###### Abstract
The aims of the evolutionary-inspired FSS algorithm include the minimization of time required to find the suboptimal solution and the elimination of the premature convergence problem, inherent to many population-based algorithms. FSS is a relatively lightweight algorithm, compared to other swarm intelligence algorithms. However, the results produced by evolutionary computation can be less accurate compared to the results that can be obtained from classical optimization methods; and classical optimization methods have a higher chance to converge to a locally optimal solution. Due to the fact that population-based algorithms process a variety of solutions at a time, by starting from different points in the search space of a given fitness function, there is a higher chance for such algorithms to converge closer to a globally optimal solution, especially when the search space is multimodal. Hence, in global optimization tasks, when high solution accuracy matters, it is reasonable to take the best from both worlds, by first applying a global search metaheuristic and then using a local search method to converge to the closest optimum. The hybridization idea of evolutionary-inspired algorithms and classical optimization methods is not new. A similar approach was proposed by [PERSON] et al. in 2006 for accurate inverse permittivity measurement of arbitrarily shaped materials [25]. In the proposed hybrid approach, the best solution obtained by a genetic algorithm was used as a starting point for gradient descent. The results demonstrate that the hybrid algorithm requires fewer iterations to obtain a similar accuracy, compared to the original genetic and gradient descent algorithms used separately, applied to the calculations of complex permittivity of materials. Using a similar strategy, [PERSON] et al. in [26] achieved better accuracy and faster convergence speed when training a qubit neural network. Another similar hybrid algorithm was proposed by [PERSON] et al. in [27], which involved post-hybridization of the enhanced bat algorithm with gradient-based local search. The algorithm proved its superiority over other bat algorithms in dealing with multidimensional test functions for optimization. [PERSON] and [PERSON] proposed the use of the population-based particle swarm optimization algorithm with a classical Quasi-Newton local search method [28]. In the proposed technique, the best solution obtained by swarm intelligence was used as a starting point for the Broyden-Fletcher-Goldfarb-Shanno optimization method. This paper extends the research presented earlier by [PERSON] and [PERSON] (2018), where we proposed a hybrid algorithm based on FSS and classical optimization methods, such as the [PERSON]'s method in optimization and gradient ascent. In this paper, we provide additional benchmarks on test functions for optimization and the results of the non-parametric statistical hypothesis Wilcoxon signed-rank test, to demonstrate the effectiveness of the proposed techniques. The test was used to determine if significant statistical differences exist among the original algorithm and the considered hybrids. We also describe the applications of the most effective hybrid algorithm, including loss function optimization during neural network training, and hyperparameter optimization of neural networks. Evolutionary-inspired algorithms can be easily distributed across multiple computational nodes using various distribution strategies ([PERSON] and [PERSON], 2018), such as master-slave model or island model. We provide the solution of the hyperparameter optimization problem of a neural network, by computing fitness function values in distributed mode, to decrease the time required to find the suboptimal solution. However, the proposed algorithms based on FSS and classical optimization techniques impose a limitation--the methods cannot optimize non-differentiable numerical functions. Hence, the discussed techniques cannot be used for neural network training wherein the derivative of the loss function does not exist.