We introduce a stochastic optimization technique to obtain self-trapped beams in the generalized nonlinear Schrödinger equation. The method is based on combining a variational approach with a bio-inspired method: the cuckoo search algorithm that relies on Lévy flights. The proposed technique can be easily adapted to generate diverse self-trapped structures in a plethora of nonlinear media. Unlike the standard variational technique and some of the numerical algorithms previously reported, this algorithm allows for the optimization of different families of self-trapped beams concurrently.

• Received 3 April 2021
• Revised 5 July 2021
• Accepted 1 September 2021

DOI:https://doi.org/10.1103/PhysRevA.104.033524