The second harmonic generation case-study as a gateway for es to quantum control problems

The Second Harmonic Generation (SHG), a process that turns out to be a good test case in the physics lab, can also be considered as a fairly simple theoretical test function for global optimization. Despite its symmetry properties, that will be derived here analytically, it seems to capture the complexity of the Fourier transform between the decision space to the evaluation space, and by that to challenge optimization routines. And indeed, counter-intuitively to some extent, locating its global maximum seems to be not an easy task for Evolutionary Algorithms (EAs). Although this research originates from the real-world applications domain, it aims to introduce a theoretical test case to Evolution Strategies (ES), being a possible theoretical gateway to the real-world physics regime of quantum control problems. After presenting some theoretical results, this paper introduces the study of the scalability of the decision space subject to optimization by specific variants of Derandomized ...

• Type: Conference
• Year: 2007
• Where: GECCO
• Authors: Ofer M. Shir, Thomas Bäck
• Keywords: Evolution Strategies, GECCO 2007, Second Harmonic Generation, Theoretical Test