Work

rDSM—A robust Downhill Simplex Method software package for high-dimensional optimization problems

Year: 2025

Type: software-paper

Abstract: The Downhill Simplex Method (DSM) is a fast-converging derivative-free optimization technique for nonlinear systems. However, the optimization process is often subject to premature convergence due to degenerate simplices or noise-induced spurious minima. This study introduces a software package for the robust Downhill Simplex Method (rDSM), which incorporates two key enhancements. First, simplex degeneracy is detected and corrected by volume maximization under constraints. Second, the real objective value of noisy problems is estimated by reevaluating the long-standing points. Thus, rDSM improves the convergence of DSM, and may increase the applicability of DSM to higher dimensions, even in the presence of noise. The rDSM software package thus provides a robust and efficient solution for both analytical and experimental optimization scenarios. This methodological advancement extends the applicability of simplex-based optimization to complex experimental systems where gradient information remains inaccessible and measurement noise proves non-negligible.

Source: SoftwareX

DOI: 10.1016/j.softx.2025.102462

Authors: Tianyu Wang, Xiaozhou He, Bernd R. Noack

Institutions: Harbin Institute of Technology, Shenzhen University

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Natural Science Foundation of China, Natural Science Foundation of Guangdong Province, Science, Technology and Innovation Commission of Shenzhen Municipality, Shenzhen Science and Technology Innovation Program