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Journal articles on the topic 'Set partitioning problems'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Sherali, Hanif D., and Youngho Lee. "Tighter representations for set partitioning problems." Discrete Applied Mathematics 68, no. 1-2 (June 1996): 153–67. http://dx.doi.org/10.1016/0166-218x(95)00060-5.

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2

El-Darzi, Elia, and Gautam Mitra. "Graph theoretic relaxations of set covering and set partitioning problems." European Journal of Operational Research 87, no. 1 (November 1995): 109–21. http://dx.doi.org/10.1016/0377-2217(94)00115-s.

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3

El-Darzi, E., and G. Mitra. "Set covering and set partitioning: A collection of test problems." Omega 18, no. 2 (January 1990): 195–201. http://dx.doi.org/10.1016/0305-0483(90)90066-i.

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4

Gomme, Paul, and Paul G. Harrald. "Applying evolutionary programming to selected set partitioning problems." Fuzzy Sets and Systems 95, no. 1 (April 1998): 67–76. http://dx.doi.org/10.1016/s0165-0114(96)00404-6.

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5

Conforti, Michele, Marco Di Summa, and Giacomo Zambelli. "Minimally Infeasible Set-Partitioning Problems with Balanced Constraints." Mathematics of Operations Research 32, no. 3 (August 2007): 497–507. http://dx.doi.org/10.1287/moor.1070.0250.

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6

El-Darzi, Elia, and Gautam Mitra. "Solution of Set-Covering and Set-Partitioning Problems Using Assignment Relaxations." Journal of the Operational Research Society 43, no. 5 (May 1992): 483. http://dx.doi.org/10.2307/2583567.

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7

El-Darzi, Elia, and Gautam Mitra. "Solution of Set-Covering and Set-Partitioning Problems Using Assignment Relaxations." Journal of the Operational Research Society 43, no. 5 (May 1992): 483–93. http://dx.doi.org/10.1057/jors.1992.74.

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8

Rokach, Lior. "Genetic algorithm-based feature set partitioning for classification problems." Pattern Recognition 41, no. 5 (May 2008): 1676–700. http://dx.doi.org/10.1016/j.patcog.2007.10.013.

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9

Benchimol, Pascal, Guy Desaulniers, and Jacques Desrosiers. "Stabilized dynamic constraint aggregation for solving set partitioning problems." European Journal of Operational Research 223, no. 2 (December 2012): 360–71. http://dx.doi.org/10.1016/j.ejor.2012.07.004.

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10

Foutlane, Omar, Issmail El Hallaoui, and Pierre Hansen. "Integral simplex using double decomposition for set partitioning problems." Computers & Operations Research 111 (November 2019): 243–57. http://dx.doi.org/10.1016/j.cor.2019.06.016.

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11

Osei-Bryson, Kweku-Muata, and Anito Joseph. "Applications of sequential set partitioning: a set of technical information systems problems." Omega 34, no. 5 (October 2006): 492–500. http://dx.doi.org/10.1016/j.omega.2005.01.008.

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12

Crawford, Broderick, Ricardo Soto, Eric Monfroy, Carlos Castro, Wenceslao Palma, and Fernando Paredes. "A Hybrid Soft Computing Approach for Subset Problems." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/716069.

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Subset problems (set partitioning, packing, and covering) are formal models for many practical optimization problems. A set partitioning problem determines how the items in one set (S) can be partitioned into smaller subsets. All items inSmust be contained in one and only one partition. Related problems are set packing (all items must be contained in zero or one partitions) and set covering (all items must be contained in at least one partition). Here, we present a hybrid solver based on ant colony optimization (ACO) combined with arc consistency for solving this kind of problems. ACO is a swarm intelligence metaheuristic inspired on ants behavior when they search for food. It allows to solve complex combinatorial problems for which traditional mathematical techniques may fail. By other side, in constraint programming, the solving process of Constraint Satisfaction Problems can dramatically reduce the search space by means of arc consistency enforcing constraint consistencies either prior to or during search. Our hybrid approach was tested with set covering and set partitioning dataset benchmarks. It was observed that the performance of ACO had been improved embedding this filtering technique in its constructive phase.

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13

Shanker, Ravi, S. R. Arora, and R. R. Saxena. "Relation between set partitioning and set covering problems with quadratic fractional objective functions." OPSEARCH 48, no. 3 (September 2011): 247–56. http://dx.doi.org/10.1007/s12597-011-0052-3.

