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1

ARAKAWA, Masao, Takaharu Shirai, Hitomi Kono, Hirotaka NAKAYAMA, and Hiroshi ISHIKAWA. "Approximate Optimization Using RBF : Mixed variable Optimization with Discrete Variables." Proceedings of Design & Systems Conference 2003.13 (2003): 108–11. http://dx.doi.org/10.1299/jsmedsd.2003.13.108.

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2

Salgueiro, Yamisleydi, Jorge L. Toro, Rafael Bello, and Rafael Falcon. "Multiobjective variable mesh optimization." Annals of Operations Research 258, no. 2 (May 18, 2016): 869–93. http://dx.doi.org/10.1007/s10479-016-2221-5.

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3

Puris, Amilkar, Rafael Bello, Daniel Molina, and Francisco Herrera. "Variable mesh optimization for continuous optimization problems." Soft Computing 16, no. 3 (August 10, 2011): 511–25. http://dx.doi.org/10.1007/s00500-011-0753-9.

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4

Liao, Tianjun, Krzysztof Socha, Marco A. Montes de Oca, Thomas Stutzle, and Marco Dorigo. "Ant Colony Optimization for Mixed-Variable Optimization Problems." IEEE Transactions on Evolutionary Computation 18, no. 4 (August 2014): 503–18. http://dx.doi.org/10.1109/tevc.2013.2281531.

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5

Singh, Prem, and Himanshu Chaudhary. "A Modified Jaya Algorithm for Mixed-Variable Optimization Problems." Journal of Intelligent Systems 29, no. 1 (October 23, 2018): 1007–27. http://dx.doi.org/10.1515/jisys-2018-0273.

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Анотація:
Abstract Mixed-variable optimization problems consist of the continuous, integer, and discrete variables generally used in various engineering optimization problems. These variables increase the computational cost and complexity of optimization problems due to the handling of variables. Moreover, there are few optimization algorithms that give a globally optimal solution for non-differential and non-convex objective functions. Initially, the Jaya algorithm has been developed for continuous variable optimization problems. In this paper, the Jaya algorithm is further extended for solving mixed-variable optimization problems. In the proposed algorithm, continuous variables remain in the continuous domain while continuous domains of discrete and integer variables are converted into discrete and integer domains applying bound constraint of the middle point of corresponding two consecutive values of discrete and integer variables. The effectiveness of the proposed algorithm is evaluated through examples of mixed-variable optimization problems taken from previous research works, and optimum solutions are validated with other mixed-variable optimization algorithms. The proposed algorithm is also applied to two-plane balancing of the unbalanced rigid threshing rotor, using the number of balance masses on plane 1 and plane 2. It is found that the proposed algorithm is computationally more efficient and easier to use than other mixed optimization techniques.
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6

Naik, Kamlesh Kumar. "Optimization of Complex Function Variable." International Journal for Research in Applied Science and Engineering Technology V, no. X (October 22, 2017): 554–57. http://dx.doi.org/10.22214/ijraset.2017.10081.

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7

Segretier, Wilfried, Martine Collard, Laurent Brisson, and Jean-Emile Symphor. "Variable optimization for flood prediction." Ingénierie des systèmes d'information 16, no. 3 (June 30, 2011): 113–39. http://dx.doi.org/10.3166/isi.16.3.113-139.

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8

Deng, Geng, and Michael C. Ferris. "Variable-Number Sample-Path Optimization." Mathematical Programming 117, no. 1-2 (July 18, 2007): 81–109. http://dx.doi.org/10.1007/s10107-007-0164-y.

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9

Tian, Hao, Xiang Fan Piao, and Cheng Zhe Xu. "Parameter Optimization of Gas Purge-Microsyringe Extraction." Advanced Materials Research 1033-1034 (October 2014): 607–10. http://dx.doi.org/10.4028/www.scientific.net/amr.1033-1034.607.

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This paper proposes parameter optimization method of GP-MSE based on extraction parameters model. First, we identify the function relationship between dependent and independent variables by using neural networks. Second, independent variable set is made by interpolating the original independent variables, and then input these independent variables to fitted function to generate the dependent variable set. Last, we find the maximum value on dependent variable set to confirm the optimal parameters. Experimental result shows that the proposed method is not only simple and fast, but also ideal for recovery of single analyte.
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10

Gao, Li, and Rong Rong Wang. "Study on Mix-Variable Collaborative Design Optimization." Applied Mechanics and Materials 215-216 (November 2012): 592–96. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.592.

