations of residual strains) in concert with restriction, limiting the maximum value of total energy dissipation, make up the adaptation conditions of the structure to given cyclic loading. Kuhn-Tucker conditions used in above—mentioned problem allow to correctly interprete the physical aspect of the degeneracy problem at shakedown. When the safety factor is larger than unity an artificial degeneracy situation for the statical formulation of analysis problem can be created. Then the mathematical models presented can be applied to the analysis of unloading elastoplastic structures. With this aim in view a fictitious equiplastic structure the behaviour of which is holonomic is derived. The displacements of the fictitious structure enclose the displacements of the actual structure subject to cyclic loading.

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Xia, S. H., and F. Tin-Loi. "Large Displacement Elastoplastic Analysis of Space Trusses as a Mathematical Programming Problem." International Journal of Space Structures 13, no. 3 (September 1998): 127–36. http://dx.doi.org/10.1177/026635119801300302.

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A mathematical programming approach is proposed for the large displacement elastoplastic analysis of space trusses. Features of the general methodology include the preservation of static-kinematic duality through the concept of fictitious forces and deformations, exact descriptions of equilibrium and compatibility for arbitrarily large displacements, albeit small strain, that can be specialized to any order of geometrical nonlinearity, and a complementarity description of the elastoplastic constitutive laws. The finite incremental formulation developed takes the form of a special mathematical programming problem known as a nonlinear complementarity problem for which a predictor-corrector type numerical scheme is proposed.

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Liu, Wenlian, Hanhua Xu, Sugang Sui, Ze Li, Xiaoyan Zhang, and Pu Peng. "Lower Bound Limit Analysis of Non-Persistent Jointed Rock Masses Using Mixed Numerical Discretization." Applied Sciences 12, no. 24 (December 16, 2022): 12945. http://dx.doi.org/10.3390/app122412945.

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The bearing capacity of a non-persistent jointed rock mass containing a rock bridge is investigated by combining the lower bound limit analysis theory, a mixed numerical discrete method, and linear mathematical programming. A mixed numerical discrete method is proposed to divide non-persistent jointed rock masses in which rigid block elements are used to simulate the rock blocks, whereas the finite element method is used to simulate the intact rock bridges. A linear mathematical programming model for the ultimate bearing capacity is constructed and solved using the interior point algorithm. The proposed formulation is validated by application to three rock slopes.

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Gil-González, Walter, Oscar Danilo Montoya, Luis Fernando Grisales-Noreña, Fernando Cruz-Peragón, and Gerardo Alcalá. "Economic Dispatch of Renewable Generators and BESS in DC Microgrids Using Second-Order Cone Optimization." Energies 13, no. 7 (April 3, 2020): 1703. http://dx.doi.org/10.3390/en13071703.

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A convex mathematical model based on second-order cone programming (SOCP) for the optimal operation in direct current microgrids (DCMGs) with high-level penetration of renewable energies and battery energy storage systems (BESSs) is developed in this paper. The SOCP formulation allows converting the non-convex model of economic dispatch into a convex approach that guarantees the global optimum and has an easy implementation in specialized software, i.e., CVX. This conversion is accomplished by performing a mathematical relaxation to ensure the global optimum in DCMG. The SOCP model includes changeable energy purchase prices in the DCMG operation, which makes it in a suitable formulation to be implemented in real-time operation. An energy short-term forecasting model based on a receding horizon control (RHC) plus an artificial neural network (ANN) is used to forecast primary sources of renewable energy for periods of 0.5h. The proposed mathematical approach is compared to the non-convex model and semidefinite programming (SDP) in three simulation scenarios to validate its accuracy and efficiency.

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Fazlollahtabar, Hamed. "An Effective Mathematical Programming Model for Production Automatic Robot Path Planning." Open Transportation Journal 13, no. 1 (March 26, 2019): 11–16. http://dx.doi.org/10.2174/1874447801913010011.

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Objective: Path planning for production robots has been investigated. The sequence of the orders to be processed in a certain planning horizon has been planned for the production system. Methods: Production automatic robots are employed to carry parts and products among all production stations and machining centers. The combination of machines in stations and autonomous robot evolves a production network. Results: The problem is to assign orders to robots so that paths are obtained to minimize total waiting times of production system and meanwhile provide collision-free paths. Conclusion: The proposed mathematical formulation is implemented to show the efficiency and effectiveness.

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