Niching methods for genetic algorithms
Niching methods for genetic algorithms
Algorithm 548: Solution of the Assignment Problem [H]
ACM Transactions on Mathematical Software (TOMS)
Genetic Algorithms and Grouping Problems
Genetic Algorithms and Grouping Problems
A Permutation Based Genetic Algorithm for Minimum Span Frequency Assignment
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Exploiting domain knowledge in system-level MPSoC design space exploration
Journal of Systems Architecture: the EUROMICRO Journal
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Many problems consist in splitting a set of objects into different groups so that each group verifies some properties. In practice, a partitioning is often encoded by an array mapping each object to its group numbering. In fact, the group number of an object does not really matter, and one can simply rename each group to obtain a new encoding. That is what we call the symmetry of the search space in a partitioning problem. This property may be prejudicial for optimization methods such as evolutionary algorithms (EA) which require some diversity during the search. This paper aims at providing a theoretical framework for breaking this symmetry. We define an equivalence relation on the encoding space. This leads us to define a non-trivial search space which eliminates symmetry. We define polynomially computable tools such as equality test, a neighborhood operator and a distance metric applied on the set of partitionings. This work has been applied to the graph coloring problem (GCP). A new distance has been proposed, which is quicker to compute and closer to the problem structure. Computing this distance has been reduced to the linear assignment problem which can be solved polynomially. Using this distance, the analysis of the landscape of the GCP has been carried out.