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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.20 n.2 San José Jul./Dec. 2013


An optimization algorithm inspired by musical composition in constrained optimization problems

Un algoritmo de optimización inspirado en composición musical para el problema de optimización con restricciones

Roman Anselmo Mora-Gutiérrez*+, Javier Ramírez-Rodríguez+, Eric Alfredo Rincón-García+, Antonin Ponsich§+, Oscar Herrera-Alcántara+, Pedro Lara-Velázquez/+

*Dirección para correspondencia:


Many real-world problems can be expressed as an instance of the constrained nonlinear optimization problem (CNOP). This problem has a set of constraints specifies the feasible solution space. In the last years several algorithms have been proposed and developed for tackling CNOP. In this paper, we present a cultural algorithm for constrained optimization, which is an adaptation of “Musical Composition Method” or MCM, which was proposed in [33] by Mora et al. We evaluated and analyzed the performance of MCM on five test cases benchmark of the CNOP. Numerical results were compared to evolutionary algorithm based on homomorphous mapping [23], Artificial Immune System [9] and anti-culture population algorithm [39]. The experimental results demonstrate that MCM significantly improves the global performances of the other tested metaheuristics on same of benchmark functions.

Keywords: Constrained nonlinear optimization, metaheuristics, cultural algorithms, system socio-cultural of creativity, musical composition.


Muchos de los problemas reales se pueden expresar como una instancia del problema de optimización no lineal con restricciones (CNOP). Este problema tiene un conjunto de restricciones, el cual especifica el espacio de soluciones factibles. En los últimos años se han propuesto y desarrollado varios algoritmos para resolver el CNOP. En este trabajo, se presenta un algoritmo cultural para optimización con restricciones, el cual es una adaptación del “Método de Composición Musical” o MCM, propuesto en [33] por Mora et al., para resolver instancias del CNOP. La adaptación propuesta del MCM se aplicó a cinco instancias de prueba del CNOP a fin de evaluar y analizar su comportamiento Los resultados experimentales del MCM se compararon con los resultados obtenidos por algoritmo evolutivo basado en homomorfismo [23] , Sistema Inmune Artificial [9] y el algoritmo de anti-cultural [39]. Los resultados experimentales muestran que el MCM genera resultados significativamente mejores que los obtenidos por las otras metaheurísticas probadas en algunos de los problemas de referencia.

Palabras clave: optimización no lineal con restricciones, metaheurísticas, algoritmos culturales, sistema socio-cultural de la creatividad, composición musical.

Mathematics Subject Classification: 97M40, 90C59, 68T20.

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*Correspondencia a:
Roman Anselmo Mora-Gutiérrez. Departamento de Sistemas, Universidad Autónoma Metropolitana - Azcapotzalco. Avenida San Pablo 180, Colonia Reynosa Tamaulipas, 02200 México D. F. E-Mail:
Javier Ramírez-Rodríguez. Departamento de Sistemas, Universidad Autónoma Metropolitana and LIA Université d’Avignon et des Pays de Vaucluse, same address that Mora,
Eric Alfredo Rincón-García. Misma dirección que/Same address as: R.A. Mora, E-Mail:
Antonin Ponsich.
Misma dirección que/Same address as: R.A. Mora, E-Mail:
Oscar Herrera-Alcántara. Misma dirección que/Same address as: R.A. Mora, E-Mail:
Pedro Lara-Velázquez. Misma dirección que/Same address as: R.A. Mora, E-Mail: pedro
*Departamento de Sistemas, Universidad Autónoma Metropolitana - Azcapotzalco. Avenida San Pablo 180, Colonia Reynosa Tamaulipas, 02200 México D. F. E-Mail:
Departamento de Sistemas, Universidad Autónoma Metropolitana and LIA Université d’Avignon et des Pays de Vaucluse, same address that Mora,
Misma dirección que/Same address as: R.A. Mora, E-Mail:
§Misma dirección que/Same address as: R.A. Mora, E-Mail:
Misma dirección que/Same address as: R.A. Mora, E-Mail:
/Misma dirección que/Same address as: R.A. Mora, E-Mail: pedro

Received: 14/Mar/2012; Revised: 22/May/2013; Accepted: 28/May/2013

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