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## 4 Summary And Further Development

A framework for the interactive resolution of multi-objective vehicle routing problems has been presented. The concept has been prototypically implemented in a computer system. Preliminary results on a benchmark instance have been reported. First investigations indicate that the concept may successfully solve vehicle routing problems under multiple objectives and complex side constraints. In this context, an interaction with the system is provided by a graphical user interface. The relative importance of the objective functions can be modified by means of a slider bar, resulting in different solutions which are computed in real time by the system, therefore providing an immediate feedback to **the user. Figure 3 shows two extreme**
solutions that have been interactively obtained by the system.

Future developments are manifold. First, other ways of representing preferences than a weighted sum approach may be beneficial to investigate. While the comparable easy interaction with the GUI by means of a slider bar enables the user to directly change the relative importance of the objective functions, it prohibits the definition of more complex preference information, e. g. involving aspiration levels. Second, different and improved ways of implementing the market mechanism have to be investigated. First results indicate that the quality of the solutions is biased with respect to the initial setting of the relative importance of the optimality criteria. It appears as if more complex reallocations of orders between vehicles are needed to address this issue. Finally, more investigations on benchmark instances will be carried out. Apart from test cases known from literature we aim to address particularly problems with unusual, complex side constraints and