Entropy 2013, 15(12), 5475-5491; doi:10.3390/e15125475

Entropy Diversity in Multi-Objective Particle Swarm Optimization

1 INESC TEC—INESC Technology and Science (formerly INESC Porto, UTAD pole), Escola de Ciências e Tecnologia, Universidade de Trás-os-Montes e Alto Douro, 5000–811 Vila Real, Portugal 2 ISEP—Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. António Bernadino de Almeida, 4200–072 Porto, Portugal
* Author to whom correspondence should be addressed.
Received: 30 August 2013; in revised form: 30 November 2013 / Accepted: 3 December 2013 / Published: 10 December 2013
(This article belongs to the Special Issue Dynamical Systems)
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Abstract: Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the final results. In the present paper, a different approach is proposed, by using Shannon entropy to analyze the MOPSO dynamics along the algorithm execution. The results indicate that Shannon entropy can be used as an indicator of diversity and convergence for MOPSO problems.
Keywords: multi-objective particle swarm optimization; Shannon entropy; diversity

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MDPI and ACS Style

Pires, E.J.S.; Machado, J.A.T.; de Moura Oliveira, P.B. Entropy Diversity in Multi-Objective Particle Swarm Optimization. Entropy 2013, 15, 5475-5491.

AMA Style

Pires EJS, Machado JAT, de Moura Oliveira PB. Entropy Diversity in Multi-Objective Particle Swarm Optimization. Entropy. 2013; 15(12):5475-5491.

Chicago/Turabian Style

Pires, Eduardo J.S.; Machado, José A.T.; de Moura Oliveira, Paulo B. 2013. "Entropy Diversity in Multi-Objective Particle Swarm Optimization." Entropy 15, no. 12: 5475-5491.

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