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Journal articles on the topic 'Directions of optimization'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Liu, XiaoGuang, and XingBao Gao. "Total Variation Image Restoration Method Based on Subspace Optimization." Mathematical Problems in Engineering 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/6921742.

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The alternating direction method is widely applied in total variation image restoration. However, the search directions of the method are not accurate enough. In this paper, one method based on the subspace optimization is proposed to improve its optimization performance. This method corrects the search directions of primal alternating direction method by using the energy function and a linear combination of the previous search directions. In addition, the convergence of the primal alternating direction method is proven under some weaker conditions. Thus the convergence of the corrected method

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Eran, Vax, Ben David Nadav, Salomon Yossi, et al. "Methodical Optimization of Mutual-Shielding Directional Gamma Detector." EPJ Web of Conferences 288 (2023): 10023. http://dx.doi.org/10.1051/epjconf/202328810023.

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Mutual-Shielding Directional Gamma Detector excels at sensitivity and can achieve good angular accuracy and a large field of view. In this paper, we present, in detail, a method to optimize a mutual shielding directional detector array regarding the scintillators positioning for a given number and size of detection units. The optimization goals are improvement of accuracy and sensitivity. The optimization uses two types of fast, non-Monte-Carlo simulations since the simulation needs to generate measurements from all directions for each array formation tested. Both these simulations are explain

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Lee, Myung W., and Sang Y. Suh. "Optimization of one‐way wave equations." GEOPHYSICS 50, no. 10 (1985): 1634–37. http://dx.doi.org/10.1190/1.1441853.

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The theory of wave extrapolation is based on the square‐root equation or one‐way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square‐root equation represents waves propagating in one direction only.

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Yamshchikovа, I. V., T. G. Doroshenko, and N. B. Mikheeva. "Directions of wage optimization in construction." E3S Web of Conferences 296 (2021): 06006. http://dx.doi.org/10.1051/e3sconf/202129606006.

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The article analyses the method proposed by the Government of the Russian Federation for adjusting the principle of determining the minimum subsistence level, based on the median salary. The article shows the result of the analysis of changes in wages in construction when calculating, using the median salary in relation to the “absolute” principle of calculating the minimum subsistence level, the calculation of the size of the minimum subsistence level in Russia as a whole, and on the territory of the Irkutsk region is analysed. It is shown that the transition to the calculation of the median

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Henig, Mordechai I., and John T. Buchanan. "Tradeoff directions in multiobjective optimization problems." Mathematical Programming 78, no. 3 (1997): 357–74. http://dx.doi.org/10.1007/bf02614361.

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.Biegler, Lorenz T. "New directions for nonlinear process optimization." Current Opinion in Chemical Engineering 21 (September 2018): 32–40. http://dx.doi.org/10.1016/j.coche.2018.02.008.

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An, Xiao-Min, Dong-Hui Li, and Yunhai Xiao. "Sufficient descent directions in unconstrained optimization." Computational Optimization and Applications 48, no. 3 (2009): 515–32. http://dx.doi.org/10.1007/s10589-009-9268-z.

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Wu, Tao, Peiqing Liu, and Jikai Liu. "Geometric Complexity Control in Topology Optimization of 3D-Printed Fiber Composites for Performance Enhancement." Materials 17, no. 9 (2024): 2005. http://dx.doi.org/10.3390/ma17092005.

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This paper investigates the impact of varying the part geometric complexity and 3D printing process setup on the resulting structural load bearing capacity of fiber composites. Three levels of geometric complexity are developed through 2.5D topology optimization, 3D topology optimization, and 3D topology optimization with directional material removal. The 3D topology optimization is performed with the SIMP method and accelerated by high-performance computing. The directional material removal is realized by incorporating the advection-diffusion partial differential equation-based filter to prev

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Lin, Hao, Ning Zhang, and Jun Chen. "Optimization of Variable Guiding Lanes'Function at Signalized Intersections." Applied Mechanics and Materials 253-255 (December 2012): 1721–25. http://dx.doi.org/10.4028/www.scientific.net/amm.253-255.1721.

