Статті в журналах: "Mathematical optimization"

1

Kulcsár, T., and I. Timár. "Mathematical optimization and engineering applications." Mathematical Modeling and Computing 3, no. 1 (July 1, 2016): 59–78. http://dx.doi.org/10.23939/mmc2016.01.059.

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Bhardwaj, Suyash, Seema Kashyap, and Anju Shukla. "A Novel Approach For Optimization In Mathematical Calculations Using Vedic Mathematics Techniques." MATHEMATICAL JOURNAL OF INTERDISCIPLINARY SCIENCES 1, no. 1 (July 2, 2012): 23–34. http://dx.doi.org/10.15415/mjis.2012.11002.

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3

Chawla, Dr Meenu. "Mathematical optimization techniques." Pharma Innovation 8, no. 2 (January 1, 2019): 888–92. http://dx.doi.org/10.22271/tpi.2019.v8.i2n.25454.

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4

Suhl, Uwe H. "MOPS — Mathematical optimization system." European Journal of Operational Research 72, no. 2 (January 1994): 312–22. http://dx.doi.org/10.1016/0377-2217(94)90312-3.

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5

Blaydа, I. A. "OPTIMIZATION OF THE COAL BACTERIAL DESULFURIZATION USING MATHEMATICAL METHODS." Biotechnologia Acta 11, no. 6 (December 2018): 55–66. http://dx.doi.org/10.15407/biotech11.06.055.

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6

Requelme Ibáñez, Rosa María, Carlos Abel Reyes Alvarado, and Jorge Luis Lozano Cervera. "Mathematical optimization for economic agents." Revista Ciencia y Tecnología 17, no. 3 (September 9, 2021): 81–89. http://dx.doi.org/10.17268/rev.cyt.2021.03.07.

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7

Sezer, Ali Devin, and Gerhard-Wilhelm Weber. "Optimization Methods in Mathematical Finance." Optimization 62, no. 11 (November 2013): 1399–402. http://dx.doi.org/10.1080/02331934.2013.863528.

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8

Stanojević, Milan, and Bogdana Stanojević. "Lua APIs for mathematical optimization." Procedia Computer Science 242 (2024): 460–65. http://dx.doi.org/10.1016/j.procs.2024.08.160.

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9

García, J. M., C. A. Acosta, and M. J. Mesa. "Genetic algorithms for mathematical optimization." Journal of Physics: Conference Series 1448 (January 2020): 012020. http://dx.doi.org/10.1088/1742-6596/1448/1/012020.

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10

Gorissen, Bram L., Jan Unkelbach, and Thomas R. Bortfeld. "Mathematical Optimization of Treatment Schedules." International Journal of Radiation Oncology*Biology*Physics 96, no. 1 (September 2016): 6–8. http://dx.doi.org/10.1016/j.ijrobp.2016.04.012.

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11

Feichtinger, Gustav. "Mathematical Optimization and Economic Analysis." European Journal of Operational Research 221, no. 1 (August 2012): 273–74. http://dx.doi.org/10.1016/j.ejor.2012.03.018.

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12

Carrizosa, Emilio, and Dolores Romero Morales. "Supervised classification and mathematical optimization." Computers & Operations Research 40, no. 1 (January 2013): 150–65. http://dx.doi.org/10.1016/j.cor.2012.05.015.

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13

BOBYLEV, A. I. "INTEGER OPTIMIZATION PROBLEM." Vestnik LSTU, no. 1 (2024): 30–37. http://dx.doi.org/10.53015/23049235_2024_1_30.

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Mathematical programming is a mathematical discipline that studies various extremal problems and develops algorithms for solving them. Among the problems are those of mathematical integer programming. Integer programming is indispensable for solving mathematical programming problems in which some or all of the variables take on integer values. The problems include the transport problem. The paper considers the transport problem and three linear programming methods for solving it: the method of potentials, the method of differential rents and the simplex method. The paper analyzes and assesses the effectiveness of the three algorithms for optimizing transport problems. Several linear optimization algorithms have been studied and presented. The paper contains the basic concepts, formulas, and algorithms of the methods used. The method of potentials, the method of differential rents and the simplex method are considered. The results of solving the problem using these methods are presented and compared. All calculations were performed using Excel.

