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  4. Applying the Harmony Search Algorithm to Combinatorial Optimization Problems

Applying the Harmony Search Algorithm to Combinatorial Optimization Problems

MMC.
2026;
Volume 13, Number 1
: pp. 329–338
https://doi.org/10.23939/mmc2026.01.329
Received: August 04, 2025
Revised: April 10, 2026
Accepted: April 12, 2026

Bouyaakoubi F., Abounaima M. C., El Ouadghiri M. D.  Applying the Harmony Search Algorithm to Combinatorial Optimization Problems.  Mathematical Modeling and Computing. Vol. 13, No. 1, pp. 329–338 (2026)

Authors:
  1. F. Bouyaakoubi
  2. M. C. Abounaima
  3. M. D. El Ouadghiri
1
IA Laboratory, Faculty of Sciences, Moulay Ismail University
2
Laboratory of Intelligent Systems and Applications, Faculty of Sciences and Technologies, Sidi Mohammed Ben Abdellah University
3
IA Laboratory, Faculty of Sciences, Moulay Ismail University

The Harmony Search Algorithm (HSA) is a metaheuristic inspired by the musical composition process that is used to solve complex optimization problems.  This study provides a detailed exploration of the application of HSA to classical combinatorial optimization problems, including the Traveling Salesman Problem (TSP), the Quadratic Assignment Problem (QAP), and the Vehicle Routing Problem (VRP).  The results demonstrate that HSA is an effective method for finding high-quality solutions, even for large-scale instances.  This study also presents an in-depth analysis of HSA parameters, its adaptation to the considered problems, and a comparison with other metaheuristic methods.

harmony search algorithm
combinatorial optimization
TSP
QAP
VRP
TSPLIB
QAPLIB
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