Continuous Multiobjective Programming

Margaret M. Wiecek (), Matthias Ehrgott () and Alexander Engau ()
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Margaret M. Wiecek: Clemson University
Matthias Ehrgott: Lancaster University
Alexander Engau: Dalhousie University

Chapter Chapter 18 in Multiple Criteria Decision Analysis, 2016, pp 739-815 from Springer

Abstract: Abstract We present our view of the state of the art in continuous multiobjective programming. After an introduction we formulate the multiobjective program (MOP) and define the most important solution concepts in Sect. 18.2. In Sect. 18.3 we summarize properties of efficient and nondominated sets. Optimality conditions are reviewed in Sect. 18.4. The main part of the chapter consists of Sects. 18.5 and 18.6 that deal with solution techniques for MOPs and approximation of efficient and nondominated sets. In Sect. 18.7 we discuss specially-structured problems including linear, nonlinear, parametric, and bilevel MOPs. In Sect. 18.8 we present our perspective on future research directions.

Keywords: Multiobjective programming; Efficient solution; Pareto point; Nondominated solution; Scalarization; Approximation; Representation; Parametric programming; Bilevel programming (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-1-4939-3094-4_18

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