scholarly journals Optimal Randomness in Swarm-Based Search

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 828 ◽  
Author(s):  
Jiamin Wei ◽  
YangQuan Chen ◽  
Yongguang Yu ◽  
Yuquan Chen
Keyword(s):  
Probability Distributions ◽  
Cauchy Distribution ◽  
Cuckoo Search ◽  
Search Algorithms ◽  
Lévy Flights ◽  
Lévy Distribution ◽  
Resource Searching ◽  
Levy Flights ◽  
Levy Distribution ◽  
Heavy Tailed

Lévy flights is a random walk where the step-lengths have a probability distribution that is heavy-tailed. It has been shown that Lévy flights can maximize the efficiency of resource searching in uncertain environments and also the movements of many foragers and wandering animals have been shown to follow a Lévy distribution. The reason mainly comes from the fact that the Lévy distribution has an infinite second moment and hence is more likely to generate an offspring that is farther away from its parent. However, the investigation into the efficiency of other different heavy-tailed probability distributions in swarm-based searches is still insufficient up to now. For swarm-based search algorithms, randomness plays a significant role in both exploration and exploitation or diversification and intensification. Therefore, it is necessary to discuss the optimal randomness in swarm-based search algorithms. In this study, cuckoo search (CS) is taken as a representative method of swarm-based optimization algorithms, and the results can be generalized to other swarm-based search algorithms. In this paper, four different types of commonly used heavy-tailed distributions, including Mittag-Leffler distribution, Pareto distribution, Cauchy distribution, and Weibull distribution, are considered to enhance the searching ability of CS. Then four novel CS algorithms are proposed and experiments are carried out on 20 benchmark functions to compare their searching performances. Finally, the proposed methods are used to system identification to demonstrate the effectiveness.

Improving Cuckoo Search Algorithm With Mittag-Leffler Distribution

2019 ◽  
Author(s):  
Jiamin Wei ◽  
YangQuan Chen ◽  
Yongguang Yu ◽  
Yuquan Chen
Keyword(s):  
Search Algorithm ◽  
Cuckoo Search ◽  
Search Space ◽  
Cuckoo Search Algorithm ◽  
Lévy Flights ◽  
Lévy Distribution ◽  
Levy Flights ◽  
Levy Distribution ◽  
Heavy Tailed ◽  
The Impact

Abstract Cuckoo search (CS), as one of the recent nature-inspired metaheuristic algorithms, has proved to be an efficient approach due to the combination of Lévy flights, local search capabilities and guaranteed global convergence. CS uses Lévy flights in global random walk to explore the search space. The Lévy step is taken from the Lévy distribution which is a heavy-tailed probability distribution. In this case, a fraction of large steps are generated, which plays an important role in enhancing search capability of CS. Besides, although many foragers and wandering animals have been shown to follow a Lévy distribution of steps, investigation into the impact of other different heavy-tailed probability distributions on CS is still insufficient up to now. Based on the above considerations, we are motivated to apply the well-known Mittag-Leffler distribution to the standard CS algorithm, and proposed an improved cuckoo search algorithm (CSML) in this paper, where a more efficient search is supposed to take place in the search space thanks to the long jumps. In order to verify the performance of CSML, experiments are carried out on a test suite of 20 benchmark functions. In terms of the observations and results analysis, CSML can be regarded as a new potentially promising algorithm for solving optimization problems.

scholarly journals Determining Optimal Link Capacity Expansions in Road Networks Using Cuckoo Search Algorithm with Lévy Flights

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ozgur Baskan
Keyword(s):  
Traffic Congestion ◽  
Road Network ◽  
Search Algorithm ◽  
Road Networks ◽  
Cuckoo Search ◽  
User Equilibrium ◽  
Network Design Problem ◽  
Lévy Flights ◽  
Link Capacity ◽  
Levy Flights

During the last two decades, Continuous Network Design Problem (CNDP) has received much more attention because of increasing trend of traffic congestion in road networks. In the CNDP, the problem is to find optimal link capacity expansions by minimizing the sum of total travel time and investment cost of capacity expansions in a road network. Considering both increasing traffic congestion and limited budgets of local authorities, the CNDP deserves to receive more attention in order to use available budget economically and to mitigate traffic congestion. The CNDP can generally be formulated as bilevel programming model in which the upper level deals with finding optimal link capacity expansions, whereas at the lower level, User Equilibrium (UE) link flows are determined by Wardrop’s first principle. In this paper, cuckoo search (CS) algorithm with Lévy flights is introduced for finding optimal link capacity expansions because of its recent successful applications in solving such complex problems. CS is applied to the 16-link and Sioux Falls networks and compared with available methods in the literature. Results show the potential of CS for finding optimal or near optimal link capacity expansions in a given road network.

scholarly journals Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

Symmetry ◽  
2018 ◽  
Vol 10 (3) ◽  
pp. 58 ◽  
Author(s):  
Andrés Iglesias ◽  
Akemi Gálvez ◽  
Patricia Suárez ◽  
Mikio Shinya ◽  
Norimasa Yoshida ◽  
...  
Keyword(s):  
Reverse Engineering ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Parametric Surface ◽  
Lévy Flights ◽  
Surface Approximation ◽  
Levy Flights

Generalized Lotka-Volterra (GLV) Models of Stock Markets

2000 ◽  
Vol 03 (01n04) ◽  
pp. 301-322 ◽  
Author(s):  
Sorin Solomon
Keyword(s):  
Power Law ◽  
Wide Class ◽  
Stock Markets ◽  
Probability Distributions ◽  
Economic Systems ◽  
Lévy Flights ◽  
Levy Flights ◽  
General Method

The Generalized Lotka-Volterra (GLV) model: [Formula: see text] provides a general method to simulate, analyze and understand a wide class of phenomena that are characterized by power-law probability distributions: [Formula: see text] and truncated Levy flights fluctuations [Formula: see text]. We show how the model applies to economic systems.

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