Algorithms for highly symmetric linear and integer programs
نویسندگان
چکیده
منابع مشابه
Branch and Bound Algorithms for Highly Constrained Integer Programs
In this paper we describe a new branch and bound algorithm for solving 0-1 integer linear programs (ILP). The algorithm is specifically targeted at ILP instances that are highly constrained, i.e. instances for which the constraints are hard to satisfy. Our approach is based on recent algorithms for solving instances of Propositional Satisfiability (SAT) which are also highly constrained. In par...
متن کاملApproximation Algorithms Based on Lp Relaxation 1 Linear Programs and Linear Integer Programs
There are two fundamental approximation algorithm design techniques based on linear programming: (a) LP-relaxation and rounding, and (b) the primal-dual method. In this lecture note, we will discuss the former. The idea of LP-relaxation and rounding is quite simple. We first formulate an optimization problem as an integer program (IP), which is like a linear program (LP) with integer variables....
متن کاملApproximation algorithms for covering/packing integer programs
Given matrices A and B and vectors a, b, c and d, all with non-negative entries, we consider the problem of computing min{cx : x ∈ Z+, Ax ≥ a, Bx ≤ b, x ≤ d}. We give a bicriteria-approximation algorithm that, given ε ∈ (0, 1], finds a solution of cost O(ln(m)/ε) times optimal, meeting the covering constraints (Ax ≥ a) and multiplicity constraints (x ≤ d), and satisfying Bx ≤ (1 + ε)b + β, wher...
متن کاملTerse Integer Linear Programs for Boolean Optimization
We present a new polyhedral approach to nonlinear Boolean optimization. Compared to other methods, it produces much smaller integer programming models, making it more efficient from a practical point of view. We mainly obtain this by two different ideas: first, we do not require the objective function to be in any normal form. The transformation into a normal form usually leads to the introduct...
متن کاملInequalities for Mixed Integer Linear Programs
This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2011
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-011-0487-6