Extensions of Firefly Algorithm for Nonsmooth Nonconvex Constrained Optimization Problems

Abstract

Firefly Algorithm (FA) is a stochastic population-based algorithm based on the flashing patterns and behavior of fireflies. Original FA was created and successfully applied to solve bound constrained optimization problems. In this paper we present extensions of FA for solving nonsmooth nonconvex constrained global optimization problems. To handle the constraints of the problem, feasibility and dominance rules and a fitness function based on the global competitive ranking, are proposed. To enhance the speed of convergence, the proposed extensions of FA invoke a stochastic local search procedure. Numerical experiments to validate the proposed approaches using a set of well know test problems are presented. The results show that the proposed extensions of FA compares favorably with other stochastic population-based methods.

Extension of the firefly algorithm and preference rules for solving MINLP problems

“…The constraint violation and the objective function values are used and compared separately in order to decide which point would be preferred between the two. The technique has been used with different metaheuristics, like the genetic algorithm, evolutionary algorithm, differential evolution, electromagnetismlike algorithm [3,4,5] Recently, a new rule has been added to the set with the goal of solving nonlinear global optimization problems [6]. The authors extended the FA to general constrained global optimization problems by exploring two strategies, one based on the global competitive ranking and the other on the below four described rules.…”

A particle swarm optimization algorithm based on an improved deb criterion for constrained optimization problems

“… Karaboga & Akay (2011) integrated the Deb criterion and an improved artificial bee colony (ABC) algorithm and used a probabilistic selection scheme for feasible solutions based on their fitness values. Francisco, Costa & Rocha (2016) combined the firefly algorithm with feasibility and dominance rules and a fitness function based on global competitive ranking to solve nonsmooth nonconvex constrained global optimization problems. Kohli & Arora (2018) proposed the chaotic grey wolf algorithm for COPs.…”