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14

Yogita D. Bhise. "Mathematical Optimization of Electric Motor Designs." Panamerican Mathematical Journal 35, no. 1s (November 13, 2024): 220–30. http://dx.doi.org/10.52783/pmj.v35.i1s.2310.

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When designing and improving the performance of electric motors, mathematical optimization is very important. The main goals are usually to make the motors more efficient, lower their costs, and work within certain limits. The main topic of this study is how to improve electric motor designs using advanced optimization methods, such as multi-objective optimization. The study looks at how to use different types of computer algorithms together, like gradient-based methods, genetic algorithms, and particle swarm optimization, to solve difficult design problems. Some of these problems are reducing energy loss, making the best use of materials, and finding the right balance between different performance measures such as speed, power density, and temperature management. Building mathematical models of the motor's physical and functional features is the first step in this method. Then, optimization methods are applied to these models. Finite element analysis (FEA) is used to correctly model the motor's electric behavior. This makes sure that the optimization process considers physical limits and nonlinearities that happen in the real world. The study also looks into how different design factors, like the shape of the motor's core, the way the windings are set up, and the materials used, affect its total performance. The study also looks at the fact that motor design has more than one goal by using Pareto front analysis to find the best ways to balance different goals. This lets people come up with motor designs that are good for speed, efficiency, and cost-effectiveness. Case studies of the design of different kinds of electric motors, such as induction motors, permanent magnet synchronous motors (PMSMs), and brushless DC motors (BLDCs), show that the proposed optimization method works well. The results show that mathematical optimization has the ability to make the planning process a lot better. This could lead to motors that work better, cost less, and are better suited to certain uses. The study ends with a talk of how optimization methods could be used in the future to improve the design of electric motors, especially for new technologies like electric cars and green energy systems.

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15

Freeman, T. L., and Melvyn W. Jeter. "Mathematical Programming: An Introduction to Optimization." Mathematical Gazette 71, no. 458 (December 1987): 350. http://dx.doi.org/10.2307/3617112.

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16

Gozuyilmaz, Seyma, and O. Erhun Kundakcioglu. "Mathematical optimization for time series decomposition." OR Spectrum 43, no. 3 (June 8, 2021): 733–58. http://dx.doi.org/10.1007/s00291-021-00637-w.

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17

Lucatero, Carlos Rodríguez, Marcelo Olivera Villaroel, and Paola Ovando. "A Mathematical Model for Agroforestry Optimization." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 17 (March 2, 2022): 108–22. http://dx.doi.org/10.37394/23203.2022.17.13.

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In the present article, we will describe some extensions of an agroforestry model that has been proposed and computationally implemented in [7]. Our generalizations consist of the inclusion of two additional species of tree, one culture, and a declaration of regeneration tours as variables definable by us as a parameter and the weight allocation by rentability of the treeless soil utilization as well as an exhaustive exploration of the different soil utilization scenarios in order to obtain the one who gives the best economic performance.

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18

McMullen, P. "MATHEMATICAL PROGRAMMING An Introduction to Optimization." Bulletin of the London Mathematical Society 19, no. 3 (May 1987): 290–91. http://dx.doi.org/10.1112/blms/19.3.290.

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19

Naidu, N. V. R. "Mathematical model for quality cost optimization." Robotics and Computer-Integrated Manufacturing 24, no. 6 (December 2008): 811–15. http://dx.doi.org/10.1016/j.rcim.2008.03.018.

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20

Zomorrodi, Ali R., Patrick F. Suthers, Sridhar Ranganathan, and Costas D. Maranas. "Mathematical optimization applications in metabolic networks." Metabolic Engineering 14, no. 6 (November 2012): 672–86. http://dx.doi.org/10.1016/j.ymben.2012.09.005.

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21

Rakesh, Vineet, and Ashim Datta. "Microwave puffing: mathematical modeling and optimization." Procedia Food Science 1 (2011): 762–69. http://dx.doi.org/10.1016/j.profoo.2011.09.115.