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14

Lin, Chi-san Althon. "GENERATIONAL MODEL GENETIC ALGORITHM FOR REAL WORLD SET PARTITIONING PROBLEMS." International Journal of Electronic Commerce Studies 4, no. 1 (June 2013): 33–46. http://dx.doi.org/10.7903/ijecs.1138.

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15

Peker, Musa, Baha Sen, and Safak Bayir. "Using Artificial Intelligence Techniques for Large Scale Set Partitioning Problems." Procedia Technology 1 (2012): 44–49. http://dx.doi.org/10.1016/j.protcy.2012.02.010.

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16

Fisher, Marshall L., and Pradeep Kedia. "Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics." Management Science 36, no. 6 (June 1990): 674–88. http://dx.doi.org/10.1287/mnsc.36.6.674.

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17

Elhallaoui, Issmail, Abdelmoutalib Metrane, François Soumis, and Guy Desaulniers. "Multi-phase dynamic constraint aggregation for set partitioning type problems." Mathematical Programming 123, no. 2 (November 14, 2008): 345–70. http://dx.doi.org/10.1007/s10107-008-0254-5.

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18

Darby-Dowman, K., and G. Mitra. "An extension of set partitioning with application to scheduling problems." European Journal of Operational Research 21, no. 2 (August 1985): 200–205. http://dx.doi.org/10.1016/0377-2217(85)90031-1.

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19

URAHAMA, KIICHI. "PERFORMANCE OF NEURAL ALGORITHMS FOR MAXIMUM-CUT PROBLEMS." Journal of Circuits, Systems and Computers 02, no. 04 (December 1992): 389–95. http://dx.doi.org/10.1142/s0218126692000246.

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The author previously developed a new neural algorithm effective for set-partitioning combinatorial optimization problems by extending the logistic transformation used in the Hopfield algorithm into its multivariable version. In this letter the performance of the algorithm is theoretically evaluated and it is proved that this algorithm is 1/p-approximate for p-partitioning maximum-cut problems.

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20

Iguider, Adil, Oussama Elissati, Abdeslam En-Nouaary, and Mouhcine Chami. "Shortest Path Method for Hardware/Software Partitioning Problems." International Journal of Information Systems and Social Change 12, no. 3 (July 2021): 40–57. http://dx.doi.org/10.4018/ijissc.2021070104.

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Smart systems are becoming more present in every aspect of our daily lives. The main component of such systems is an embedded system; this latter assures the collection, the treatment, and the transmission of the accurate information in the right time and for the right component. Modern embedded systems are facing several challenges; the objective is to design a system with high performance and to decrease the cost and the development time. Consequently, some robust methodologies like the Codesign were developed to fulfill those requirements. The most important step of the Codesign is the partitioning of the systems' functionalities between a hardware set and a software set. This article deals with this problem and uses a heuristic approach based on shortest path optimizations to solve the problem. The aim is to minimize the total hardware area and to respect a constraint on the overall execution time of the system. Experiments results demonstrate that the proposed method is very fast and gives better results compared to the genetic algorithm.

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21

Ryan, D. M. "The Solution of Massive Generalized Set Partitioning Problems in Aircrew Rostering." Journal of the Operational Research Society 43, no. 5 (May 1992): 459. http://dx.doi.org/10.2307/2583565.

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22

Ziadi, D. "Sorting and doubling techniques for set partitioning and automata minimization problems." Theoretical Computer Science 231, no. 1 (January 2000): 75–87. http://dx.doi.org/10.1016/s0304-3975(99)00018-3.

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23

Ryan, D. M. "The Solution of Massive Generalized Set Partitioning Problems in Aircrew Rostering." Journal of the Operational Research Society 43, no. 5 (May 1992): 459–67. http://dx.doi.org/10.1057/jors.1992.72.

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24

Ghoniem, A., and H. D. Sherali. "Set partitioning and packing versus assignment formulations for subassembly matching problems." Journal of the Operational Research Society 62, no. 11 (November 2011): 2023–33. http://dx.doi.org/10.1057/jors.2010.165.

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25

Samer, Phillippe, Evellyn Cavalcante, Sebastián Urrutia, and Johan Oppen. "The matching relaxation for a class of generalized set partitioning problems." Discrete Applied Mathematics 253 (January 2019): 153–66. http://dx.doi.org/10.1016/j.dam.2018.05.033.

