Relevant bibliographies by topics / Set partitioning problems

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Set partitioning problems'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Set partitioning problems"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Set partitioning problems"

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Ryoo, Moo Bong. "A constraint branch-and-bound method for set partitioning problems." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA227092.

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Thesis (M.S. in Operations Research)--Naval Postgraduate School, March 1990.
Thesis Advisor(s): Wood, R. Kevin. Second Reader: Brown, Gerald Gerard. "March 1990." Description based on signature page as viewed on October 21, 2009. Author(s) subject terms: Set partitioning problem, constraint branch and bound method, enumeration tree. Includes bibliographical references (p. 34-36). Also available online.
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El-Darzi, E. "Methods for solving the set covering and set partitioning problems using graph theoretic (relaxation) algorithms." Thesis, Brunel University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381678.

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Liu, Ya. "Methods to solve set partitioning problems and applications in packing and operating room scheduling." Troyes, 2009. http://www.theses.fr/2009TROY0021.

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Cette thèse traite des problèmes qui peuvent être considérés comme un problème de partitionnement. Ces problèmes peuvent être distingués en deux familles : les problèmes dont le coût dépend de la séquence et ceux dont le coût est indépendant de la séquence. Cette thèse se concentre sur cette dernière famille, et en particulier sur la planification des salles opératoires et le problème de découpe en deux dimensions. Bien que le problème de partitionnement soit largement étudié, la littérature est encore pauvre en heuristiques, par rapport aux algorithmes exacts. Cette thèse développe une heuristique pour résoudre une série de problèmes de partitionnement basée sur un schéma général émanant de la programmation dynamique. Dans ce schéma, on doit résoudre un sous-problème qui consiste à contenir une configuration de coût réduit minium en affectant une ressource à un sous-ensemble activités doit être résolu. Un tel sous problème est résolu différemment pour chaque application. Pour chaque problème, nous décrivons les formulations mathématiques, les réalisations d'algorithmes. La performance des algorithmes proposés est évaluée à l’aide des instances, en comparant les solutions obtenues avec des bornes inférieures ou les solutions approchées connues. Les résultats montrent que les algorithmes développés sont très efficaces, tant en termes de qualité de solution qu’en termes de temps de calcul. En outre, les algorithmes peuvent être facilement implémentés. Ces résultats satisfaisants nous laissent penser que le schéma proposé peut devenir une approche générale pour résoudre une série de problèmes de partitionnement
This thesis considers problems that can be considered as set partitioning. Such problems can be distinguished into two families: problems with sequence-dependent costs and those with sequence-independent costs. This thesis is focused on the latter family, in particular operating room scheduling and two-dimensional bin packing. Although the set partitioning problem is widely studied, the literature is still very limited in heuristics, compared to exact algorithms. This thesis develops heuristic algorithms to solve a series of set partitioning problems based on a general schema stemming from dynamic programming idea. In this schema, a subproblem consisting of constructing a pattern with the least cost by affecting a resource to a subset of activities must be solved. Such a subproblem is solved differently for each application. For each problem, we describe mathematical formulations, implementation of algorithms. The performance of the proposed algorithms is evaluated on benchmark instances found in the literature, by comparing the obtained solutions with lower bounds or known near optimal solutions. The computational results show that the developed algorithms are very efficient both in terms of the quality of the solutions and in terms of computation time. Further-more, the algorithms can be easily implemented. The satisfactory results make us believe that the proposed schema can become a general approach to solve a series of set partitioning problems
