Simple lifted cover inequalities and hard knapsack problems
نویسندگان
چکیده
منابع مشابه
Simple lifted cover inequalities and hard knapsack problems
We consider a class of random knapsack instances described by Chvátal, who showed that with probability going to 1, such instances require an exponential number of branch-and-bound nodes. We show that even with the use of simple lifted cover inequalities, an exponential number of nodes is required with probability going to 1. It is not surprising that there exist integer programming (IP) instan...
متن کاملLocal and global lifted cover inequalities for the 0-1 multidimensional knapsack problem
The 0-1 Multidimensional Knapsack Problem (0-1 MKP) is a wellknown (and strongly NP-hard) combinatorial optimization problem with many applications. Up to now, the majority of upper bounding techniques for the 0-1 MKP have been based on Lagrangian or surrogate relaxation. We show that good upper bounds can be obtained by a cutting plane method based on lifted cover inequalities (LCIs). As well ...
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We investigate several complexity issues related to branch and cut algorithms for integer programming based on lifted cover inequalities LCIs We show that given a fractional point determining a violated LCI over all minimal covers is NP hard The main result is that there exists a class of knapsack instances for which any branch and cut algorithm based on LCIs has to evaluate an exponential numb...
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We investigate the algorithmic and implementation issues related to the e ective and e cient use of lifted cover inequalities and lifted GUB cover inequalities in a branch and cut algorithm for integer programming We have tried various strategies on several test problems and we identify the best ones for use in practice
متن کاملThe Complexity of Lifted Inequalities for the Knapsack Problem
Hartvigsen, D. and E. Zemel, The complexity of lifted inequalities for the knapsack problem, Discrete Applied Mathematics 39 (1992) 11. 123. It is well known that one can obtain facets and valid inequalities for the knapsack polytope by lifting simple inequalities associated with minimal covers. We study the complexity of lifting. We show that recognizing integral lifted facets or valid inequal...
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ژورنال
عنوان ژورنال: Discrete Optimization
سال: 2005
ISSN: 1572-5286
DOI: 10.1016/j.disopt.2005.06.003