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22

Hales, Roland Oliver, and Sergio García. "Congress seat allocation using mathematical optimization." TOP 27, no. 3 (April 29, 2019): 426–55. http://dx.doi.org/10.1007/s11750-019-00515-3.

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23

Liou, Y. C., X. Q. Yang, and J. C. Yao. "Mathematical Programs with Vector Optimization Constraints." Journal of Optimization Theory and Applications 126, no. 2 (August 2005): 345–55. http://dx.doi.org/10.1007/s10957-005-4720-4.

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24

Shah, Nita, and Poonam Mishra. "Oil production optimization: a mathematical model." Journal of Petroleum Exploration and Production Technology 3, no. 1 (November 2, 2012): 37–42. http://dx.doi.org/10.1007/s13202-012-0040-z.

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25

Billionnet, Alain. "Mathematical optimization ideas for biodiversity conservation." European Journal of Operational Research 231, no. 3 (December 2013): 514–34. http://dx.doi.org/10.1016/j.ejor.2013.03.025.

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26

Venkayya, V. B. "Mathematical optimization in multi-disciplinary design." Mathematical and Computer Modelling 14 (1990): 29–36. http://dx.doi.org/10.1016/0895-7177(90)90144-c.

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27

Russenschuck, S., and T. Tortschanoff. "Mathematical optimization of superconducting accelerator magnets." IEEE Transactions on Magnetics 30, no. 5 (September 1994): 3419–22. http://dx.doi.org/10.1109/20.312673.

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28

Sakhapov, R. L., R. V. Nikolaeva, M. H. Gatiyatullin, and M. M. Makhmutov. "Mathematical model of highways network optimization." Journal of Physics: Conference Series 936 (December 2017): 012032. http://dx.doi.org/10.1088/1742-6596/936/1/012032.

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29

Şen, Alper, Kamyar Kargar, Esma Akgün, and Mustafa Ç. Pınar. "Codon optimization: a mathematical programing approach." Bioinformatics 36, no. 13 (April 20, 2020): 4012–20. http://dx.doi.org/10.1093/bioinformatics/btaa248.

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Abstract Motivation Synthesizing proteins in heterologous hosts is an important tool in biotechnology. However, the genetic code is degenerate and the codon usage is biased in many organisms. Synonymous codon changes that are customized for each host organism may have a significant effect on the level of protein expression. This effect can be measured by using metrics, such as codon adaptation index, codon pair bias, relative codon bias and relative codon pair bias. Codon optimization is designing codons that improve one or more of these objectives. Currently available algorithms and software solutions either rely on heuristics without providing optimality guarantees or are very rigid in modeling different objective functions and restrictions. Results We develop an effective mixed integer linear programing (MILP) formulation, which considers multiple objectives. Our numerical study shows that this formulation can be effectively used to generate (Pareto) optimal codon designs even for very long amino acid sequences using a standard commercial solver. We also show that one can obtain designs in the efficient frontier in reasonable solution times and incorporate other complex objectives, such as mRNA secondary structures in codon design using MILP formulations. Availability and implementation http://alpersen.bilkent.edu.tr/codonoptimization/CodonOptimization.zip.

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30

Heyer, Laurie J. "A Mathematical Optimization Problem in Bioinformatics." PRIMUS 18, no. 1 (January 17, 2008): 101–18. http://dx.doi.org/10.1080/10511970701744992.

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31

Zowe, Jochem, Michal Kočvara, and Martin P. Bendsøe. "Free material optimization via mathematical programming." Mathematical Programming 79, no. 1-3 (October 1997): 445–66. http://dx.doi.org/10.1007/bf02614328.

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32

Norkin, B. V. "Mathematical models for insurance business optimization." Cybernetics and Systems Analysis 47, no. 1 (January 2011): 117–33. http://dx.doi.org/10.1007/s10559-011-9295-5.

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33

Ahmad Mala, Firdous. "Mathematical Analysis and Optimization for Economists." Technometrics 65, no. 2 (April 3, 2023): 300–301. http://dx.doi.org/10.1080/00401706.2023.2201131.

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34

Petridis, Konstantinos, Garyfallos Arabatzis, and Angelo Sifaleras. "Mathematical optimization models for fuelwood production." Annals of Operations Research 294, no. 1-2 (October 31, 2017): 59–74. http://dx.doi.org/10.1007/s10479-017-2697-7.

