Title: Decision making under conflict and uncertainty: parametric and robust paradigms in multiobjective optimization
Speaker: Prof. Dr. Margaret M. Wiecek, School of Mathematical and Statistical Sciences, Clemson University, USA
Time: 24 April 2023, 4:00-5:00 PM.
Many real-life problems in engineering, business, and management are characterized by multiple and conflicting objectives, as well as the presence of uncertainty. The conflicting criteria originate from various ways to assess the system performance and multiplicity of decision makers, while uncertainty results from inaccurate or unknown data, imperfect models and measurements, lack of knowledge, and volatility of the global environment. Mathematical sciences offer three modeling and methodological paradigms to address uncertainty: probabilistic, possibilistic, and deterministic. The probabilistic type relies on distributions to evaluate the event probability, the possibilistic type uses fuzzy sets and membership functions to assess the event plausibility, and the deterministic type uses crisp sets to define domains within which uncertainties vary. The latter perspective is employed by two types of optimization, parametric and robust, that have been developed initially in single-objective settings and independently of each other. In parametric optimization, the optimal solution and objective values are computed for all values of the uncertainty parameters and are expressed as functions of these parameters, while the parameter space is partitioned into invariancy regions for which these functions are valid. In contrast, robust optimization provides optimal solutions specifically for the worst-case realizations of uncertain data. In this talk, we first present sources of uncertainty, and place each type of uncertainty in the general multiobjective optimization problem (MOP), yielding several types of uncertain MOPs (UMOPs). Some of the sources are adopted from earlier studies in single-objective optimization, while the others result from the multiobjective optimization modus operandi. We then focus on parameter uncertainty located in the objective functions and/or the constraints and present methods and algorithms of robust optimization and parametric optimization to solve the resulting UMOPs. We recognize that the location of the uncertainty in the left or right-hand side of the constraints significantly affects the solvability of these problems. We include applications in internet routing, engineering design, and portfolio optimization.