An oracle penalty and modified augmented Lagrangian methods with firefly algorithm for constrained optimization problems

Abstract

Almost all engineering optimization problems in the real world are constrained in nature. Swarm intelligence is a bio-inspired technique based on studying and observing fireflies, ants, birds and fish in nature. Firefly algorithm (FA) is the most prominent swarm based metaheuristic algorithm used for solving a global optimization problem. This paper presents two new constrained optimization algorithms: (1) firefly algorithm with extended oracle penalty method (FA-EOPM) and (2) modified augmented Lagrangian with firefly algorithm (MAL-FA). These proposed algorithms are applied for solving classic thirteen benchmark constraint problems as well as a few good engineering problem designs. The efficiency, effectiveness, and performance of MAL-FA and FA-EOPM algorithms are estimated on the basis of statistical analysis such as best optimal value, worst value, mean value, p value and standard deviation value against the existing methods. The experimental results show that the proposed MAL-FA algorithm offers better outcomes for most of the cases in terms of the number of function evaluations compared to various optimization algorithms.