Comparison of Single- and Multi- Objective Optimization Quality for
  Evolutionary Equation Discovery
Mikhail Maslyaev Alexander Hvatov
Evolutionary differential equation discovery proved to be a tool to obtain
equations with less a priori assumptions than conventional approaches, such as
sparse symbolic regression over the complete possible terms library. The
equation discovery field contains two independent directions. The first one is
purely mathematical and concerns differentiation, the object of optimization
and its relation to the functional spaces and others. The second one is
dedicated purely to the optimizational problem statement. Both topics are worth
investigating to improve the algorithm's ability to handle experimental data a
more artificial intelligence way, without significant pre-processing and a
priori knowledge of their nature. In the paper, we consider the prevalence of
either single-objective optimization, which considers only the discrepancy
between selected terms in the equation, or multi-objective optimization, which
additionally takes into account the complexity of the obtained equation. The
proposed comparison approach is shown on classical model examples -- Burgers
equation, wave equation, and Korteweg - de Vries equation.