灰狼优化算法优化SVM_MATLAB代码分享.zip

S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey Wolf Optimizer, Advances in Engineering Software , vol. 69, pp.

46-61, 2014, DOI: http://dx.doi.org/10.1016/j.advengsoft.2013.12.007

Grey Wolf Optimizer

1

Seyedali Mirjalili,

2

Seyed Mohammad Mirjalili,

1

Abstract: This work proposes a new meta-heuristic called Grey Wolf Optimizer (GWO) inspired by grey wolves

(Canis lupus). The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in

nature. Four types of grey wolves such as alpha, beta, delta, and omega are employed for simulating the

leadership hierarchy. In addition, the three main steps of hunting, searching for prey, encircling prey, and

attacking prey, are implemented. The algorithm is then benchmarked on 29 well-known test functions, and the

results are verified by a comparative study with Particle Swarm Optimization (PSO), Gravitational Search

Algorithm (GSA), Differential Evolution (DE), Evolutionary Programming (EP), and Evolution Strategy (ES).

The results show that the GWO algorithm is able to provide very competitive results compared to these well-

known meta-heuristics. The paper also considers solving three classical engineering design problems

1. Introduction

some of them such as Genetic Algorithm (GA) [1], Ant Colony Optimization (ACO) [2], and Particle Swarm

Optimization (PSO) [3] are fairly well-known among not only computer scientists but also scientists from

different fields. In addition to the huge number of theoretical works, such optimization techniques have been

applied in various fields of study. There is a question here as to why meta-heuristics have become remarkably

common. The answer to this question can be summarized into four main reasons: simplicity, flexibility,

derivation-free mechanism, and local optima avoidance.

mostly assume problems as black boxes. In other words, only the input(s) and output(s) of a system are

important for a meta-heuristic. So, all a designer needs is to know how to represent his/her problem for meta-

heuristics.

optimization approaches, meta-heuristics optimize problems stochastically. The optimization process starts with

random solution(s), and there is no need to calculate the derivative of search spaces to find the optimum. This

makes meta-heuristics highly suitable for real problems with expensive or unknown derivative information.

techniques. This is due to the stochastic nature of meta-heuristics which allow them to avoid stagnation in local

solutions and search the entire search space extensively. The search space of real problems is usually unknown

S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey Wolf Optimizer, Advances in Engineering Software , vol. 69, pp.

46-61, 2014, DOI: http://dx.doi.org/10.1016/j.advengsoft.2013.12.007

results in enhancing current approaches and proposing new meta-heuristics every year. This also motivates our

attempts to develop a new meta-heuristic with inspiration from grey wolves.

population-based. In the former class (Simulated Annealing [5] for instance) the search process starts with one

candidate solution. This single candidate solution is then improved over the course of iterations. Population-

based meta-heuristics, however, perform the optimization using a set of solutions (population). In this case the

search process starts with a random initial population (multiple solutions), and this population is enhanced over

the course of iterations. Population-based meta-heuristics have some advantages compared to single solution-

based algorithms:

 Multiple candidate solutions share information about the search space which results in sudden jumps

concepts of SI was first proposed in 1993 [6]. According to Bonabeau et al. [1], SI is “The emergent collective

intelligence of groups of simple agents”. The inspirations of SI techniques originate mostly from natural

colonies, flock, herds, and schools. Some of the most popular SI techniques are ACO [2], PSO [3], and Artificial

Bee Colony (ABC) [7]. A comprehensive literature review of the SI algorithms is provided in the next section.

Some of the advantages of SI algorithms are:

 SI algorithms preserve information about the search space over the course of iteration, whereas

Evolutionary Algorithms (EA) discard the information of the previous generations

 SI algorithms often utilize memory to save the best solution obtained so far

 SI algorithms usually have fewer parameters to adjust

stochastic operators to randomly and globally search the search space in order to support this phase. However,

exploitation refers to the local search capability around the promising regions obtained in the exploration phase.

Finding a proper balance between these two phases is considered a challenging task due to the stochastic nature

of meta-heuristics. This work proposes a new SI technique with inspiration from the social hierarchy and

hunting behavior of grey wolf packs. The rest of the paper is organized as follows:

results and discussion of benchmark functions, semi-real problems, and a real application are presented in

Section 4, Section 5, and Section 6, respectively. Finally, Section 7 concludes the work and suggests some

directions for future studies.

combination and mutation of the individuals in the previous generation. Since the best individuals have higher

probability of participating in generating the new population, the new population is likely to be better than the

previous generation(s). This can guarantee that the initial random population is optimized over the course of

generations. Some of the EAs are Differential Evolution (DE) [15], Evolutionary Programing (EP) [16, 17], and

S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey Wolf Optimizer, Advances in Engineering Software , vol. 69, pp.

46-61, 2014, DOI: http://dx.doi.org/10.1016/j.advengsoft.2013.12.007

Evolution Strategy (ES) [18, 19], Probability-Based Incremental Learning (PBIL), Genetic Programming (GP)

[20], and Biogeography-Based Optimizer (BBO) [21].

algorithm has been inspired by biogeography which refers to the study of biological organisms in terms of

geographical distribution (over time and space). The case studies might include different islands, lands, or even

continents over decades, centuries, or millennia. In this field of study different ecosystems (habitats or

[22], Big-Bang Big-Crunch (BBBC) [23], Gravitational Search Algorithm (GSA) [24], Charged System Search

(CSS) [25], Central Force Optimization (CFO) [26], Artificial Chemical Reaction Optimization Algorithm

(ACROA) [27], Black Hole (BH) [28] algorithm, Ray Optimization (RO) [29] algorithm, Small-World

Optimization Algorithm (SWOA) [30], Galaxy-based Search Algorithm (GbSA) [31], and Curved Space

Optimization (CSO) [32]. The mechanism of these algorithms is different from EAs, in that a random set of

search agents communicate and move throughout search space according to physical rules. This movement is

implemented, for example, using gravitational force, ray casting, electromagnetic force, inertia force, weights,

and so on.

BBBC are scattered from a point in random directions in a search space according to the principles of the big

masses in proportion to their distances.

of swarms, herds, flocks, or schools of creatures in nature. The mechanism is almost similar to physics-based

algorithm, but the search agents navigate using the simulated collective and social intelligence of creatures. The

most popular SI technique is PSO. The PSO algorithm was proposed by Kennedy and Eberhart [3] and inspired

from the social behavior of birds flocking. The PSO algorithm employs multiple particles that chase the position

of the best particle and their own best positions obtained so far. In other words, a particle is moved considering

its own best solution as well as the best solution the swarm has obtained.

by the social behavior of ants in an ant colony. In fact, the social intelligence of ants in finding the shortest path

S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey Wolf Optimizer, Advances in Engineering Software , vol. 69, pp.

46-61, 2014, DOI: http://dx.doi.org/10.1016/j.advengsoft.2013.12.007

S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey Wolf Optimizer, Advances in Engineering Software , vol. 69, pp.

46-61, 2014, DOI: http://dx.doi.org/10.1016/j.advengsoft.2013.12.007

caretakers belong to this category. Scouts are responsible for watching the boundaries of the territory and