A Dynamic Treatment Criterion of Population Sizes in PSO

Resumo

Populational algorithms are strongly dependent on parameters, and among them, the size of the pop-
ulation directly impacts the search for optimized solutions and computational cost. As the population grows, the

slice of the inspected search space also tends to expand, allowing new optimums to be discovered. However, the

increase in this population also implies an increase in the objective function calls, consequently increasing the al-
gorithms’ computational effort and execution time. When the objective function calls are the execution bottleneck,

the number of individuals observed at each iteration is decisive for the weight given to exploration and exploita-
tion. In general, the choice of population size happens empirically, through the user’s experience. However, the

dynamic treatment of population size can be a more interesting choice. In optimization problems that require a
simulator, such as optimization in mechanical and structural engineering, the decrease in computational cost is

very significant. Moreover, many simulations have high computational costs, motivating the study of a less empir-
ical approach in population size choosing. Here we propose and study an approximation metamodel in the form

of a criterion for dynamic treatment of the population size of a Particle Swarm Optimization algorithm applied to
mechanical engineering optimization problems. This metamodel considers that particles that are very close and
with similar speeds will have similar behavior, tending to the same solution, thus allowing one of the particles to
be eliminated. Comparative results are presented using the proposed strategy, showing that it achieved the desired
expectations.