Papers by Nicos Christofides
Journal of Global Optimization, 2006
In this paper a Branch-and-Bound (BB) algorithm is developed to obtain an optimal solution to the... more In this paper a Branch-and-Bound (BB) algorithm is developed to obtain an optimal solution to the single source uncapacitated minimum cost Network Flow Problem (NFP) with general concave costs. Concave NFPs are NP-Hard, even for the simplest version therefore, there is a scarcity of exact methods to address them in their full generality. The BB algorithm presented here can be used to solve optimally single source uncapacitated minimum cost NFPs with any kind of concave arc costs. The bounding is based on the computation of lower bounds derived from state space relaxations of a dynamic programming formulation. The relaxations, which are the subject of the paper (Fontes et al., 2005b) and also briefly discussed here, involve the use of non-injective mapping functions, which guarantee a reduction on the cardinality of the state space. Branching is performed by either fixing an arc as part of the final solution or by removing it from the final solution. Computational results are reported and compared to available alternative methods for addressing the same type of problems. It could be concluded that our BB algorithm has better performance and the results have also shown evidence that it has a sub-exponential time growth.
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European Journal of Operational Research, 2006
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Networks, 2003
... Dalila BMM Fontes Faculdade de Economia da Universidade do Porto, Rua Dr. Roberto Frias, 4200... more ... Dalila BMM Fontes Faculdade de Economia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal ... Computational results on dif-ferent classes of test problems indicate the effective-ness of the proposed method in generating basic feasi-ble solutions for ...
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Journal of Global Optimization, 2006
In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are der... more In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go
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Studies in Computational Finance, 2000
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We propose a new corporate bond portfolio management based on a multi-factor hedging. Our risk fa... more We propose a new corporate bond portfolio management based on a multi-factor hedging. Our risk factors are the parameters of the popular Nelson-Siegel-Svensson exponential forward rate models. The multi-factor hedging goes beyond duration and convexity hedging, capturing level, slope and curvature factors. We also propose quasi-Newton methods to solve the non- linear optimization problem encountered in the Nelson-Siegel-Svensson exponential forward
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SIAM Journal on Applied Mathematics, 1976
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SIAM Journal on Applied Mathematics, 1970
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Mathematical Programming, 1974
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Journal of the London Mathematical Society, 1985
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Journal of Combinatorial Theory, Series B, 1981
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Discrete Applied Mathematics, 1987
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Mathematical Programming Studies, 1986
The problem examined in this paper is as follows: Given a feasible optimum basic solution (f.o.b.... more The problem examined in this paper is as follows: Given a feasible optimum basic solution (f.o.b.s) of the minimum cost network flow problem, find all the f.o.b.s of this problem. The existence of alternative f.o.b.s is characterized by means of elementary circuits of zero cost and length greater than two in the incremental graph associated to the given f.o.b.s. It
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Journal of Global Optimization, 2006
In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are der... more In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go
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... RECHERCHE OPÉRATIONNELLE. RECHERCHE OPÉRATIONNELLE NICOS CHRISTOFIDES The vehicle routing pro... more ... RECHERCHE OPÉRATIONNELLE. RECHERCHE OPÉRATIONNELLE NICOS CHRISTOFIDES The vehicle routing problem Revue française d'automatique, d'informatique et de rechercheopérationnelle. Recherche opérationnelle, tome 10, no V1 (1976), p. 55-70. ...
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European Journal of Operational Research, Jun 30, 1987
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Siamam, 1976
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... Graph theory: An algorithmic approach. Post a Comment. CONTRIBUTORS: Author: Christofides, Ni... more ... Graph theory: An algorithmic approach. Post a Comment. CONTRIBUTORS: Author: Christofides, Nicos. PUBLISHER: ... VOLUME/EDITION: PAGES (INTRO/BODY): xv, 400 p. SUBJECT(S): Graph theory; Data processing. DISCIPLINE: No discipline assigned. ...
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... of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents... more ... of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents a 50% reduction over the value 2 which was the previously best known such ratio for the performance of other polynomial-growth algorithms for the TSP.*COMBINATORIAL ANALYSIS. ...
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Papers by Nicos Christofides