Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 151590, 20 pages
Research Article

Hybrid Optimization Approach for the Design of Mechanisms Using a New Error Estimator

1Calculation Department, MTOI, C/Maria Viscarret 1, Ártica (Berrioplano), 31013 Navarra, Spain
2Department of Structual and Mechanical Engineering, University of Cantabria, Avenida de los Castros s/n, 39005 Santander, Spain
3Mechatronics Department, Tekniker, Avenida Otaola 20, 20600 Eibar, Spain

Received 24 February 2012; Revised 24 April 2012; Accepted 14 May 2012

Academic Editor: Yi-Chung Hu

Copyright © 2012 A. Sedano et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A hybrid optimization approach for the design of linkages is presented. The method is applied to the dimensional synthesis of mechanism and combines the merits of both stochastic and deterministic optimization. The stochastic optimization approach is based on a real-valued evolutionary algorithm (EA) and is used for extensive exploration of the design variable space when searching for the best linkage. The deterministic approach uses a local optimization technique to improve the efficiency by reducing the high CPU time that EA techniques require in this kind of applications. To that end, the deterministic approach is implemented in the evolutionary algorithm in two stages. The first stage is the fitness evaluation where the deterministic approach is used to obtain an effective new error estimator. In the second stage the deterministic approach refines the solution provided by the evolutionary part of the algorithm. The new error estimator enables the evaluation of the different individuals in each generation, avoiding the removal of well-adapted linkages that other methods would not detect. The efficiency, robustness, and accuracy of the proposed method are tested for the design of a mechanism in two examples.