Questions tagged [lp-relaxation]
For questions relating to the relaxation of linear integer or mixed-integer-linear programming (MILP) problems where the integer constraints are removed.
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Modeling of a special form of the precedence constraint
There exists a scheduling problem in which some tasks should be processed on some resources. Additionally, each task needs to be assigned to a specific position on each resource. Let the decision ...
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How do we branch a Cutting Stock problem using Branch and Price?
I'm sure this is a straightforward question, but since I started learning integer programming recently this isn't clear to me.
Consider solving a 1 dimensional cutting stock problem using delayed ...
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Big M and convergence of LP to IP
I have been working on an applied problem with Big M constraints (due to several security issues in the company, I cannot write the formulation I am working on).
While solving with a partially LP-...
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Totally unimodular towards linear programming relaxation
I'm currently studying about totally unimodular.
I was reading this link: https://ostad.nit.ac.ir/upload/Integer_Programming_1.pdf, from page 38-41 and I came across the statement:
'It is clear that ...
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How to transform this BIP into LP with the help of penalty function?
I have an BIP problem as below
$$\underset{\bf b}{\max}{\bf u}^T\bf b$$
$$\text{subject to}$$
$${\bf Ab}\le1$$
Here, ${\bf b}=\{b_1,b_2,\cdots,b_N\}$ is a column vector of decision/optimization ...
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I ran a relaxed MIP and got some integer results; how can I constrain MIP to match those integers?
Suppose I run a relaxation of an MIP. If my result is all integers, I have achieved the same min/max that the MIP would achieve. However, what can I say if some portion of my result is integer?
If ...
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KKT conditions analysis for binary constraints
I am wondering if boolean constraints in a linear program can be solved (after linear relaxation from $x\in\{0,1\}$ to both $x\ge0$ and $x\le1$) using KKT analysis.
Most of the algorithms that I have ...
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Linear Relaxation of Boolean Constraint for Solving Integer Linear Program Using KKT
I am trying to convert a boolean LP to LP using LP relaxation by converting $x \in {0,1}$ to both $x \ge 0$ and $x \le 1$.
Then to use it in my problem analysis, I am trying to build the KKT ...
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Is there any academic reference which suggests/uses dual values as initialization of Lagrangian multipliers?
The Lagrangian relaxation approach is used to generate lower (upper) bounds for minimization (maximization) problems by moving some constraints to the objective function and multiplying them by "...
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Obtaining linear relaxation objective value from MILP model coded in Pyomo
I would like to seek some advice on modeling the following:
I am currently using Pyomo to generate my MILP model in Pyomo. It seems that it is not possible to cast the integer and binary variables to ...
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Specific algorithms to compute the LP-relaxation of the Set-Cover problem
One of the most commonly known combinatorial problems is the set cover problem, which states that given a collection of sets $S = \{s_1, \dots, s_m\}$ and a universe of elements $U = \bigcup_{i=1}^m ...
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What is a general procedure to prove that the LP relaxation of an IP delivers the optimal IP solution?
Say that I have a binary IP
$$z=\max_x \{c^\top x: Ax=b, x\in B^n\}$$
where $B^n$ is the set of $n$-dimensional $0-1$ vectors.
Its LP relaxation will be
$$z^{LP}=\max_x \{c^\top x: Ax=b, 0\leq x\leq 1\...
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What is the difference between root relaxation and LP relaxation
(I apologize. I saw this question but, I do not know these may be the same or not.)
I am trying to solve a MIP problem and have an issue about that. The problem's LP relaxation has the objective ...
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Problem related to machine's performance while solving an LP-relaxation of a set-covering problem using the Column Generation
PS: I am familiar with performance variability encountered while solving large-scale MIPs. My question may not be explicitly related to it but maybe to the inefficiency of python packages.
I have ...
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Cplex 12.10: How can I solve an LP relaxation?
I have an IloCplex object which contains a MILP.
Is there a way to obtain the objective value of its LP relaxation, without having to rewrite the entire model as ...
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What to do with cuts (constraints) when a fixation is contrary to a RHS in a ILP / LP relaxation?
I am trying to understand an algorithm in a paper by Crévits et al. (2012)1 (see algorithm 2, the cuts I'm referring to are from the reduced costs). It uses a series of successive cuts on a linear ...
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Is This Constraint Convex?
I have a constraint that I believe to be convex and not affine which I think means that I can implement a relaxation. I will first define the full constraint, and then build up my (informal) reasoning ...
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How to compare two different formulations of a problem?
I somewhat know how to compare two MILP formulations of a problem that both use the same set of decision variables (as in the classical MTZ vs DFJ formulations of the TSP). I was wondering how two ...
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Symmetric undirected $p$-median instance with fractional LP solution?
The $p$-median problem is NP-hard, so its LP relaxation does not naturally have all-integer solutions. However, it very often does; in fact, it can be hard to find an instance for which the LP ...
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Efficiency of solving LP relaxation
I'm building a mixed-integer programming model, and the solver is experiencing a very long run time. So I tried to solve the LP relaxation to the MIP, and I get a similarly long solve time, which ...
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