DETC99/DAC-8586
A Fuzzy Adaptive Simplex Search Optimization Algorithm
|
Mohamed B. Trabia Associate
Professor University
of Nevada, Las Vegas Department of Mechanical Engineering Las
Vegas, NV 89154-4027 Telephone:
(702) 895-0957 E-mail: mbt@me.unlv.edu |
Xiao Bin Lu Graduate
Student University
of Nevada, Las Vegas Department of Mathematical Sciences |
Optimization algorithms
usually use fixed parameters that are empirically chosen to reach the minimum
for various objective functions. This paper shows how to incorporate fuzzy
logic in optimization algorithms to make the search adaptive to various
objective functions. This idea is applied to produce a new algorithm for
minimization of a function of n
variables using an adaptive form of the simplex method. The search starts by
generating a simplex with n+1
vertices. The algorithm replaces the point with the highest function value by a
new point. This process comprises reflecting the point with the highest
function value in addition to expanding or contracting the simplex using fuzzy
logic controllers whose inputs incorporate the relative weights of the function
values at the simplex points. The efficiency of the algorithm is studied using
a set of standard minimization test problems. This algorithm generally results
in a faster convergence toward the minimum. The algorithm is also applied
successfully to two engineering design problems.
Keywords: Optimization Algorithms, Nonlinear Programming,
Simplex, Fuzzy Logic