765 research outputs found
The Generalized Bin Packing Problem
In the Generalized Bin Packing Problem a set of items characterized by volume and profit and a set of bins of different types characterized by volume and cost are given. The goal consists in selecting those items and bins which optimize an objective function which combines the cost of the used bins and the profit of the selected items. We propose two methods to tackle the problem: branch-and-price as an exact method and beam search as a heuristics, derived from the branch-and-price. Our branch-and-price method is characterized by a two level branching strategy. At the first level the branching is performed on the number of available bins for each bin type. At the second level it consists on pairs of items which can or cannot be loaded together. Exploiting the branch-and-price skeleton, we then present a variegated beam search heuristics, characterized by different beam sizes. We finally present extensive computational results which show a high accuracy of the exact method and a very good efficiency of the proposed heuristics
Adaptive Improvements of Multi-Objective Branch and Bound
Branch and bound methods which are based on the principle "divide and
conquer" are a well established solution approach in single-objective integer
programming. In multi-objective optimization branch and bound algorithms are
increasingly attracting interest. However, the larger number of objectives
raises additional difficulties for implicit enumeration approaches like branch
and bound. Since bounding and pruning is considerably weaker in multiple
objectives, many branches have to be (partially) searched and may not be pruned
directly. The adaptive use of objective space information can guide the search
in promising directions to determine a good approximation of the Pareto front
already in early stages of the algorithm. In particular we focus in this
article on improving the branching and queuing of subproblems and the handling
of lower bound sets.
In our numerical test we evaluate the impact of the proposed methods in
comparison to a standard implementation of multiobjective branch and bound on
knapsack problems, generalized assignment problems and (un)capacitated facility
location problems
Lagrangian-based methods for single and multi-layer multicommodity capacitated network design
Le problème de conception de réseau avec coûts fixes et capacités (MCFND) et le problème
de conception de réseau multicouches (MLND) sont parmi les problèmes de
conception de réseau les plus importants. Dans le problème MCFND monocouche, plusieurs
produits doivent être acheminés entre des paires origine-destination différentes
d’un réseau potentiel donné. Des liaisons doivent être ouvertes pour acheminer les produits,
chaque liaison ayant une capacité donnée. Le problème 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 problème MLND, il existe plusieurs réseaux potentiels,
chacun correspondant à une couche donnée. Dans chaque couche, les demandes pour un
ensemble de produits doivent être satisfaites. Pour ouvrir un lien dans une couche particulière,
une chaîne de liens de support dans une autre couche doit être ouverte. Nous
abordons le problème de conception de réseau multiproduits multicouches à flot unique
avec coûts fixes et capacités (MSMCFND), où les produits doivent être acheminés uniquement
dans l’une des couches.
Les algorithmes basés sur la relaxation lagrangienne sont l’une des méthodes de résolution
les plus efficaces pour résoudre les problèmes de conception de réseau. Nous
présentons de nouvelles relaxations à base de noeuds, où le sous-problème résultant se
décompose par noeud. Nous montrons que la décomposition lagrangienne améliore significativement
les limites des relaxations traditionnelles.
Les problèmes de conception du réseau ont été étudiés dans la littérature. Cependant,
ces dernières années, des applications intéressantes des problèmes MLND sont apparues,
qui ne sont pas couvertes dans ces études. Nous présentons un examen des problèmes 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 problème 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
Optimisation of an integrated transport and distribution system
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