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PRAIS, MARCELO. "A STUDY ON CUTTING PLANE AND FIXING VARIABLE TECHNIQUES APPLIED TO THE RESOLUTION OF SET PARTITIONING PROBLEMS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1987. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10249@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Este trabalho consiste da aplicação de métodos de planos de corte (euclideano acelerado e cortes disjuntivos) na solução de problemas de programação inteira pura do tipo 0- 1 e suas especializações para o problemas de particionamento, quando combinados com técnicas de penalidades para fixação de variáveis. Desenvolve-se um estudo de técnicas de penalidades, que permitem fixar variáveis a valores inteiros a partir da solução ótima da relaxação linear do problema inteiro. As variáveis fixadas são eliminadas do problema e este é reescrito, tendo suas dimensões originais reduzidas. Sugerem-se melhorias no cálculo destas penalidades, levando-se em conta a estrutura particular do problema de particionamento. Finalmente, propõe-se um novo enfoque para a solução de problemas de particionamento: um algoritmo de planos de corte que utiliza técnicas de penalidades, com a finalidade de acelerar a convergência dos métodos puros de planos de corte e de reduzir os problemas por estes apresentados. Resultados computacionais são apresentados, comparando-se o desempenho (i) do algoritmo euclideano acelerado, (ii) do algoritmo de cortes disjuntivos e (iii) do algoritmo de cortes disjuntivos utilizando-se técnicas de penalidades. Para este último algoritmo, são comparados os resultados obtidos utilizando-se técnicas de penalidades genéricas para problemas inteiros do tipo 0-1 e as melhorias destas penalidades, especificas para problemas de particionamento. Considerando-se o problemas de particionamento e as melhorias propostas no cálculo de penalidades, mostra-se que é, freqüentemente, possível fixar um maior número de variáveis ou até mesmo resolver-se diretamente o problema 0-1 original. Em alguns casos, ao aplicar-se o algoritmo de planos de corte com técnicas de penalidades não só pode- se acelerar a convergência, como também superar os problemas de degenerescência dual e erros por arredondamento apresentados pelos algoritmos puros de plano de corte.
This work consists on the application of cutting plane techniques (accelerated euclidean algorithm and disjunctive cuts) for solving pure 0-1 integer problems and their specializations for the set partitioning problem, when combined to penalty techniques for fixing variables. A study on penalty techniques, which allows the fixation of variables to integer values, is also developed. These penalties are directly derived from the optimal tableau nof the linear relaxation of the integer problem. The variables fixed due to penalties are eliminated and the problem is reformulated, having its initial dimensions reduced. Some improvements on the evaluation of penalties are suggested, taking into account the special structure of the set partitioning problem. Finally, a new approach to the solution of set partitioning problems is proposed: a cutting plane algorithm which uses penalty techniques, in order to accelerate the convergence of pure cutting plane methods and overcome the problems arising from their use. Computational results are shown, allowing to compare the performance of (i) the accelerated euclidean algorithm, (ii) the disjunctive cut algorithm and (iii) the last one combined with penalty techniques. For the latter, the results obained by the use of generic penalties for 0-1 integer programs are compared with those obtained by the use of the improved penalties for ser partitioning problems. Taking into account set partitioninng problems and the improvements proposed for the evaluation of penalties, it is shown that very often it is possible to fix more variables to integer values and even to solve directly the original 0-1 problem. For some cases, by applying the cutting plane algorithm together with penalties, it is possible to accelerate the convergence and overcome dual degeneracy and round-off errors arising from the use of pure cutting plane algorithms.
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Brommesson, Peter. "Solving the Generalized Assignment Problem by column enumeration based on Lagrangian reduced costs." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5583.

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In this thesis a method for solving the Generalized Assignment Problem (GAP) is described. It is based on a reformulation of the original problem into a Set Partitioning Problem (SPP), in which the columns represent partial solutions to the original problem. For solving this problem, column generation, with systematic overgeneration of columns, is used. Conditions that guarantee that an optimal solution to a restricted SPP is optimal also in the original problem are given. In order to satisfy these conditions, not only columns with the most negative Lagrangian reduced costs need to be generated, but also others; this observation leads to the use of overgeneration of columns.