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35

Stanimirović, Predrag S., and Artem Stupin. "Dynamic programming in package Mathematica." ITM Web of Conferences 72 (2025): 01001. https://doi.org/10.1051/itmconf/20257201001.

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Dynamic programming (DP) is a powerful algorithmic technique for solving optimization problems by breaking them down into simpler subproblems. This paper presents an implementation of DP algorithms for two classic optimization problems: the Knapsack problem and the Traveling Salesman Problem (TSP). The solutions are developed and demonstrated using the Mathematica® programming language. For the Knapsack problem, we present two variants: with and without item repetition. The paper describes the mathematical formulation of each variant and provides detailed Mathematica code for their implementation. Examples are given to illustrate the effectiveness of the algorithms in finding optimal solutions. The TSP implementation demonstrates how DP can be applied to find the shortest Hamiltonian contour in a given network. The paper outlines the mathematical model, recurrent formula, and step-by-step solution process. An example with a four-node network is provided to showcase the algorithm's application. This work highlights the versatility of dynamic programming in solving complex optimization problems and demonstrates the effectiveness of Mathematica as a tool for implementing and visualizing these solutions. The presented algorithms and code snippets serve as valuable resources for researchers and practitioners working on similar optimization challenges.

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36

Ulitinas, Tomas, and Stanislovas Kalanta. "OPTIMIZATION OF TRUSS HEIGHT." Mokslas - Lietuvos ateitis 2, no. 6 (December 31, 2010): 56–60. http://dx.doi.org/10.3846/mla.2010.112.

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The article analyzes the task in truss height and in the optimization of the cross-sections of their elements. Element cross-sections are designed of steel profiles considering requirements for strength, stability and rigidity. A mathematical model is formulated as a nonlinear mathematical programming problem. It is solved as an iterative process, using mathematical software package “MATLAB” routine “fmincon”. The ratio of buckling is corrected in the each iteration. Optimization results are compared with those obtained applying software package “Robot Millennium”.

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37

Xie, Hua Long, Hui Min Guo, Qing Bao Wang, and Yong Xian Liu. "The Spindle Structural Optimization Design of HTC3250µn NC Machine Tool Based on ANSYS." Advanced Materials Research 457-458 (January 2012): 60–64. http://dx.doi.org/10.4028/www.scientific.net/amr.457-458.60.

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The optimization of spindle has important significance. The optimization method based on ANSYS is introduced and spindle mathematical mode of HTC3250µn NC machine tool is given. By scanning of design variables, the main optimized design variables are determined. The single objective and multi-objective optimizations are done. In the end, the main size comparison of spindle before and after optimization is given.

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38

Ma, Yunpeng, Xiaolu Wang, and Wanting Meng. "A Reinforced Whale Optimization Algorithm for Solving Mathematical Optimization Problems." Biomimetics 9, no. 9 (September 22, 2024): 576. http://dx.doi.org/10.3390/biomimetics9090576.

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The whale optimization algorithm has several advantages, such as simple operation, few control parameters, and a strong ability to jump out of the local optimum, and has been used to solve various practical optimization problems. In order to improve its convergence speed and solution quality, a reinforced whale optimization algorithm (RWOA) was designed. Firstly, an opposition-based learning strategy is used to generate other optima based on the best optimal solution found during the algorithm’s iteration, which can increase the diversity of the optimal solution and accelerate the convergence speed. Secondly, a dynamic adaptive coefficient is introduced in the two stages of prey and bubble net, which can balance exploration and exploitation. Finally, a kind of individual information-reinforced mechanism is utilized during the encircling prey stage to improve the solution quality. The performance of the RWOA is validated using 23 benchmark test functions, 29 CEC-2017 test functions, and 12 CEC-2022 test functions. Experiment results demonstrate that the RWOA exhibits better convergence accuracy and algorithm stability than the WOA on 20 benchmark test functions, 21 CEC-2017 test functions, and 8 CEC-2022 test functions, separately. Wilcoxon’s rank sum test shows that there are significant statistical differences between the RWOA and other algorithms

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39

Monabbati, S. E., and H. Torabi. "Mathematical modeling of finite topologies." Carpathian Mathematical Publications 12, no. 2 (December 29, 2020): 434–42. http://dx.doi.org/10.15330/cmp.12.2.434-442.

