Preserving and Approximating Efficient Solutions in Multiobjective Optimization under Function Uncertainty
Optimization Eruditorum, Volume 4, Issue 1, April 2027, Pages 22–52
Hervé Kerivin
Clermont-Auvergne Institute of Technology, LIMOS, CNRS UMR 6158, University Clermont Auvergne, Clermont-Ferrand, France
School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina, USA
Margaret M. Wiecek
School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina, USA
Rushabh Sadiwala
Department of Mechanical Engineering, Clemson University, Clemson, South Carolina, USA
Erin K. Doolittle
School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina, USA
Abstract
Many engineering systems are designed to satisfy multiple and conflicting objectives while their performance with respect to these objectives is uncertain. Motivated by such design problems, we develop a model of uncertain multiobjective optimization problem (UMOP) under function uncertainty and present two robust counterparts whose efficient solutions are robust efficient for the UMOP. While the counterparts account for all, possibly infinitely many scenarios, their efficient sets are preserved in or approximated by the efficient sets of associated finite MOPs. The properties of preservation and approximation require that the uncertain functions be constructed by order-preserving operators applied to basis functions making up the objective functions of the finite MOPs. The proposed model of UMOPs under function uncertainty and its resolution are applicable to monotone and linear systems in science and engineering because their performance is governed by order-preserving operators. Examples of linear operators making up a big class of order-preserving operators are included. An engineering design problem illustrates the UMOP model and solution approaches.
Cite this Article as
Hervé Kerivin, Margaret M. Wiecek, Rushabh Sadiwala, and Erin K. Doolittle, Preserving and Approximating Efficient Solutions in Multiobjective Optimization under Function Uncertainty, Optimization Eruditorum, 4(1), 22–52, 2027