Solving Bi-objective Many-Constraint Bin Packing Problems in Automobile Sheet Metal Forming Processes

The solution of bi-objective bin packing problems with many constraints is of fundamental importance for a wide range of engineering applications such as wireless communication, logistics, or automobile sheet metal forming processes. When the bi-objective bin packing problem is single-constrained, state-of-the-art multi-objective genetic algorithms such as NSGA-II combined with standard constraint handling techniques can be used. In the case of many-constraint bin packing problems, problems with thousand of additional constraints, it is not easy to solve this kind of problem accurately and fast with classical methods. Our approach relies on two key ingredients, NSGA-II and a clustering algorithm in order to generate always feasible solutions independent of the number of constraints. The method allows to tackle bi-objective many-constraint bin packing problems. We will present results for challenging artificial bin packing problems which model typical bi-objective bin packing problems with many constraints arising in the automobile industry.