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The Gaussian process regression can be computed in scikit learn using an object of class GaussianProcessRegressor as:

 gp= GaussianProcessRegressor(alpha=1e-10, copy_X_train=True,
    kernel=1**2 + Matern(length_scale=2, nu=1.5) + WhiteKernel(noise_level=1),
    n_restarts_optimizer=0, normalize_y=False,
    optimizer='fmin_l_bfgs_b', random_state=None)

Here, we see that the L-BFGS-B algorithm has been used to optimize the hyperparameters. Is there any alternative (for example trust-region-reflective algorithm) to this algorithm available in sklearn?

EDIT: It provides some Constrained multivariate methods for optimization. Is there such functions available for other methods like trust-region-reflective algorithm and swarm intelligence (eg. Firefly algorithm)?

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Scikit-learn package has a limited selection of optimizers. The scipy package has many more optimitizers, including trust-region-reflective algorithm. You would have to use another third party package for Firefly algorithm.

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