The Differential Evolution (DE) is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular\nfor its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but\nseveral modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has\nbeen mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial\ndata analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which\nmeet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE)\napplying the principle of the discrete-coded DE in discrete point clouds (PCs). The paper examines the local searching abilities of\nthe MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered\nto get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator\nutilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial\ndatasets and optimization problems.The experiments show that the MDDE is an efficient and fast method for discrete optimizations\nin the multidimensional point clouds.
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