Multiobjective optimization: Quasi-even generation of pareto frontier and its local approximation

Sergei V. Utyuzhnikov

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

3 Citations (Scopus)

Abstract

In multidisciplinary optimization the designer needs to fi d a solution to an optimization problem that includes a number of usually contradicting criteria. Such a problem is mathematically related to the fiel of nonlinear vector optimization with constraints. It is well-known that the solution to this problem is far from unique and given by a Pareto surface. In the real-life design the decision-maker is able to analyze only several Pareto optimal (trade-off) solutions. Therefore, a well-distributed representation of the entire Pareto frontier is especially important. At present, there are only a few methods that are capable of even generating a Pareto frontier in a general formulation. In the present work they are compared to each other, with the main focus being on a general strategy combining the advantages of the known algorithms. The approach is based on shrinking a search domain to generate a Pareto optimal solution in a selected area on the Pareto frontier. The search domain can be easily conducted in the general multidimensional formulation. The efficien y of the method is demonstrated on different test cases. For the problem in question, it is also important to carry out a local analysis. This provides an opportunity for a sensitivity analysis and local optimization. In general, the local approximation of a Pareto frontier is able to complement a quasi-even generated Pareto set.

Original languageEnglish
Title of host publicationHandbook of Optimization Theory
Subtitle of host publicationDecision Analysis and Application
PublisherNova Science Publishers, Inc.
Pages211-235
Number of pages25
ISBN (Print)9781608765003
Publication statusPublished - Jan 2011
Externally publishedYes

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