Applying the Median and Genetic Algorithm to Construct D- and G-optimal Robust Designs Against Missing Data

Abstract

In practice, there is a circumstance in which some observed values in well-planned experiments are missing. In this research, small optimal robust response surface designs against missing data were constructed using a Genetic Algorithm (GA) with a Minimum (Min) of alphabetic criteria such as D- and G-optimality for a second-order model. The resulting designs from GA were compared to designs generated from Exchange Algorithm (EA). Unlike EA, GA uses a set of continuous design points as candidate points, so GA produces more optimal and robust designs. For D-optimality, the results showed that the values for D-efficiency, Min D, Med D, and leave- 1-out D criteria of designs generated by GA were all greater than or equal to those from EA. Calculated by EA and GA methods, all G-related criteria values were less than 0.6 apart, except in the case of N = 7. Furthermore, a median of alphabetic optimality criteria has been proposed for use as a criterion to construct robust designs. This approach compromises between optimality criteria such as usual D- and G-optimality and pessimisticoriented criteria such as Min D- and Min G-optimality. For general missing points, the Med D-optimal designs would be superior to the Min D-optimal designs, especially for very small designs. The Med G-optimal designs are far better than the G-optimal designs, although the sample size is increased.