We present a mathematical formulation of a emph{frequency assignment problem} encountered in cellular phone networks: frequencies have to be assigned to stationary transceivers (carriers) such that as little interference as possible is induced while obeying several technical and legal restrictions. The optimization problem is NP-hard, and no good approximation can be guaranteed---unless P = NP. We sketch some starting and improvement heuristics, and report on their successful application for solving the frequency assignment problem under consideration. Computational results on real-world instances with up to 2877 carriers and 50 frequencies are presented.
{"title":"A frequency assignment problem in cellular phone networks","authors":"A. Eisenblätter","doi":"10.1090/dimacs/040/07","DOIUrl":"https://doi.org/10.1090/dimacs/040/07","url":null,"abstract":"We present a mathematical formulation of a emph{frequency assignment problem} encountered in cellular phone networks: frequencies have to be assigned to stationary transceivers (carriers) such that as little interference as possible is induced while obeying several technical and legal restrictions. The optimization problem is NP-hard, and no good approximation can be guaranteed---unless P = NP. We sketch some starting and improvement heuristics, and report on their successful application for solving the frequency assignment problem under consideration. Computational results on real-world instances with up to 2877 carriers and 50 frequencies are presented.","PeriodicalId":115016,"journal":{"name":"Network Design: Connectivity and Facilities Location","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117272895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. O. Krumke, M. Marathe, H. Noltemeier, R. Ravi, S. Ravi
The authors study budget constrained optimal network improvement problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. As an example, consider the following prototypical problem: Let G = (V, E) be an undirected graph with two cost values L(e) and C(e) associated with each edge e, where L(e) denotes the length of e and C(e) denotes the cost of reducing the length of e by a unit amount. A reduction strategy specifies for each edge e, the amount by which L(e) is to be reduced. For a given budget B, the goal is to find a reduction strategy such that the total cost of reduction is at most B and the minimum cost tree (with respect to some measure M) under the modified L costs is the best over all possible reduction strategies which obey the budget constraint. Typical measures M for a tree are the total weight and the diameter. They provide both hardness and approximation results for the two measures M mentioned above. For the problem of minimizing the total weight of a spacing tree, they provide an algorithm that, for any fixed {gamma},{var_epsilon} > 0, finds a solution whose weight is at most (1 + 1/{gamma}) times that of a minimum length spanning tree plus an additive constant of at most {var_epsilon} and the total cost of improvement is at most (1 + {gamma}) times the budget B. This result can be extended to obtain approximation algorithms for more general network design problems considered in [GW, GG+94].
{"title":"Network improvement problems","authors":"S. O. Krumke, M. Marathe, H. Noltemeier, R. Ravi, S. Ravi","doi":"10.1090/dimacs/040/15","DOIUrl":"https://doi.org/10.1090/dimacs/040/15","url":null,"abstract":"The authors study budget constrained optimal network improvement problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. As an example, consider the following prototypical problem: Let G = (V, E) be an undirected graph with two cost values L(e) and C(e) associated with each edge e, where L(e) denotes the length of e and C(e) denotes the cost of reducing the length of e by a unit amount. A reduction strategy specifies for each edge e, the amount by which L(e) is to be reduced. For a given budget B, the goal is to find a reduction strategy such that the total cost of reduction is at most B and the minimum cost tree (with respect to some measure M) under the modified L costs is the best over all possible reduction strategies which obey the budget constraint. Typical measures M for a tree are the total weight and the diameter. They provide both hardness and approximation results for the two measures M mentioned above. For the problem of minimizing the total weight of a spacing tree, they provide an algorithm that, for any fixed {gamma},{var_epsilon} > 0, finds a solution whose weight is at most (1 + 1/{gamma}) times that of a minimum length spanning tree plus an additive constant of at most {var_epsilon} and the total cost of improvement is at most (1 + {gamma}) times the budget B. This result can be extended to obtain approximation algorithms for more general network design problems considered in [GW, GG+94].","PeriodicalId":115016,"journal":{"name":"Network Design: Connectivity and Facilities Location","volume":"201 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115699655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A greedy randomized adaptive search procedure for the multitarget multisensor tracking problem","authors":"R. Murphey, P. Pardalos, L. Pitsoulis","doi":"10.1090/dimacs/040/17","DOIUrl":"https://doi.org/10.1090/dimacs/040/17","url":null,"abstract":"","PeriodicalId":115016,"journal":{"name":"Network Design: Connectivity and Facilities Location","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115813875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A scalable TWDM lightwave network based on generalized de Bruijn digraph","authors":"P. Wan, A. Pavan","doi":"10.1090/dimacs/040/22","DOIUrl":"https://doi.org/10.1090/dimacs/040/22","url":null,"abstract":"","PeriodicalId":115016,"journal":{"name":"Network Design: Connectivity and Facilities Location","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128433489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Brazil, J. Rubinstein, Doreen A. Thomas, J. Weng, N. Wormald
