Fundamental research at GERAD contributes to the development of digital intelligence. We have four research axes. The first (valuing data for decision-making) relates to descriptive and predictive analytics (two of the three pillars of digital intelligence). The other three areas relate to prescriptive analytics (the third pillar of digital intelligence) where mathematical optimization methods are mainly implemented to guide decision-making.
There are many strategic advantages to using data. Data often present methodological challenges due to their complex nature or structure, their large size, their degree of confidentiality or even sometimes their scarcity or poor quality. This line of research focuses on the design of mathematical, statistical and machine learning tools for processing, analyzing and modelling data for descriptive, predictive and prescriptive purposes.
The complexity of decision support systems can take many forms. Some optimization problems involve millions of variables and constraints. Others are made up of highly nonlinear functions, obtained by simulations requiring a long computation time. Complexity can also be due to the large number of agents who act without coordination on the system. This line of research aims to design a range of algorithms adapted to the characteristics of these systems, to apply them to real problems, and to analyze their convergence.
Uncertainty is inherent in many decision and optimization problems for a variety of reasons: imperfect models, random inputs, noisy measurements of variables, and imprecise knowledge of dynamic parameters. Added to this is the frequent complexity of large contemporary systems. This axis groups together decision-making methods in complex and uncertain systems. These methods include state estimation, hierarchical optimal control, robust optimization, and mean field game theory.
This axis brings together theoretical developments and applications for continuous and discrete real-time decision-making with information on future needs over a shorter or longer horizon. Several GERAD researchers who are experts on optimization algorithms for planning in many fields also undertake research activities on operational decisions. They innovate by using the results of planning for better decisions in real time. The Canada Excellence Research Chair in Data Science for Real-Time Decision Making is a member of GERAD.