Comparative Study of the Quick Convergent Inflow Algorithm (QCIA) and the Modified Quick Convergent Inflow Algorithm (MQCIA)

Abstract

The performance of two line search algorithms, the Quick Convergent Inflow Algorithm and the Modified Quick Convergent Inflow Algorithm, used in locating the optimizers of response functions is studied. The methodology requires the use of the same starting experimental design. The indicator variables are the number of iterations and the optimal point reached at each iteration. The Modified Quick Convergent Inflow Algorithm seems to perform generally better than the Quick Convergent Inflow Algorithm in the sense that solutions obtained are much closer to the exact solutions than those obtained using the Quick Convergent Inflow Algorithm. As a consequence to the study, a new algorithm is developed for solving Linear Programming problems. The algorithm iteratively eliminates from an N-sized starting design a point that contributes less to the process as measured by the predictive variances at the design points. The design size is immediately recoverd by adding to the resulting N-1 sized design a design point from the candidate set that optimizes performance. The new algorithm offers approximate solutions to Linear Programming problems as demonstrated with some numerical illustrations.