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
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.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

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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

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