CleverAlgorithms

The C++ implementation of Clever Algorithms.

Overview

Clever Algorithms: Nature-Inspired Programming Recipes is an open source book that describes a large number of algorithmic techniques from the the fields of Biologically Inspired Computation, Computational Intelligence and Metaheuristics in a complete, consistent, and centralized manner such that they are accessible, usable, and understandable. This is a repository for the source code (C++ implementation) of the book project.

Algorithm List

Stochastic Algorithms

Evolutionary Algorithms

Physical Algorithms

Probabilistic Algorithms

Population-Based Incremental Learning
Univariate Marginal Distribution Algorithm
Compact Genetic Algorithm
Bayesian Optimization Algorithm
Cross-Entropy Method

Swarm Algorithms

Immune Algorithms

Neural Algorithms

Test Functions

ACKLEY FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-32.768, 32.768]$ , and $a=20, b=0.2, c=2\pi$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, ..., 0)$

BUKIN FUNCTION N.6

Input Domain:

The function is usually evaluated on the $x_1 \in [-15, 5],x_2\in[-3,3]$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (-10, 1)$

CROSS-IN-TRAY FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-10, 10]\text{for all}i=1, 2$ .

Global Minimum:

$f(x^{*}) = -2.06261, \text{at} x^{*} = (1.3491, -1.3491),(1.3491, 1.3491),(-1.3491, 1.3491),\text{and}(-1.3491, -1.3491)$

Drop-Wave Function

Input Domain:

The function is usually evaluated on the $x_i \in [-5.12, 5.12]\text{for all}i=1, 2$ .

Global Minimum:

$f(x^{*}) = -1, \text{at} x^{*} = (0, 0)$

EGGHOLDER FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-512, 512]\text{for all}i=1, 2$ .

Global Minimum:

$f(x^{*}) = -959.6407, \text{at} x^{*} = (512, 404.2319)$

Gramacy & Lee Function

Input Domain:

The function is usually evaluated on the $x \in [0.5, 2.5]$ .

Griewank Function

Input Domain:

The function is usually evaluated on the $x_i \in [-600, 600]\text{for all}i=1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0,..., 0)$

Holder Table Function

Input Domain:

The function is usually evaluated on the $x_i \in [-10, 10]\text{for all}i=1, 2$ .

Global Minimum:

$f(x^{*}) = -19.2085, \text{at} x^{*} = (8.05502, 9.66459),(8.05502, -9.66459),(-8.05502, 9.66459),(-8.05502, -9.66459)$

Levy Function

Input Domain:

The function is usually evaluated on the $x_i \in [-10, 10]\text{for all}i=1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (1,..., 1)$

Levy Function N. 13

Input Domain:

The function is usually evaluated on the $x_i \in [-10, 10]\text{for all}i=1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (1, 1)$

Rastrigin Function

Input Domain:

The function is usually evaluated on the $x_i \in [-5.12, 5.12]\text{for all}i=1,..., d$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0,..., 0)$

Schaffer Function N. 2

Input Domain:

The function is usually evaluated on the $x_i \in [-100, 100] \text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0)$

Schaffer Function N. 4

Input Domain:

The function is usually evaluated on the $x_i \in [-100, 100] \text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0)$

Schwefel Function

Input Domain:

The function is usually evaluated on the $x_i \in [-500, 500] \text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (420.9687,..., 420.9687)$

Shubert Function

Input Domain:

The function is usually evaluated on the $x_i \in [-5.12, 5.12] \text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = -186.7309$

Bohachevsky Function

Input Domain:

The function is usually evaluated on the $x_i \in [-100, 100] \text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0)$

Perm Function 0, D, Beta

Input Domain:

The function is usually evaluated on the $x_i \in [-d, d] \text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (1, \frac{1}{2}, ..., \frac{1}{d})$

Rotated Hyper-ellipsoid Function

Input Domain:

The function is usually evaluated on the $x_i \in [-65.536, 65.536] \text{for all} i = 1, 2, ..., d$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0, ..., 0)$

Sphere Function

Input Domain:

The function is usually evaluated on the $x_i \in [-5.12, 5.12] \text{for all} i = 1, 2, ..., d$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0, ..., 0)$

Sum of Different Powers Function

Input Domain:

The function is usually evaluated on the $x_i \in [-1, 1] \text{for all} i = 1, 2, ..., d$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0, ..., 0)$

SUM SQUARES FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-5.12, 5.12] \text{for all} i = 1, 2, ..., d$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0, ..., 0)$

TRID FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-d^2, d^2] \text{for all} i = 1, 2, ..., d$ .

Global Minimum:

$f(x^{*}) = -d(d 4)(d-1)/6, \text{at} x_i = i(d 1 -i) \text{for all } i=1,2,...,d$

BOOTH FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-10, 10] \text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (1, 3)$

BATYAS FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-10, 10] \text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0)$

MCCORMICK FUNCTION

Input Domain:

The function is usually evaluated on the $x_1 \in [-1.5, 4] ,x_2 \in [-3, 4]$ .

Global Minimum:

$f(x^{*}) = -1.9133, \text{at} x^{*} = (-0.54719, -1.54719)$

POWER OF SUM FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [0, d]\,\text{for all}\,i=1,...,d$ .

