In many areas in engineering, economics and science new
developments are only possible by the application of modern
optimization methods.
Theoptimizationproblemsarisingnowadaysinapplicationsaremostly
multiobjective, i.e. many competing objectives are aspired all at
once. These optimization problems with a vector-valued objective
function have in opposition to scalar-valued problems generally not
only one minimal solution but the solution set is very large. Thus
the devel- ment of e?cient numerical methods for special classes of
multiobj- tive optimization problems is, due to the complexity of
the solution set, of special interest. This relevance is pointed
out in many recent publications in application areas such as
medicine ([63, 118, 100, 143]),
engineering([112,126,133,211,224],referencesin[81]),environmental
decision making ([137, 227]) or economics ([57, 65, 217, 234]).
Consideringmultiobjectiveoptimizationproblemsdemands?rstthe
de?nition of minimality for such problems. A ?rst minimality notion
traces back to Edgeworth [59], 1881, and Pareto [180], 1896, using
the naturalorderingintheimagespace.A?rstmathematicalconsideration
ofthistopicwasdonebyKuhnandTucker[144]in1951.Sincethattime
multiobjective optimization became an active research ? eld.
Several books and survey papers have been published giving
introductions to this topic, for instance [28, 60, 66, 76, 112,
124, 165, 188, 189, 190, 215].
Inthelastdecadesthemainfocuswasonthedevelopmentofinteractive
methods for determining one single solution in an iterative
process.
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