###### Abstract  
The parameter estimation (PE) of biochemical reactions is one of the most challenging tasks in systems biology given the pivotal role of these kinetic constants in driving the behavior of biochemical systems. PE is a non-convex, multi-modal, and non-separable optimization problem with an unknown fitness landscape; moreover, the quantities of the biochemical species appearing in the system can be low, making biological noise a non-negligible phenomenon and mandating the use of stochastic simulation. Finally, the values of the kinetic parameters typically follow a log-uniform distribution; thus, the optimal solutions are situated in the lowest orders of magnitude of the search space. In this work, we further elaborate on a novel approach to address the PE problem based on a combination of adaptive swarm intelligence and dilation functions (DFs). DFs require prior knowledge of the characteristics of the fitness landscape; therefore, we leverage an alternative solution to evolve optimal DFs. On top of this approach, we introduce surrogate Fourier modeling to simplify the PE, by producing a smoother version of the fitness landscape that excludes the high frequency components of the fitness function. Our results show that the PE exploiting evolved DFs has a performance comparable with that of the PE run with a custom DF. Moreover, surrogate Fourier modeling allows for improving the convergence speed. Finally, we discuss some open problems related to the scalability of our methodology. p 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 202  
Similar to other real-world optimization problems, PE is typically characterized by many local optima that impede reaching the global optimum due to premature convergence of any optimization meta-heuristics. Moreover, when dealing with the PE of stochastic biochemical models, the multidimensional fitness landscape is rugged, making the optimization process even harder and more time-consuming [2; 3; 4]. Many works proposed solutions focused on the simplification of the optimization task by exploiting specific transformation functions to re-map the original candidate solutions into a modified search space or by using \"smoothed\" surrogate fitness landscapes [5]. The manipulation of the fitness landscape can be realized by exploiting the so-called dilation functions (DFs) [6], which can \"compress\" and \"dilate\" localized areas of the search space, or other approaches such as the Shrinking Space Technique [7; 8; 9], which alters the search space to concentrate the search on specific areas, and the Space Transformation Search, [10], which transforms the original search space and simultaneously evaluates the solutions in both the original and transformed spaces. The generation of surrogate models has been shown to be particularly advantageous when algorithms that generally require a huge number of fitness evaluations to converge to the optimal solution--e.g., evolutionary computation and swarm intelligence--are used to tackle the optimization problem. As a matter of fact, the surrogate model is based on an approximated fitness function that can be evaluated with a reduced computational effort [11]. Multi-modal, rugged, and noisy fitness landscapes--such as those typically associated with the PE problem of stochastic biochemical models--can be efficiently tackled with a surrogate modeling method called surf [12], which exploits the discrete Fourier transform. While surf is applied here on the landscape induced by a _stochastic_ model, it can clearly be applied to a deterministic landscape, as carried out, for example, in [12; 13]. A peculiarity of surf is that the number of low frequency spectral coefficients used for the inverse Fourier transform can be set to adjust the smoothness of the created surrogate model. In [5], DFs and surf were coupled with FST-PSO [14], a settings-free version of particle swarm optimization (PSO) [15], to investigate the PE problem of biochemical systems.