there has been considerable interest in the identification of structural properties of combinatorial problems that lead;directly or indirectly, to the development of efficient algorithms for solving them. One such con...
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ISBN:
(纸本)9783642019289
there has been considerable interest in the identification of structural properties of combinatorial problems that lead;directly or indirectly, to the development of efficient algorithms for solving them. One such concept is that of a backdoor set-a set of variables such that once they are instantiated, the remaining problem simplifies to a tractable form. While backdoor sets were originally defined to capture structure in decision problems with discrete variables, here we introduce a notion of backdoors that;captures structure in optimization problems;which often have both discrete and continuous variables. We show that finding a feasible solution and proving optimality are characterized by backdoors of different kinds and size. Surprisingly;in certain mixed integerprogramming problems, proving optimality involves a smaller backdoor set, than finding the optimal solution. We also show extensive results on the number of backdoors of various sizes in optimization problems. Overall;this work demonstrates that backdoors;appropriately generalized;are also effective in capturing problem structure in optimization problems.
Millions of containers are stowed ever.), week with goods worth billions of dollars, but container vessel stowage is an all but neglected combinatorialoptimization problem. In this paper, we introduce a model for sto...
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ISBN:
(纸本)9783642042430
Millions of containers are stowed ever.), week with goods worth billions of dollars, but container vessel stowage is an all but neglected combinatorialoptimization problem. In this paper, we introduce a model for stowing containers in a vessel bay which is the result of probably the longest collaboration to date with a liner shipping company on automated stowage planning. We then show how to solve this model efficiently in - to our knowledge - the first;application of CP to stowage planning using state-of-the-art techniques such as extensive use of global constraints, viewpoints, static and dynamic symmetry breaking, decomposed branching strategies, and early failure detection. Our CP approach outperforms an integerprogramming and column generation approach in a preliminary study. Since a complete model of this problem includes even more logical constraints, we believe that stowage planning is a new application area, for CP with a high impact potential.
We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear optimization oracle. We provide a polynomial-time algorithm that determines an r-best solu...
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ISBN:
(纸本)9783642021572
We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear optimization oracle. We provide a polynomial-time algorithm that determines an r-best solution for nonlinear functions of the total weight of an independent set, where r is a constant depending on certain Frobenius numbers of the weights and is independent of the size of the ground set. In contrast, we show that finding an optimal (0-best) solution requires exponential time even in a very special case of the problem.
this paper presents a hybrid Constraint programming (CP) and Semidefinite programming (SDP) approach to the k-clustering minimum biclique completion problem on bipartite graphs. the problem consists in partitioning a ...
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Automatic review assignment can significantly improve the productivity of many people such as conference organizers, journal editors and grant administrators. Most previous works have set the problem up as using a pap...
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ISBN:
(纸本)9781605585123
Automatic review assignment can significantly improve the productivity of many people such as conference organizers, journal editors and grant administrators. Most previous works have set the problem up as using a paper as a query to independently "retrieve" a set of reviewers that should review the paper. A more appropriate formulation of the problem would be to simultaneously optimize the assignments of all the papers to an entire committee of reviewers under constraints such as the review quota. In this paper, we solve the problem of committee review assignment with multi-aspect expertise matching by casting it as an integer linear programming problem. the proposed algorithm can naturally accommodate any probabilistic or deterministic method for modeling multiple aspects to automate committee review assignments. Evaluation using an existing data set shows that the proposed algorithm is effective for committee review assignments based on multi-aspect expertise matching. Copyright 2009 ACM.
In analyzing the proteome using mass spectrometry, the mass values help identify the molecules, and the intensities help quantify them, relative to their abundance in other samples. Peptides that are shared across dif...
