Extensions of firefly algorithm for nonsmooth nonconvex constrained optimization problems

Publicado em: "Computational science and its applications – ICCSA 2016: 16th International Conference, Beijing, China, July 4-7, 2016, Proceedings, Part I". ISBN 978-3-319-42084-4Firefly 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.COMPETE: POCI-01-0145- FEDER-007043FCT – Fundação para a Ciência e Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/201

Heuristic-based firefly algorithm for bound constrained nonlinear binary optimization

Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper,we address the practical testing of aheuristic-based FA (HBFA) for computing optimaof discrete nonlinear optimization problems,where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid ‘erf’ function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid ‘erf’ function with ‘movements in continuous space’ is the best, both in terms of computational requirements and accuracy.Fundação para a Ciência e a Tecnologia (FCT

Theoretical and practical convergence of a self-adaptive penalty algorithm for constrained global optimization

This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems.The authors would like to thank the referees, the Associate Editor and the Editor-in-Chief for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Funda¸c˜ao para a Ciˆencia e Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

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

An extension of the firefly algorithm (FA) for solving mixed-integer nonlinear programming (MINLP) problems is presented. Although penalty functions are nowadays frequently used to handle integrality conditions and inequality and equality constraints, this paper proposes the implementation within the FA of a simple rounded-based heuristic and four preference rules to find and converge to MINLP feasible solutions. Preliminary numerical experiments are carried out to validate the proposed methodology.This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundac¸ao para a Ci ˜ encia e Tecnologia, ˆ within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Parameter calibration of a system dynamics model. A comparison of three evolutionary algorithms

This research seeks to improve the parameter calibration process of a System Dynamics model. A movie release strategies" model has been developed in 2012 using a gradient-based optimization algorithm to estimate all the parameters. On this research, three modern optimization algorithms are initially compared using mathematical benchmark functions and then tested with the model to compare results. The tested algorithms are modifications of the Artificial Bee Colony algorithm, the Cuckoo Search and the Genetic Sampler. The results show that by using the Artificial Bee Colony algorithm, better performance is achieved in terms of speed and fitness. It is also shown how the optimization problem definition was improved resulting from a better optimization process.GEO-SD360JMASV-SYS

Designs of Digital Filters and Neural Networks using Firefly Algorithm

Firefly algorithm is an evolutionary algorithm that can be used to solve complex multi-parameter problems in less time. The algorithm was applied to design digital filters of different orders as well as to determine the parameters of complex neural network designs. Digital filters have several applications in the fields of control systems, aerospace, telecommunication, medical equipment and applications, digital appliances, audio recognition processes etc. An Artificial Neural Network (ANN) is an information processing paradigm that is inspired by the way biological nervous systems, such as the brain, processes information and can be simulated using a computer to perform certain specific tasks like clustering, classification, and pattern recognition etc. The results of the designs using Firefly algorithm was compared to the state of the art algorithms and found that the digital filter designs produce results close to the Parks McClellan method which shows the algorithm’s capability of handling complex problems. Also, for the neural network designs, Firefly algorithm was able to efficiently optimize a number of parameter values. The performance of the algorithm was tested by introducing various input noise levels to the training inputs of the neural network designs and it produced the desired output with negligible error in a time-efficient manner. Overall, Firefly algorithm was found to be competitive in solving the complex design optimization problems like other popular optimization algorithms such as Differential Evolution, Particle Swarm Optimization and Genetic Algorithm. It provides a number of adjustable parameters which can be tuned according to the specified problem so that it can be applied to a number of optimization problems and is capable of producing quality results in a reasonable amount of time