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26

Coslovich, Luca, Raffaele Pesenti, and Walter Ukovich. "LARGE-SCALE SET PARTITIONING PROBLEMS: SOME REAL‐WORLD INSTANCES HIDE A BENEFICIAL STRUCTURE." Technological and Economic Development of Economy 12, no. 1 (March 31, 2006): 18–22. http://dx.doi.org/10.3846/13928619.2006.9637717.

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In this paper we consider large‐scale set partitioning problems. Our main purpose is to show that real‐world set partitioning problems originating from the container‐trucking industry are easier to tackle in respect to general ones. We show such different behavior through computational experiments: in particular, we have applied both a heuristic algorithm and some exact solution approaches to real‐world instances as well as to benchmark instances from Beasley OR‐library. Moreover, in order to gain an insight into the structure of the real-world instances, we have performed and evaluated various instance perturbations.

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27

URAHAMA, KIICHI, and HIROSHI NISHIYUKI. "PERFORMANCE OF THE RELAXATION ALGORITHM FOR MAXIMUM-CUT PROBLEMS." Journal of Circuits, Systems and Computers 06, no. 04 (August 1996): 375–84. http://dx.doi.org/10.1142/s021812669600025x.

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A relaxation algorithm is presented for solving a class of combinatorial optimization problems called set-partitioning tasks. The convergence property of the presented algorithm is investigated theoretically. A performance guarantee is derived theoretically for the present algorithm applied to an NP-hard example problem called the maximum-cut graph partitioning. The experimental examination of its performance manifests its superiority in computational speed to the conventional gradient method.

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28

Gao, Ya, and Xia Gao. "An Optical Distribution Network Partitioning Method Based on the Branch-and-Bound." Applied Mechanics and Materials 427-429 (September 2013): 2399–402. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.2399.

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Optical Distribution Network is a kind of optical transmission path connecting Optical Line Terminal and Optical Network Unit. This article mainly studies how to optimize broadband loan problems of the backbone network. In order to get the best allocation scheme of the Optical Distribution Network problems, we propose a solution which is converting the Optical Distribution Network partitioning problem into a graph partitioning model, and solve the problem by adopting Graph partitioning algorithms. Graph partitioning is about the undirected graph , is the collection of all vertexes. is the collection of all sides. Any vertex in the vertex set has weight value of a positive integer. Any side in a side set has weight value of a positive integer. The vertex set is divided into non-intersecting subsets , and .As to every subset , it has ,,.What we need to solve is to get the minimum sum of weight values between m non-intersecting subsets. The experimental results show that Graph partitioning algorithm is efficient.

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29

Shaikh, M. Bilal, M. Abdul Rehman, and Attaullah Sahito. "Optimizing Distributed Machine Learning for Large Scale EEG Data Set." Sukkur IBA Journal of Computing and Mathematical Sciences 1, no. 1 (June 30, 2017): 114. http://dx.doi.org/10.30537/sjcms.v1i1.14.

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Distributed Machine Learning (DML) has gained its importance more than ever in this era of Big Data. There are a lot of challenges to scale machine learning techniques on distributed platforms. When it comes to scalability, improving the processor technology for high level computation of data is at its limit, however increasing machine nodes and distributing data along with computation looks as a viable solution. Different frameworks and platforms are available to solve DML problems. These platforms provide automated random data distribution of datasets which miss the power of user defined intelligent data partitioning based on domain knowledge. We have conducted an empirical study which uses an EEG Data Set collected through P300 Speller component of an ERP (Event Related Potential) which is widely used in BCI problems; it helps in translating the intention of subject w h i l e performing any cognitive task. EEG data contains noise due to waves generated by other activities in the brain which contaminates true P300Speller. Use of Machine Learning techniques could help in detecting errors made by P300 Speller. We are solving this classification problem by partitioning data into different chunks and preparing distributed models using Elastic CV Classifier. To present a case of optimizing distributed machine learning, we propose an intelligent user defined data partitioning approach that could impact on the accuracy of distributed machine learners on average. Our results show better average AUC as compared to average AUC obtained after applying random data partitioning which gives no control to user over data partitioning. It improves the average accuracy of distributed learner due to the domain specific intelligent partitioning by the user. Our customized approach achieves 0.66 AUC on individual sessions and 0.75 AUC on mixed sessions, whereas random / uncontrolled data distribution records 0.63 AUC.

