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- W2221612995 abstract "Hartikainen, Markus Approximation through Interpolation in Nonconvex Multiobjective Optimization Jyvaskyla: University of Jyvaskyla, 2011, 74 p.(+included articles) (Jyvaskyla Studies in Computing ISSN 1456-5390; 141) ISBN ISBN 978-951-39-4535-0 (nid.) ISBN 978-951-39-4536-7 (PDF) Finnish summary Diss. In this thesis, we develop a PAINT method that constructs a Pareto front approximation by interpolating between a given set of Pareto optimal solutions to a (possibly nonconvex) multiobjective optimization problem. The Pareto front approximation produced by the PAINT method implies a computationally inexpensive mixed integer linear surrogate problem for the original multiobjective optimization problem. The PAINT method is especially useful in alleviating the computational burden of solving computationally expensive multiobjective optimization problems with interactive multiobjective optimization methods. The theory behind the PAINT method is based on the concept of inherent nondominance, which is also introduced in this thesis. We show that inherent nondominance is a desired property for a Pareto front approximation. In addition, the PAINTmethod utilizes concepts from computational geometry by using the Delaunay triangulation as the basis for the approximation. We illustrate the usefulness of the PAINT method by solving two multiobjective optimization problems with the PAINT method and the interactive NIMBUS method. The first problem is a three-objective heat exchanger network synthesis problem and the second one is a five-objective problem of designing and operating a wastewater treatment plant. In both problems, the PAINT method proved to be a very useful tool. In addition, we introduce a new IND-NIMBUS® PAINT module. With this new module, one can use the PAINT method together with the interactive NIMBUS method within a single graphical user interface. The PAINT module is used in the wastewater treatment plant problem mentioned above." @default.
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- W2221612995 date "2011-01-01" @default.
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- W2221612995 title "Approximation through interpolation in nonconvex multiobjective optimization" @default.
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