Comparative Analysis of Nonlinear Programming Solvers: Performance Evaluation, Benchmarking, and Multi-UAV Optimal Path Planning

Abstract

In this paper, we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. We conduct a comparative analysis of the convergence performances of commonly used solvers for both unconstrained and constrained nonlinear programming problems. The comparison metrics involve accuracy, convergence rate, and computational time. MATLAB is chosen as the implementation platform due to its widespread adoption in academia and industry. Our study includes solvers which are either freely available or require a license, or are extensively documented in the literature. Moreover, we differentiate solvers if they allow the selection of different optimal search methods. We assess the performance of 24 algorithms on a set of 60 benchmark problems. We also evaluate the capability of each solver to tackle two large-scale UAV optimal path planning scenarios, specifically the 3D minimum time problem for UAV landing and the 3D minimum time problem for UAV formation flying. To enrich our analysis, we discuss the effects of each solver’s inner settings on accuracy, convergence rate, and computational time.

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“…An optimization problem is categorized as nonlinear when its functions, goals, and constraints have a nonlinear form. Nonlinear programming can be classified into two categories, namely nonlinear programming that involves constraints (constrained) and that does not involve constraints (unconstrained), which will affect the method of solving it (Lavezzi et al, 2023).…”