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Анотація:
In order to deal with complex product design optimization problems with both discrete and continuous variables, mix-variable collaborative design optimization algorithm is put forward based on collaborative optimization, which is an efficient way to solve mix-variable design optimization problems. On the rule of “divide and rule”, the algorithm decouples the problem into some relatively simple subsystems. Then by using collaborative mechanism, the optimal solution is obtained. Finally, the result of a case shows the feasibility and effectiveness of the new algorithm.
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11

Wang, Weiting, Yonghuan Yun, Baichuan Deng, Wei Fan, and Yizeng Liang. "Iteratively variable subset optimization for multivariate calibration." RSC Advances 5, no. 116 (2015): 95771–80. http://dx.doi.org/10.1039/c5ra08455e.

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12

Ramanujam, Rahul, and A. Abhishek. "Performance Optimization of Variable-Speed and Variable-Geometry Rotor Concept." Journal of Aircraft 54, no. 2 (March 2017): 476–89. http://dx.doi.org/10.2514/1.c033869.

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13

Mehrdel, Pouya, Josep Farre Llados, Jasmina Casals, and Shadi Karimi. "Optimization of Variable Radius Spiral Micromixer." Proceedings 1, no. 8 (December 6, 2017): 819. http://dx.doi.org/10.3390/proceedings1080819.

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14

Liao, Shan-Hui, Ming-Nan Fu, Kung-Hsu Hou, and Ching-Chung Li. "Variable Optimization for Chemical Mechanical Polishing." Japanese Journal of Applied Physics 44, no. 5A (May 10, 2005): 2961–66. http://dx.doi.org/10.1143/jjap.44.2961.

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15

Davey, K. R. "Magnet design optimization using variable metrics." IEEE Transactions on Magnetics 31, no. 6 (1995): 3566–68. http://dx.doi.org/10.1109/20.489571.

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16

Homem-De-Mello, Tito. "Variable-sample methods for stochastic optimization." ACM Transactions on Modeling and Computer Simulation 13, no. 2 (April 2003): 108–33. http://dx.doi.org/10.1145/858481.858483.

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17

Kuindersma, Scott R., Roderic A. Grupen, and Andrew G. Barto. "Variable risk control via stochastic optimization." International Journal of Robotics Research 32, no. 7 (June 2013): 806–25. http://dx.doi.org/10.1177/0278364913476124.

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18

Fukushima, Masao. "Parallel Variable Transformation in Unconstrained Optimization." SIAM Journal on Optimization 8, no. 3 (August 1998): 658–72. http://dx.doi.org/10.1137/s1052623496309879.

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19

Marduel, Xavier, Christophe Tribes, and Jean-Yves Trépanier. "Variable-fidelity optimization: Efficiency and robustness." Optimization and Engineering 7, no. 4 (December 2006): 479–500. http://dx.doi.org/10.1007/s11081-006-0351-3.

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20

Li, Yong Xian, Song Ping Chen, and Wen Qiong Zhang. "A Prevalent Error in Optimization Design of Helical Springs." Advanced Materials Research 1006-1007 (August 2014): 324–27. http://dx.doi.org/10.4028/www.scientific.net/amr.1006-1007.324.

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Анотація:
This paper reveals the popular error and problem in optimization design of helical springs. Most of the engineers and researchers regard wire diameter d, mean coil diameter D and number of active coils n as design variables in the mathematical model of optimization design for helical springs. In fact, only two variables are independent variables in the three design variables. The dependent variable in the optimization design model influences the behavior of the systems to be optimized, which is also possible to calculate wrong results. This paper analyses relationship of wire diameter d, mean coil diameter D and number of active coils n. To take number of active coils n as the dependent variable is reasonable. It can lead to wrong results to take n as the independent variable. The right independent variables in optimization design of helical spring are wire diameter d and mean coil diameter D.
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21

Ketabi, Abbas, and Mohammad Javad Navardi. "Optimization Shape of Variable-Capacitance Micromotor Using Seeker Optimization Algorithm." Journal of Electrical Engineering and Technology 7, no. 2 (March 1, 2012): 212–20. http://dx.doi.org/10.5370/jeet.2012.7.2.212.

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22

Wang, Feng, Heng Zhang, and Aimin Zhou. "A particle swarm optimization algorithm for mixed-variable optimization problems." Swarm and Evolutionary Computation 60 (February 2021): 100808. http://dx.doi.org/10.1016/j.swevo.2020.100808.

