Genetic algorithms have proven to be a well-suited technique for solving selected combinatorial optimization problems. When solving real-world problems, often the main task is to find a proper representation for the candidate solutions. Strings of elementary data types with standard genetic operators may tend to create infeasible individuals during the search because of the discrete and often constrained search space. This article introduces a generally applicable representation for two-dimensional combinatorial placement and packing problems. Empirical results are presented for two constrained placement problems, the facility layout problem and the generation of VLSI macro-cell layouts. For multi-objective optimization problems, common approaches often deal with the different objectives in different phases, thus are unable to efficiently solve the global problem. Due to a tree-structured genotype representation and hybrid, problem-specific operators, the proposed approach is able to deal with different constraints and objectives in one optimization step.
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