A constrained optimization algorithm based on the simplex search method

In this article, a robust method is presented for handling constraints with the Nelder and Mead simplex search method, which is a direct search algorithm for multidimensional unconstrained optimization. The proposed method is free from the limitations of previous attempts that demand the initial simplex to be feasible or a projection of infeasible points to the nonlinear constraint boundaries. The method is tested on several benchmark problems and the results are compared with various evolutionary algorithms available in the literature. The proposed method is found to be competitive with respect to the existing algorithms in terms of effectiveness and efficiency.

[1]  C. Coello,et al.  CONSTRAINT-HANDLING USING AN EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION TECHNIQUE , 2000 .

[2]  M. Mahdavi,et al.  ARTICLE IN PRESS Available online at www.sciencedirect.com , 2007 .

[3]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[4]  K. M. Ragsdell,et al.  Optimal Design of a Class of Welded Structures Using Geometric Programming , 1976 .

[5]  Tetsuyuki Takahama,et al.  Constrained optimization by applying the /spl alpha/ constrained method to the nonlinear simplex method with mutations , 2005, IEEE Transactions on Evolutionary Computation.

[6]  Tapabrata Ray,et al.  Society and civilization: An optimization algorithm based on the simulation of social behavior , 2003, IEEE Trans. Evol. Comput..

[7]  M. J. Box.  A New Method of Constrained Optimization and a Comparison With Other Methods , 1965, Comput. J..

[8]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[9]  Pearson India,et al.  Applied Mathematical Methods , 1999 .

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

[11]  M. Fesanghary,et al.  An improved harmony search algorithm for solving optimization problems , 2007, Appl. Math. Comput..

[12]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

[13]  F. Zirilli,et al.  An Extension of the Simplex Method to Constrained Nonlinear Optimization , 2022 .

[14]  K. Lee,et al.  A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice , 2005 .

[15]  H. Ghiasi,et al.  Constrained Globalized Nelder—Mead Method for Simultaneous Structural and Manufacturing Optimization of a Composite Bracket , 2008 .

[16]  Carlos A. Coello Coello,et al.  Solving Engineering Optimization Problems with the Simple Constrained Particle Swarm Optimizer , 2008, Informatica.

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

[18]  G. R. Hext,et al.  Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation , 1962 .

[19]  K. Lee,et al.  A new metaheuristic algorithm for continuous engineering optimization : harmony search theory and practice , 2005 .

[20]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[21]  Carlos A. Coello Coello,et al.  Useful Infeasible Solutions in Engineering Optimization with Evolutionary Algorithms , 2005, MICAI.

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

[23]  Duc Truong Pham,et al.  Optimal design of mechanical components using the Bees Algorithm , 2009 .