The Generalized Assignment Problem has shown to be NP-hard and therefore efficient algorithms are needed, especially for large problems. The application of the proposed method decomposes GAP into several knapsack problems via Lagrangian relaxation, and enumerates solutions to each of these problems. The solutions obtained from the knapsack problems form a Set Partitioning Problem, which consists of combining one solution from each knapsack problem to obtain a solution to the original problem. The algorithm has been tested on problems with 10 agents and 60 jobs. This leads to 10 knapsack problems, each with 60 variables.

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Qiu, Shengli. "Airline crew pairing optimization problems and capacitated vehicle routing problems." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/51717.

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Crew pairing and vehicle routing are combinatorial optimization problems that have been studied for many years by researchers worldwide. The aim of this research work is to investigate effective methods for solving large scale crew pairing problems and vehicle routing problems. In the airline industry, to address the complex nature of crew pairing problems, we propose a duty tree method followed by a primal-dual subproblem simplex method. The duty tree approach captures the constraints that apply to crew pairings and generate candidate pairings taking advantage of various proposed strategies. A huge number of legal pairings are stored in the duty tree and can be enumerated. A set partitioning formulation is then constructed, and the problem is solved using a primal-dual subproblem simplex method tailored to the duty tree approach. Computational experiments are conducted to show the effectiveness of the methods. We also present our efforts addressing the capacitated vehicle routing problem (CVRP) that is the basic version of many other variants of the problem. We do not attempt to solve the CVRP instances that have been solved to optimality. Instead, we focus on investigating good solutions for large CVRP instances, with particular emphasis on those benchmark problems from the public online library that have not yet been solved to optimality by other researchers and determine whether we can find new best-known solutions. In this research, we propose a route network that can store a huge number of routes with all routes being legal, a set partitioning formulation that can handle many columns, and the primal-dual subproblem simplex method to find a solution. The computational results show that our proposed methods can achieve better solutions than the existing best-known solutions for some difficult instances. Upon convergence of the primal-dual subproblem simplex method on the giant-tour based networks, we use the near optimal primal and dual solution as well as solve the elementary shortest path problem with resource constraints to achieve the linear programming relaxation global optimal solution.
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Rönnberg, Elina. "Methods and Applications in Integer Programming : All-Integer Column Generation and Nurse Scheduling." Licentiate thesis, Linköping University, Linköping University, Optimization, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-15143.

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Integer programming can be used to provide solutionsto complex decision and planning problems occurring in a wide varietyof situations. Applying integer programming to a real life problembasically involves a first phase where a mathematical model isconstructed, and a second phase where the problem described by themodel is solved. While the nature of the challenges involved in therespective two phases differ, the strong relationship between theproperties of models, and which methods that are appropriate for theirsolution, links the two phases. This thesis constitutes of threepapers, of which the third one considers the modeling phase, while thefirst and second one consider the solution phase.

 

Many applications of column generation yield master problems of setpartitioning type, and the first and second papers presentmethodologies for solving such problems. The characteristics of themethodologies presented are that all successively found solutions arefeasible and integral, where the retention of integrality is a majordistinction from other column generation methods presented in theliterature.

 

The third paper concerns nurse scheduling and describes the results ofa pilot implementation of a scheduling tool at a Swedish nursing ward.This paper focuses on the practical aspects of modeling and thechallenges of providing a solution to a complex real life problem.

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Ayik, Mehmet. "Exploiting consecutive ones structure in the set partitioning problem." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2000. http://handle.dtic.mil/100.2/ADA387501.

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Fernández, Elena (Fernández Aréizaga). "Diseño y estudio computacional de algotimos híbridos para problemas de set partitioning." Doctoral thesis, Universitat Politècnica de Catalunya, 1988. http://hdl.handle.net/10803/5920.

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Sachdeva, Sandeep. "Development of a branch and price approach involving vertex cloning to solve the maximum weighted independent set problem." Thesis, Texas A&M University, 2004. http://hdl.handle.net/1969.1/3251.