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Integer programming is a tool for solving some combinatorial optimization problems. In this paper, we deal with combinatorial optimization problems on finite topologies. We use the binary representation of the sets to characterize finite topologies as the solutions of a Boolean quadratic system. This system is used as a basic model for formulating other types of topologies (e.g. door topology and $T_0$-topology) and some combinatorial optimization problems on finite topologies. As an example of the proposed model, we found that the smallest number $m(k)$ for which the topology exists on an $m(k)$-elements set containing exactly $k$ open sets, for $k = 8$ and $k = 15$ is $3$ and $5$, respectively.

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40

Gupta, Arnav, Ananya Sharma, Chen Li Wei, and Mehta Ravi. "Integrating Evolutionary Algorithms and Mathematical Modeling for Efficient Neural Network Optimization." Advances in Machine Learning & Artificial Intelligence 5, no. 4 (December 3, 2024): 01–06. https://doi.org/10.33140/amlai.05.04.01.

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Optimizing neural network architectures presents significant challenges due to the vast search spaces and computational costs involved. This study explores the integration of evolutionary algorithms (EAs) and mathematical modeling techniques to enhance neural network optimization. We propose a novel framework combining EAs with dimensionality reduction, surrogate modeling, and hybrid optimization strategies to reduce computational complexity and improve performance. Our results demonstrate that the adapted EAs significantly increase accuracy and F1-scores while reducing the number of generations required for convergence. The hybrid approach, combining EAs with local search techniques, achieves superior performance and robustness across various datasets. These findings provide a foundational basis for future research in advanced optimization methods for neural networks

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41

Zhang, Hongxin. "Optimization Strategies for Mathematical Algorithms in Computer Programming." Journal of Big Data and Computing 1, no. 1 (March 2023): 16–19. http://dx.doi.org/10.62517/jbdc.202301104.

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Computer programming is an important part of computing information technology, mathematical operation is one of the main modules of computer programming, through the optimization of mathematical operation to simple computer programming algorithm, can improve the efficiency of computer software. Therefore, in order to improve the efficiency of computer operation, it is particularly important to optimize the mathematical algorithms. Based on this, this paper studies the optimization strategy of mathematical algorithm in computer programming. Firstly, a brief overview of mathematical algorithm and computer programming is made, secondly, the role of mathematical algorithm in computer programming is analyzed, and finally, the optimization strategy of mathematical algorithm in computer programming is given.

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42

Journal, IJSREM. "Reviewing the Role of Mathematical Optimization in Operations Research: Algorithms, Applications, and Challenges." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 08, no. 02 (February 8, 2024): 1–11. http://dx.doi.org/10.55041/ijsrem28578.

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This review paper examines the pivotal role of mathematical optimization in operations research, focusing on its algorithms, applications, and challenges. Mathematical optimization, a cornerstone of operations research, offers powerful tools for addressing complex decision-making problems. We discuss a variety of optimization algorithms, from classical methods like linear programming to modern metaheuristic techniques such as genetic algorithms. Through specific case studies, we highlight the diverse applications of mathematical optimization in industries such as logistics, finance, and manufacturing. Additionally, analyze challenges like computational complexity and scalability issues, providing insights into the practical implementation of optimization solutions in real world scenarios. Keywords: Mathematical Optimization, Operations Research, Algorithms, Decision-Making Problems, Challenges, Applications

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43

Zhong, Mei Peng. "Parameter Optimization of Compressor Based on an Ant Colony Optimization." Applied Mechanics and Materials 201-202 (October 2012): 916–19. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.916.

