Particle Swarms for Linearly Constrained Optimisation

Article type: Research Article

Authors: Paquet, Ulrich | Engelbrecht, Andries P.

Affiliations: Department of Computer Science University of Pretoria Pretoria, 0002, South Africa. E-mail: [email protected]; [email protected]

Abstract: Particle Swarm Optimisation (PSO) has proved to be a very useful algorithm to optimise unconstrained functions. This paper extends PSO to a Linear PSO (LPSO) to optimise functions constrained by a set of equality constraints of the form Ax=b. By initialising particles within a constrained hyperplane, the LPSO is guaranteed to 'fly' only through this hyperplane. A criterion on the initial swarm stipulates when the optimum solution can possibly be reached. The Linear PSO is modified to the Converging Linear PSO, for which it is proved to always find at least a local minimum. Experimental results are given, which compare the LPSO and CLPSO with Genocop II.

Keywords: Particle Swarm Optimisation, Constrained Optimisation, Convergence Proofs

Journal: Fundamenta Informaticae, vol. 76, no. 1-2, pp. 147-170, 2007