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We propose a novel branch-and-price (B&P) approach to solve the maximum weighted independent set problem (MWISP). Our approach uses clones of vertices to create edge-disjoint partitions from vertex-disjoint partitions. We solve the MWISP on sub-problems based on these edge-disjoint partitions using a B&P framework, which coordinates sub-problem solutions by involving an equivalence relationship between a vertex and each of its clones. We present test results for standard instances and randomly generated graphs for comparison. We show analytically and computationally that our approach gives tight bounds and it solves both dense and sparse graphs quite quickly.
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Books on the topic "Set partitioning problems"

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El-Darzi, Elia. Methods for solving the set covering and set partitioning problems using graph theoretic (relaxation) algorithms. Uxbridge: Brunel University, 1988.

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Wassenhove, Luk N. van. A set partitioning heuristic for the generalized assignment problem. Fontainebleau: INSEAD, 1991.

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Exploiting Consecutive Ones Structure in the Set Partitioning Problem. Storming Media, 2000.

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Newman, Mark. Mathematics of networks. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805090.003.0006.

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An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.
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A Combined Adaptive Tabu Search and Set Partitioning Approach for the Crew Scheduling Problem with an Air Tanker Crew Application. Storming Media, 2002.

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Book chapters on the topic "Set partitioning problems"

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Saldanha, Ricardo, and Ernesto Morgado. "Solving Set Partitioning Problems with Global Constraint Propagation." In Progress in Artificial Intelligence, 101–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-24580-3_18.

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Mumford, Christine L. "An Order Based Memetic Evolutionary Algorithm for Set Partitioning Problems." In Studies in Computational Intelligence, 881–925. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78293-3_21.

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Rönnberg, Elina, and Torbjörn Larsson. "Integral Simplex Methods for the Set Partitioning Problem: Globalisation and Anti-Cycling." In Open Problems in Optimization and Data Analysis, 285–303. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99142-9_15.

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Ziadi, D. "Sorting and doubling techniques for set partitioning and automata minimization problems." In Lecture Notes in Computer Science, 241–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0031397.

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Shevchenko, Tetyana, Elena Kiseleva, and Larysa Koriashkina. "The Features of Solving of the set Partitioning Problems with Moving Boundaries Between Subsets." In Operations Research Proceedings 2008, 533–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00142-0_86.

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Crawford, Broderick, and Carlos Castro. "Integrating Lookahead and Post Processing Procedures with ACO for Solving Set Partitioning and Covering Problems." In Artificial Intelligence and Soft Computing – ICAISC 2006, 1082–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11785231_113.

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Gass, Saul I., and Carl M. Harris. "Set-partitioning problem." In Encyclopedia of Operations Research and Management Science, 746. New York, NY: Springer US, 2001. http://dx.doi.org/10.1007/1-4020-0611-x_942.

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Levine, David. "A Parallel Genetic Algorithm for the Set Partitioning Problem." In Meta-Heuristics, 23–35. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1361-8_2.

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Derigs, U., and A. Metz. "Über die Matching Relaxation für das Set Partitioning Problem." In Operations Research Proceedings 1991, 398–406. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-46773-8_103.

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Ali, Agha Iqbal, Hyun-Soo Han, and Jeffery L. Kennington. "Use of hidden network structure in the set partitioning problem." In Integer Programming and Combinatorial Optimization, 172–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-59408-6_50.

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Conference papers on the topic "Set partitioning problems"

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Alexandre, Dolgui,. "An Approach to Transfer Line Balancing Via a Special Set Partitioning Problem." In Information Control Problems in Manufacturing, edited by Bakhtadze, Natalia, chair Dolgui, Alexandre and Bakhtadze, Natalia. Elsevier, 2009. http://dx.doi.org/10.3182/20090603-3-ru-2001.00123.

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Crawford, Broderick, Carlos Castro, and Eric Monfroy. "A New ACO Transition Rule for Set Partitioning and Covering Problems." In 2009 International Conference of Soft Computing and Pattern Recognition. IEEE, 2009. http://dx.doi.org/10.1109/socpar.2009.89.

