In this paper, we have investigated a new spectral Quasi-Newton (QN) Algorithm. New search directions of the proposed Algorithm increase its stability and increase the arrival to the optimum solution with a lowest cost value and our numerical applications on the standard Firefly Algorithm (FA)and the new proposed Algorithm are powerful as in meta-heuristic field. Our new proposed Algorithm has quite common uses in several sciences and engineering problems. Finally, our numerical results show that the proposed technique is the best and its accuracy higher than the accuracy of the standard FA. These numerical results are compared using statistical analysis to evaluate the efficiency and the robustness of new proposed Algorithm.

Evolutionary Algorithms are among the most powerful Algorithms for Optimization, Firefly Algorithm (FA) is one of them that inspired by nature. It is an easily implementable, robust, simple and flexible technique. On the other hand, Integration of this Algorithm with other Algorithms, can be improved the performance of FA. Particle Swarm Optimization (PSO) and Gravitational Search Algorithm (GSA) are suitable and effective for integration with FA. Some method and operation in GSA and PSO can help to FA for fast and smart searching. In one version of the Gravitational Search Algorithm (GSA), selecting the K-best particles with bigger mass, and examining its effect on other masses has a great help for achieving the faster and more accurate in optimal answer. As well as, in Particle Swarm Optimization (PSO), the candidate answers for solving Optimization problem, are guided by local best position and global best position to achieving optimal answer. These operators and their combination with the Firefly Algorithm (FA) can improve the performance of the search Algorithm. This paper intends to provide models for improvement Firefly Algorithm using GSA and PSO operation. For this purpose, 5 scenarios are defined and then, their models are simulated using MATLAB software. Finally, by reviewing the results, It is shown that the performance of introduced models are better than the standard Firefly Algorithm.

In this paper, a new and an effective combination of two metaheuristic Algorithms, namely Firefly Algorithm and the Differential evolution, has been proposed. This hybridization called as HFADE, consists of two phases of Differential Evolution (DE) and Firefly Algorithm (FA). Firefly Algorithm is the nature-inspired Algorithm which has its roots in the light intensity attraction process of Firefly in the nature. Differential evolution is an Evolutionary Algorithm that uses the evolutionary operators like selection, recombination and mutation. FA and DE together are effective and powerful Algorithms but FA Algorithm depends on random directions for search which led into retardation in finding the best solution and DE needs more iteration to find proper solution. As a result, this proposed method has been designed to cover each Algorithm deficiencies so as to make them more suitable for Optimization in real world domain. To obtain the required results, the experiment on a set of benchmark functions was performed and findings showed that HFADE is a more preferable and effective method in solving the high-dimensional functions.

Software testing is an expensive and time-consuming process. These costs can be significantly reduced using automated methods. Recently, many researchers have focused on automating this process using search Algorithms. Many different methods have been proposed, all of which using a means of heuristic or meta-heuristic search Algorithms. The main problem with these methods is that they are usually stuck in local optima. In this paper, to overcome such a problem, we have combined the Firefly Algorithm (FA) and asexual reproduction Optimization Algorithm (ARO). FA is a bio-inspired Algorithm that is very efficient at exploitation and local searches; however, it suffers from poor exploration and is prone to local optima problem. On the other hand, ARO can be used for escaping from local optima. For this combination, we have inserted ARO into the steps of FA for increasing the population diversity. We have utilized this combination for automatic test case generation with the aim of covering all finite paths of the control flow graph. To evaluate the performance of the proposed method, we have utilized it for generating test cases for a number of programs. Results have indicated that, while giving similar results in terms of the test coverage, the proposed method is significantly better than the existing state of the art Algorithms in terms of the number of fitness evaluations. Compared Algorithms are FA, ARO, traditional genetic Algorithm (TGA), adaptive genetic Algorithm (AGA), adaptive particle swarm Optimization (APSO), hybrid genetic tabu search Algorithm (HGATS), random search (RS), differential evolution (DE), and hybrid cuckoo search and genetic Algorithm (CSGA).

Water distribution networks are one of the important and costly infrastructures of cities and many meta-heuristic Algorithms in standard or hybrid forms were used for optimizing water distribution networks. These Algorithms require a large amount of computational cost. Therefore, the converging speed of Algorithms toward the Optimization goal is as important as the goal itself. In this paper, a new method is developed by linking the charged system search Algorithm and Firefly Algorithm for optimizing water distribution networks. For evaluating the proposed method, some popular benchmark examples are considered. Simulation results demonstrate the efficiency of the proposed Algorithm compared to others.

In this paper, the effect of carboxyl methyl cellulose (CMC), konjac gum (KG) and sage seed gum (SSG) and their mixtures on dynamic rheological properties of the instant camel yogurt samples were investigated, Then, these properties were optimized using mixture design models and Firefly Algorithm. The results of the stress sweep tests for different samples showed that the elastic modulus (G') values were greater than viscous modulus (G') indicating behavior essentially like that of solids. Results showed the synergistic effect of these three gums, especially the synergistic effect of SSG and CMC on the critical strain and the yield stress of instant camel yogurt samples. Frequency sweep test results showed that samples had a typical weak gellike structure behavior at any given frequency and complex viscosity ( *) had a linear correlation with frequency. SSG had the most positive effect on k’ , k" and k* but the combination with CMC and KG could also improve this effect. All the linear terms in the predicted models for the n’ , n" and n* parameters were insignificant (p<0. 01) and it was observed that each gum had an identical effect on these parameters. The optimal results of different gum percentages to achieve maximum γ c, n′ , k′ , n″ , n*, k* and minimum G˝ LVE using the Firefly Algorithm in PC space, it has been shown that the optimum amounts of KG and SSG were close to each other and had more variance of the data which shows the similarity of the effect of these two gums on the rheological parameters. Promising result of this study also showed that SSG as a novel source of hydrocolloid could act very capable and produce desirable properties in instant camel yogurt.

Taking into account that the stability analysis of the earth slopes is a complicated geotechnical problem and conventional methods of analyses because of circular slip surface assumption, are incapable to estimate the location of the slip surface especially in non-homogeneous earth slopes. Therefore, the new methods for the study of these types of slopes are necessary. Nowadays, the methods based on Optimization principles are developed and the main point in the application of these new methods is the evaluation of the capability of these methods. Therefore, optimizing these problems needs robust Algorithms. In this research, three meta- heurestic Algorithms were applied for the slope stability analyzing of three studied and selected cases from literature. For all three cases of study, a non-circular slip surface is considered. Factor of safety was computed and compared with the same cases analysed analytically. The obtained results indicated that ICA had the best performance and FA had the worst results for the cases studied in this research.