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This paper brings forward a method to improve the efficiency of the variable guiding lanes. It shows the proper time to change the direction of variable guiding lanes, and a new method to clean out the vehicles on the variable guiding lanes. In condition of a low flow of left-turning vehicle but a high flow of straight vehicle, or the opposite situation, the directions of the variable guiding lanes are different. In the certain of the signal cycle, we changed the direction and gave the proper time to clean out vehicle on the variable guiding lanes, and then the vehicle of different directions

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Galeev, A. S., Y. A. Boltneva, G. I. Bikbulatova, and R. N. Suleymanov. "OPTIMIZATION OF OPERATION MODES OF THE PLUNGER PUMP OF THE FORMATION PRESSURE MAINTENANCE SYSTEM." Petroleum Engineering 21, no. 6 (2023): 164–70. http://dx.doi.org/10.17122/ngdelo-2023-6-164-170.

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The efficiency of pumping equipment in the context of continuous growth in electricity prices is a priority for any oil and gas production department (OGPD). The pumping stations of the reservoir pressure maintenance system are the main consumers of electricity in the OGPD. The efficiency of pumping units, as a rule, is reduced primarily to the value of their efficiency, and the criterion for the efficiency of the injection system is usually the consumption of electrical energy per unit volume of pumped liquid. At the same time, they often focus only on maintaining high pump efficiency, which

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11

Li, Chongqing. "Multi-objective Structural Optimization of Column based on Topology Optimization and NSGA-Ⅱ Algorithm." Academic Journal of Science and Technology 11, no. 3 (2024): 261–63. http://dx.doi.org/10.54097/qdg7mj86.

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In order to realize the lightweight design of CNC machine tool and optimize the important structural columns in gantry structure, this paper proposes a combination of variable density topology optimization and multi-objective optimization based on NSGA-Ⅱ algorithm, which realizes the pursuit of lighter and better structure without changing the performance of the columns, and also puts forward suggestions and improvement directions for the subsequent optimization direction. A new theoretical basis for structural optimization is proposed.

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Wang, Xianjie, Fan Zhang, Zhenjiang Weng, et al. "Space Node Topology Optimization Design Considering Anisotropy of Additive Manufacturing." Applied Sciences 12, no. 18 (2022): 9396. http://dx.doi.org/10.3390/app12189396.

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At present, a large number of scholars have conducted related research on topology optimization for additive manufacturing (AM). However, there are few relevant research reports on the impact of different directions of additive manufacturing on the optimal design and manufacturing results. In this paper, using the bidirectional evolutionary optimization (BESO) method, anisotropic optimization analysis was carried out on space nodes that are currently popular in the field of additive manufacturing and topology optimization. The elastic constants in different directions were used as anisotropic

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TAMURA, Kenichi, and Keiichiro YASUDA. "Spiral Optimization Algorithm Using Periodic Descent Directions." SICE Journal of Control, Measurement, and System Integration 9, no. 3 (2016): 134–43. http://dx.doi.org/10.9746/jcmsi.9.134.

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Zubareva, K. Ju, E. G. Simonova, S. R. Raichich, A. A. Shabejkin, and A. M. Guljukin. "MODERN DIRECTIONS IN OPTIMIZATION OF RABIES SURVEILLANCE." Russian Journal of Infection and Immunity 8, no. 4 (2019): 553. http://dx.doi.org/10.15789/2220-7619-2018-4-4.30.

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Lobanova, I. I. "Driving Style: Determining Factors, Characteristics, Optimization Directions." Rossiiskii Gumanitarnyi Zhurnal 4, no. 1 (2015): 76. http://dx.doi.org/10.15643/libartrus-2015.1.10.

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Davidon, William C., and Jorge Nocedal. "Evaluation of step directions in optimization algorithms." ACM Transactions on Mathematical Software 11, no. 1 (1985): 12–19. http://dx.doi.org/10.1145/3147.3164.

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Ding, Siew-Hong, and Shahrul Kamaruddin. "Maintenance policy optimization—literature review and directions." International Journal of Advanced Manufacturing Technology 76, no. 5-8 (2014): 1263–83. http://dx.doi.org/10.1007/s00170-014-6341-2.

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Reiner, Bruce, Eliot Siegel, and John A. Carrino. "Workflow Optimization: Current Trends and Future Directions." Journal of Digital Imaging 15, no. 3 (2002): 141–52. http://dx.doi.org/10.1007/s10278-002-0022-7.

