Optimal Synthesis of Mechanisms by using an EDA based on the Normal distribution

Sergio Ivván Valdez Peña, Arturo Hernández Aguirre, Salvador Botello Rionda, Eusebio E. Hernández-Martínez

Abstract


The problem of synthesis of mechanisms is to find the adequate dimensions in the elements in order to perform a given task. The task is defined by a set of points named: precision points. The problem is defined as minimizing the distance among the precision points and the actual position of the mechanism, the decision variables are the elements dimensions, the position and rotation of the relative coordinate system and two parameters related with the initial position and velocity. The proposal of this work is an algorithm for automatized synthesis of mechanisms. We use an Estimation of Distribution Algorithm (EDA), to approximate the optimum, by sampling and estimating a Normal multivariate probability distribution. Each sample is a candidate solution (a candidate mechanism), then we measure the difference between the precision points and the actual positions of the mechanism, the best candidate solutions are used to update the probability distribution, and the process is repeated until convergence is reached. We apply the proposed method for the synthesis of a Four-bar planar mechanism with closed chain. The obtained results are near-optimal designs that are better than others reported in the literature. The proposed method is a competitive alternative for the automatized synthesis of mechanism. We obtain high quality results when compare our approach with other reported in the literature. Additionally, the proposal presents other interesting features: the number of precision points can be increased without the need of increasing the dimension of the search space, in addition, the algorithm can be used for optimizing any mechanism. The results suggest that EDAs can successfully approach this kind of problems, hence, future work contemplate to use the same strategy for tackling more complex problems, possibly involving control parameters, or intending to design singularity-free closed kinematic chains.

Keywords


Synthesis of mechanisms; Evolutionary techniques; Estimation for distribution algorithms; optimization

References


Bosman P. A., Grahl J. y Rothlauf F. (2007). SDR: A Better Trigger for Adaptive Variance Scaling in Normal EDAs. In: GECCO ’07: Proceedings of the 8th annual conference on Genetic and evolutionary computation, 516–522.

Bulatovic R. y Djordjevic S. R. (2004). Optimal Synthesis of a Four bar Linkage by Method of Controlled Deviation. The first Conference on Computational Mechanics (CM04), 31(4), 265-280.

Cabrera J. A., Simon A. y Prado M. (2002). Optimal Synthesis of Mechanisms with Genetic Algortihms. Mechanism and Machine Theory, 37, 1165-1177.

Cabrera J. A., Nadal F., Muñoz J. P. y Simon A. (2007). Multiobjective Constrained Optimal Synthesis of Planar Mechanisms using a New Evolutionary Algorithm. Mechanism and Machine Theory, 42, 791-806.

Cai Y., Sun X., Xu H. y Jia P. (2007). Cross Entropy and Adaptive Variance Scaling in Continuous EDA. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, GECCO ’07. ACM, New York, NY, USA, 609–616.

Dong W. y Yao X. (2002). NichingEDA: Utilizing the Diversity inside a Population of EDAs for Continuous Optimization. In: IEEE Congress on Evolutionary Computation, 1260–1267.

Dong W. y Yao X. (2008). Unified Eigen Analysis on Multivariate Gaussian based Estimation of Distribution Algorithms. Information Sciences, 178(15), 3000 – 3023.

Fang, W. E. (1994). Simultaneous Type and Dimensional Synthesis of Mechanisms by Genetic Algorithms-DE. Mechanism Synthesis Analysis, 70.

Freudenstein F. (1954). An Analytical Approach to the Design of Four-link Mechanisms. Transactions of the ASME, 76, 483–492.

Grahl J., Bosman P. A. N. y Minner S. (2007). Convergence Phases, Variance Trajectories, and Runtime Analysis of Continuos EDAs. In: GECCO ’07: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, ACM, 516–522.

Grahl J., Bosman P. A. N. y Rothlauf F. (2006). The Correlation-triggered Adaptive Variance Scaling IDEA. In: GECCO ’06: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, ACM Press, 397–404.

Handa H. (2007). The Effectiveness of Mutation Operation in the Case of Estimation of Distribution Algorithms. Biosystems, 87(23), 243 – 251.

Hartenberg R. y Denavit J. (1964). Kinematic Synthesis of Linkages, McGraw-Hill, New York.

Hrones, J. A. y Nelson G. L. (1951). Analysis of the Four Bar Linkage. MIT Press and Wiley, New York.

Kalnas R. y Kota S. (2001). Incorporating Uncertaintly into Mechanism Synthesis. Mechanism and Machine Theory, 36(3), 843-851.

Kunjur, J. A. y Krisshnamurty S. (1997). Genetic Algorithms in Mechanical Synthesis. Journal of Applied Mechanisms and Robotics, 4(2), 18-24.

Larrañaga P. y Lozano J. A. (2001). Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Norwell, MA, USA .

Laribi M. A., Milak A., Romdhane L. y Zegloul S. (2004). A Combined Genetic Algorithm Fuzzy Logic Method (GA-FL) in Mechanisms Synthesis. Mechanism and Machine Theory, 39, 717-735.

