Physics problems requiring optimization? I would like to know if there are simple benchmark physics problems to test a Genetic Algorithm C++ library I developed. The library supports single and multi-objective constrained optimization and I would like to publish the code showing its performance in the optimization of some physics examples.
 A: One example of a physics problem which is ultimately an optimization problem is that of determining the ground state for a spin glass.  The simplest model of a spin glass is an Ising model with random bonds between all of the sites.  That is the hamiltonian is defined as
$$ H = - \sum_{i<j} J_{ij} s_i s_j - \sum_{i} h_i s_i $$
Here $s_i$ denotes the spin on each lattice site, $J_{ij}$ the strengths of the interactions between sites, $h_i$ is an external magnetic field.  Typically, the spins are said to only take two values $\{ 1, -1 \}$, and their interactions might be limited to only occur between nearest neighbors.  The problem is to determine the particular set of plus and minus ones that minimizes this hamiltonian.  With various choices for what the $h$s or $J$s are allowed to be, you can actually make this problem equivalent to many other known problems in computer science, and has been shown to be NP-hard in general. For more information see: Ising formulations of many NP problems, Andrew Lucas arXiv/1302.5843. 
In fact, finding solutions to this problem was in the news recently, you may remember D-Wave.  D-Wave claimed to have built a quantum annealing computer that could efficiently solve a restricted version of this problem.  For instance see one of their papers on the particular problem they studied.
This caused some controversy, with people like Scott Aaronson initially showing a great deal of skepticism, and Nature being less pessimistic.  As a result, people started collecting benchmarks for classical algorithms to vet some of the numbers coming out of D-Wave.
In particular, Alex Selby has a nice rundown, as well as github repository of a canonical set of problems and the timing results for a couple canonical classical algorithms as well as D-Wave.  The classical algorithms outperform the D-Wave results.
You could test your optimization routines against those benchmarks.
