A note on construction of heuristically optimal Pena’s synthetic indicators by the particle swarm method of global optimization

Pena’s method of construction of a synthetic indicator is very sensitive to the order in which the constituent variables (whose linear aggregation yields the synthetic indicator) are arranged. Due to this, Pena’s method can at present give only an arbitrary synthetic indicator whose representativeness is indeterminate and uncertain, especially when the number of constituent variables is not very small. This paper uses discrete global optimization method based on the Particle Swarms to obtain a heuristically optimal order in which the constituent variables can be arranged so as to yield Pena’s synthetic indicator that maximizes the minimal absolute (or squared) correlation with its constituent variables.