Adaptive discretization on multidimensional continuous search spaces

This paper extends an adaptive discretization method, Split-on-Demand (SoD), to be capable of handling multidimensional continuous search spaces. The proposed extension is called multidimensional Split-on-Demand (mSoD), which considers multiple dimensions of the search space as a whole instead of independently discretizing each dimension as SoD does. In this study, we integrate mSoD and SoD with the extended compact genetic algorithm (ECGA) to numerically examine the effectiveness and performance of mSoD and SoD on the problems with and without linkage among dimensions of the search space. The experimental results indicate that mSoD outperforms SoD on both types of the test problems and that mSoD can offer better scalability, stability, and accuracy. The behavior of mSoD is discussed, followed by the potential future work.

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