Numerical hybrid Taguchi-random coordinate search algorithm for path synthesis

Abstract We present a new algorithm for application to path synthesis of a four-bar linkage with continuous variables called the Hybrid Taguchi random coordinate search algorithm (HTRCA). The HTRCA combines two algorithms of the Taguchi method (TM) and the random coordinate search algorithm (RCA). The RCA adjusts one variable simultaneously with two directions and various step sizes in random order to escape a local minimum. Since the RCA modifies one variable at a time according to the random order, the result of the RCA is sensitive to an initial condition of variables. The TM was adopted to generate nearly optimal initial conditions. Using the TM, the approximate optimal value can be found in even multi-modal functions. Also, the TM is used with different setting values to escape a local minimum point by changing two or more variables in one step. By combining the two methods, a global optimal value can be found efficiently. Seven test functions were optimized and the robust and efficient performance was verified by comparison with other hybrid optimization algorithms. Finally, path synthesis of four-bar linkage is done by the developed optimization algorithm, and the result is compared to previous works on the same problem with evolutionary algorithm.

[1]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[2]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[3]  Sundar Krishnamurty,et al.  Optimal synthesis of mechanisms using nonlinear goal programming techniques , 1992 .

[4]  Erwie Zahara,et al.  A hybrid genetic algorithm and particle swarm optimization for multimodal functions , 2008, Appl. Soft Comput..

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

[6]  TaeWon Seo,et al.  A new design methodology for four-bar linkage mechanisms based on derivations of coupler curve , 2016 .

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

[8]  M. Piccioni,et al.  Random tunneling by means of acceptance-rejection sampling for global optimization , 1989 .

[9]  A. Morgan,et al.  Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages , 1992 .

[10]  William L. Goffe,et al.  SIMANN: FORTRAN module to perform Global Optimization of Statistical Functions with Simulated Annealing , 1992 .

[11]  Glen Mullineux,et al.  Atlas of spherical four-bar mechanisms , 2011 .

[12]  Jinkui Chu,et al.  Numerical atlas method for path generation of spherical four-bar mechanism , 2010 .

[13]  Nikolaos V. Sahinidis,et al.  Derivative-free optimization: a review of algorithms and comparison of software implementations , 2013, J. Glob. Optim..

[14]  Wen Yi Lin,et al.  A GA–DE hybrid evolutionary algorithm for path synthesis of four-bar linkage , 2010 .

[15]  R. Howard,et al.  Local convergence analysis of a grouped variable version of coordinate descent , 1987 .

[16]  John Stufken,et al.  Taguchi Methods: A Hands-On Approach , 1992 .

[17]  Nam P. Suh,et al.  Axiomatic Design: Advances and Applications , 2001 .

[18]  S. M. Varedi,et al.  Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm , 2013 .

[19]  G. R. Gogate,et al.  Optimum synthesis of path generating four-bar mechanisms using differential evolution and a modified error function , 2012 .

[20]  F. Peñuñuri,et al.  Synthesis of mechanisms for single and hybrid tasks using differential evolution , 2011 .

[21]  Tung-Kuan Liu,et al.  Hybrid Taguchi-genetic algorithm for global numerical optimization , 2004, IEEE Transactions on Evolutionary Computation.

[22]  A. V. Levy,et al.  The Tunneling Algorithm for the Global Minimization of Functions , 1985 .

[23]  Andrew D. Dimarogonas.  Machine Design: A CAD Approach , 2000 .

[24]  Jongwon Kim,et al.  Optimal design of the front linkage of a hydraulic excavator for multi-objective function , 2014 .

[25]  Rasim Alizade,et al.  Analytical synthesis of function generating spherical four-bar mechanism for the five precision points , 2005 .

[26]  Brigitte Moench,et al.  Engineering Design A Systematic Approach , 2016 .

[27]  Han Chi-Yeh,et al.  A general method for the optimum design of mechanisms , 1966 .

[28]  Xianwen Kong,et al.  Type Synthesis of Parallel Mechanisms , 2010, Springer Tracts in Advanced Robotics.

[29]  T. R. Bement,et al.  Taguchi techniques for quality engineering , 1995 .

[30]  John Anthony Hrones,et al.  Analysis of the four-bar linkage , 1951 .

[31]  H. Zhou,et al.  Optimal synthesis of crank–rocker linkages for path generation using the orientation structural error of the fixed link , 2001 .

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

[33]  Chunshien Li,et al.  Optimization by random search with jumps , 2004 .