A hybrid approach to approximate the Pareto front of the MOST problem

Authors

  • Asma Boumesbah Faculty of Mathematics, University of Science and Technology Houari Boumediene, RECITS Laboratory, Algiers, Algeria.
  • Mohamed El-Amine Chergui Faculty of Mathematics, University of Science and Technology Houari Boumediene, RECITS Laboratory, Algiers, Algeria

Abstract

This study introduces a hybrid NSGA-II algorithm with Multi-VNS for approximating the Pareto front of the multi-objective spanning tree (MOST) problem, building on recent approaches that have adapted NSGA-II combined with local search heuristics. By exploiting the property that a spanning tree is acyclic and that the addition of an edge generates a unique cycle, our mutation operator adds edges to a given spanning tree $T$ of a connected graph $G$, thereby reducing the size of the MOST problem. By applying the exact mutation operator with low probability, this reduced problem is solved, producing a set of mutant solutions. The NSGA-II selection operator then approximates the Pareto front, which is further refined by a Multi-VNS metaheuristic to balance diversification and intensification. Comparative experiments with both exact and approximate methods demonstrate promising results.

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Published

2026-01-23

Issue

Vol. 17 No. 1 (2026): CRORR

Section

CRORR Journal Regular Issue

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