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23

Xiao-Min Hu, Jun Zhang, Henry Shu-Hung Chung, Yun Li, and Ou Liu. "SamACO: Variable Sampling Ant Colony Optimization Algorithm for Continuous Optimization." IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 40, no. 6 (December 2010): 1555–66. http://dx.doi.org/10.1109/tsmcb.2010.2043094.

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24

Chen, Shih-Pin. "Simulation response optimization via an alternating variable methodsimulation response optimization." Engineering Optimization 35, no. 6 (December 2003): 675–84. http://dx.doi.org/10.1080/03052150310001620722.

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25

Akulinin, E. I., A. A. Ishin, S. A. Skvortsov, D. S. Dvoretsky, and S. I. Dvoretsky. "Optimization of Adsorption Processes with Cyclic Variable Pressure in Gas Mixture Separation." Advanced Materials & Technologies, no. 3 (2017): 051–60. http://dx.doi.org/10.17277/amt.2017.03.pp.051-060.

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26

Kota, László, and Károly Jármai. "Application of a Multilevel Firefly Algorithm on a Large Variable Number Logistic Problem." Advanced Logistic Systems - Theory and Practice 13, no. 2 (2019): 21–28. http://dx.doi.org/10.32971/als.2020.002.

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Анотація:
During our research and industrial projects, we often meet difficult optimization problems, a lot of variables, a lot of constraints, nonlinear and mostly discrete problems, where the running time can be calculated sometimes in weeks with the usual optimization methods on an average computer. In the most cases in the logistic industry the strongest constraint is the time. The optimizations are running on a usual office configuration and the company accepts the suboptimal solution what the optimization method gives in the appropriate time limit. In this article we will investigate a multilevel method on supply chain problem, to increase the effectivity, improve the solution in a strict time condition.
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27

Hensch, S. A., and C. Donald Heth. "Optimization of reward rate on concurrent variable-interval variable-interval schedules." Animal Learning & Behavior 17, no. 3 (September 1989): 339–48. http://dx.doi.org/10.3758/bf03209807.

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28

Wu, Guohua, Witold Pedrycz, Manhao Ma, Dishan Qiu, Haifeng Li, and Jin Liu. "A Particle Swarm Optimization Variant with an Inner Variable Learning Strategy." Scientific World Journal 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/713490.

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Although Particle Swarm Optimization (PSO) has demonstrated competitive performance in solving global optimization problems, it exhibits some limitations when dealing with optimization problems with high dimensionality and complex landscape. In this paper, we integrate some problem-oriented knowledge into the design of a certain PSO variant. The resulting novel PSO algorithm with an inner variable learning strategy (PSO-IVL) is particularly efficient for optimizing functions with symmetric variables. Symmetric variables of the optimized function have to satisfy a certain quantitative relation. Based on this knowledge, the inner variable learning (IVL) strategy helps the particle to inspect the relation among its inner variables, determine the exemplar variable for all other variables, and then make each variable learn from the exemplar variable in terms of their quantitative relations. In addition, we design a new trap detection and jumping out strategy to help particles escape from local optima. The trap detection operation is employed at the level of individual particles whereas the trap jumping out strategy is adaptive in its nature. Experimental simulations completed for some representative optimization functions demonstrate the excellent performance of PSO-IVL. The effectiveness of the PSO-IVL stresses a usefulness of augmenting evolutionary algorithms by problem-oriented domain knowledge.
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29

Liu, Yi Xiang, and Xiang Yang Jin. "Application of Chaos PSO Algorithm in the Decelerator Optimization." Key Engineering Materials 392-394 (October 2008): 532–37. http://dx.doi.org/10.4028/www.scientific.net/kem.392-394.532.

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The problems of slow convergence speed and being prone to converge to minimum were solved by combining the characteristics of chaos dynamics in the paper, whose characteristic of combining chaos optimal ergodicity and particle swarm optimal rapidness conquered deficiency of the traditional PSO algorithm. The proposed algorithm used for the decelerator of the electric submersible progressive cavity pump (ESPCP) design optimization compared with that of which was based on the standard PSO and genetic algorithm. By use of property mentioned, optimization searching could be carried out, firstly a series of chaos variables were produced as same number as optimization variable, then chaos was lead into optimization variable by the way of similar to carrier, that made the optimization variable into a chaos state, at the same time, the extent of chaos emotion was magnified to the value range of optimization variable, at last searched by chaos variable, searching technique based on chaos had more superiority than other searching technique. The results showed that the proposed algorithm was superior to the other two algorithms with a better astringency and stability. This article offered a new optimization method in machine.
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30

Wang, Ling, Ji Pei, Muhammad Ilyas Menhas, Jiaxing Pi, Minrui Fei, and Panos M. Pardalos. "A Hybrid-coded Human Learning Optimization for mixed-variable optimization problems." Knowledge-Based Systems 127 (July 2017): 114–25. http://dx.doi.org/10.1016/j.knosys.2017.04.015.

