Particle swarm optimization (analysis)
- Analysis title
- Particle swarm optimization
- Provider
- Institute of Systems Biology
- Class
MOPSOOptMethod
- Plugin
- ru.biosoft.analysis.optimization (Common methods of data optimization analysis plug-in)
Multi-objective particle swarm optimization (MOPSO)
The particle swarm optimization (PSO) algorithm, initially proposed by Kennedy and Eberhart^{1}, is a direct search algorithm based on the simulation of the social behavior of birds within a flock. The swarm is typically modeled by particles in the multidimensional space that have a position and a velocity. These particles fly through hyperspace and have two essential reasoning capabilities: their memory of their own best position and knowledge of the global or their neighborhood's best.
Let x_{i}(t) denote the position of particle p_{i} at time step t. The position of p_{i} is then changed by adding a velocity v_{i}(t) to its current position, i.e.
x_{i}(t) = x_{i}(t − 1) + v_{i}(t). |
Let gbest is the position of the best particle from the entire swarm and pbest is the position of the neighborhood best that the particle obtained by communicating with a subset of the swarm. In this case, velocity equation is given by
v_{i}(t) = W·v_{i}(t − 1) + C_{1}r_{1}(x_{pbest} − x_{i}(t)) + C_{2}r_{2}(x_{gbest} − x_{i}(t)), |
where W is the inertia weight, C_{1} and C_{2} are the learning factors (usually defined as constants), and r_{1}, r_{2} ∈ [0,1] are random values.
Here we used a multiple-objective particle swarm optimizers based on the paper of Sierra and Coello^{2}. This optimizer allows to take into account parametric constraints and uses a crowding factor for the leaders selection as well as the following mutation operators: an uniform mutation operator, where the variability range allowed for each decision variable is constant over generations, and a non-uniform mutation operator, where such range decreases over time. These operators modify the values of the particle decision variables with a certain probability.
References
- J Kennedy, RC Eberhart. "Particle Swarm Optimization". Proceedings of the 1995 IEEE International Conference on Neural Networks, Piscataway, New Jersey, IEEE Service Center, 1995, 1942-1948.
- MR Sierra and CA Coello Coello "Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and e-Dominance." Evolutionary Multi-Criterion Optimization, 3410/2005: 505-519, Springer Berlin/Heidelberg.