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Kel'manov, Alexander. "Efficient approximation algorithms for some NP-hard problems of partitioning a set and a sequence." In 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON). IEEE, 2017. http://dx.doi.org/10.1109/sibircon.2017.8109843.

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Huang, Jun, and Satyandra K. Gupta. "Accessibility Driven Spatial Partitioning for Generating Sacrificial Multi-Piece Molds." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/dfm-34173.

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This paper describes an algorithm based on accessibility-driven partitioning approach to the design of sacrificial multi-piece molds. We construct gross shape of the mold by subtracting the part model from the mold enclosure and analyze its accessibility. The gross mold shape is partitioned using accessibility information. Each partitioning improves accessibility and we produce a set of mold components that are accessible and therefore can be produced using milling and drilling operations. Our approach has the following advantages. First, by using multi-piece molds we can create geometrically complex objects that are impossible to create using traditional two-piece molds. Second, we make use of sacrificial molds. Therefore, using multi-piece sacrificial molds, we can create parts that pose disassembly problems for permanent molds. Third, mold design steps are significantly automated in our methodology. Therefore, we can create the functional part from the CAD model of the part in a matter of hours and so our approach can be used in small batch manufacturing environments.
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Gandini, Martina, and Suela Ruffa. "A DOE Approach for Sensitivity Analysis of a Shape Partitioning Algorithm." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59175.

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In the field of geometrical product specification and verification, one of the main problems is classification and segmentation of 3D shapes. Shape recognition and segmentation is a widespread research area with different application fields (image processing, shape searching, pattern recognition, reverse engineering, etc.). Many methodologies and algorithms have been developed within such different fields, each one exhibiting optimized performances with respect to the set of objects and targets in each application [1, 11, 12]. Nevertheless, for manufactured parts a unique description of shape during the whole product lifecycle is still envisaged, and GPS (“Geometrical Product Specification and Verification”) project seems to be the most promising approach, but it should be stated that the partitioning process is still to be improved both theoretically and operationally. The ISO Technical Committee 213 (TC213), entrusted to develop the GPS project, founded the partitioning process on the classification of shapes based on symmetrical properties of surfaces [5, 6]. The aim of this paper is to describe the method proposed by Gelfand and Guibas [4] and analyze its performances on sampled surfaces by varying parameters of the method that basically affect its efficiency. In fact, the ISO research is currently devoted to identify a segmentation method characterized by efficiency, reliability, robustness and applicability with the aim to standardize the methodology for the verification phase of the manufacturing process. In this paper, a DOE analysis has been performed, in order to search an optimal parameter configuration, necessary to consider the method as a standard for shape partitioning.
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Prabhu, D. R., and D. L. Taylor. "Some Issues in the Generation of the Topology of Systems With Constant Power-Flow Input-Output Requirements." In ASME 1988 Design Technology Conferences. American Society of Mechanical Engineers, 1988. http://dx.doi.org/10.1115/detc1988-0006.

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Abstract In this paper, we examine design problems in which requirements consist of constant power-flows with constant effort and flow variables in various domains. The use of an outgrowth of bond graph structure for design is explored. A spanning set of functional primitives is determined which can assemble an arbitrary system meeting the above functional requirements. Some basic theorems are developed regarding generic assembly algorithms to build systems using elements belonging to the chosen set. Maximum and minimum bounds on complexity are determined. An optimal partitioning of specified requirements is obtained to minimize the number of primitives needed. Power-flows through each primitive used is subsequently minimized to obtain a minimal power-flow graph.
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Fan, Gaojian, Martin Müller, and Robert Holte. "Additive Merge-and-Shrink Heuristics for Diverse Action Costs." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/599.

