483 research outputs found
Designing Satellite Communication Networks by Zero-One Quadratic Programming
In satellite communications networks, distinctive facilities called homing stations perform special transmission functions. Local demand nodes clustered around each homing station communicate with each other via a local switch at the homing station; demand nodes in different clusters communicate with each other via satellite earth stations at the homing stations. Designing such a communication network requires choices on the locations of the earth stations and on the assignments of demand nodes to the local clusters at the earth stations. We formulate this problem as a zero-one quadratic facility location problem and transform it into an equivalent zero-one integer linear program. Computational experience on real data shows that a branch and bound procedure is effective in solving problems with up to forty demand nodes (major cities) and that the solutions that this algorithm finds improve considerably upon management generated solutions. We also show that a greedy add heuristic, as implemented on an IBM PC, consistently generates optimal or near-optimal solutions
Lagrangian-based methods for single and multi-layer multicommodity capacitated network design
Le problÚme de conception de réseau avec coûts fixes et capacités (MCFND) et le problÚme
de conception de réseau multicouches (MLND) sont parmi les problÚmes de
conception de réseau les plus importants. Dans le problÚme MCFND monocouche, plusieurs
produits doivent ĂȘtre acheminĂ©s entre des paires origine-destination diffĂ©rentes
dâun rĂ©seau potentiel donnĂ©. Des liaisons doivent ĂȘtre ouvertes pour acheminer les produits,
chaque liaison ayant une capacité donnée. Le problÚme est de trouver la conception
du réseau à coût minimum de sorte que les demandes soient satisfaites et que les capacités
soient respectées. Dans le problÚme MLND, il existe plusieurs réseaux potentiels,
chacun correspondant à une couche donnée. Dans chaque couche, les demandes pour un
ensemble de produits doivent ĂȘtre satisfaites. Pour ouvrir un lien dans une couche particuliĂšre,
une chaĂźne de liens de support dans une autre couche doit ĂȘtre ouverte. Nous
abordons le problÚme de conception de réseau multiproduits multicouches à flot unique
avec coĂ»ts fixes et capacitĂ©s (MSMCFND), oĂč les produits doivent ĂȘtre acheminĂ©s uniquement
dans lâune des couches.
Les algorithmes basĂ©s sur la relaxation lagrangienne sont lâune des mĂ©thodes de rĂ©solution
les plus efficaces pour résoudre les problÚmes de conception de réseau. Nous
prĂ©sentons de nouvelles relaxations Ă base de noeuds, oĂč le sous-problĂšme rĂ©sultant se
décompose par noeud. Nous montrons que la décomposition lagrangienne améliore significativement
les limites des relaxations traditionnelles.
Les problÚmes de conception du réseau ont été étudiés dans la littérature. Cependant,
ces derniÚres années, des applications intéressantes des problÚmes MLND sont apparues,
qui ne sont pas couvertes dans ces études. Nous présentons un examen des problÚmes de
MLND et proposons une formulation générale pour le MLND. Nous proposons également
une formulation générale et une méthodologie de relaxation lagrangienne efficace
pour le problÚme MMCFND. La méthode est compétitive avec un logiciel commercial
de programmation en nombres entiers, et donne généralement de meilleurs résultats.The multicommodity capacitated fixed-charge network design problem (MCFND) and
the multilayer network design problem (MLND) are among the most important network
design problems. In the single-layer MCFND problem, several commodities have to
be routed between different origin-destination pairs of a given potential network. Appropriate
capacitated links have to be opened to route the commodities. The problem
is to find the minimum cost design and routing such that the demands are satisfied and
the capacities are respected. In the MLND, there are several potential networks, each
at a given layer. In each network, the flow requirements for a set of commodities must
be satisfied. However, the selection of the links is interdependent. To open a link in a
particular layer, a chain of supporting links in another layer has to be opened. We address
the multilayer single flow-type multicommodity capacitated fixed-charge network
design problem (MSMCFND), where commodities are routed only in one of the layers.