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31

Shu, Leshi, Ping Jiang, Qi Zhou, and Tingli Xie. "An online variable-fidelity optimization approach for multi-objective design optimization." Structural and Multidisciplinary Optimization 60, no. 3 (May 9, 2019): 1059–77. http://dx.doi.org/10.1007/s00158-019-02256-0.

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32

Jiang, Li Feng, Dong Xiang, Duo Zeng, Hong Lei Wang, and Guang Hong Duan. "Automotive Crashworthiness Optimization Using Energy Flow Based Variable Screening." Key Engineering Materials 450 (November 2010): 133–36. http://dx.doi.org/10.4028/www.scientific.net/kem.450.133.

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Анотація:
A variable screening method based on energy flow analysis is provided for significant variables selection in crashworthiness optimizing. Two quantities, significance and specific energy absorption, are used to screen design variables. These quantities are calculated from energy relation matrix and energy absorption of parts. Energy relation matrix is built from finite element crash simulation result to describe energy flow path in parts during impact. The method is applied in the case of a car engine room under frontal impact. Optimization for lightweight using response surface method is performed on the reduced variable set at a relatively low computational cost.
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33

Krivulin, Nikolai. "Algebraic Solution of Tropical Polynomial Optimization Problems." Mathematics 9, no. 19 (October 3, 2021): 2472. http://dx.doi.org/10.3390/math9192472.

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We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with idempotent addition and invertible multiplication). The problems are to minimize the objective functions given by tropical analogues of multivariate Puiseux polynomials, subject to box constraints on the variables. A technique for variable elimination is presented that converts the original optimization problem to a new one in which one variable is removed and the box constraint for this variable is modified. The novel approach may be thought of as an extension of the Fourier–Motzkin elimination method for systems of linear inequalities in ordered fields to the issue of polynomial optimization in ordered tropical semifields. We use this technique to develop a procedure to solve the problem in a finite number of iterations. The procedure includes two phases: backward elimination and forward substitution of variables. We describe the main steps of the procedure, discuss its computational complexity and present numerical examples.
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34

Ren, Jie, and Jian She Tian. "Simulation on Multi-Objective Wind Power Integration Using Genetic Algorithm with Adaptive Weight." Advanced Materials Research 986-987 (July 2014): 529–32. http://dx.doi.org/10.4028/www.scientific.net/amr.986-987.529.

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Aiming at problems which were brought by large-scale wind power integration, and the problem of multi-objective reactive power optimization considering the coexistence of discrete variables and continuous variables, a method of simulation based on genetic algorithm with adaptive weight is brought out. A solving thinking presents that capacitor switching and transformer tap adjusting and other discrete equipments are first, and the action sequence of generator and dynamic reactive power compensation (DRPC) devices and other continuous equipments setting follows, which is presented that optimization problem is decomposed into continuous variable optimization and discrete variable optimization, then they are solved respectively and cross iteration until convergence. In view of the optimization complexity and the coexistence of discrete variables and continuous variables, genetic algorithm with adaptive weight is presented for finding global optimal solution. Case studies show that the proposed thinking and algorithm for solving multi-objective reactive power optimization are reasonable.
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35

Ao, Liang Bo, Yuan Sheng Li, Lei Li, Zhi Xun Wen, and Zhu Feng Yue. "Turbine Blade Aerodynamic Optimization Based on Variable Dimensionality Model." Advanced Materials Research 287-290 (July 2011): 2801–4. http://dx.doi.org/10.4028/www.scientific.net/amr.287-290.2801.

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The aerodynamic optimization for turbocharger turbine blade is studied using variable dimensionality analysis technology. The aerodynamic optimization procedure is decomposed to two steps: two-dimensional (2D) optimization and three-dimensional (3D) optimization based on the 2D optimal results. The quintic polynomial method with continuous three order derivatives is used to present section profile of three sections, root, middle and tip of blade. The 2D aerodynamic analysis and optimization are carried separately for different sections. Aerodynamic optimization for turbine blade is driven by the combination of global and local optimization arithmetic, with the 2D optimization blade as initial value, and profile parameter as design variable. The result shows that the calculation time is shortened and the optimization efficiency is improved, compared with the full 3D optimization under the same effect.
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36

JIAO, Hongyu. "Periodic Topology Optimization Using Variable Density Method." Journal of Mechanical Engineering 49, no. 13 (2013): 132. http://dx.doi.org/10.3901/jme.2013.13.132.