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30

Linderoth, Jeff T., Eva K. Lee, and Martin W. P. Savelsbergh. "A Parallel, Linear Programming-based Heuristic for Large-Scale Set Partitioning Problems." INFORMS Journal on Computing 13, no. 3 (August 2001): 191–209. http://dx.doi.org/10.1287/ijoc.13.3.191.12630.

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31

Bredström, D., K. Jörnsten, M. Rönnqvist, and M. Bouchard. "Searching for optimal integer solutions to set partitioning problems using column generation." International Transactions in Operational Research 21, no. 2 (October 17, 2013): 177–97. http://dx.doi.org/10.1111/itor.12050.

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32

Huang, Han, Weijia Lin, Zhiyong Lin, Zhifeng Hao, and Andrew Lim. "An evolutionary algorithm based on constraint set partitioning for nurse rostering problems." Neural Computing and Applications 25, no. 3-4 (January 3, 2014): 703–15. http://dx.doi.org/10.1007/s00521-013-1536-2.

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33

GREENE, WILLIAM A. "GENETIC ALGORITHMS FOR PARTITIONING SETS." International Journal on Artificial Intelligence Tools 10, no. 01n02 (March 2001): 225–41. http://dx.doi.org/10.1142/s0218213001000490.

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We first revisit a problem from the literature, that of partitioning a given set of numbers into subsets such that their sums are as nearly equal as possible. We devise a new genetic algorithm, Eager Breeder, for this problem. The algorithm is distinctive in its novel and aggressive way of extracting parental genetic material when forming a child partition, and its results are a substantial improvement upon prior results from the literature. Then we extend our algorithm to the more general setting, of partitioning a set in the case that the environment provides us a measure of the fitness of individual subsets in the partition. We apply the extension to two artificial problems, one with a targeted partition whose subsets are of very diverse sizes, and one whose subsets are the same size. Finally, we apply our approach to several map coloring problems, and obtain good results there as well. In our different stages of work, we exploit different heuristics, which are attuned to the particular partitioning problem under attack.

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34

Yang, Chuan-Kai. "An Optimal Balanced Partitioning of a Set of 1D Intervals." International Journal of Artificial Life Research 1, no. 2 (April 2010): 72–79. http://dx.doi.org/10.4018/jalr.2010040106.

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Given a set of 1D intervals and a desired partition number, in this paper, the author examines how to make an optimal partitioning of these intervals, such that the number of intervals between the largest partition and smallest partition is minimal among all possible partitioning schemes. This problem has its difficulty due to the fact that an interval “striding” multiple partitions should be counted multiple times. Previously the author proposed an approximated solution to this problem by employing a simulated annealing approach (Yang & Chiueh, 2006), which could give satisfactory results in most cases; however, there is no theoretical guarantee on its optimality. This paper proposes a method that could both optimally and deterministically partition a given set of 1D intervals into a given number of partitions. The author shows that some load balancing problems could also be formulated as a balanced interval partitioning problem.

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35

Koriashkina, Larisa S. "Methods of Optimal Set Partitioning for Some Start Control Problems with Quadratic Functional." Journal of Automation and Information Sciences 32, no. 5 (2000): 29–39. http://dx.doi.org/10.1615/jautomatinfscien.v32.i5.40.

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36

Kiseleva, Elena M., Alexandra A. Zhiltsova, and Viktoriya A. Stroyeva. "General Scheme to Obtain Necessary Optimality Conditions for Continuous Optimal Set Partitioning Problems." Journal of Automation and Information Sciences 44, no. 9 (2012): 51–65. http://dx.doi.org/10.1615/jautomatinfscien.v44.i9.50.

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37

Kel’manov, A. V., and A. V. Pyatkin. "NP-Hardness of Some Euclidean Problems of Partitioning a Finite Set of Points." Computational Mathematics and Mathematical Physics 58, no. 5 (May 2018): 822–26. http://dx.doi.org/10.1134/s0965542518050123.

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38

Shor, N. Z., Yu V. Voitishin, and V. M. Glushkov. "Using dual network bounds in algorithms for solving generalized set packing partitioning problems." Computational Optimization and Applications 6, no. 3 (November 1996): 293–303. http://dx.doi.org/10.1007/bf00247796.

