Get Computational Combinatorial Optimization: Optimal or PDF

By Alexander Martin (auth.), Michael Jünger, Denis Naddef (eds.)

ISBN-10: 3540428771

ISBN-13: 9783540428770

This educational comprises written types of 7 lectures on Computational Combinatorial Optimization given through prime individuals of the optimization group. The lectures introduce glossy combinatorial optimization innovations, with an emphasis on department and reduce algorithms and Lagrangian leisure techniques. Polyhedral combinatorics because the mathematical spine of profitable algorithms are coated from many views, specifically, polyhedral projection and lifting recommendations and the significance of modeling are largely mentioned. purposes to admired combinatorial optimization difficulties, e.g., in construction and shipping making plans, are taken care of in lots of areas; particularly, the ebook incorporates a cutting-edge account of the main profitable options for fixing the touring salesman challenge to optimality.

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28. R. E. Gomory. An algorithm for integer solutions to linear programming. In R. L. Graves and P. Wolfe, editors, Recent Advances in Mathematical Programming, pages 269 – 302, New York, 1969. McGraw-Hill. 29. J. Gondzio. Presolve analysis of linear programs prior to apply an interior point method. INFORMS Journal on Computing, 9:73 – 91, 1997. 30. M. Gr¨ otschel, L. Lov´ asz, and A. Schrijver. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica, 1:169 – 197, 1981.

If, on the other hand, we use the so called “strong” formulation of the uncapacitated plant location problem, namely min (cj xj : j ∈ N ) (uij : j ∈ Ni ) ≥ 1 i ∈ M −uij + xj ≥ 0 i ∈ M, j ∈ N ; uij ≥ 0, xj ∈ {0, 1}, i ∈ M, j ∈ N ; then the projected inequalities include (xj : j ∈ Ni ) ≥ 1, xj ≥ 0 i ∈ M; j∈N thus yielding the same LP relaxation as that of (SC). Nonlinear 0-1 Programming. Consider the nonlinear inequality aj ( π xi ) ≤ b, aj > 0, j ∈ N j∈N i∈Qj xi ∈ {0, 1}, i ∈ Qj , j ∈ N where π denotes product.

Lifting (sequential or simultaneous) has also been applied to general mixed integer programs, see, for instance, [34,48] or in connection with lift-and-project cuts, see [7,5] and [−→ Balas]. Computational results about the success of knapsack inequalities with or without GUB constraints are given, for instance, in [20,11,19,33,49]. The papers consistently show that knapsack cuts are crucial for the solution of integer programs that contain knapsack problems as a substructure. Of course, knapsack relaxations are not the only ones considered in mixed integer programming solvers.

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Computational Combinatorial Optimization: Optimal or Provably Near-Optimal Solutions by Alexander Martin (auth.), Michael Jünger, Denis Naddef (eds.)

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