Naegele, Philipp Alexander (2010)
Ph.D. thesis, University of Birmingham.
The subject area of multiobjective optimisation deals with the investigation of optimisation problems that possess more than one objective function. Usually, there does not exist a single solution that optimises all functions simultaneously, quite the contrary, in general the set of so-called efficient points, these are solutions to multiobjective optimisation problems, is large. Since it is important for the decision maker to obtain as much information as possible about this set, our research objective is to determine a well-defined and meaningful approximation of the solution set for nonlinear multiobjective optimisation problems. In order to achieve this target we develop an algorithm that employs the optimality conditions introduced by Karush, Kuhn and Tucker for a scalarised objective function and computes solutions to the corresponding system of equations via a modified Newton method. In particular, we utilise an infeasible interior-point technique which determines solutions in the neighbourhood of a central path and therefore, constitutes a path-following approach. We proof the convergence of our algorithm under certain assumptions and develop a warm-start strategy to compute different solutions for varying weighting parameters. Furthermore we examine our numerical implementation in MATLAB and present the results we obtained for several suites of test problems from the literature.
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