Adaptive Scalarization Methods in Multiobjective Optimization Paperback / softback

by Gabriele Eichfelder

Part of the Vector Optimization series

Paperback / softback

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Description

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.