Originally posted by: SystemAdmin

[pmarley2 said:]

Hi all,

Does anyone know if there are any academic references that look at how CPLEX works? Specifically, I am looking at the mixed integer optimizer, and I would like to know how it finds the solution to a given nonlinear function/constraint program.

Thanks for your help,
Piku
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Originally posted by: SystemAdmin

[aroso said:]

Hi Piku,

There are several academic papers produced from people within the ILOG organization that propose new methods for solving a wide range of problems, that are later incorporated into newer versions of CPLEX (e.g., the RINS and Polishing methods). I have never read anything about how CPLEX deals with nonlinear functions/constraints, but I'm sure that, if they exist, you can find them in any major repository.

Antonio
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Originally posted by: SystemAdmin

[pmarley2 said:]

Hi Antonio

I have checked out a couple of repositories including Google Scholar, but I haven't been able to find any academic paper that discusses the methodology behind CPLEX's mixed integer optimizer.

If you do know of anything related to this I'd be grateful to know.

Thanks
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Originally posted by: SystemAdmin

[jgregory said:]

The CPLEX User's Manual is intended to give insights into how the branch and cut algorithm works, from the perspective of helping users understand the ways to control various aspects of that algorithm.  Have a look in the Discrete Optimization chapter, in particular the section titled "Tuning performance features of the mixed integer optimizer". 

The only nonlinearity that CPLEX explicitly supports is convex quadratic, either in the objective function or in constraints or both.  Apart from the algorithms that handle the continuous subproblems (LP, QP, or QCP), the way that the mixed-integer problem is solved is more or less unaffected when quadratics are involved.

Because CPLEX is a proprietary commercial product, publication in academic journals is not a primary goal. Howver several years ago, the team published a paper that I like to recommend, “MIP: Theory and practice -- closing the gap".  You can find a copy at http://www.ilog.com/products/optimization/tech/research/mip.pdf .  The principles found there still apply.

Other papers about ILOG products, including CPLEX, may be found listed at http://www.ilog.com/products/optimization/info/randlit.cfm .
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Originally posted by: SystemAdmin

[pmarley2 said:]

Hi jgregory,

Thanks, that helps a lot. I see the section you're referring to and I'll review it now.

The links to the papers helped as well.
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