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39

FLORIDO, J. P., H. POMARES, and I. ROJAS. "GENERATING BALANCED LEARNING AND TEST SETS FOR FUNCTION APPROXIMATION PROBLEMS." International Journal of Neural Systems 21, no. 03 (June 2011): 247–63. http://dx.doi.org/10.1142/s0129065711002791.

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In function approximation problems, one of the most common ways to evaluate a learning algorithm consists in partitioning the original data set (input/output data) into two sets: learning, used for building models, and test, applied for genuine out-of-sample evaluation. When the partition into learning and test sets does not take into account the variability and geometry of the original data, it might lead to non-balanced and unrepresentative learning and test sets and, thus, to wrong conclusions in the accuracy of the learning algorithm. How the partitioning is made is therefore a key issue and becomes more important when the data set is small due to the need of reducing the pessimistic effects caused by the removal of instances from the original data set. Thus, in this work, we propose a deterministic data mining approach for a distribution of a data set (input/output data) into two representative and balanced sets of roughly equal size taking the variability of the data set into consideration with the purpose of allowing both a fair evaluation of learning's accuracy and to make reproducible machine learning experiments usually based on random distributions. The sets are generated using a combination of a clustering procedure, especially suited for function approximation problems, and a distribution algorithm which distributes the data set into two sets within each cluster based on a nearest-neighbor approach. In the experiments section, the performance of the proposed methodology is reported in a variety of situations through an ANOVA-based statistical study of the results.

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40

Zhiltsova, Alexandra A., and Elena M. Kiseleva. "The Necessary Optimality Conditions for Continuous Problems of Set Partitioning in Terms of the Theory of Set Functions." Journal of Automation and Information Sciences 40, no. 12 (2008): 14–26. http://dx.doi.org/10.1615/jautomatinfscien.v40.i12.20.

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41

Dayar, Tuǧrul, and M. Can Orhan. "CARTESIAN PRODUCT PARTITIONING OF MULTI-DIMENSIONAL REACHABLE STATE SPACES." Probability in the Engineering and Informational Sciences 30, no. 3 (May 18, 2016): 413–30. http://dx.doi.org/10.1017/s0269964816000085.

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Markov chains (MCs) are widely used to model systems which evolve by visiting the states in their state spaces following the available transitions. When such systems are composed of interacting subsystems, they can be mapped to a multi-dimensional MC in which each subsystem normally corresponds to a different dimension. Usually the reachable state space of the multi-dimensional MC is a proper subset of its product state space, that is, Cartesian product of its subsystem state spaces. Compact storage of the matrix underlying such a MC and efficient implementation of analysis methods using Kronecker operations require the set of reachable states to be represented as a union of Cartesian products of subsets of subsystem state spaces. The problem of partitioning the reachable state space of a three or higher dimensional system with a minimum number of partitions into Cartesian products of subsets of subsystem state spaces is shown to be NP-complete. Two algorithms, one merge based the other refinement based, that yield possibly non-optimal partitionings are presented. Results of experiments on a set of problems from the literature and those that are randomly generated indicate that, although it may be more time and memory consuming, the refinement based algorithm almost always computes partitionings with a smaller number of partitions than the merge-based algorithm. The refinement based algorithm is insensitive to the order in which the states in the reachable state space are processed, and in many cases it computes partitionings that are optimal.

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42

Baldacci, Roberto, Eleni Hadjiconstantinou, Vittorio Maniezzo, and Aristide Mingozzi. "A new method for solving capacitated location problems based on a set partitioning approach." Computers & Operations Research 29, no. 4 (April 2002): 365–86. http://dx.doi.org/10.1016/s0305-0548(00)00072-1.

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43

Kel’manov, A. V., and A. V. Pyatkin. "On the complexity of some Euclidean problems of partitioning a finite set of points." Doklady Mathematics 94, no. 3 (November 2016): 635–38. http://dx.doi.org/10.1134/s1064562416060089.

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44

Atamt�rk, A., G. L. Nemhauser, and M. W. P. Savelsbergh. "A combined Lagrangian, linear programming, and implication heuristic for large-scale set partitioning problems." Journal of Heuristics 1, no. 2 (1996): 247–59. http://dx.doi.org/10.1007/bf00127080.

