Letter: Application of optimization algorithms to engineering design problems and discrepancies in mathematical formulas

Abstract

Engineering design optimization problems have attracted the attention of researchers since they appeared. Those who work on developing optimization algorithms, in particular, apply their developed algorithms to these problems in order to test their new algorithms’ capabilities. The mathematical discrepancy emerges during the implementation of equations and constraints related to these engineering problems. This is due to an error occurring in writing or transmitting these equations from one paper to another. Maintaining these discrepancies will have a negative impact on the assessment and model performance verification of the newly developed algorithms, as well as the decision-making process. To address this issue, this study investigates the mathematical discrepancies occurred by researchers in four well-known engineering design optimization problems (Welded Beam Design WBD, Speed Reducer Design SRD, Cantilever Beam Design CBD, and Multiple Disk Clutch Brake Design MDCBD). We have investigated some of the recently published papers in the literature, identifying discrepancies in their mathematical formulas, and fixing them appropriately by referring and comparing them to the original problem. Furthermore, all mathematical discrepancies , references, parameters, cost functions, constraints, and constraint errors are highlighted, arranged and organized in tables. As a result, this work can help readers and researchers avoid being confused and wasting time when working on these engineering design optimization problems.