Dimensional synthesis of mechanisms using Differential Evolution with auto-adaptive control parameters

Abstract This paper presents how an algorithm based on Differential Evolution (DE) with no constant control parameters solves the dimensional synthesis of four and six-bar mechanisms for path generation. The selection of values of DE control parameters is not always an easy and obvious job. In this paper a DE with auto-adaptive control parameters is proposed which includes a new mutation operator to solve stagnation in local minima and, on top of all this, the choice of a control parameters value in a simple way. For a set of 6 representative cases related to dimensional synthesis from bibliography, the performance of this new DE algorithm, called Ingenieria Mecanica Malaga (IMMa) Optimization Algorithm with Self-Adaptive Technique, IOA s-at , has been tested. An explanation of how the new mutation operator works is also included. The results obtained, compared with other synthesis techniques from literature, present significant improvements for every case studied. The new version does not require control input parameters to be chosen by the user. Those are auto-tuned during the algorithm execution, that is, we use an algorithm with adaptive control parameters and it continues being easy-to-use, robust and fast.

[1]  Liang Gao,et al.  A differential evolution algorithm with self-adapting strategy and control parameters , 2011, Comput. Oper. Res..

[2]  Vitaliy Feoktistov.  Differential Evolution: In Search of Solutions , 2006 .

[3]  Antonio Moreno Ortiz,et al.  The IMMa optimisation algorithm without control input parameters , 2009 .

[4]  Qingfu Zhang,et al.  DE/EDA: A new evolutionary algorithm for global optimization , 2005, Inf. Sci..

[5]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[6]  David Redekop.  Design Analysis and Synthesis. , 1984 .

[7]  Panos S. Shiakolas,et al.  On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique , 2005 .

[8]  Zbigniew Michalewicz,et al.  Parameter control in evolutionary algorithms , 1999, IEEE Trans. Evol. Comput..

[9]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[10]  Ajith Abraham,et al.  A simple adaptive Differential Evolution algorithm , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[11]  Sanjib Kumar Acharyya,et al.  Performance of EAs for four-bar linkage synthesis , 2009 .

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[13]  J. A. Cabrera,et al.  An Alternative Method to Determine the Magic Tyre Model Parameters Using Genetic Algorithms , 2004 .

[14]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[15]  J. A. Cabrera,et al.  Optimal synthesis of mechanisms with genetic algorithms , 2002 .