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45

Cohn, Amy, Michael Magazine, and George Polak. "Rank-Cluster-and-Prune: An algorithm for generating clusters in complex set partitioning problems." Naval Research Logistics (NRL) 56, no. 3 (February 24, 2009): 215–25. http://dx.doi.org/10.1002/nav.20343.

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46

Minoux, M. "A class of combinatorial problems with polynomially solvable large scale set covering/partitioning relaxations." RAIRO - Operations Research 21, no. 2 (1987): 105–36. http://dx.doi.org/10.1051/ro/1987210201051.

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47

CHEN, DANNY Z., XIAOBO S. HU, SHUANG (SEAN) LUAN, CHAO WANG, and XIAODONG WU. "GEOMETRIC ALGORITHMS FOR STATIC LEAF SEQUENCING PROBLEMS IN RADIATION THERAPY." International Journal of Computational Geometry & Applications 14, no. 04n05 (October 2004): 311–39. http://dx.doi.org/10.1142/s0218195904001494.

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The static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to accomplish the delivery of a radiation prescription to a target tumor in the minimum amount of delivery time. Geometrically, the SLS problem can be formulated as a 3-D partition problem for which the 2-D problem of partitioning a polygonal domain (possibly with holes) into a minimum set of monotone polygons is a special case. In this paper, we present new geometric algorithms for a basic case of the 3-D SLS problem (which is also of clinical value) and for the general 3-D SLS problem. Our basic 3-D SLS algorithm, based on new geometric observations, produces guaranteed optimal quality solutions using O(1) Steiner points in polynomial time; the previously best known basic 3-D SLS algorithm gives optimal outputs only for the case without considering any Steiner points, and its time bound involves a multiplicative factor of a factorial function of the input. Our general 3-D SLS algorithm is based on our basic 3-D SLS algorithm and a polynomial time algorithm for partitioning a polygonal domain (possibly with holes) into a minimum set of x-monotone polygons, and has a fast running time. Experiments of our SLS algorithms and software in clinical settings have shown substantial improvements over the current most popular commercial treatment planning system and the most well-known SLS algorithm in medical literature. The radiotherapy plans produced by our software not only take significantly shorter delivery times, but also have a much better treatment quality. This proves the feasibility of our software and has led to its clinical applications at the Department of Radiation Oncology at the University of Maryland Medical Center. Some of our techniques and geometric procedures (e.g., for partitioning a polygonal domain into a minimum set of x-monotone polygons) are interesting in their own right.

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48

Kel’manov, A. V., A. V. Pyatkin, and V. I. Khandeev. "On the complexity of some partition problems of a finite set of points in Euclidean space into balanced clusters." Доклады Академии наук 488, no. 1 (September 24, 2019): 16–20. http://dx.doi.org/10.31857/s0869-5652488116-20.

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We consider some problems of partitioning a finite set of N points in d-dimension Euclidean space into two clusters balancing the value of (1) the quadratic variance normalized by a cluster size, (2) the quadratic variance, and (3) the size-weighted quadratic variance. We have proved the NP-completeness of all these problems.

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49

Kiseliova, O. M., O. M. Prytomanova, and V. H. Padalko. "APPLICATION OF THE THEORY OF OPTIMAL SET PARTITIONING BEFORE BUILDING MULTIPLICATIVELY WEIGHTED VORONOI DIAGRAM WITH FUZZY PARAMETERS." EurasianUnionScientists 6, no. 2(71) (2020): 30–35. http://dx.doi.org/10.31618/esu.2413-9335.2020.6.71.615.

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An algorithm for constructing a multiplicatively weighted Voronoi diagram involving fuzzy parameters with the optimal location of a finite number of generator points in a limited set of n-dimensional Euclidean space 𝐸𝑛 has been suggested in the paper. The algorithm has been developed based on the synthesis of methods of solving the problems of optimal set partitioning theory involving neurofuzzy technologies modifications of N.Z. Shor 𝑟 -algorithm for solving nonsmooth optimization problems.

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50

Vasilyeva, Natalya K. "Analytical, Geometrical and Numerical Investigations of a Class of Multicriteria Continuous Problems of Set Partitioning." Journal of Automation and Information Sciences 34, no. 11 (2002): 12. http://dx.doi.org/10.1615/jautomatinfscien.v34.i11.50.

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