    Performance of the Simulated Annealing and Genetic Algorithms for the Design of Periodic Devices Loay D. Khalaf, 1 Andrew F. Peterson 2 1 Philadelphia University, P.O. Box 1101, Sweileh, Jordan 2 Georgia Institute of Technology, Atlanta, Georgia 30332; e-mail: peterson@ee.gatech.edu Recei  ed 14 March, 1996; re ised 17 July, 1996 ABSTRACT: The performance of the simulated annealing and genetic algorithms is investi- gated when used for microwave device design. A finite-element method for 2D structures having 1D periodicity is used to generate the objective function used in the optimization. A comparison of the optimization algorithms is described based on a number of design examples.  1997 John Wiley & Sons, Inc. Int J Microwa  e Millimeter-Wa e CAE 7: 108–116, 1997. Keywords: optimization; finite element; design; scattering matrix; scattering coefficients; reflection coefficient; transmission coefficient; quad-section; tri-section 1. INTRODUCTION The increasing computer power available to engi- neers and the demanding performance specifica- tions associated with microwave and optical de- vices motivate the growth of optimization-driven design. Recently optimization algorithms based on local search methods such as the steepest descent method have been superceded by Monte Carlo random search methods such as simulated annealing and genetic algorithms. These methods employ random variables in order to admit candi- date solutions that might be very different from the current best estimate of the solution, and avoid being trapped in local minimas encountered with highly nonlinear objective functions. These global algorithms have been studied in a Ž variety of problems combinatorial, electromag- . netic, and structural for different types of opti- Ž . mization geometrical and topological . In many cases, results obtained with the use of simulated annealing and genetic algorithms could not have been achieved with local optimization methods. Simulated annealing produces one optimal or Correspondence to: A. F. Peterson nearly optimal solution, and the genetic algorithm produces several nearly optimal solutions, which might include the optimal solution. Thus a solu- tion can be selected while considering other vari- ables not incorporated into the objective function, such as manufacturability or cost. The literature on optimization shows a consid- erable amount of application in mechanical, civil, and electrical engineering. The results achieved with the use of random search methods were far superior to those produced by local optimization methods. For example, numerical optimization was used to minimize ohmic losses in a conductor  1, in the optimization of a nonlinear mag-  netostatic problem 2 , in topological design of  structural objects 3 , for optimization of three-  dimensional structures 4 , and for mixed discrete  optimization problems in structures 5. Others used the simulated annealing algorithm  in an MRI system design 6 and concluded that the simulated annealing algorithm can be used to search a large multidimensional space for the global minima, but it is computationally expen- sive. The simulated annealing algorithm has been used with the finite-element method for solving  nonlinear magnetics problems 7 , and simulated  1997 John Wiley & Sons, Inc. CCC 1050-182797010108-09 108