IFA-EO: An Improved Firefly Algorithm Hybridized With Extremal Optimization for Continuous Unconstrained Optimization Problems

As one of the evolutionary algorithms, firefly algorithm (FA) has been widely used to solve various complex optimization problems. However, FA has significant drawbacks in slow convergence rate and is easily trapped into local optimum. To tackle these defects, this paper proposes an improved FA combined with extremal optimization (EO), named IFA-EO, where three strategies are incorporated. First, to balance the tradeoff between exploration ability and exploitation ability, we adopt a new attraction model for FA operation, which combines the full attraction model and the single attraction model through the probability choice strategy. In the single attraction model, small probability accepts the worse solution to improve the diversity of the offspring. Second, the adaptive step size is proposed based on the number of iterations to dynamically adjust the attention to the exploration model or exploitation model. Third, we combine an EO algorithm with powerful ability in local-search into FA. Experiments are tested on two group popular benchmarks including complex unimodal and multimodal functions. Our experimental results demonstrate that the proposed IFA-EO algorithm can deal with various complex optimization problems and has similar or better performance than the other eight FA variants, three EO-based algorithms, and one advanced differential evolution variant in terms of accuracy and statistical results.

Firefly Algorithm based on Euclidean Metric and Dimensional Mutation

Firefly algorithm is a meta-heuristic stochastic search algorithm with strong robustness and easy implementation. However, it also has some shortcomings, such as the "oscillation" phenomenon caused by too many attractions, which makes the convergence speed is too slow or premature. In the original FA, the full attraction model makes the algorithm consume a lot of evaluation times, and the time complexity is high. Therefore, In this paper, a novel firefly algorithm (EMDmFA) based on Euclidean metric (EM) and dimensional mutation (DM) is proposed. The EM strategy makes the firefly learn from its nearest neighbors. When the firefly is better than its neighbors, it learns from the best individuals in the population. It improves the FA attraction model and dramatically reduces the computational time complexity. At the same time, DM strategy improves the ability of the algorithm to jump out of the local optimum. The experimental results show that the proposed EMDmFA significantly improves the accuracy of the solution and better than most state-of-the-art FA variants.

LAND USE IN THE BAB AL-MOADHAM AREA

The Bab al- moadham area is distinguished by the diversity of land uses, and the main objective of this is to study the land uses in the region. To achieve the study objective, the study area is divided into two zones. A conversation mechanism has been adopted to collect data. The data collection included all education centers, state institutions, shopping centers and health centers, and their numbers were 21 educational centers, 10 centers belonging to state institutions, 5 shopping centers, 12 health centers. The use of land for educational purposes is very wide compared to the rest of the types of land uses, and the study area is a non –residential area. The number of daily personal trips for educational use is 51549 between students and employees. Because of this varied use of land in the study area, it is considered a high attraction for trips, which helps this study to create an attraction model for the Bab al-Moadham area.

Enhancing firefly algorithm with multiple swarm strategy

Firefly algorithm (FA) is one of most important nature-inspired algorithm based on swarm intelligence. Meanwhile, FA uses the full attraction model, which results too many unnecessary movements and reduces the efficiency of searching the optimal solution. To overcome these problems, this paper presents a new job, how the better fireflies move, which is always ignored. The novel algorithm is called multiple swarm strategy firefly algorithm (MSFFA), in which multiple swarm attraction model and status adaptively switch approach are proposed. It is characterized by employing the multiple swarm attraction model, which not only improves the efficiency of searching the optimal solution, but also quickly finds the better fireflies that move in free status. In addition, the novel approach defines that the fireflies followed different rules in different status, and can adaptively switch the status of fireflies between the original status and the free status to balance the exploration and the exploitation. To verify the robustness of MSFFA, it is compared with other improved FA variants on CEC2013. In one case of 30 dimension on 28 test functions, the proposed algorithm is significantly better than FA, DFA, PaFA, MFA, NaFA,and NSRaFA on 24, 23, 23, 17, 15, and 24 functions, respectively. The experimental results prove that MSFFA has obvious advantages over other FA variants.