Mixed-integer linear programming, Integer quadratic programming, Territory design, Location, Valid inequalities,

In 2017, approximately 5 million Americans were living with Alzheimer’s disease (AD), and it is estimated that by 2050 this number could increase to 16 million. In this study, we apply mathematical optimization to approach microarray analysis to detect differentially expressed genes and determine the most correlated structure among their expression changes. The analysis of GSE4757 microarray dataset, which compares expression between AD neurons without neurofibrillary tangles (controls) and with neurofibrillary tangles (cases), was casted as a multiple criteria optimization (MCO) problem. Through the analysis it was possible to determine a series of Pareto efficient frontiers to find the most differentially expressed genes, which are here proposed as potential AD biomarkers. The Traveling Sales Problem (TSP) model was used to find the cyclical path of maximal correlation between the expression changes among the genes deemed important from the previous stage. This leads to a structure capable of guiding biological exploration with enhanced precision and repeatability. Ten genes were selected (FTL, GFAP, HNRNPA3, COX1, ND2, ND3, ND4, NUCKS1, RPL41, and RPS10) and their most correlated cyclic structure was found in our analyses. The biological functions of their products were found to be linked to inflammation and neurodegenerative diseases and some of them had not been reported for AD before. The TSP path connects genes coding for mitochondrial electron transfer proteins. Some of these proteins are closely related to other electron transport proteins already reported as important for AD.

Microarray experiments are capable of determining the relative expression of tens of thousands of genes simultaneously, thus resulting in very large databases. The analysis of these databases and the extraction of biologically relevant knowledge from them are challenging tasks. The identification of potential cancer biomarker genes is one of the most important aims for microarray analysis and, as such, has been widely targeted in the literature. However, identifying a set of these genes consistently across different experiments, researches, microarray platforms, or cancer types is still an elusive endeavor. Besides the inherent difficulty of the large and nonconstant variability in these experiments and the incommensurability between different microarray technologies, there is the issue of the users having to adjust a series of parameters that significantly affect the outcome of the analyses and that do not have a biological or medical meaning. In this study, the identification of potential cancer biomarkers from microarray data is casted as a multiple criteria optimization (MCO) problem. The efficient solutions to this problem, found here through data envelopment analysis (DEA), are associated to genes that are proposed as potential cancer biomarkers. The method does not require any parameter adjustment by the user, and thus fosters repeatability. The approach also allows the analysis of different microarray experiments, microarray platforms, and cancer types simultaneously. The results include the analysis of three publicly available microarray databases related to cervix cancer. This study points to the feasibility of modeling the selection of potential cancer biomarkers from microarray data as an MCO problem and solve it using DEA. Using MCO entails a new optic to the identification of potential cancer biomarkers as it does not require the definition of a threshold value to establish significance for a particular gene and the selection of a normalization procedure to compare different experiments is no longer necessary.

Modelling and simulation in reactive polymer processing have been active research areas for the past decades in academic institutions as well as within the industry. Both areas have played a key role in advancing and optimizing reactive polymer processing operations. The objective of this paper is to review the two major classifications of models used to simulate polymer processes: physics based models and empirical models. Additionally, a section on multiple criteria optimization using data envelopment analysis has been included for completeness. The work presented here helps define a decisionmaking framework for the creation of reactive polymer process models and for the effective selection of settings of the process variables based on these models.