Automated Two Stage Adjustable Ratio Simplex Algorithm for Two Parameter Optimization

Multivariable optimization is an essential mathematical exercise in daily engineering design and troubleshooting. To this end, simplex multivariable optimization method is a powerful optimization approach that has served many engineering disciplines well over the years. One such simplex algorithm is the Nelder Mead algorithm. But, the reflection step of the Nelder Mead algorithm may increase the number of iterations needed to arrive at the optimal point, as it reflects the starting point to the opposite side of the function. This work proposes an automated two-stage adjustable ratio simplex optimization method that first search within and around the optimization surface for a good starting point, followed by a narrow and more refined search for the optimal point. For both stages of the new simplex algorithm, only contraction and extension steps are used, and this helps to remove possible oscillatory effects common to other simplex algorithms as the iterations progress. Demonstrative use of the new simplex algorithm on optimizing the coefficients of a quadratic function reveals good accuracy and speed as compared to the Nelder Mead algorithm which uses significantly more iterations. Future testing should be conducted with other optimization functions as well as objective functions. Interested readers are invited to explore and expand on the work reported herein.