ZAKHAROV FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-5, 10] ,\text{at all} i = 1, ..., d$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0,..., 0)$

THREE-HUMP CAMEL FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-5, 5] ,\text{at all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (0, 0)$

SIX-HUMP CAMEL FUNCTION

Input Domain:

The function is usually evaluated on the $x_1 \in [-3, 3] , x_2 \in [-2, 2]$ .

Global Minimum:

$f(x^{*}) = -1.0316,\text{at } x^{*} = (0.0898, -0.7126) \text{and} (-0.0898, 0.7126)$

Dixon-Price FUNCTION

Input Domain:

The function is usually evaluated on the $x_i \in [-10, 10], \text{for all } i = 1, ..., d$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x_i = 2^{-\frac{2^i-2}{2^i}},\text{for} i=1,...,d$

Rosenbrock Function

Input Domain:

The function is usually evaluated on the $x_i \in [-10, 10], \text{for all } i = 1, ..., d$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x_i = (1,...,1),\text{for} i=1,...,d$

Easom Function

Input Domain:

The function is usually evaluated on the $x_i \in [-100, 100], \text{for all } i = 1, 2$ .

Global Minimum:

$f(x^{*}) = -1, \text{at} X^{*} = (\pi,\pi)$

Michalewicz Function

Input Domain:

The function is usually evaluated on the $x_i \in [0, \pi], \text{for all } i = 1, 2,...,d$ .

Global Minimum:

$\text{at }d = 2: f(x^{*}) = -1.8013, \text{at} X^{*} = (2.20,1.57)$

$\text{at }d = 5: f(x^{*}) = -4.687658$

$\text{at }d = 10: f(x^{*}) = -9.66015$

Beale Function

Input Domain:

The function is usually evaluated on the $x_i \in [-4.5, 4.5], \text{for all } i = 1, 2$ .

Global Minimum:

$\text{at }d = 2: f(x^{*}) = 0, \text{at} X^{*} = (3,0.5)$

Branin Function

Input Domain:

The function is usually evaluated on the $x_1 \in [-5, 10], x_2 \in [0, 15]$ .

Global Minimum:

$f(x^{*}) = -0.397887, \text{at} x^{*} = (\pi,12.275),(\pi,2.275)\text{and}(9.42478,2.475)$

COLVILLE FUNCTION

Input Domain:

The function is usually evaluated on the $x_1 \in [-10, 10],\text{for all } i = 1, 2, 3, 4$ .

Global Minimum:

$f(x^{*}) = 0, \text{at} x^{*} = (1,1,1,1)$

Forrester et al. (2008) Function

Input Domain:

The function is usually evaluated on the $x_1 \in [0, 1]$ .

Goldstein-Price Function

Input Domain:

The function is usually evaluated on the $x_1 \in [-2, 2],\text{for all} i = 1, 2$ .

Global Minimum:

$f(x^{*}) = 3, \text{at} x^{*} = (0,-1)$

How to build the source code

gcc -g -Wall -std=c++11 <algorithm>.cpp -lstdc++ -o <algorithm>

Thanks

This project has been supported by JetBrains Free License Programs - Licenses for Open Source Development. Thanks JetBrains!

Name		Name	Last commit message	Last commit date
Latest commit History 191 Commits
.github/ISSUE_TEMPLATE		.github/ISSUE_TEMPLATE
docs		docs
examples		examples
include		include
test		test
.gitignore		.gitignore
CMakeLists.txt		CMakeLists.txt
CODE_OF_CONDUCT.md		CODE_OF_CONDUCT.md
LICENSE		LICENSE
README.md		README.md

License

GreatV/CleverAlgorithms

Folders and files

Latest commit

History

Repository files navigation

CleverAlgorithms

Overview

Algorithm List

Stochastic Algorithms

Evolutionary Algorithms

Physical Algorithms

Probabilistic Algorithms

Swarm Algorithms

Immune Algorithms

Neural Algorithms

Test Functions

ACKLEY FUNCTION

BUKIN FUNCTION N.6

CROSS-IN-TRAY FUNCTION

Drop-Wave Function

EGGHOLDER FUNCTION

Gramacy & Lee Function

Griewank Function

Holder Table Function

Levy Function

Levy Function N. 13

Rastrigin Function

Schaffer Function N. 2

Schaffer Function N. 4

Schwefel Function

Shubert Function

Bohachevsky Function

Perm Function 0, D, Beta

Rotated Hyper-ellipsoid Function

Sphere Function

Sum of Different Powers Function

SUM SQUARES FUNCTION

TRID FUNCTION

BOOTH FUNCTION

BATYAS FUNCTION

MCCORMICK FUNCTION

POWER OF SUM FUNCTION

ZAKHAROV FUNCTION

THREE-HUMP CAMEL FUNCTION

SIX-HUMP CAMEL FUNCTION

Dixon-Price FUNCTION

Rosenbrock Function

Easom Function

Michalewicz Function

Beale Function

Branin Function

COLVILLE FUNCTION

Forrester et al. (2008) Function

Goldstein-Price Function

How to build the source code

Thanks

About

Resources

License

Code of conduct

Stars

Watchers

Forks

Languages