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<p>A mathematical model of a multi-objective problem for combinatorial configurations of polypermutations is proposed, and its features are analyzed taking into account the properties of combinatorial configurations and their graphs. A new algorithm for a horizontal approach to solving such problems of finding a set of Pareto-optimal solutions is developed, based on adaptive combinatorial search and heuristic methods. The operation of the proposed algorithm is illustrated by solving a test problem. Based on numerical experiments, the effectiveness of the algorithm on Euclidean configurations of polypermutations and permutations with repetitions is justified, taking into account modern approaches in combinatorial and vector optimization.</p>

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Solving a Multi-Objective Optimization Problem on Combinatorial Point Configurations

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • N. V. Semenova,
  • L. M. Koliechkina,
  • O. A. Dvirna

摘要

A mathematical model of a multi-objective problem for combinatorial configurations of polypermutations is proposed, and its features are analyzed taking into account the properties of combinatorial configurations and their graphs. A new algorithm for a horizontal approach to solving such problems of finding a set of Pareto-optimal solutions is developed, based on adaptive combinatorial search and heuristic methods. The operation of the proposed algorithm is illustrated by solving a test problem. Based on numerical experiments, the effectiveness of the algorithm on Euclidean configurations of polypermutations and permutations with repetitions is justified, taking into account modern approaches in combinatorial and vector optimization.