Photonic inverse design has emerged as an indispensable engineering tool for complex optical systems. In many instances it is important to optimize for both material and geometry configurations, which results in complex non-smooth search spaces with multiple local minima. Finding solutions approaching global optimum may present a computationally intractable task. Here, we develop a framework that allows expediting the search of solutions close to global optimum on complex optimization spaces. We study the way representative black box optimization algorithms work, including genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA), and mesh adaptive direct search (NOMAD). We then propose and utilize a two-step approach that identifies best performance algorithms on arbitrarily complex search spaces. We reveal a connection between the search space complexity and algorithm performance and find that PSO and NOMAD consistently deliver better performance for mixed integer problems encountered in photonic inverse design, particularly with the account of material combinations. Our results differ from a commonly anticipated advantage of GA. Our findings will foster more efficient design of photonic systems with optimal performance.
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