Adaptations in the simulated annealing algorithm to generate D-optimal mixing experiments both in the absence and presence of biases in the specification of the proportions

Abstract

The mixture designs are represented in terms of variables (x_i, $i=1,·,q$) called by components. The components display an experimental region described in a simplex space, where each variable has values between 0 and 1, portraying the specification of proportions. With these characteristics, the practice of the designs both in several industrial and in pharmaceutical sectors becomes justifiable. The issue is that defining a structure with N experimental points becomes complex since we can generate infinite configurations. Therefore, we used D-optimal mixture designs, which, in summary, guarantee more accurate confidence regions for parameter estimates as we develop these designs conditioned to a statistical criterion. For this reason, we have undertaken this approach to fulfill the aim of this study. We propose a modification in the simulated annealing algorithm combined with the Monte Carlo procedure in the generation of D-optimal mixture designs classified both by the presence and by the absence of bias in the proportion specifications. We conclude that the proposed modification in the simulated annealing algorithm provides the search with generation of D-optimal designs, supporting the control of the distribution of experimental points either near or far from the edges of the observed region limited by the simplex space. The optimal strategies generated in a biased way are less sensitive in relation to the number of components.

KEYWORDS:

• D-optimal design
• Monte Carlo simulation
• simulated annealing

Acknowledgments

The authors thank the Brazilian Agencies, CNPq and CAPES for providing them support for the valuable contribution on the topic studied. Both of us thank the anonymous reviewer who pointed out specific question which enhance the manuscript.

Disclosure statement

The authors declare no potential conflict of interests.

Additional information

Funding

Marcelo Angelo Cirillo wishes to thank the Brazilian Agency CNPq for providing support through the project number 304939/2021-8.