A New Study on Optimization of Four-Bar Mechanisms Based on a Hybrid-Combined Differential Evolution and Jaya Algorithm

Nguyen-Van, Sy; Lieu, Qui X.; Xuan-Mung, Nguyen; Nguyen, Thi Thanh Nga

doi:10.3390/sym14020381

Cited by 12 publications

(7 citation statements)

References 45 publications

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“…Because of this, the metaheuristic techniques from evolutionary computation and swarm intelligence [36] are alternatives used to obtain adequate solutions to this type of problem at an affordable computational cost [27]. As previously discussed, the metaheuristic technique of Differential Evolution (DE) [30] has been very successful in finding the solutions of dimensional synthesis problems of mechanisms [31][32][33].…”

Section: Differential Evolutionmentioning

confidence: 99%

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

Rodríguez-Molina,

Villarreal-Cervantes,

Rueda-Gutiérrez

et al. 2023

Applied Sciences

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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.

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Section: Differential Evolutionmentioning

confidence: 99%

“…However, the operation of these alternatives takes as a starting point the operation of state-of-the-art metaheuristics [29]. Among these metaheuristic techniques, Differential Evolution (DE) [30] along with its various variants, are recurring options for solving mechanism synthesis problems [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

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

Rodríguez-Molina,

Villarreal-Cervantes,

Rueda-Gutiérrez

et al. 2023

Applied Sciences

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“…In this study, the design domain exhibits a large size with 18 target points. There are slight differences in the limit of design parameters in various studies, such as the GA-CSP [41], GA-DE [47], MUMSA [48], IOA S-at [53], HCDJ [77] methods, r 1 , r 2 , r 3 , r 4 ∈ [0, 50]; x 0 , y 0 , r cx , r cy ∈ [−50, 50], DE-SRT [56] and BAS [37] methods, r 1 , r 2 , r 3 , r 4 ∈ [0, 5]; r cx , r cy , x 0 , y 0 ∈ [−5, 5]. Hereafter, in the following cases, the existence of difference in the limits of design variables will not be mentioned again.…”

Section: Five Problems Of the Dimensional Synthesis Of The Path-gener...mentioning

confidence: 99%

“…The REA consists of two repulsive mutation behaviors, which exhibit two common characteristics: (i) the population no longer learns from the current global optimum to prevent the population from falling into the local optimum region; (ii) the offspring searches any direction except the location of the parent. Sy et al [77] proposed a hybrid-combined differential evolution and Jaya (HCDJ) algorithm, which uses a modified initialization, a hybrid-combined mutation between the DE and Jaya algorithm, and an elitist selection for the dimensional synthesis of pathgenerating four-bar mechanisms with symmetrical motions. Five representative problems were tested, and the HCDJ algorithm was confirmed to provide an improved optimal solution than the original DE and Jaya methods and some algorithms presented in the literature.…”

Section: Introductionmentioning

confidence: 99%

Comparative Study on the Synthesis of Path-Generating Four-Bar Linkages Using Metaheuristic Optimization Algorithms

Kang¹,

Jun²,

You³

2022

Applied Sciences

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Four-bar linkages are one of the most widely used mechanisms in industries. This paper presents a comparative study on the accuracy and efficiency of the optimum synthesis of path-generating four-bar linkages using five metaheuristic optimization algorithms. The utilized metaheuristic methods included two swarm intelligence-based algorithms, i.e., particle swarm optimization and hybrid particle swarm optimization, and three evolutionary-based algorithms, i.e., differential evolution, ensemble of parameters and mutation strategies in differential evolution, and linearly ensemble of parameters and mutation strategies in differential evolution. The objective function to be minimized is the sum of squares of the distance between the generated points and the precision points of a coupler point. The optimal design of four-bar linkages must meet the Grashof’s criteria and exhibit sequential constraints that can prevent the occurrence of order defect. This study investigated five representative cases of the dimensional synthesis of four-bar path generators with and without prescribed timing and compared the optimal solutions of the utilized five metaheuristic methods to those of previously reported algorithms in literature. The improved metaheuristic methods exhibited superior optimal solution and enhanced reliability compared to the original methods. Moreover, three improved metaheuristic methods were not only easy implemented, but also more efficient for solving the optimal synthesis problems, particularly for high dimensional problems.

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“…The swarm intelligence algorithm is still the most productive solution based on the characteristics of biological swarms. Various swarm intelligence methods [33,34] have been proposed, such as PSO (Particle Swarm Optimization), GA (Genetic Algorithm), AA (Ant Algorithm), and DE (Differential Evolution). The swarm intelligence algorithms have become the most effective method to solve the IK problem.…”

Section: Introductionmentioning

confidence: 99%

A Review and Comparative Study of Differential Evolution Algorithms in Solving Inverse Kinematics of Mobile Manipulator

Qiao

2023

Symmetry

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Mobile manipulator robots have become important pieces of equipment due to the high mobility of mobile subsystems and the high flexibility of manipulator subsystems. Considering the increasing degrees of freedom and the need to avoid singular locations, one of the most challenging problems is solving the inverse kinematics problem of mobile manipulator robots (IKMM). Of all the popular optimization algorithms, the differential evolution (DE) algorithm is the most effective method for quickly solving the IKMM problem with sufficient solutions. Currently, many strategies have been proposed for DE algorithms to improve the performance of solving mathematical problems; some symmetry strategies or symmetry functions have been introduced to DE algorithms. However, the effects of various DE algorithms on solving the actual IKMM lack a comprehensive explanation. Therefore, we divide various DE algorithms into three categories considering the control parameter selection and compare the specific optimization of various DE algorithms. Then, we compare the performance of various DE algorithms when solving the inverse kinematics problems of mobile manipulators with different degrees of freedom. Considering the effectiveness and the speed of the DE algorithm on the IKMM problem, we determine the best DE algorithm by comparing the error and time required to reach 100 random mission points and tracking the typical trajectories. Finally, the best-performing DE method is further improved by studying the selection of fundamental parameters in the best DE algorithm. Valuable conclusions are obtained from these experimental simulations, which can help with choosing an algorithm that is suitable for solving the inverse kinematics problem of mobile manipulator robots in practice.

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A New Study on Optimization of Four-Bar Mechanisms Based on a Hybrid-Combined Differential Evolution and Jaya Algorithm

Cited by 12 publications

References 45 publications

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

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

Comparative Study on the Synthesis of Path-Generating Four-Bar Linkages Using Metaheuristic Optimization Algorithms

A Review and Comparative Study of Differential Evolution Algorithms in Solving Inverse Kinematics of Mobile Manipulator

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