Modified Krill Herd (MKH) algorithm and its application in dimensional synthesis of a four-bar linkage

Abstract The paper considers the application of the modified Krill Herd (KH) algorithm for obtaining optimal solutions in dimensional synthesis of a four-bar linkage as a path generator. Certain modifications have been made for the purpose of increasing the performance of the standard KH algorithm for the considered examples of synthesis. In the first modification, besides the initialization of fitness functions, there is also the initialization of the vectors which represent the food location. This modification reflects the actual behavior of krills in their natural environment, i.e. the tendency for optimum swarm density and the best position in relation to the food. The second modification relates to the replacement of the crossover operator with the combination of columns of fitness functions obtained in one iteration. The newly obtained sequence of krills is corrected by the value of physical diffusion, which results in repeated search of the solution space, in the same iteration, in order to improve the optimum found. This is how the Modified Krill Herd (MKH) algorithm tested on four benchmark examples from the synthesis of a four-bar linkage has been obtained. The results obtained by this algorithm confirm its efficiency, i.e. they considerably outperform the results obtained in the cited literature.

[1]  G. R. Gogate,et al.  Optimum synthesis of motion generating four-bar mechanisms using alternate error functions , 2012 .

[2]  F. Freudenstein.  Advanced mechanism design: Analysis and synthesis: Vol. 2, by G. N. Sandor and A. G. Erdman. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1984, 688 p , 1985 .

[3]  Wen Yi Lin,et al.  Dimensional synthesis of a five-point double-toggle mould clamping mechanism using a genetic algorithm—differential evolution hybrid algorithm , 2010 .

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

[5]  J. McGarva.  Rapid search and selection of path generating mechanisms from a library , 1994 .

[6]  S. Kota,et al.  Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods , 1997 .

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

[8]  Amir Hossein Alavi,et al.  Krill herd: A new bio-inspired optimization algorithm , 2012 .

[9]  I A Sultan,et al.  On the kinematics and synthesis of a geared five-bar slider–crank mechanism , 2011 .

[10]  L. Romdhane,et al.  A combined genetic algorithm-fuzzy logic method (GA-FL) in mechanisms synthesis , 2004 .

[11]  Jianbin Qiu,et al.  Model Reduction for Discrete-Time Markovian Jump Systems with Deficient Mode Information , 2013 .

[12]  J. A. Cabrera,et al.  Multiobjective constrained optimal synthesis of planar mechanisms using a new evolutionary algorithm , 2007 .

[13]  Chun-Che Lee,et al.  On a hybrid particle swarm optimization method and its application in mechanism design , 2014 .

[14]  Sundar Krishnamurty,et al.  A generalized exact gradient method for mechanism synthesis , 1996 .

[15]  Antonio Moreno Ortiz,et al.  Dimensional synthesis of mechanisms using Differential Evolution with auto-adaptive control parameters , 2013 .

[16]  A. Smaili,et al.  Optimum Synthesis of Mechanisms Using Tabu-Gradient Search Algorithm , 2005 .

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

[18]  Jiang Li,et al.  Erratum to: Incorporating mutation scheme into krill herd algorithm for global numerical optimization , 2013, Neural Computing and Applications.

[19]  Radovan R. Bulatović,et al.  Cuckoo Search algorithm: A metaheuristic approach to solving the problem of optimum synthesis of a six-bar double dwell linkage , 2013 .

[20]  Seyed Mohammad Mirjalili,et al.  Chaotic krill herd optimization algorithm , 2014 .

[21]  Amir Hossein Gandomi,et al.  A chaotic particle-swarm krill herd algorithm for global numerical optimization , 2013, Kybernetes.

[22]  Amir Hossein Alavi,et al.  Levy-flight krill herd algorithm , 2013 .

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

[24]  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 .

[25]  John M. Hansen.  Synthesis of Mechanisms Using Time-Varying Dimensions , 2002 .

[26]  Xin-Ping Guan,et al.  An improved krill herd algorithm: Krill herd with linear decreasing step , 2014, Appl. Math. Comput..

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

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

[29]  Antonio Moreno Ortiz,et al.  An evolutionary algorithm for path synthesis of mechanisms , 2011 .

[30]  Amir Hossein Gandomi,et al.  Krill herd algorithm for optimum design of truss structures , 2013, Int. J. Bio Inspired Comput..

[31]  Radovan R. Bulatović,et al.  On the optimum synthesis of a four-bar linkage using differential evolution and method of variable controlled deviations , 2009 .

[32]  Ahmad Smaili,et al.  Optimum synthesis of hybrid-task mechanisms using ant-gradient search method , 2007 .