Solving Extremum Problems with Linear Fractional Objective Functions on the Combinatorial Configuration of Permutations Under Multicriteriality

Multiobjective Optimization on Permutations with Applications

“…For instance, an element of the set ( 6) is called an ideal solution [4,10,[23][24][25], and it is the best for all the particular criteria, respectively, for MP as well. At the same time, Pareto optimality (see (7)) means that the value of any of the particular criteria can be increased only by reducing the value of at least one of the other particular criteria. For a weakly effective estimate/solution (8) there will be no such estimate/solution that would be better with respect to all particular criteria.…”

“…In [4,6,7,10,20,22,25], methods for solving multiobjective optimization problems are considered, both constrained and unconstrained. In such studies [4,6,7,10,20,22,25], various approaches to 1 2 * their solution are offered. In particular, methods of a search and examining the whole feasible domain are described in [4,10,20].…”

“…Since real-world systems are discrete-continuous by nature, they are modeled as partially integer programs. In particular, numerous problems of planning, management, design, and placement are modeled with the help of multiobjective problems whose solutions are of combinatorial nature, e.g., permutations, partial permutations, combinations, compositions, partitions, as well as their composition images [5,7,8,[22][23][24]. In this case, the search for an optimal solution is conducted on the correspondent combinatorial set or its proper subset.…”

“…MCP approaches take mainly are based on structural peculiarities of a particular combinatorial set. In [7,8], a multiobjective optimization on permutations without repetitions is considered. The formulation of MCP on poly-partial permutations is formulated in [22,23], and an approach to its solution using polyhedral relaxation is offered from the group of cutting methods.…”