Vector optimization problems with linear criteria over a fuzzy combinatorial set of alternatives

Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations

“…The present paper continues the studies in combinatorial optimization under multicriteriality condition [3,[8][9][10][11][12]. Our purpose is to develop a modified approach to the solution of the multicriteria problem on the set of permutations, to construct an algorithm for the modified approach, and to carry out a numerical experiment.…”

“…As the number of optimization criteria increases, the problem complexity grows [6][7][8][9][10][11] and the need arises to develop a new approach to the solution of vector combinatorial problems since the general algorithm can not always be adapted and applied efficiently. Therefore, the form of its mathematical formulation and search for solution methods are important.…”

Continuous Extensions On Euclidean Combinatorial Configurations

“…Further, we intend to proceed to the study of genetic algorithms for optimization problems on C-sets in view of previous research [50][51][52]. Of interest are methods of parametric and multicriteria optimization on C-sets, taking into account the results of [5,30]. We also plan to focus further research on the development of methods for solving the problems of clustering, packing, layout, and covering [6, 10, 16, 17, 31, 33-35, 44, 48].…”

A mathematical programming problem with the fuzzy set of indices of constraints

“…Various forms of the description of fuzzy initial data can lead to different formulations of fuzzy mathematical programming (FMP) problems: attaining a fuzzy objective under fuzzy constraints [1]; with a fuzzy set of alternatives [2]; with an objective specified by a fuzzy mapping [2]; with a "softened" objective function and (or) constraints [3]; with fuzzy coefficients [3]; vector optimization on a fuzzy combinatorial set of alternatives [4], etc.…”

“…This concept allows determining the set of Pareto optimal alternatives of the two-criteria problem (5), which is the support set of the fuzzy set of solutions of problem (4). For x X Î denote it as…”