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37

Casalino, Lorenzo, and Guido Colasurdo. "Optimization of Variable-Specific-Impulse Interplanetary Trajectories." Journal of Guidance, Control, and Dynamics 27, no. 4 (July 2004): 678–84. http://dx.doi.org/10.2514/1.11159.

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38

Hamed, Eman, and Marwa Hamad. "Self-Scaling Variable Metric in Constrained Optimization." AL-Rafidain Journal of Computer Sciences and Mathematics 14, no. 1 (June 1, 2020): 33–42. http://dx.doi.org/10.33899/csmj.2020.164673.

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39

Lim, Woochul, Junyong Jang, Jungho Kim, Jongho Na, Changkun Lee, Yongsuk Kim, and Tae Hee Lee. "Reliability-Based Design Optimization Considering Variable Uncertainty." Transactions of the Korean Society of Mechanical Engineers A 38, no. 6 (June 1, 2014): 649–53. http://dx.doi.org/10.3795/ksme-a.2014.38.6.649.

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40

Guo, Chuang-xin, Jia-sheng Hu, Bin Ye, and Yi-jia Cao. "Swarm intelligence for mixed-variable design optimization." Journal of Zhejiang University-SCIENCE A 5, no. 7 (July 2004): 851–60. http://dx.doi.org/10.1631/jzus.2004.0851.

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41

Feehery, William F., and Paul I. Barton. "Dynamic optimization with state variable path constraints." Computers & Chemical Engineering 22, no. 9 (August 1998): 1241–56. http://dx.doi.org/10.1016/s0098-1354(98)00012-x.

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42

HU, Peifeng, Zongzhong TIAN, Zhenzhou YUAN, and Shunping JIA. "Variable-Bandwidth Progression Optimization in Traffic Operation." Journal of Transportation Systems Engineering and Information Technology 11, no. 1 (February 2011): 61–72. http://dx.doi.org/10.1016/s1570-6672(10)60101-8.

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43

Su, Yu-Shih, Da-Chung Wang, Shih-Chieh Chang, and Malgorzata Marek-Sadowska. "Performance Optimization Using Variable-Latency Design Style." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 19, no. 10 (October 2011): 1874–83. http://dx.doi.org/10.1109/tvlsi.2010.2058874.

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44

Sun, Yuan, Michael Kirley, and Saman K. Halgamuge. "Quantifying Variable Interactions in Continuous Optimization Problems." IEEE Transactions on Evolutionary Computation 21, no. 2 (April 2017): 249–64. http://dx.doi.org/10.1109/tevc.2016.2599164.

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45

Thokala, Praveen, and Joaquim R. R. A. Martins. "Variable-complexity optimization applied to airfoil design." Engineering Optimization 39, no. 3 (April 2007): 271–86. http://dx.doi.org/10.1080/03052150601107976.

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46

Bogdan, Małgorzata, Ewout van den Berg, Chiara Sabatti, Weijie Su, and Emmanuel J. Candès. "SLOPE—Adaptive variable selection via convex optimization." Annals of Applied Statistics 9, no. 3 (September 2015): 1103–40. http://dx.doi.org/10.1214/15-aoas842.

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47

Gano, Shawn E., John E. Renaud, Harish Agarwal, and Andrés Tovar. "Reliability-based design using variable-fidelity optimization." Structure and Infrastructure Engineering 2, no. 3-4 (September 2006): 247–60. http://dx.doi.org/10.1080/15732470600590408.

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48

Tengs, Erik, Pål-Tore Storli, and Martin Holst. "Optimization procedure for variable speed turbine design." Engineering Applications of Computational Fluid Mechanics 12, no. 1 (January 2018): 652–61. http://dx.doi.org/10.1080/19942060.2018.1507950.

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49

Udawalpola, Rajitha, Eddie Wadbro, and Martin Berggren. "Optimization of a variable mouth acoustic horn." International Journal for Numerical Methods in Engineering 85, no. 5 (December 29, 2010): 591–606. http://dx.doi.org/10.1002/nme.2982.

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50

Anilkumar, P. M., Ayan Haldar, Eelco Jansen, B. N. Rao, and Raimund Rolfes. "Design optimization of multistable variable-stiffness laminates." Mechanics of Advanced Materials and Structures 26, no. 1 (January 2, 2019): 48–55. http://dx.doi.org/10.1080/15376494.2018.1512022.

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