Currently, computational algorithms for global stochastic (random) optimization and optimal control are widely used in the literature to solve various scientific and applied problems, including ecology and epidemiology. In particular, such algorithms are used in the development of optimal control of epidemics of infectious diseases in humans and farm animals. For example, one of the most important tasks is to minimize the number of infected organisms after a fixed amount of time with limited financial resources to solve the problem. Note that global optimization methods differ from local ones in that a global one is sought, i.e. biggest maximum.
However, the computational methods of global optimization existing in the literature, in particular those using stochastic algorithms, have an important drawback. Mathematically, in high-dimensional spaces, the convergence of the solution to the global maximum is not guaranteed, i.e. there is a possibility of getting “stuck” in some local maximum, which is a gross error of the algorithm. In this case, optimal control of the system is impossible. This paper proposes a unique approach to the development of global optimization methods based on the classical Darwinian idea of evolutionary selection, in particular, the work uses the principle of survival of the fittest species in the presence of competition from other species. The mathematical optimization method constructed in the work (generation of random mutations followed by selection of the fittest species) guarantees convergence, which is a problem for previously proposed methods, which are known in the literature as “nature-like” methods.
The convergence of the proposed optimization algorithm is mathematically rigorously proven. The proposed algorithm is also compared with previous algorithms in its class and its high efficiency is shown. An important role in the effectiveness of the new algorithm is played by modeling the process of random mutations, for which the anisotropy effect is introduced (in a hypothetical multi-dimensional parameter space, mutations occur differently in different dimensions). Next, the proposed algorithm is used to construct a strategy for optimal control of an epidemic in a population consisting of interacting groups (agents) with different characteristics, such as infectivity, frequency of contacts with other groups, etc. In the considered model, optimal control of the epidemic is carried out under restrictions on program funding implementation of control.
The work was published in the journal Communications in Nonlinear Science and Numerical Simulation. Kuzenkov, Oleg A., Andrew Yu Morozov, and Samvel A. Nalchajyan. "Revisiting ‘survival of the fittest’principle in global stochastic optimisation: Incorporating anisotropic mutations." Communications in Nonlinear Science and Numerical Simulation 130 (2024): 107768. https://doi.org/10.1016/j.cnsns.2023.107768