Iemets O.O., Barbolina T.M.
Lexicographic equivalence in mixed combinatorial optimization of linear-fractional functions on arrangements

The paper substantiates the method of constructing the lexicographic equivalence to solve mixed combinatorial 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. © 2017, Springer Science+Business Media New York.

Keywords: Euclidian problem of combinatorial optimization, lexicographic equivalence, linear-fractional function, optimization problem on arrangements, Combinatorial optimization, Equivalence classes, Optimization, Approximate methods, Combinatorial optimization problems, Directed searches, Equivalence relations, lexicographic equivalence, Objective function values, Objective functions, Optimization problems, Functions

Cite:
Iemets O.O., Barbolina T.M. (2017). Lexicographic equivalence in mixed combinatorial optimization of linear-fractional functions on arrangements. Cybernetics and Systems Analysis, 53 (2), 94-106. doi: https://doi.org/10.1007/s10559-017-9924-8 http://jnas.nbuv.gov.ua/article/UJRN-0000670414 [In Russian].