Many real-life problems in engineering, business, and management are characterized by multiple, conflicting objectives, as well as the presence of uncertainty. The conflicting criteria originate from various ways to assess system performance and the multiplicity of decision makers, while uncertainty results from inaccurate or unknown data due to imperfect models and measurements, lack of knowledge, and volatility of the global environment.
In this talk, the deterministic approaches to uncertainty that are integrated with multiobjective optimization to address decision making under uncertainty and conflict are discussed. The approaches are based on robust optimization and parametric optimization, both developed for single-objective settings. Six sources of uncertainty are presented, and each type of uncertainty is placed in the multiobjective optimization problem (MOP), yielding several types of uncertain MOPs (UMOPs). Some of the sources are adopted from earlier studies in (single-objective) engineering optimization, while the others result from the multiobjective optimization modus operandi. The UMOP models are classified first according to the location of the uncertainty in their formulation, second with respect to the undertaken optimization approach, and third on the basis of the proposed definition of robust efficient solutions. The models are presented along with the accompanying results on solution concepts, properties, methods, and applications that are specific to each case.
Margaret M. Wiecek is Professor in the Department of Mathematical Sciences at Clemson University in Clemson, South Carolina, USA. She has obtained a Ph.D. degree in Systems Engineering from the AGH University of Science and Technology in Krakow, Poland. Her research area includes theory, methodology, and applications of mathematical programming with special interest in multiobjective optimization and decision-making. Part of her work has been interdisciplinary since she introduced new multiobjective optimization concepts and methods into engineering optimization to enrich the field of automotive and structural design. She has published over 140 articles in peer-refereed journals, book chapters, and conference proceedings. She has advised eleven doctoral students, 41 Master’s students, and four postdoctoral scholars. Her work has been funded by agencies in the US, Finland and Germany. She is on the editorial boards of the International Journal of Multicriteria Decision Making and Decision Making in Manufacturing and Services. She currently serves as the President of the INFORMS Section on Multiple Criteria Decision Making.