Abstract. The authors consider the extremum optimization problem with fractional-linear objective functions on combinatorial configuration of permutations under multicriteria condition. The solution methods for fractional-linear problems are analyzed to choose the approach to problem’s solution. A solution technique based on graph theory is proposed. The algorithm of the modified coordinate method’s subprogram with search optimization is described. This subprogram forms a set of points that satisfy additional constraints of the problem. The general solution algorithm without linearization of the objective function and it’s block diagram are proposed. Examples of the algorithm operation are described.

Keywords: extremum problems, combinatorial configurations, fractional-linear functions, multicriteriality condition, modified coordinate method, optimization of search.