A hybrid method for multidimensional scaling using city-block distances

The problem of multidimensional scaling with city-block distances in the embedding space is reduced to a two level optimization problem consisting of a combinatorial problem at the upper level and a quadratic programming problem at the lower level. A hybrid method is proposed combining randomized search for the upper level problem with a standard quadratic programming algorithm for the lower level problem. Several algorithms for the combinatorial problem have been tested and an evolutionary global search algorithm has been proved most suitable. An experimental code of the proposed hybrid multidimensional scaling algorithm is developed and tested using several test problems of two- and three-dimensional scaling.