The German Research Foundation (DFG) is financing a research project on the particular challenges arising in many-objective optimization, where more than two conflicting objective functions are considered simultaneously. Such objective functions can model ecological and economical criteria, the quality, reliability and cost of a technical structure, or the travel time, travel cost and convenience in routing applications. The focus lies in combinatorial problems like multiobjective knapsack problems, multiobjective assignment problems, and multiobjective network optimization problems including shortest path and spanning tree problems.
The complexity of multiobjective combinatorial optimization problems largely depends on the number of considered objective functions. In this project, the geometrical and combinatorial structure of the Pareto set, i.e., the set of all those solutions that can not be improved in one objective without deterioration in at least one other objective, will be used to achieve a new level of understanding for higher-dimensional problems. This includes the determination of concise representations of the search area and of representative subsets as well as the analysis of different preference structures and quality indicators.