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Psiaki, M. L., and K. H. Park. "Parallel solver for trajectory optimization search directions." Journal of Optimization Theory and Applications 73, no. 3 (1992): 519–46. http://dx.doi.org/10.1007/bf00940054.

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Zou, Yiyang. "Advancing Mathematical Optimization Methods: Applications, Challenges, and Future Directions." Theoretical and Natural Science 79, no. 1 (2025): 119–25. https://doi.org/10.54254/2753-8818/2025.20116.

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Mathematical optimization methods have seen substantial advancements and applications in diverse fields, including industry, agriculture, commerce, and scientific research, due to advances in computer science and artificial intelligence. These methods improve production efficiency, resource allocation, and structural optimization. This paper reviews key optimization techniques such as gradient descent, Newtons method, and heuristic algorithms, discussing their advantages, limitations, and applicability. Although optimization methods offer powerful tools for solving complex equations and optimi

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Shaikh, Mohammad Shahnawaz, Prithviraj S. Chouhan, Imran Baig, and Syed Ibad Ali. "QUANTUM COMPUTING FOR OPTIMIZATION PROBLEMS: A REVIEW AND FUTURE DIRECTIONS." COMPUSOFT: An International Journal of Advanced Computer Technology 11 (June 22, 2022): 3995–97. https://doi.org/10.5281/zenodo.15087230.

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Quantum computing, leveraging principles of quantum mechanics, has shown potential in solving complex optimization problems more efficiently than classical approaches. This paper reviews recent advancements in quantum algorithms designed for optimization tasks and evaluates their performance against classical methods. We present a comprehensive analysis of quantum optimization algorithms such as Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing, discussing their applications, advantages, and limitations. Future directions are proposed, focusing on improving algorithm effi

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22

Kuzheliev, Mykhailo, and Volodymyr Plahotniuk. "Directions of optimization of investment climate in Ukraine." University Economic Bulletin, no. 41 (March 30, 2019): 119–26. http://dx.doi.org/10.31470/2306-546x-2019-41-119-126.

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The subject of the research is the economic relations arising in the conditions of functioning of the investment market of Ukraine. The purpose of the work is to assess the investment climate of Ukraine on the basis of a system analysis, to reveal problem aspects and deterrents of its formation in modern conditions and also to define the priority directions it optimization. Methodological basis of the article became the methods of analysis and synthesis, statistical methods, including graphical method, methods of comparison and generalization. The results of the work. The article contains a st

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23

Beck, Amir, and Nadav Hallak. "The regularized feasible directions method for nonconvex optimization." Operations Research Letters 50, no. 5 (2022): 517–23. http://dx.doi.org/10.1016/j.orl.2022.07.005.

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Myrzakhanova, D. Zh, R. U. Smagulova, G. A. Taspenova, and B. S. Utegulova. "MAIN DIRECTIONS OF OPTIMIZATION TAX SYSTEMS OF RK." REPORTS 4, no. 326 (2019): 104–11. http://dx.doi.org/10.32014/2019.2518-1483.124.

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L. A., Prashanth, Shalabh Bhatnagar, Michael Fu, and Steve Marcus. "Adaptive System Optimization Using Random Directions Stochastic Approximation." IEEE Transactions on Automatic Control 62, no. 5 (2017): 2223–38. http://dx.doi.org/10.1109/tac.2016.2600643.

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Lee, G. M., and H. Nakayama. "Generalized trade-off directions in multiobjective optimization problems." Applied Mathematics Letters 10, no. 1 (1997): 119–22. http://dx.doi.org/10.1016/s0893-9659(96)00122-x.

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Herskovits, José, Wilhelm P. Freire, Mario Tanaka Fo, and Alfredo Canelas. "A feasible directions method for nonsmooth convex optimization." Structural and Multidisciplinary Optimization 44, no. 3 (2011): 363–77. http://dx.doi.org/10.1007/s00158-011-0634-y.

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28

Arora, Jasbir S. "Computational design optimization: A review and future directions." Structural Safety 7, no. 2-4 (1990): 131–48. http://dx.doi.org/10.1016/0167-4730(90)90063-u.

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29

Loeffler, Jay S., and Marco Durante. "Charged particle therapy—optimization, challenges and future directions." Nature Reviews Clinical Oncology 10, no. 7 (2013): 411–24. http://dx.doi.org/10.1038/nrclinonc.2013.79.

