Optimization of problems with multivariate multiple functional responses: A case study in air quality

ABSTRACT

Optimization of multi-response problems is a popular subject in the literature. However, the problem becomes complicated when the responses are functional due to the existence of signal factors. In this article, we have proposed a combined index to optimize multivariate multiple functional responses by considering functional specification limits and a target. The relation among the responses and controllable factors is characterized by polynomial equations to consider the curvature of the response functions. The validity of the proposed method is checked by a simulation example. To show the applicability of the proposed method, a real case about Tehran air quality is analyzed. Latitude and longitude are considered to be signal factors, and different pollutant values are responses of the experiment. Government policies in each time interval are considered as controllable factors. Finally, an optimization algorithm is used to find the best decisions for government policies.

KEYWORDS:

• Air pollution
• Air quality
• Experimental design
• Functional response
• Multi-response optimization
• Process capability index

MATHEMATICS SUBJECT CLASSIFICATION:

• 62-XX Statistics
• 62Kxx Design of experiments
• 62K99