Influence of the Binomial Crossover in the DE Variants Based on the Robot Design with Optimum Mechanical Energy

 

Miguel G. Villarreal-Cervantes, Daniel De-la-Cruz-Muciño, Carlos Ricaño-Rea, Jesus Said Pantoja-García

 

Instituto Politécnico Nacional, CIDETEC, Mechatronic Section, Postgraduate Department, Juan de Dios Bátiz s/n, 07700, DF, México. (e-mail: mvillarrealc@ipn.mx, ddelacruzm@ipn.mx, cricanor@ipn.mx, jpantjag@ipn.mx).

 

Manuscript received on July 02, 2014,
Accepted for publication on January 20, 2015,
Published on June 15, 2015.

 

Abstract

Differential evolution (DE) is a powerful algorithm to find an optimal solution in real world problems. Nevertheless, the binomial crossover parameter is an important issue for the success of the algorithm. The proper selection of the binomial crossover parameter depends on the problem at hand. In this work, the effect of the binomial crossover in the DE/Rand/1/bin, DE/Best/1/Bin and DE/Current to rand/1/Bin is empirically studied and analyzed in the optimum design of the kinematic and the dynamic parameters of links for a parallel robot. The optimum design minimizes mechanical energy and consequently reduces the energy provided by the actuator. Based on the experimental results, the range of crossover parameter values that properly explores the search space is obtained. The importance of finding a proper crossover parameter is highlighted. In addition, the optimal design shows a decrease in the parallel robot mechanical energy compared with non-optimal design.

Key words: Differential evolution, binomial crossover, optimum design, mechatronic design.

 

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ACKNOWLEDGEMENTS

This work is supported by the Secretaría de Investigación y Posgrado del Instituto Politécnico Nacional (SIP-IPN) under project number SIP-20151212 and the CONACYT under project number 182298. The second to the fourth authors acknowledge support from CoNACYT through a scholarship to pursue graduate studies at Instituto Politécnico Nacional.

 

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