In this paper we study a generalization of the classical feasibility problem in integer linear programming, where an ILP needs to have a prescribed number of solutions to be considered solved. We first provide a gener...
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the paper deals with low-power adaptive scheduling of synchronous and flexible real-time OS tasks. A software reconfiguration scenario is assumed to be any run-time operation allowing the addition-removal-update of OS...
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the paper deals with low-power adaptive scheduling of synchronous and flexible real-time OS tasks. A software reconfiguration scenario is assumed to be any run-time operation allowing the addition-removal-update of OS tasks to adapt the system to its environment under well-defined conditions. the problem is that any reconfiguration can push the system to an unfeasible behavior where temporal properties are violated or the energy consumption is possibly high and unacceptable. A task in the system can change its characteristics at any time when a reconfiguration scenario is applied, it can also be stopped or replaced by another one. the difficulty is how to find the new temporal parameters of the systems tasks after any reconfiguration. We use a DVS processor which is with a variable speed to support run-time solutions that re-obtain the system's feasibility. the challenge is how to compute the best combinations between available processor speeds for a good compromise between execution time and energy consumption. We propose a combinatorialoptimization method based on integerprogramming and heuristics. We propose also a solution when the available speeds do not allow the feasibility of the system. Both approaches include a mechanism to adjust the deadlines of tasks to satisfy the feasibility conditions and overcome the problem of rejected tasks. this mechanism makes the scheduling more flexible and able to react in accordance with its environment.
In optimization problems such as integer programs or their relaxations, one encounters feasible regions of the form {x ∈ +n : Rx ∈ S} where R is a general real matrix and S ⊂ q is a specific closed set with 0 ∉ S. F...
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We consider a problem arising in the context of industrial production planning, namely the multi-product discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. We aim at developping an ex...
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ISBN:
(纸本)9782960053241
We consider a problem arising in the context of industrial production planning, namely the multi-product discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. We aim at developping an exact solution approach based on a standard Branch & Bound procedure for this combinatorialoptimization problem. To achieve this, we propose a new family of multi-product valid inequalities which enables us to better take into account in the mixed integer linear programming formulation the conflicts between different products simultaneously requiring production on the resource. We then present both an exact and a heuristic separation algorithm in order to identify the most violated valid inequalities to be added in the initial MILP formulation within a cutting-plane generation algorithm. We finally discuss preliminary computational results which confirm the practical usefulness of the proposed valid inequalities at strengthening the MILP formulation and at reducing the overall computation time.
the proceedings contain 34 papers. the topics discussed include: solving LP relaxations of large-scale precedence constrained problems;computing minimum multiway cuts in hypergraphs from hypertree packings;eigenvalue ...
ISBN:
(纸本)3642130356
the proceedings contain 34 papers. the topics discussed include: solving LP relaxations of large-scale precedence constrained problems;computing minimum multiway cuts in hypergraphs from hypertree packings;eigenvalue techniques for convex objective, nonconvex optimization problems;restricted b-matchings in degree-bounded graphs;zero-coefficient cuts;prize-collecting steiner network problems;on lifting integer variables in minimal inequalities;efficient edge splitting-off algorithms maintaining all-pairs edge-connectivities;on generalizations of network design problems with degree bounds;a polyhedral study of the mixed integer cut;symmetry matters for the sizes of extended formulations;a 3-approximation for facility location with uniform capacities;and approximability of 3- and 4-hop bounded disjoint paths problems.
Mixed polynomial matrices are polynomial matrices with two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. the comp...
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ISBN:
(纸本)9783642208072
Mixed polynomial matrices are polynomial matrices with two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. the computation of their maximum degrees of minors is known to be reducible to valuated independent assignment problems, which can be solved by polynomial numbers of additions, subtractions, and multiplications of rational functions. However, these arithmetic operations on rational functions are much more expensive than those on constants. In this paper, we present a new algorithm of combinatorial relaxation type. the algorithm finds a combinatorial estimate of the maximum degree by solving a weighted bipartite matching problem, and checks if the estimate is equal to the true value by solving independent matching problems. the algorithm mainly relies on fast combinatorial algorithms and performs numerical computation only when necessary. In addition, it requires no arithmetic operations on rational functions. As a byproduct, this method yields a new algorithm for solving a linear valuated independent assignment problem.
We model maximum cross-free matchings and minimum biclique covers of two-directional orthogonal ray graphs (2-dorgs) as maximum independent sets and minimum hitting sets of an associated family of rectangles in the pl...
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ISBN:
(纸本)9783642208072
We model maximum cross-free matchings and minimum biclique covers of two-directional orthogonal ray graphs (2-dorgs) as maximum independent sets and minimum hitting sets of an associated family of rectangles in the plane, respectively. We then compute the corresponding maximum independent set using linear programming and uncrossing techniques. this procedure motivates an efficient combinatorial algorithm to find a cross-free matching and a biclique cover of the same cardinality, proving the corresponding min-max relation. We connect this min-max relation withthework ofGyori [19], Lubiw[23], and Frank and Jordan [16] on seemingly unrelated problems. Our result can be seen as a non-trivial application of Frank and Jord ' an's theorem. As a direct consequence, we obtain the first polynomial algorithm for the jump number problem on 2-dorgs. For the subclass of convex graphs, our approach is a vast improvement over previous algorithms. Additionally, we prove that the weighted maximum cross-free matching problem is NP-complete for 2-dorgs and give polynomial algorithms for some subclasses.
We present an exact rational solver for mixed-integer linear programmingthat avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. this allows the solver to be used ...
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ISBN:
(纸本)9783642208072
We present an exact rational solver for mixed-integer linear programmingthat avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. this allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. the software is incorporated into the SCIP optimization framework, using the exact LP solver QSOPT-EX and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann collections.
the proceedings contain 33 papers. the topics discussed include: an excluded minor characterization of seymour graphs;complexity analyses of bienstock-zuckerberg and lasserre relaxations on the matching and stable set...
ISBN:
(纸本)9783642208065
the proceedings contain 33 papers. the topics discussed include: an excluded minor characterization of seymour graphs;complexity analyses of bienstock-zuckerberg and lasserre relaxations on the matching and stable set polytopes;a probabilistic analysis of the strength of the split and triangle closures;partial convexification of general MIPs by Dantzig-Wolfe reformulation;lift-and-project cuts for mixed integer convex programs;TSP on cubic and subcubic graphs;approximability of capacitated network design;facility location with client latencies: linear programming based techniques for minimum latency problems;an exact rational mixed-integerprogramming solver;valid inequalities for the pooling problem with binary variables;design and verify: a new scheme for generating cutting-planes;and contact center scheduling with strict resource requirements.
A new exact approach to the stable set problem is presented, which attempts to avoids the pitfalls of existing approaches based on linear and semidefinite programming. the method begins by constructing an ellipsoid th...
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ISBN:
(纸本)9783642208072
A new exact approach to the stable set problem is presented, which attempts to avoids the pitfalls of existing approaches based on linear and semidefinite programming. the method begins by constructing an ellipsoid that contains the stable set polytope and has the property that the upper bound obtained by optimising over it is equal to the Lovasz theta number. this ellipsoid is then used to derive cutting planes, which can be used within a linear programming-based branch-and-cut algorithm. Preliminary computational results indicate that the cutting planes are strong and easy to generate.
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