Abstract. The paper substantiates the method of constructing the lexicographic equivalence to solve mixed c ombinatorial optimization problems on arrangements with linear-fractional objective function and linear additional constraints. The method involves directed search of equivalence classes obtained by splitting polyhedral set using equivalence relation. The authors propose exact methods as well as an approximate one. The approximate method allows getting the objective function value that differs from the optimum by no more than a predetermined value.

Keywords: Euclidian problem of combinatorial optimization, optimization problem on arrangements, lexicographic equivalence, linear-fractional function.