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A mathematical model of operation on air compressors is set up in order to improve the efficiency of air compressors. Parameter of Compressor is optimized by an Ant Colony Optimization (ACO) Particle approach. Volume and its weight of the new compressor are little, and its efficiency is high. An Ant Colony Optimization embed BLDCM module which optimizating the air compressor was put forward. Optimizated target of an Ant Colony Optimization is the efficiency of BLDCM. Optimizated variables are the diameter of low pressure cylinder, the diameter of high pressure cylinder, the journey of low pressure piston, the journey of high pressure piston and the rotate speed of BLDCM. Simulated result shows that the efficiency of BLDCM is more than that before optimizating. The test is done. The result shows that the specifc Power of air compressor is much less than before optimizating on 2.5Mpa. The result also shows that an Ant Colony Optimization which optimizating the air compressor is availability and practicality.

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44

Montoro, Johnny Moisés Valverde, Milton Milciades Cortez Gutiérrez, and Hernán Oscar Cortez Gutiérrez. "Optimization of the mathematical programming and applications." South Florida Journal of Development 2, no. 5 (December 9, 2021): 7902–11. http://dx.doi.org/10.46932/sfjdv2n5-114.

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The present investigation responds to the need to solve optimization problems with optimality conditions. The KKT conditions are considered for multiobjective optimization problems with interval-valued objective functions.

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45

Kutova, О. V., and R. V. Sahaidak-Nikitiuk. "Optimization methods for multi-criteria decisions in pharmacy." Social Pharmacy in Health Care 9, no. 4 (November 17, 2023): 3–10. http://dx.doi.org/10.24959/sphhcj.23.302.

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Optimization methods for multi-criteria decisions in pharmacy In pharmaceutical technological research, the determination of the quantitative composition of granules is considered as a task of multi-criteria selection. Today, to solve this problem, the regression analysis and multi-criteria optimization methods are widely used; they are based on mathematical models obtained for the object under study. Aim. To identify a decision-making method in a multi-criteria space that is effective for use in pharmaceutical technology research with quantitative factors. Materials and methods. The study uses tools of the popular computer mathematics system Mathcad (MathSoft Ins., USA) to automate the solution of mathematical problems. To automatically search for the type and coefficients of regression equations, the MS Excel application was used, namely: the data analysis package (regression analysis). The MS Word processor was used to edit the code. Results. A variety of approaches to the formalization of the multi-criteria optimization task have been studied. The optimal quantitative content of excipients when developing the granule technology has been found using two different optimization criteria, which are formed according to different methodical approaches. The method proposed does not provide for the mandatory introduction of gradation of individual criteria or their weighting factors. Conclusions. As a result of the comparison of multi-criteria optimization methods, the effectiveness of the decision-making method in the multi-criteria space has been shown; it synthesizes a mathematical procedure related to the vector of criteria and is based on determining the ideal point and introducing the concept of a norm into the space of functionals; it has not been mathematically proven, but it is practically useful decision-making algorithm compared to the mathematical method of convolution of criteria. The optimization method proposed has advantages that are manifested in the possibility of using a relatively simple mathematical apparatus and simplified logic of obtaining a solution.

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46

Lebedev, Vladimir, and Ekaterina Yushkova. "Mathematical model for optimization of heat exchange systems." E3S Web of Conferences 164 (2020): 02011. http://dx.doi.org/10.1051/e3sconf/202016402011.

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The article is devoted to the issue of thermodynamic optimization of heat transfer systems. Optimization is carried out by an exergy pinch method. This method includes the advantages of exergy analysis and pinch method. Exergy analysis takes into account the quantitative and qualitative characteristics of thermal processes, the pinch method allows structural and parametric optimization of heat transfer systems. The article presents a mathematical model for optimization by exergy pinch analysis. This model allows automated system optimization. Exergy pinch analysis allows more efficient use of energy and resources at the enterprise, which is relevant today.

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47

Carrizosa, Emilio, Cristina Molero-Río, and Dolores Romero Morales. "Mathematical optimization in classification and regression trees." TOP 29, no. 1 (March 17, 2021): 5–33. http://dx.doi.org/10.1007/s11750-021-00594-1.

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AbstractClassification and regression trees, as well as their variants, are off-the-shelf methods in Machine Learning. In this paper, we review recent contributions within the Continuous Optimization and the Mixed-Integer Linear Optimization paradigms to develop novel formulations in this research area. We compare those in terms of the nature of the decision variables and the constraints required, as well as the optimization algorithms proposed. We illustrate how these powerful formulations enhance the flexibility of tree models, being better suited to incorporate desirable properties such as cost-sensitivity, explainability, and fairness, and to deal with complex data, such as functional data.