Lagrangian-based algorithms are one of the most effective solution methods to solve
network design problems. The traditional Lagrangian relaxations for the MCFND problem
are the flow and knapsack relaxations, where the resulting Lagrangian subproblems
decompose by commodity and by arc, respectively. We present new node-based
relaxations, where the resulting subproblem decomposes by node. We show that the
Lagrangian dual bound improves significantly upon the bounds of the traditional relaxations.
We also propose a Lagrangian-based algorithm to obtain upper bounds.
Network design problems have been the object of extensive literature reviews. However,
in recent years, interesting applications of multilayer problems have appeared that
are not covered in these surveys. We present a review of multilayer problems and propose
a general formulation for the MLND. We also propose a general formulation and
an efficient Lagrangian-based solution methodology for the MMCFND problem. The
method is competitive with (and often significantly better than) a state-of-the-art mixedinteger
programming solver on a large set of randomly generated instances
Hybrid Statistical Data Mining Framework for Multi-Commodity Fixed Charge Network Flow Problem
This paper presents a new approach to analyze the network structure in multi-commodity fixed charge network flow problems (MCFCNF). This methodology uses historical data produced from repeatedly solving the traditional MCFCNF mathematical model as input for the machine-learning framework. Further, we reshape the problem as a binary classification problem and employ machine-learning algorithms to predict network structure. This predicted network structure is further used as an initial solution for our mathematical model. The quality of the initial solution generated is judged on the basis of predictive accuracy, feasibility and reduction in solving time
Avoiding unnecessary demerging and remerging of multiâcommodity integer flows
Resource flows may merge and demerge at a network node. Sometimes several demerged flows may be immediately merged again, but in different combinations compared to before they were demerged. However, the demerging is unnecessary in the first place if the total resources at each of the network nodes involved remains unchanged. We describe this situation as âunnecessary demerging and remerging (UDR)â of flows, which would incur unnecessary operations and costs in practice. Multiâcommodity integer flows in particular will be considered in this paper. This deficiency could be theoretically overcome by means of fixedâcharge variables, but the practicality of this approach is restricted by the difficulty in solving the corresponding integer linear program (ILP). Moreover, in a problem where the objective function has many cost elements, it would be helpful if such operational costs are optimized implicitly. This paper presents a heuristic branching method within an ILP solver for removing UDR without the use of fixedâcharge variables. We use the concept of âflow potentialsâ (different from âflow residuesâ for maxâflows) guided by which underutilized arcs are heuristically banned, thus reducing occurrences of UDR. Flow connection bigraphs and flow connection groups (FCGs) are introduced. We prove that if certain conditions are met, fully utilizing an arc will guarantee an improvement within an FCG. Moreover, a location subâmodel is given when the former cannot guarantee an improvement. More importantly, the heuristic approach can significantly enhance the full fixedâcharge model by warmâstarting. Computational experiments based on realâworld instances have shown the usefulness of the proposed methods
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A cycle-based evolutionary algorithm for the fixed-charge capacitated multi-commodity network design problem
This paper presents an evolutionary algorithm for the fixed-charge multicommodity network design problem (MCNDP), which concerns routing multiple commodities from origins to destinations by designing a network through selecting arcs, with an objective of minimizing the fixed costs of the selected arcs plus the variable costs of the flows on each arc. The proposed algorithm evolves a pool of solutions using principles of scatter search, interlinked with an iterated local search as an improvement method. New cycle-based neighborhood operators are presented which enable complete or partial re-routing of multiple commodities. An efficient perturbation strategy, inspired by ejection chains, is introduced to perform local compound cycle-based moves to explore different parts of the solution space. The algorithm also allows infeasible solutions violating arc capacities while performing the "ejection cycles", and subsequently restores feasibility by systematically applying correction moves. Computational experiments on benchmark MCNDP instances show that the proposed solution method consistently produces high-quality solutions in reasonable computational times
Matheuristics: using mathematics for heuristic design
Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks.
In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development
Optimisation of an integrated transport and distribution system
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