Abstract
We introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires a small amount of expensive function evaluations. We share the implementation of O-NAUTILUS as open source code. Thanks to its graphical user interface, a decision maker can see in real time how the preferences provided affect the direction of the search. We demonstrate the potential and benefits of O-NAUTILUS with a problem related to the design of vehicles.
Highlights
Multiobjective optimization deals with the simultaneous minimization or maximization of multiple conflicting objective functions
Relevant questions include: How can we scale to problems with a large number of objectives? How can we solve problems with realistic, computationally expensive objective function formulations? How can an algorithm conveniently integrate a decision maker (DM)’s preferences into the search? This article answers these questions by proposing a novel method called Optimistic NAUTILUS Navigator method, for short, O-NAUTILUS, which extends the interactive NAUTILUS Navigator method [38] to an online data-driven approach [18], sparingly needing new objective function evaluations during the interactive solution process and displaying additional information to support the DM
In this paper we have proposed a novel method in the NAUTILUS family, termed ONAUTILUS for interactive multiobjective optimization
Summary
Multiobjective optimization deals with the simultaneous minimization or maximization of multiple conflicting objective functions. Trade-off-free interactive methods such as the NAUTILUS family [30] have been proposed They start from an inferior solution and iteratively approach Pareto optimal solutions by simultaneously improving all the objectives while following the DM’s preferences. We use uncertainty quantification in the form of (confidence) bounds from Kriging or Lipschitzian models, to build and update an optimistic approximation of the Pareto optimal set and use this information in the interactive method. The DM has an option to extend the search area and cross the current borders of the estimated Pareto optimal set for further discovery towards optimistic boundaries This will trigger an exploration phase: new evaluations with the costly objective functions are conducted in a targeted way in order to assess possibilities to extend the Pareto optimal set and find an improvement in the preferred direction.
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