Optimization algorithms in engineering design: a comparative analysis of SciPy module methods

Abstract

The aim of this study is to analyze the application of various optimization algorithms for solving engineering problems. The formulation of the optimal design problem is presented in the form of nonlinear programming as a constrained extremum problem. Classical optimization methods inclu-

ded in the SciPy library of the Python programming language are considered. The study focuses on three unconstrained minimization methods: the Nelder – Mead simplex method, Powell’s method, and the Broyden – Fletcher – Goldfarb – Shanno (BFGS) method, which were integrated into the authors’ optimization algorithm. This algorithm transforms the original problem into an unconstrained extremum problem based on a modified Lagrangian function. Additionally, a separate module of the SciPy library for constrained minimization using the Sequential Least Squares Quadratic Programming (SLSQP) method is examined. To evaluate the efficiency of the studied methods, a well-known benchmark optimization problem of a cantilever plate is solved. The obtained solutions are analyzed in terms of convergence rate and accuracy. It is found that all three unconstrained minimization methods produced similar results, with a near-optimal solution obtained as early as the third iteration of the search process, followed by minor adjustments in subsequent iterations. This demonstrates the successful integration of these methods into the authors’ optimization algorithm. The SLSQP method exhibited less stable convergence, as a near-optimal solution was obtained only by the ninth iteration. Thus, the algorithm based on the modified Lagrangian function, developed by the authors, in combination with the unconstrained minimization modules of the SciPy library, can be recommended for further use in large-scale optimization problems.