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30

Hu, Si Bo, Yi Ding, Jing Ru Bao, and Ping Hu. "Crashworthiness Optimization for a Two-Layered Front Rail Considering Front Oblique Impact." Applied Mechanics and Materials 365-366 (August 2013): 3–13. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.3.

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This paper is concerned with the crashworthiness design of the front rail on a vehicle chassis frame structure considering uncertain crash directions. The front rail, as a typical thin-walled structure, is sensitive to the loading direction for crashworthiness requirements. Multi-step multi-domain optimization method was applied to obtain a new single-layered front rail (SFR) which has better adaptability to crash loading directions. To further improve the front rail crashworthiness, a two-layered front rail (TFR) is proposed. Response surface method is conducted to pursue the optimal thicknes

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31

Billah, Arisona Lestari, Deddy P. Koesrindartoto, and Taufik Faturohman. "Advancing ESG Portfolio Optimization: Methods, Progress, and Future Directions." GATR Accounting and Finance Review 9, no. 2 (2024): 65–73. http://dx.doi.org/10.35609/afr.2024.9.2(2).

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Objective - The integration of environmental, social, and governance (ESG) criteria into investment portfolios has emerged as a critical field of study, underscoring the interconnectedness between financial markets and global sustainability objectives. Methodology/Technique - This systematic literature review analyzes 157 academic documents, focusing on ESG portfolio optimization methodologies and identifying emerging trends. Key methods reviewed include genetic algorithms, dynamic optimization models, multi-objective optimization frameworks, and machine learning techniques. Findings - Despite

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Cai, Enxiang, Shihong Long, Ling Li, et al. "Optimization of Rural Residential Areas in Flood Detention Basins Based on Dual Minimum Accumulation Resistance Model: A Case Study of Xun County in Central China." Land 13, no. 12 (2024): 2217. https://doi.org/10.3390/land13122217.

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Optimizing rural residential areas (RRAs) in environmentally fragile areas such as flood detention basins is of great significance for improving the human–land relationship and achieving sustainable rural development. This study took Xun County in central China as a case study, established a dual minimum cumulative resistance model (DMCR) that considered the dual factors of natural attributes and policy regulations to evaluate the optimization resistance of RRAs and determined the optimization directions and strategies accordingly. The main results are: (1) RRAs are relatively small and scatte

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Zhang, Ming-Liang, Yun-Hai Xiao, and Dangzhen Zhou. "A Simple Sufficient Descent Method for Unconstrained Optimization." Mathematical Problems in Engineering 2010 (2010): 1–9. http://dx.doi.org/10.1155/2010/684705.

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We develop a sufficient descent method for solving large-scale unconstrained optimization problems. At each iteration, the search direction is a linear combination of the gradient at the current and the previous steps. An attractive property of this method is that the generated directions are always descent. Under some appropriate conditions, we show that the proposed method converges globally. Numerical experiments on some unconstrained minimization problems from CUTEr library are reported, which illustrate that the proposed method is promising.

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Ventura, Tiago, Humberto Rocha, Brigida da Costa Ferreira, Joana Dias, and Maria do Carmo Lopes. "Comparison of non-coplanar optimization of static beams and arc trajectories for intensity-modulated treatments of meningioma cases." Physical and Engineering Sciences in Medicine 44, no. 4 (2021): 1273–83. http://dx.doi.org/10.1007/s13246-021-01061-8.

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AbstractTwo methods for non-coplanar beam direction optimization, one for static beams and another for arc trajectories, were proposed for intracranial tumours. The results of the beam angle optimizations were compared with the beam directions used in the clinical plans. Ten meningioma cases already treated were selected for this retrospective planning study. Algorithms for non-coplanar beam angle optimization (BAO) and arc trajectory optimization (ATO) were used to generate the corresponding plans. A plan quality score, calculated by a graphical method for plan assessment and comparison, was

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Charles, Mfon, David T. O. Oyedokun, and Mqhele Dlodlo. "Power Maximization and Turbulence Intensity Management through Axial Induction-Based Optimization and Efficient Static Turbine Deployment." Energies 14, no. 16 (2021): 4943. http://dx.doi.org/10.3390/en14164943.

