Abstract
The article considers multiobjective combinatorial problems on a general configuration of permutations. As is known, combinatorial optimization problems arise in many areas and are associated with solving complex problems. These problems are usually relatively easy to formulate mathematically, but most are computationally complex and require a systematic approach to solve them. The solution to such problems becomes more complicated if two or more objective functions appear in the problem statement, which can characterize different statistical and economic performance indicators. A horizontal method (HM) is proposed for solving multiobjective combinatorial problems on a general set of permutations. The main idea of this method is to use the properties of combinatorial configurations and polytopes of these configurations. The proposed method reduces the search area to solving auxiliary unbounded combinatorial problems and cuts off a part of the polyhedron based on the properties of linear objective functions on graphs. The applicability of the horizontal method to the general configuration of permutations is substantiated. The proposed method for solving multiobjective combinatorial problems belongs to the group of branch and bound methods.
Published Version
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