The Cost-Sorted Distance Method for Identifying Minima Within Firefly Optimization Results: Application to Engineering Design

Abstract

Abstract This paper provides a detailed description of the cost-sorted distance (CSD) method for visually and computationally identifying objective function minima within clustered population-based optimization results. CSD requires sorting the design vector population by cost and computing Euclidean distances between each pair of designs. It may be applied in conjunction with any population-based optimization method (e.g., particle swarm, genetic algorithm, simulated annealing, ant colony, firefly), but it is naturally compatible with the firefly algorithm (FA) because FA also requires the distances between each pair of design vectors and benefits from cost-sorting the population (the computational work required for CSD is a byproduct of FA). A modified FA is presented that uses CSD to more thoroughly search near potential minima and a systematic method for tuning the algorithm to reliably identify multiple minima is documented. The tuned algorithm's efficacy is demonstrated using a class of benchmark problems and a “real world” electromechanical design problem, where the identification of attractive design alternatives can be challenging.