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Layout optimization is capable of increasing turbine density and reducing wake effects in wind plants. However, such optimized layouts do not guarantee fixed T-2-T distances in any direction and would be disadvantageous if reduction in computational costs due to turbine set-point updates is also a priority. Regular turbine layouts are considered basic because turbine coordinates can be determined intuitively without the application of any optimization algorithms. However, such layouts can be used to intentionally create directions of large T-2-T distances, hence, achieve the gains of standard/

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Schlesinger, Mykhaylo I. "Solution of Soft Constrains Problems via their Reparametrization." Control Systems and Computers, no. 1 (297) (2022): 15–23. http://dx.doi.org/10.15407/csc.2022.01.015.

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Introduction. The past quarter-century is characterized by the birth of a new scientific direction, formed as a result of combining research in pattern recognition problems and constraint satisfaction problems. These two scientific directions traditionally belong to the problem of artificial intelligence, but they formalize different aspects of intellectual activity. The formation of a single formal scheme that combines these two directions expands and concretizes the concept of machine thinking, on the formalization of which they are oriented, and necessitates the development of new and impro

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Соколов, С. А. "Directions of optimization of companies' strategies optimization of the organization's personnel motivation system." Scientific Journal ECONOMIC SYSTEMS 1, no. 142 (2023): 106–12. http://dx.doi.org/10.29030/2309-2076-2023-16-4-106-112.

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В условиях современной конкурентной среды компании стремятся не просто производить товар или предоставлять услугу, но и качественно выстраивать взаимодействие с важными партнерами, клиентами, налаживать логистическую цепочку поставок и выходить на мировой рынок. Для эффективного выполнения таких задач компании уделяют внимание квалификации персонала, навыкам и, соответственно, мотивации. Мотивация является важнейшей составляющей кадровой политики.В представленной научно-практической работе выявлены наиболее частые ошибки при построении мотивационной системы, которые могут негативным образом от

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Yuan, Fujiang, Xia Huang, Long Zheng, et al. "The Evolution and Optimization Strategies of a PBFT Consensus Algorithm for Consortium Blockchains." Information 16, no. 4 (2025): 268. https://doi.org/10.3390/info16040268.

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With the rapid development of blockchain technology, consensus algorithms have become a significant research focus. Practical Byzantine Fault Tolerance (PBFT), as a widely used consensus mechanism in consortium blockchains, has undergone numerous enhancements in recent years. However, existing review studies primarily emphasize broad comparisons of different consensus algorithms and lack an in-depth exploration of PBFT optimization strategies. The lack of such a review makes it challenging for researchers and practitioners to identify the most effective optimizations for specific application s

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Chen, Yong, and Bailin Li. "A Modification of Feasible Direction Optimization Method for Handling Equality Constraints." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 3 (1989): 442–45. http://dx.doi.org/10.1115/1.3259018.

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The Feasible Direction Method of Zoutendijk has proven to be one of the most efficient algorithms currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of equality type constraints, there exists no nonzero direction close to the feasible region, the traditional algorithm cannot work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tang

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Zhang, Deng Xia, An Tong Gao, Lin Sha, Ze Feng Wei, and Jun Han. "Optimization of the Stamping Direction for Complex Parts Based on 3D Mesh Model." Advanced Materials Research 482-484 (February 2012): 2508–11. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.2508.

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A new algorithm directly based on 3D mesh model is presented to determine the reasonable stamping direction in CAE software. Compared with former similar optimization algorithms of the stamping direction, it can simplify the procedure and avoid the missing of some necessary details of complex parts, and it is automatic and intellective to determine the reasonable stamping direction. The feasibility of the algorithm has been proved by the creation of stamping directions of the automobile fender.

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Buryy, O., B. Olchovyk, O. Hrinchenko, A. Andrushchak, and M. Andrushchak. "OPTIMIZATION OF GEOMETRY OF PIEZORESISTIVE EFFECT ON THE EXAMPLE OF CUBIC CRYSTALS." Information and communication technologies, electronic engineering 4, no. 1 (2024): 126–36. http://dx.doi.org/10.23939/ictee2024.01.126.

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On the example of semiconductor crystals Ge, Si, PbTe, PbS, InSb with different levels of doping and different types of conductivity, the geometry of the piezoresistive effect was optimized, namely, such directions of voltage measuring and uniaxial pressure applying were determined, which ensure the maximum achievable value of the effect. The optimization is based on an approach using the construction and analysis of extreme surfaces that represent all possible maxima of the objective function (the magnitude of the effect) under different spatial orientations of interacting factors. The optimi

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Li, Weiqi, Fan Lyu, Fanhua Shang, Liang Wan, and Wei Feng. "Long-Tailed Learning as Multi-Objective Optimization." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 4 (2024): 3190–98. http://dx.doi.org/10.1609/aaai.v38i4.28103.

