Numerical integration based on evolutionary functional network

In this paper, a novel evolutionary functional network (EFN) is introduced. Firstly the generalized basis function is introduced, and then genetic programming is improved by changing the objects and structure of encoding. Sequences of generalized basis functions acts as individuals, general tree structure is used to encode them. Least square method (LSM) is used to design fitness function and by a number of evolutions, the optimum approximated model is achieved. The algorithm is used to compute the numerical integrals of all kinds of functions. Finally, results of 5 experiments show that this algorithm is effectively feasible and more accurate.

[1]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[2]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[3]  Ricardo Landa Becerra,et al.  Efficient evolutionary optimization through the use of a cultural algorithm , 2004 .

[4]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[5]  K. V. Price,et al.  Differential evolution: a fast and simple numerical optimizer , 1996, Proceedings of North American Fuzzy Information Processing.

[6]  Yang Qi.  A Survey of Differential Evolution Algorithms , 2008 .

[7]  Ling Wang,et al.  A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization , 2007, Appl. Math. Comput..

[8]  Jasbir S. Arora,et al.  12 – Introduction to Optimum Design with MATLAB , 2004 .

[9]  R. Eberhart,et al.  Fuzzy adaptive particle swarm optimization , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[10]  Kalyanmoy Deb,et al.  Optimal design of a welded beam via genetic algorithms , 1991 .

[11]  Yongquan Zhou,et al.  A Hybrid Co-evolutionary Particle Swarm Optimization Algorithm for Solving Constrained Engineering Design Problems , 2010, J. Comput..

[12]  Ling Wang,et al.  An effective co-evolutionary particle swarm optimization for constrained engineering design problems , 2007, Eng. Appl. Artif. Intell..