Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Finding smooth maps is NP-complete
Information Processing Letters
On Multi-Dimensional Encoding/Crossover
Proceedings of the 6th International Conference on Genetic Algorithms
Finding smooth maps is NP-complete
Information Processing Letters
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We study the combinatorial optimization task of choosing the smoothest map from a given family of maps, which is motivated from motor control unit calibration. The problem is of a particular interest because of its characteristics: it is NP-hard, it has a direct and important industrial application, it is easy-to-state and it shares some properties of the wellknown Ising spin glass model. Moreover, it is appropriate for the application of randomized algorithms: for local search heuristics because of its strong 2-dimensional local structure, and for Genetic Algorithms since there is a very natural and direct encoding which results in a variable alphabet. We present the problem from two points of view, an abstract view with a very simple definition of smoothness and the real-world application. We run local search, Genetic and Memetic Algorithms. We compare the direct encoding with unary and binary codings, and we try a 2-dimensional encoding. For a simple smoothness criterion, the Memetic Algorithm clearly performs best. However, if the smoothness citerion is more complex, the local search needs many function evaluations. Therefore we prefer the pure Genetic Algorithm for the application.