Current Research Directions

A summary of the current research interests is the following:
  • interactive multiobjective optimization methods
  • solving problems with computationally expensive function evaluations
  • software development
  • real-world applications
  • data-driven decision support, prescriptive and decision analytics
  • explainable artificial intelligence
  • robustness
Methods developed include
  • NIMBUS - classification-based interactive method
  • Pareto Navigator - interactive method in particular for computationally expensive problems
  • NAUTILUS - family of interactive methods where the decision maker can gain without sacrifice
  • PAINT - method preparing a comultationally inexpensive surrogate problem
  • K-RVEA - evolutionary method for computationally expensive problems

The most well-known interactive method developed in the group is NIMBUS. NIMBUS is a classification-based method where the decision maker classifies objective functions to indicate the kind of changes that are desired in the current Pareto optimal solution to make it better. Several variants of the method have been published during the years and the synchronous version is currently in use. Examples of thesis topics relating to the current research direction for bachelor, master and doctoral students are available here.

Among more recently developed interactive methods we can mention Pareto Navigator which has been directed for computationally expensive problems. The idea is to create an approximation of the Pareto optimal set and enable the decision maker to navigate on it. On the approximation, changes of trade-offs can be seen in real-time and then any interesting solution can be projected to the real Pareto optimal set. Without the approximation, the navigation would be too slow because calculating new Pareto optimal solutions would take too much time. On the other hand, the interactive NAUTILUS method questions the idea of considering only Pareto optimal solutions throughout the solution process. Instead, the method starts from the nadir point and allows finding the most preferred solution without anchoring and the need of giving up in some objectives. This can be useful also for group decision making situations. We have developed several variants of NAUTILUS where the decision maker has different ways to specify preference information in order to direct the solution process

Because many methods developed in the group are motivated by practical applications, it is important that this work is also brought close to people that in real-life face the actual problems and apply the methods. Therefore, the group has developed and is developing several different interactive tools for multiobjective optimization.

One can say that the most widely available interactive multiobjective optimization software is WWW-NIMBUS (available at, an implementation of the NIMBUS method. WWW-NIMBUS is a web-based software freely available for academic teaching and research use around the world (the first version was published as early as in 1995). Based on the WWW-NIMBUS software, the group has also developed a commercial optimization tool IND-NIMBUS, which is a desktop application operating on Linux and Windows platforms. IND-NIMBUS has been lately used for most industrial applications considered. It is available for industrial partners and a demo-version is available for interested parties (

After testing with demo versions, the implementation of the new interactive methods Pareto Navigator and NAUTILUS has been started so that they can become more widely applicable. In method and related software development, the group is paying special attention to intuitive human-computer interaction. Because interactive methods are supposed to support learning, the way preference information is acquired from and new insight into the problem is presented to the decision maker plays a very important role in the success of the solution process. This research contains user interface and interaction design, usability research, information visualization and visual analytic environments.

The group has been active in building bridges between the MCDM and evolutionary multiobjective optimization (EMO) communities. Examples of hybrid method development include approaches for estimating the nadir point utilizing EMO and achievement scalarizing functions. In addition, the efficiency and accuracy of EMO methods have been improved by hybridizing scalarizing functions and local search in them. Preference information has been also incorporated in EMO methods in the form of a reference point improving efficiency and enabling concentration on interesting Pareto optimal solutions.

Alongside the general theoretical and methodological development, recently, the development of so-called approximation methods has been considered in the group. These methods aim, in a way or another at building or utilizing an approximation of the objective functions or the Pareto optimal set (e.g. meta models, polyhedral and tangent plane approximations). An approximation of the Pareto optimal set is especially useful in the case of industrial applications because problem related models are typically computationally very time-consuming to operate.

Another research direction is related how to tackle with uncertainty in multiobjective optimization problems, that is, how to compare solution alternatives under uncertainty and in changing environments. This research contains studies related to uncertainties in process parameters, optimization of the production plant concepts under different production tasks and production plant design through bilevel multiobjective problem formulation.