# Questions tagged [mixed-integer-programming]

For questions about mathematical optimization problems involving both continuous and binary or general integer variables.

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### “Best practices” for formulating MIPs

Often there are many alternatives ways for formulating a MIP. For example: The model contains inequality constraints that must hold with equality in an optimal solution. The model contains ...
681 views

### Read an LP/MPS file in the PuLP

I was trying to read a MPS file by using the PuLP package in the Python, but I can't find any related documents on it. Does ...
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### Heuristics for mixed integer linear and nonlinear programs

What are some primal heuristics that mixed-integer linear and nonlinear program solvers use to quickly obtain a reasonably good feasible solution?
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### Has the expressibility of 'non-integrality testing' as extension to MILP been studied before?

It turns out that extending MILP with any of the constraints $y=\lfloor x\rfloor$, $y=\lceil x\rceil$, $0 < x$, or $x\notin \mathbb{Z}$ is 'equally hard'. (see my answer here, and below) ...
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### Solving MIP in Java with free software

I would like to solve mixed integer programs in Java. I need an approach that relies purely on software that is free (not only for academic use, but also for people outside academia). What would be ...
213 views

### 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 ...
212 views

### Applicability of Lagrange Multipliers in the analysis of large-scale MILPs?

Qualitatively, in my experience in the solving of large scale MILPs, it is common that binary variables corresponding to "edge possibility" components are frequently chosen. Intuitively, these seem ...
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### What is the impact of making flow fractional rather than integer?

When creating a network flow formulation you can set up sinks with integer flow requirement $\ge 1$. This yields solutions with the total amount of flow along an edge. I have also seen this as a ...
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### Cellular Automata and MIP Resource Repository? [closed]

Apologies if this is not an appropriate question for the SE, however, considering that it is in beta testing it might be worthwhile. Note that "Cellular Automata" is not yet a tag, so perhaps there is ...
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### Application of complex numbers in Linear Programming?

The theory surrounding Linear Programming is based on variables, bounds and coefficients that take on values in $\mathbb R$, the set of real numbers. I have long wondered whether there might be ...