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ISBN:
(纸本)9783642020070
In analyzing the proteome using mass spectrometry, the mass values help identify the molecules, and the intensities help quantify them, relative to their abundance in other samples. Peptides that are shared across different protein sequences are typically discarded as being uninformative w.r.t each of the parent proteins. In this paper, we investigate the use of shared peptides which are ubiquitous (similar to 50% of peptides) in mass spectrometric data-sets. In many cases, shared peptides can help compute the relative amounts of different proteins that share the same peptide. Also, proteins with no unique peptide in the sample can still be analyzed for relative abundance. Our paper is the first attempt to use shared peptides in protein quantification, and makes use of combinatorialoptimization to reduce the error in relative abundance measurements. We describe the topological and numerical properties required for robust estimates, and use them to improve our estimates for ill-conditioned systems. Extensive simulations validate our approach even in the presence of experimental error. We apply our method to a model of Arabidopsis root knot nematode infection, and elucidate the differential role of many protein family members in mediating host response to the pathogen.
Given rational numbers C-0,...,C-m and b(0),...,b(m), the mixing set with arbitrary capacities is the mixed-integer set defined by conditions s + C(t)z(t) >= b(t), 0 = 0, z(t) integer, 0 <= t <= m. Such a set...
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ISBN:
(纸本)9783540688860
Given rational numbers C-0,...,C-m and b(0),...,b(m), the mixing set with arbitrary capacities is the mixed-integer set defined by conditions s + C(t)z(t) >= b(t), 0 <= t <= m, s >= 0, z(t) integer, 0 <= t <= m. Such a set has applications in lot-sizing problems. We study the special case of divisible capacities, i.e. C-t/Ct-1 is a positive integer for 1 < t <= m. Under this assumption, we give an extended formulation for the convex hull of the above set that uses a quadratic number of variables and constraints.
In this paper, we present a new integer Program (IP) for the Air Traffic Flow Management (ATFM) problem. the model we propose provides a complete representation of all the phases of each flights, i.e., the phase of ta...
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ISBN:
(纸本)9783540688860
In this paper, we present a new integer Program (IP) for the Air Traffic Flow Management (ATFM) problem. the model we propose provides a complete representation of all the phases of each flights, i.e., the phase of taking-off, of cruising and of landing;suggesting all the actions to be implemented to achieve the goal of safe, efficient, and expeditious aircraft movement. the distinctive feature of the model is that it allows rerouting decisions. these decisions are formulated by means of "local" conditions, which allow us to represent such decisions in a very compact way by only introducing new constraints. Moreover, to strengthen the polyhedral structure of the underlying relaxation, we also present three classes of valid inequalities. We report short computational times (less than 15 minutes) on instances of the size of the US air traffic control system that make it realistic that our approach can be used as the main engine of managing air traffic in the US.
We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytope...
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ISBN:
(纸本)9783540688860
We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and well-known integer polytopes - the cut, boolean quadric, multicut and clique partitioning polytopes - are shown to arise as projections of binary psd polytopes. Finally, we present various valid inequalities for binary psd polytopes, and show how they relate to inequalities known for the simpler polytopes mentioned. Along the way, we answer an open question in the literature on the max-cut problem, by showing that the so-called k-gonal inequalities define a polytope.
Orbital branching is a method for branching on variables in integerprogrammingthat reduces the likelihood of evaluating redundant, isomorphic nodes in the branch-and-bound procedure. In this work, the orbital branch...
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ISBN:
(纸本)9783540688860
Orbital branching is a method for branching on variables in integerprogrammingthat reduces the likelihood of evaluating redundant, isomorphic nodes in the branch-and-bound procedure. In this work, the orbital branching methodology is extended so that the branching disjunction can be based on an arbitrary constraint. Many important families of integer programs are structured such that small instances from the family are embedded in larger instances. this structural information can be exploited to define a group of strong constraints on which to base the orbital branching disjunction. the symmetric nature of the problems is further exploited by enumerating non-isomorphic solutions to instances of the small family and using these solutions to create a collection of typically easy-to-solve integer programs. the solution of each integer program in the collection is equivalent to solving the original large instance. the effectiveness of this methodology is demonstrated by computing the optimal incidence width of Steiner Triple Systems and minimum cardinality covering designs.
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