SMPSO (Speed constrained Multi-objective PSO) is a metaheuristic based on the OMOPSO algorithm (BIBTEX) that was designed to cope with difficulties of this technique when solving multi-modal problems. The SMPSO approach is to apply a constraint velocity scheme to control the so-called swarm explosion

• Velocity constriction mechanism
• External archive to store the non-dominated solutions (leaders)
  • Density estimator: crowding distance
• Leader selection: binary tournament from the leaders archive taking into account the crowding distance
• Mutation (turbulence) operator: polynomial mutation

The SMPSOhv variant, presented in CEC 2013, has the following features:

• Density estimator: hypervolume contribution
• Leader selection: binary tournament from the leaders archive taking into account the hypervolume contribution

Leader selection:

• SMPSO: the particles in the archive having larger crowding distance have more chances to be choosen as a leader
• SMPSOhv: the particles in the archive contributing the most to the hypevolume have more chances to be choosen as a leader

Leader replacement:

• SMPSO: the particle in the archive having the smallest crowding distance is removed
• SMPSOhv: the particle in the archive contributing the least to the hypevolume is removed

• A.J. Nebro, J.J. Durillo, J. García-Nieto, C.A. Coello Coello, F. Luna and E. Alba. SMPSO: A New PSO-based Metaheuristic for Multi-objective Optimization. IEEE Symposium on Computational Intelligence in Multicriteria Decision-Making (MCDM 2009), pp: 66-73. March 2009. BIBTEX
• J.J. Durillo, J. García-Nieto, A.J. Nebro, C.A. Coello Coello, F. Luna and E. Alba. Multi-Objective Particle Swarm Optimizers: An Experimental Comparison. 5th International Conference, EMO 2009, pp: 495-509. April 2009. BIBTEX
• J.J. Durillo, A.J. Nebro, C.A. Coello Coello, J. García-Nieto, F. Luna, E. Alba. A Study of Multi-Objective Metaheuristics when Solving Parameter Scalable Problems. IEEE Transactions on Evolutionary Computation. Vol. 14, No. 4 (August 2010), pp. 618-635. BIBTEX DOI
• A.J Nebro, J.J. Durillo, C.A. Coello Coello. Analysis of Leader Selection Strategies in a Multi-Objective Particle Swarm Optimizer. 2013 IEEE Congress on Evolutionary Computation. June 2013.