Study of Differential Evolution Variants in the Dimensional Synthesis of Four-Bar Grashof-Type Mechanisms

Abstract

Mechanisms have allowed for the automation of complex, repetitive, demanding, or dangerous tasks for humans. Among the different mechanisms, those with a closed kinematic chain are more precise and robust compared to open chain ones, which makes them suitable for many applications. One of the most widely used closed-chain alternatives is the four-bar Grashof-type mechanism, as it can generate highly nonlinear closed trajectories with a single degree of freedom. However, the dimensional synthesis of these mechanisms to generate specific trajectories is a complex task. Fortunately, computational methods known as metaheuristics can solve such problems effectively. Differential Evolution (DE) is a metaheuristic commonly used to tackle the dimensional synthesis problem. This paper presents a comparative study of the most commonly used variants of DE in solving the dimensional synthesis problem of four-bar Grashof-type mechanisms. The purpose of the study is to provide guidelines to choose the best DE alternative for solving problems of this type, as well as to support the development of DE-based algorithms that can solve more specific cases effectively. After analysis, the rand/1/exp variant was found to be the most effective in solving the dimensional synthesis problem, which was followed by best/1/bin. Based on these results, a Simple and Improved DE (SIDE) variant based on these two was proposed. The competitive performance of the SIDE with respect to the studied DE variants and in contrast to the results of algorithms used in the recent specialized literature for mechanism synthesis illustrates the usefulness of the study.