Abstract
Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect that the solution set forms at least locally a manifold. Recently, the Pareto Tracer (PT) has been proposed, which is such a multi-objective continuation method. While the method works reliably for MOPs with box and equality constraints, no strategy has been proposed yet to adequately treat general inequalities, which we address in this work. We formulate the extension of the PT and present numerical results on some selected benchmark problems. The results indicate that the new method can indeed handle general MOPs, which greatly enhances its applicability.
Highlights
In many real-world applications, the problem occurs that several conflicting and incommensurable objectives have to be optimized concurrently
We show the respective results obtained by the normal boundary intersection (NBI, [16]), the -constraint method [5], and the multi-objective evolutionary algorithm NSGA-II
No comparison to a multi-objective continuation method can be presented since none of the respective codes are publicly available
Summary
In many real-world applications, the problem occurs that several conflicting and incommensurable objectives have to be optimized concurrently. Many different methods for the numerical treatment of MOPs and MaOPs can be found (see the discussion ) One class of such methods is given by specialized continuation methods that take advantage of the fact that the solution set forms—at least locally and under certain mild assumption on the model as discussed in [1]—a manifold. We extend the PT for the treatment of general inequality constraints To this end, we utilize and adapt elements from active set methods to decide which of the inequalities have to be treated as equalities at each candidate solution.
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