Navigation on a Pareto-optimal front utilizing gradient information in interactive multiobjective optimization

1. Abstract In this paper, utilizing gradient (i.e. derivative) information to navigate through multiobjective optimization solutions is studied. Targets in multiobjective optimization are conflicting, and thus it is impossible to satisfy all of them at the same time. Therefore, new ways to assist the solution process and navigation through a Pareto-optimal front in multiobjective optimization are needed. When using gradient-based multiobjective optimization methods, gradients are needed to be calculated for the optimization problem solver. However, existing gradient information can be utilized thorougher: we present two different ways to control and direct the optimization process interactively by utilizing gradient information. First, gradients can be used for approximating a Pareto-optimal front, and secondly, calculating trade-offs between the optimization targets. Results from the numerical examples indicate that these approaches enable more efficient search for the best possible solution because the approaches predict how the conflicting objectives will behave and they indicate what changes to the current solution are productive to make during the optimization process. This decreases the number of uninteresting solutions calculated, and better solutions can be obtained by finding advantageous trade-offs. 2. Keywords: Nonlinear multiobjective optimization, Interactive methods, Gradient information, Trade-off information, Decision Support.

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