Shapley-guided global optimization algorithm with applications in integrated photonics inverse design

This study introduces an optimization algorithm, Shapley-Guided Stochastic Optimization (SGSO), which incorporates Shapley values to steer the search towards optimal solutions. The algorithm was tested on some well-known global optimization benchmark functions, like the Easom and Ackley functions, to validate its efficiency before applying it to more complex real-world scenarios, like the inverse design of photonic structures, specifically a 3dB splitter, a grating coupler, and a multilayer broadband mirror. The SGSO algorithm demonstrated its capability to direct the search process to generate highly performing designs while maintaining computational efficiency. Additionally, we propose a simplified approach for computing the Shapley values that can lower the algorithm's computational cost while still achieving satisfactory convergence to the global optimum. The results were benchmarked against Basin Hopping, one of the established metaheuristic optimization techniques, highlighting the potential of SGSO in navigating complex optimization landscapes. The SGSO is linked to Basin Hopping through the shared local optimization step and also shares connections with Genetic Algorithms, particularly in the crossover process between the different obtained solutions.