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Medved, I., Yu Otrosh, and N. Rashkevich. "Optimization of building structures." Mechanics And Mathematical Methods 6, no. 1 (March 28, 2024): 17–25. http://dx.doi.org/10.31650/2618-0650-2024-6-1-17-25.

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In the field of the theory of calculation of building structures, there is a constant refinement of the actual operation of these structures, i.e. design schemes are created that most accurately correspond to actual operating conditions. Creating optimal structures is a very urgent task facing designers. Therefore, it is quite natural to try to solve this problem using mathematical programming methods, which involve: selecting dependent and independent variables, constructing mathematical models and establishing criteria for the effectiveness of the selected model. In this case, the model should be a function that fairly accurately describes the research being carried out using mathematical apparatus (various types of functions, equations, systems of equations and inequalities, etc.). In mathematical programming, any set of independent (controlled) variables is called a solution. Optimal solutions are those that, for one reason or another, are preferable to others. The preference (effectiveness) of the study is quantified by the numerical value of the objective function. “Solution Search” is an add-in for Microsoft Excel that is used to solve optimization problems. Simply put, with the Solver add-in, you can determine the maximum or minimum value of one cell by changing other cells. Most often, this add-in is used to find optimal solutions to problems economically. There are not enough results of using this approach for calculating building structures in the public domain. Therefore, it is quite logical to try to use this add-on in problems of optimization of building structures. In this work, an attempt was made to use mathematical programming methods and this add-on to optimize the geometric dimensions of the structure, when the numerical value of the bending moment in a specific section was chosen as an optimization criterion.

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49

Stanojević, Bogdana, Simona Dzitac, and Ioan Dzitac. "Fuzzy Numbers and Fractional Programming in Making Decisions." International Journal of Information Technology & Decision Making 19, no. 04 (July 2020): 1123–47. http://dx.doi.org/10.1142/s0219622020300037.

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This study surveys the use of fuzzy numbers in classic optimization models, and its effects on making decisions. In a wide sense, mathematical programming is a collection of tools used in mathematical optimization to make good decisions. There are many sectors of economy that employ it. Finance and government, logistics and manufacturing, the distribution of the electrical power are worth to be first mentioned. When real life problems are modeled mathematically, there is always a trade-off between model’s accuracy and complexity. By this survey, we aim to present in a concise form some mathematical models from the literature together with the methods to solve them. We will focus mainly on fuzzy fractional programming problems. We will also refer to but not describe in detail the multi-criteria decision-making problems involving fuzzy numbers and linear fractional programming models.

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Azizi, Tahmineh. "Mathematical Modelling of Cancer Treatments, Resistance, Optimization." AppliedMath 5, no. 2 (April 4, 2025): 40. https://doi.org/10.3390/appliedmath5020040.

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Mathematical modeling plays a crucial role in the advancement of cancer treatments, offering a sophisticated framework for analyzing and optimizing therapeutic strategies. This approach employs mathematical and computational techniques to simulate diverse aspects of cancer therapy, including the effectiveness of various treatment modalities such as chemotherapy, radiation therapy, targeted therapy, and immunotherapy. By incorporating factors such as drug pharmacokinetics, tumor biology, and patient-specific characteristics, these models facilitate predictions of treatment responses and outcomes. Furthermore, mathematical models elucidate the mechanisms behind cancer treatment resistance, including genetic mutations and microenvironmental changes, thereby guiding researchers in designing strategies to mitigate or overcome resistance. The application of optimization techniques allows for the development of personalized treatment regimens that maximize therapeutic efficacy while minimizing adverse effects, taking into account patient-related variables such as tumor size and genetic profiles. This study elaborates on the key applications of mathematical modeling in oncology, encompassing the simulation of various cancer treatment modalities, the elucidation of resistance mechanisms, and the optimization of personalized treatment regimens. By integrating mathematical insights with experimental data and clinical observations, mathematical modeling emerges as a powerful tool in oncology, contributing to the development of more effective and personalized cancer therapies that improve patient outcomes.

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