Wednesday, April 21, 2021

Lagrangean Relaxation: The Sequel

In a previous post, I looked at a way to solve a multiple assignment problem (where multiple users can be assigned to each server and each user can be assigned to multiple servers) using Lagrangean relaxation (LR). I won't repeat the details of the problem, or why LR was of interest, here. The post included some computational experiments in R, using CPLEX to get the optimal solution (for confirmatory purposes) and then trying out various nonlinear optimization algorithms on the Lagrangean function.

I've been looking for an open-source, derivative-free nonlinear optimizer (capable of taking box constraints) in Java, and I came across a couple in the Apache Commons Mathematics Library. Wanting to test one of them out, I repeated the experiment with the assignment problem in Java, again using CPLEX to get the optimal solution, and using the BOBYQA algorithm for minimizing the Lagrangean. As is my habit, I've made my Java code available via a GitLab repository for anyone who might want to see it. The Apache Commons library is a bit funky when it comes to using the optimization classes, so I had to do a little trial and error (and considerable staring at the Javadocs), along with a web search for examples. Hopefully my code is simple enough to be easy to digest.

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