Optimiser

The equations of beamtracer.optimization.search, declared on the code that implements them and checked by the tests.

optimize

functionsource

Minimize the problem's first objective with SciPy's differential evolution.

problem

$$\min_{\mathbf p \in [\mathbf l, \mathbf u]} f(\mathbf p) \quad \text{subject to} \quad g_i(\mathbf p) \le 0, \quad g_\mathrm{penalty}(\mathbf p) \le 0$$

seen

$$(f, g_1, \dots, g_m, g_\mathrm{penalty}) = \begin{cases} (f, g_1, \dots, g_m, 0) & \text{ok (a NaN } g_i \text{ read as } +\infty) \\ (+\infty, +\infty, \dots, +\infty, 1) & \text{failed or unconverged} \end{cases}$$

Assumes

• SciPy's differential evolution with Lampinen's constraint rules: a feasible design beats an infeasible one, two feasible ones compare by $f$, two infeasible ones by their violations
• one generation per batch (updating='deferred', vectorized=True), evaluated in a process pool; no gradient polish
• every evaluation recorded under the key of its normalised parameters, so a rerun with the same seed resumes from the record

References

• Storn and Price, J. Global Optim. 11, 341 (1997)
• Lampinen, Proc. CEC'02, vol. 2, 1468 (2002)

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