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Real-world data is extremely imbalanced and presents a long-tailed distribution, resulting in models biased towards classes with sufficient samples and performing poorly on rare classes. Recent methods propose to rebalance classes but they undertake the seesaw dilemma (what is increasing performance on tail classes may decrease that of head classes, and vice versa). In this paper, we argue that the seesaw dilemma is derived from the gradient imbalance of different classes, in which gradients of inappropriate classes are set to important for updating, thus prone to overcompensation or undercomp

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Wang, Yuqing, Ying Shen, Xiujian Zhu, Pei Wu, Jie Lin, and Chenyuan Li. "34‐2: Research on Power Saving Solutions for medium‐sized AMOLED Display." SID Symposium Digest of Technical Papers 56, S1 (2025): 297–99. https://doi.org/10.1002/sdtp.18789.

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With the development of display technology, the functions of display panels have become increasingly rich and diverse, but the power consumption has also increased accordingly. Given that the battery life of mobile devices with medium‐sized panels has drawn attention and that AMOLED medium‐sized panels are a standard configuration of high‐end mobile devices, reducing their power consumption has become a research focus. From the perspective of power consumption paths, reducing the power consumption of medium‐sized AMOLED panels can start from four major directions, namely IC optimization, array

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Faizulin, Oleh, and Yaroslav Kis. "Optimization of the infrastructure of the distributed information system of goods accounting." Vìsnik Nacìonalʹnogo unìversitetu "Lʹvìvsʹka polìtehnìka". Serìâ Ìnformacìjnì sistemi ta merežì 12 (December 15, 2022): 219–29. http://dx.doi.org/10.23939/sisn2022.12.219.

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An existing goods accounting information system was assessed for possible infrastructure optimization. A various parts of the system were analyzed to improve infrastructure costs without having a significant degradation of non-functional requirements. Modeling of the optimized system was performed, and evaluation of the infrastructure costs was made. Several optimization directions were evaluated, analyzed and either recommended or rejected. As the result, the final information system model was designed which allows to achieve significant infrastructure cost savings by applying multiple optimi

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Shevchuk, Viktor. "Innovative optimization directions of investigative (detective) activity in modern conditions." Theory and Practice of Forensic Science and Criminalistics 24, no. 2 (2021): 8–25. http://dx.doi.org/10.32353/khrife.2.2021.02.

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This article is devoted to optimization issues of investigative (detective) activity by introducing innovative approaches in solving issues of criminal proceedings and introducing their provisions and recommendations into law enforcement practice. The most important innovative development directions of criminalistics at the present stage directed on optimization of investigative (detective) activity in the conditions of crime transformation, information and epidemiological threats to a society are defined and considered. It is substantiated that issue of optimization of investigative (detectiv

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Shakirova, Y. S. "Priority directions for optimization tax load in the economy." ACADEMICIA: An International Multidisciplinary Research Journal 11, no. 11 (2021): 500–505. http://dx.doi.org/10.5958/2249-7137.2021.02472.1.

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Hoffman, Karla L. "Combinatorial optimization: Current successes and directions for the future." Journal of Computational and Applied Mathematics 124, no. 1-2 (2000): 341–60. http://dx.doi.org/10.1016/s0377-0427(00)00430-1.

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Miettinen, Kaisa, and Marko M. Mäkelä. "On generalized trade-off directions in nonconvex multiobjective optimization." Mathematical Programming 92, no. 1 (2002): 141–51. http://dx.doi.org/10.1007/s101070100282.

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Rozvany, G. I. N. "Topological optimization of grillages: Past controversies and new directions." International Journal of Mechanical Sciences 36, no. 6 (1994): 495–512. http://dx.doi.org/10.1016/0020-7403(94)90029-9.

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Csébfalvi, A. "Structural optimization under uncertainty in loading directions: Benchmark results." Advances in Engineering Software 120 (June 2018): 68–78. http://dx.doi.org/10.1016/j.advengsoft.2016.02.006.

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