Grey Wolf Optimizer

Inspiration

Are considered as apex predator. Live in a pack. The group size is 5–12 on average. Very strict social dominant hierarchy:

• Alphas: The leaders (dominant wolf ).
• Beta: Subordinate wolves.
• Delta: Have to submit to alphas and betas, but they dominate the omega. Omega: lowest ranking.

Hunting phases:

• Tracking, chasing.
• Encircling.
• Attack the prey.

Social hierarchy

Fittest solution respectively: α β δ ω

Mathematical Model

Hunting

Guided by the alpha. We have no idea about the location of the optimum(prey). Therefore, we save the first three best solutions obtained so far and oblige the other search agents (including the omegas) to update their positions according to the position of the best search agents.

• Attack prey (exploitation), |A| < 1
• Search for prey (exploration), |A| > 1

Search Process

• Creating a random population of grey wolves.
• Alpha, beta, and delta wolves estimate the probable position of the prey.
• Each candidate solution updates its distance from the prey.
• The parameter a is decreased from 2 to 0 in order to emphasize exploration and exploitation.
• Candidate solutions tend to diverge from the prey when |A| > 1 and converge towards the prey when |A| < 1.
• GWO algorithm is terminated by the satisfaction of an end criterion.

Motivation

There is no meta-heuristic best suited for solving all optimization problems. NFL makes this field of study highly active. Hence motivates authors of GWO to develop a new meta-heuristic with inspiration from grey wolves.

What is Meta-heuristics ?

Why meta-heuristics have become remarkably common:

• Fairly simple: The simplicity assists scientists to learn meta-heuristics quickly and apply them to their problems.
• Flexibility: Applicability of meta-heuristics to different problems without any special changes in the structure of the algorithm.
• Derivation-free: The optimization process starts with random solution(s), and there is no need to calculate the derivative of search spaces to find the opti-mum.
• Avoid local optima: Due to the stochastic nature of meta-heuristics which allow them to avoid stagnation in local solutions and search the entire search space.

Meta-heuristics search process

• Exploration: The process of investigating the promising area(s) of the search space as broadly as possible, (an algorithm needs to have stochastic operators to randomly search).
• Exploitation: 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-heuristic.

Development toolchains:

The proposed algorithm was developed under Debian Linux 64bit operating system (version 8.1.0), with the following toolchains:

Tool name	Version	Description
g++	5.4.0	C++ compiler (standard 0x11)
ld	2.26.1	GNU linker
make	4.1	GNU make (builder)

How to compile:

Locate the root source code, then type the folowing:

$ make clean
$ make

If the compilation process proceeds successfully, you will see "gwo" binary under build directory.

Benchmark usage:

./gwo -name [-population_size] [-iterations] [-debug]
where:
    -name               [required]    Benchmark name: F1, F2, F3, F4, F5, F6, F7
    -population_size    [optinal ]    integer >= 0, default(30)
    -iterations         [optinal ]    integer >= 0, defualt(500)
    -debug              [optinal ]    show debugging info, defualt(false)

Run benchmarks:

In this release, I only added support for seven benchmarks: F1, F2, F3, F4, F5, F6 and F7; which represent the Unimodal functions. For more information about the benchmarks, please see the reference section.

Example

$ build/gwo -name F3 -population_size 100 -iterations 1000

Author

Ahmad Dajani Email: [email protected]

Reference

• Grey Wolf Optimizer: http://dx.doi.org/10.1016/j.advengsoft.2013.12.007