(This is a post that I started a long time ago (Aug 10, 2010), but hung on to because it is only half-baked. But based on the philosophy that avoiding foolishness is a recipe for silence, I’m sending it out into the world. Coming next: the simplest useful open problem in DCP optimization.)

Acronyms are like candy in Global Health, and Operations Research is full of them, too. This post is a place for me to collect information about software available for solving the Mixed Integer Programming (MIP) problem that the Disease Control Priorities (DCP) project is going to put together.

DCP is a massive effort to quantify the cost-effectiveness of hundreds of health interventions across tens of “health platforms” (big hospitals, small clinics, pharmacies, etc). The output of this large, coordinated effort will be (as far as I’m concerned) a collection of giant matrices, that say, for different subsets of interventions across different platforms, (1) the cost of setting up the interventions, (2) the cost of operating the interventions, (3) the health gain from the interventions. Undoubtedly, there will be some quantification of the uncertainty in each of these quantities. Also, there is something called platform improvement, which can be thought of as a special type of intervention that makes a bunch of other interventions more effective on a certain platform. And there are a number of side-constraints; some interventions come together on certain platforms, some interventions are mutually exclusive, etc.

Some unknowns: (how) will the uncertainty in the entries of these matrices be quantified? Are the intervention choices all “yes/no” or do you choose how much you want of some of them, i.e a non-negative continuous variable?

This is the optimization that mixed integer programming was born for (except for the uncertainty, which takes us into less charted waters). So how we are going to do it, in theory, is just the sort of thing my OR classes focused on when I was in grad school. We didn’t talk much about how to do it in practice. Some of the hard-working students who sat in the business school and actually solved large integer programs would mutter about CPLEX once in a while at parties, but I didn’t pay it much heed.

Heed I must now pay. So I am collecting up the available MIP solvers here, and (eventually) evaluating them for my DCP optimization task. Got suggestions? I would love to hear them.

- Gurobi – 1 2 3
- ILOG/CPLEX – 1 2
- GAMS – 1
- AMPL – 1
- NEOS – 1

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There’s an open source mip solver Cbc from COIN-OR that might get you started and prototyping, and might be good enough altogether (the docs could use a bit of work but it does the job).

There are standard formats like MPS that most solvers understand so you could start with COIN, dump out problems in a standard format, and use those to benchmark/evaluate commercial ones if you need more speed.

Gurobi is pretty fast, but has a few missing features like SOCP/QCQP which you could conceivably want to do uncertainty modelling. Maybe you can get their academic licensing? They also license by the day on amazon instances I think.

There’s a text book “convex optimization” by Boyd and Vanderberghe which you can get free online that might be helpful with formulating robust models with some types of uncertainty. Video lectures to go with it are on academic earth I think. Doesn’t cover simplex method and MIP though.

Technically speaking, GAMS and AMPL are not solvers. They are modeling languages that call a solver to solve the model (they have links to many different solvers, including Gurobi and CPLEX). I’d also add the XPRESS solver to your list. It’s now owned by FICO. Here’s the link:

http://www.fico.com/en/Products/DMTools/Pages/FICO-Xpress-Optimization-Suite.aspx

Thanks both! For those of you wondering about the additional acronyms which were dropped in the first comment:

SOCP – Second-order Cone Programming

QCQP – Quadratically constrained quadratic programming

You may also consider SCIP.

http://scip.zib.de/

Thanks for this link. It has a strange license, but otherwise looks great.