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In many planning applications, actions can have highly diverse costs. Recent studies focus on the effects of diverse action costs on search algorithms, but not on their effects on domain-independent heuristics. In this paper, we demonstrate there are negative impacts of action cost diversity on merge-and-shrink (M&S), a successful abstraction method for producing high-quality heuristics for planning problems. We propose a new cost partitioning method for M&S to address the negative effects of diverse action costs. We investigate non-unit cost IPC domains, especially those for which diverse action costs have severe negative effects on the quality of the M&S heuristic. Our experiments demonstrate that in these domains, an additive set of M&S heuristics using the new cost partitioning method produces much more informative and effective heuristics than creating a single M&S heuristic which directly encodes diverse costs.
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Kim, Hyung Min, Nestor F. Michelena, Panos Y. Papalambros, and Tao Jiang. "Target Cascading in Optimal System Design." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/dac-14265.

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Abstract Target cascading is a key challenge in the early product development stages of large complex artifacts: How to propagate the desirable top level design specifications (or targets) to appropriate specifications for the various subsystems and components in a consistent and efficient manner. Consistency means that all parts of the designed system should end up working well together, while efficiency means that the process itself should avoid iterations at later stages, which are costly in time and resources. In the present article target cascading is formalized in a process modeled as a multilevel optimal design problem. Design targets are cascaded down to lower levels using partitioning of the original problem into a hierarchical set of sub-problems. For each design problem at a given level, an optimization problem is formulated to minimize deviations from the propagated targets and thus achieve intersystem compatibility. A coordination strategy links all subproblem decisions so that the overall system performance targets are met. The process is illustrated with an explicit analytical problem and a simple chassis design model that demonstrates how the process can be applied in practice.
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9

Fan, Xuhui, Bin Li, Ling Luo, and Scott A. Sisson. "Bayesian Nonparametric Space Partitions: A Survey." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/602.

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Bayesian nonparametric space partition (BNSP) models provide a variety of strategies for partitioning a D-dimensional space into a set of blocks, such that the data within the same block share certain kinds of homogeneity. BNSP models are applicable to many areas, including regression/classification trees, random feature construction, and relational modelling. This survey provides the first comprehensive review of this subject. We explore the current progress of BNSP research through three perspectives: (1) Partition strategies, where we review the various techniques for generating partitions and discuss their theoretical foundation, `self-consistency'; (2) Applications, where we detail the current mainstream usages of BNSP models and identify some potential future applications; and (3) Challenges, where we discuss current unsolved problems and possible avenues for future research.
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Wang, Ruiwei, and Roland H. C. Yap. "Bipartite Encoding: A New Binary Encoding for Solving Non-Binary CSPs." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/165.

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Constraint Satisfaction Problems (CSPs) are typically solved with Generalized Arc Consistency (GAC). A general CSP can also be encoded into a binary CSP and solved with Arc Consistency (AC). The well-known Hidden Variable Encoding (HVE) is still a state-of-the-art binary encoding for solving CSPs. We propose a new binary encoding, called Bipartite Encoding (BE) which uses the idea of partitioning constraints. A BE encoded CSP can achieve a higher level of consistency than GAC on the original CSP. We give an algorithm for creating compact bipartite encoding for non-binary CSPs. We present a AC propagator on the binary constraints from BE exploiting their special structure. Experiments on a large set of non-binary CSP benchmarks with table constraints using the Wdeg, Activity and Impact heuristics show that BE with our AC propagator can outperform existing state-of-the-art GAC algorithms (CT, STRbit) and binary encodings (HVE with HTAC).
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Reports on the topic "Set partitioning problems"

1

Levine, D. A parallel genetic algorithm for the set partitioning problem. Office of Scientific and Technical Information (OSTI), December 1996. http://dx.doi.org/10.2172/435291.

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2

Levine, D. A parallel genetic algorithm for the set partitioning problem. Office of Scientific and Technical Information (OSTI), May 1994. http://dx.doi.org/10.2172/10161119.

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