Levitskii N. L. y Shakvazian K. K. (1960). Synthesis of Four Element Spatial Mechanisms with Lower Pairs. International Journal of Mechanical Sciences, 2, 76-92.

Mallik A. K., Ghosh A. (1994). Kinematic Analysis and Synthesis of Mechanisms. CRC-Press 1 edition, 688.

Marcelin J. (2010). Integrated Optimization of Mechanisms with Genetic Algorithms. Engineering, 2, 438-444.

Pelikan M., Goldberg D. E. y Cantú-Paz E. (1999). The Bayesian Optimization Algorithm. In: Proceedings of the 1999 Conference on Genetic and Evolutionary Computation, GECCO ’99, ACM, Orlando, FL,USA, 525-532.

Quintero R. H., Calle-Trujillo G. y Díaz-Arias A. (2004). Síntesis de generación de trayectorias y de movimiento para múltiples posiciones en mecanismos, utilizando algoritmos genéticos. Scientia et Technica, 10(25).

Roston G. P. y Sturges R. H. (1996). Genetic Algorithm Synthesis of Four Bar Mechanisms. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 10, 371-390.

Sancibrian R., Viadero F., Garcia P. y Fernandez A. (2004). Gradient-based Optimization of Path Synthesis Problems in Planar Mechanisms. Mechanism and Machine Theory, 39, 839-856.

Sandor, G. N. (1959). A General Complex Number Method for Plane Kinematic Synthesis. PhD Thesis, Columbia University, New York.

Shapiro J. L. (2006). Diversity Loss in General Estimation of Distribution Algorithms. In: Proceedings of the 9th International Conference on Parallel Problem Solving from Nature, PPSN’06, Springer-Verlag, Berlin, Heidelberg, 92–101.

Starosta R., (2008). Application of Genetic Algorithm and Fourier Coefficients (GA-FC) in Mechanisms Synthesis. Journal of Theoretical and Applied Mechanics, 46(2), 395-411.

Suh C. H. y Radcliffe C. W. (1967). Synthesis of Plane Linkages with use of Displacement Matrix. Journal of Engineering for Industry, 89(2), 206-214.

Teytaud F. y Teytaud O. (2009). Why one Must Use Reweighting in Estimation of Distribution Algorithms. In: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, GECCO ’09, ACM, New York, NY, USA, 453–460.

Tzong-Mou W. y Chao-Kuang C. (2005). Mathematical Model and its Simulation of Exactly Mechanism Synthesis with Adjustable Link. Applied Mathematics and Computation, 160, 309-316.

Valdez S. I., Hernández A. y Botello S. (2010). Efficient Estimation of Distribution Algorithms by Using the Empirical Selection Distribution. In: P. Korosec (ed.) New Achievements in Evolutionary Computation. InTech. 229-250.

Valdez I., Hernández-Aguirre y Botello S. (2012). Adequate Variance Maintenance in a Normal EDA via the Potential-Selection Method. Advances in Intelligent Systems and Computing, Springer Berlin Heidelberg, 221-235.

Vasiliu A. y Yannou B. (2001). Dimensional Synthesis of Planar Mechanism using Neural Net work: Application to Path Generator Linkages. Mechanism and Machine Theory, 36(2), 229-310.

Walczak T. (2006). Mechanism Synthesis with the Use of Neural Network. Annual Meeting of GAMM, Book of abstracts. Berlin.

Yuan B. y Gallagher M. (2005). On the Importance of Diversity Maintenance in Estimation of Distribution Algorithms. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, GECCO ’05, ACM, New York, NY, USA, 719–726.

Zhang Q. y Muhlenbein H. (2004). On the Convergence of a Class of Estimation of Distribution Algorithms. IEEE Transactions on Evolutionary Computation 8(2), 127–136.




DOI: https://doi.org/10.21640/ns.v6i11.65

Refbacks

  • There are currently no refbacks.


Copyright (c) 2015 Nova Scientia

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Scope

Nova Scientia is a multidisciplinary, electronic publication that publishes twice a year in the months of May and November; it is published by the Universidad De La Salle Bajío and aims to distribute unpublished and original papers from the different scientific disciplines written by national and international researchers and academics. It does not publish reviews, bibliographical revisions, or professional applications.

Nova Scientia, year 11, issue 23, November 2019 – April 2020, is a biannual journal printed by the Universidad De La Salle Bajío, with its address: Av. Universidad 602, Col. Lomas del Campestre, C. P. 37150, León, Gto. México. Phone: (52) 477 214 3900, http://novascientia.delasalle.edu.mx/. Chief editor: Ph.D. Ramiro Rico Martínez. ISSN 2007 - 0705. Copyright for exclusive use No. 04-2008-092518225500/102, Diffusion rights via computer net 04 - 2008 – 121011584800-203 both granted by the Instituto Nacional del Derecho de Autor.

Editor responsible for updating this issue: Direction of Research Department of the Universidad De La Salle Bajío, last updated on November 30th, 2019.