Extending the Speed-Constrained Multi-objective PSO (SMPSO) with Reference Point Based Preference Articulation

Antonio J. Nebro, Juan José Durillo, José García-Nieto, Cristóbal Barba-González, Javier Del Ser, Carlos A. Coello Coello, Antonio Benítez-Hidalgo, José Francisco Aldana Montes

Abstract: The Speed-constrained Multi-objective PSO (SMPSO) is an approach featuring an external bounded archive to store non-dominated solutions found during the search and out of which leaders that guide the particles are chosen. Here, we introduce SMPSO/RP, an extension of SMPSO based on the idea of reference point archives. These are external archives with an associated reference point so that only solutions that are dominated by the reference point or that dominate it are considered for their possible addition. SMPSO/RP can manage several reference point archives, so it can effectively be used to focus the search on one or more regions of interest. Furthermore, the algorithm allows interactively changing the reference points during its execution. Additionally, the particles of the swarm can be evaluated in parallel. We compare SMPSO/RP with respect to three other reference point based algorithms. Our results indicate that our proposed approach outperforms the other techniques with respect to which it was compared when solving a variety of problems by selecting both achievable and unachievable reference points. A real-world application related to civil engineering is also included to show up the real applicability of SMPSO/RP.