Computational Combinatorial Optimization: Optimal or by Alexander Martin (auth.), Michael Jünger, Denis Naddef

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

This instructional includes written types of 7 lectures on Computational Combinatorial Optimization given via major participants of the optimization group. The lectures introduce sleek combinatorial optimization strategies, 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 options and the significance of modeling are generally mentioned. purposes to well-liked combinatorial optimization difficulties, e.g., in creation and shipping making plans, are taken care of in lots of locations; specifically, the e-book encompasses a cutting-edge account of the main profitable options for fixing the touring salesman challenge to optimality.

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W. H. Freeman and Company, 1983. 18. M. Clochard and D. Naddef. Using path inequalities in a branch-and-cut code for the symmetric traveling salesman problem. In Lawrence Wolsey and Giovanni Rinaldi, editors, Proceedings on the Third IPCO Conference, pages 291–311, 1993. 19. C. Cordier, H. Marchand, R. Laundy, and L. A. Wolsey. bc – opt: a branch-and-cut code for mixed integer programs. Mathematical Programming, 86:335 – 354, 1999. 20. H. Crowder, E. Johnson, and M. W. Padberg. Solving large-scale zero-one linear programming problems.

Sometimes going to an extended formulation is referred to as lifting. For instance, many problems defined on graphs that are usually formulated in terms of arc variables, can also be formulated in the higher dimensional space of arc- and node-variables; and we will see examples where this is advantageous. Typically, extended formulations are not unique, and it takes some insight to recognize those which offer some advantage. One possible advantage might be that the extended formulation gives rise to a polyhedron with desirable properties.

30. M. Gr¨ otschel, L. Lov´ asz, and A. Schrijver. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica, 1:169 – 197, 1981. 31. M. Gr¨ otschel, L. Lov´ asz, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization. Springer, 1988. 32. Z. Gu, G. L. Nemhauser, and M. W. P. Savelsbergh. Cover inequalities for 0 − 1 linear programs: complexity. INFORMS Journal on Computing, 11:117 – 123, 1998. 33. Z. Gu, G. L. Nemhauser, and M. W. P. Savelsbergh. Cover inequalities for 0 − 1 linear programs: computation.

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