{"title":"Shortest networks on spheres","authors":"M. Brazil, J. Rubinstein, Doreen A. Thomas, J. Weng, N. Wormald","doi":"10.1090/dimacs/040/26","DOIUrl":"https://doi.org/10.1090/dimacs/040/26","url":null,"abstract":"","PeriodicalId":115016,"journal":{"name":"Network Design: Connectivity and Facilities Location","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115216167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the Process Synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process owsheets that convert raw materials into desired products. In recent years, the optimization approach to process synthesis has shown promise in tackling this challenge. It requires the development of a network of interconnected units, the process superstructure, that represents the alternative process owsheets. The mathematical model-ing of the superstructure has a mixed set of binary and continuous variables and results in a mixed-integer optimization model. Due to the nonlinearity of chemical models, these problems are generally classiied as Mixed-Integer Nonlinear Programming (MINLP) problems. A number of local optimization algorithms for MINLP problems are outlined in this paper: Generalized Benders Decomposition (GBD), Outer Approximation (OA), Generalized Cross Decomposition (GCD), Extended Cutting Plane (ECP), Branch and Bound (BB), and Feasibility Approach (FA), with particular emphasis on the Generalized Benders Decomposition. Recent developments for the global optimization of nonconvex MINLPs are then introduced. In particular, two branch-and-bound approaches are discussed: the Special structure Mixed Integer Nonlinear BB (SMIN-BB), where the binary variables should participate linearly or in mixed-bilinear terms, and the General structure Mixed Integer Nonlinear BB (GMIN-BB), where the continuous relaxation of the binary variables must lead to a twice-diierentiable problem. Both algorithms are based on the BB global optimization algorithm for nonconvex continuous problems. Once some of the theoretical issues behind local and global optimization algorithms for MINLPs have been exposed, attention is directed to their practical use. The algorithmic framework MINOPT is discussed as a computational tool for the solution of process synthesis problems. It is an implementation of a number of local optimization algorithms for the solution of MINLPs. The synthesis problem for a heat exchanger network is then presented to demonstrate the application of some local MINLP algorithms and the global optimization SMIN-BB algorithm.
{"title":"Nonlinear and mixed-integer optimization in chemical process network systems","authors":"C. Adjiman, C. Schweiger, C. Floudas","doi":"10.1090/dimacs/040/25","DOIUrl":"https://doi.org/10.1090/dimacs/040/25","url":null,"abstract":"The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the Process Synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process owsheets that convert raw materials into desired products. In recent years, the optimization approach to process synthesis has shown promise in tackling this challenge. It requires the development of a network of interconnected units, the process superstructure, that represents the alternative process owsheets. The mathematical model-ing of the superstructure has a mixed set of binary and continuous variables and results in a mixed-integer optimization model. Due to the nonlinearity of chemical models, these problems are generally classiied as Mixed-Integer Nonlinear Programming (MINLP) problems. A number of local optimization algorithms for MINLP problems are outlined in this paper: Generalized Benders Decomposition (GBD), Outer Approximation (OA), Generalized Cross Decomposition (GCD), Extended Cutting Plane (ECP), Branch and Bound (BB), and Feasibility Approach (FA), with particular emphasis on the Generalized Benders Decomposition. Recent developments for the global optimization of nonconvex MINLPs are then introduced. In particular, two branch-and-bound approaches are discussed: the Special structure Mixed Integer Nonlinear BB (SMIN-BB), where the binary variables should participate linearly or in mixed-bilinear terms, and the General structure Mixed Integer Nonlinear BB (GMIN-BB), where the continuous relaxation of the binary variables must lead to a twice-diierentiable problem. Both algorithms are based on the BB global optimization algorithm for nonconvex continuous problems. Once some of the theoretical issues behind local and global optimization algorithms for MINLPs have been exposed, attention is directed to their practical use. The algorithmic framework MINOPT is discussed as a computational tool for the solution of process synthesis problems. It is an implementation of a number of local optimization algorithms for the solution of MINLPs. The synthesis problem for a heat exchanger network is then presented to demonstrate the application of some local MINLP algorithms and the global optimization SMIN-BB algorithm.","PeriodicalId":115016,"journal":{"name":"Network Design: Connectivity and Facilities Location","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123781239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A model for network design","authors":"R. Wessäly","doi":"10.1090/dimacs/040/24","DOIUrl":"https://doi.org/10.1090/dimacs/040/24","url":null,"abstract":"","PeriodicalId":115016,"journal":{"name":"Network Design: Connectivity and Facilities Location","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129657310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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