Multi-objective design of a combinatorial structure
Peter Lindroth, Michael Patriksson, Ann‐Brith Strömberg · 2011
Engineering design problems are often formulated as multi-objective optimization problems. We consider the problem of designing an optimal population of configurations, where the configurations are composed by common elements. Searching for a population of solutions that are good with respect to different combinations of the multiple objectives can be seen as a search for a clustering of the Pareto optimal set to the multi-objective optimization problem. Further, a natural wish is to use common parts to construct the population of design solutions. This paper proposes a (single-objective) optimization problem through which the clustering is performed in a way such that the resulting solutions approximate the Pareto optimal solution well, while at the same time the variables in the decision space are, by construction, required to be common. The procedure is applied to instances constructed from test functions from the literature with interesting results. The usefulness of applying the procedure to practical problems and what types of sensitivity analyses that can be performed are discussed and demonstrated. Suggestions are also made on how to adapt the developed methodology to simulation-based multi-objective optimization problems.