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

Random Search
Adaptive Random Search
Stochastic Hill Climbing
Iterated Local Search
Guided Local Search
Variable Neighborhood Search
Greedy Randomized Adaptive Search
Scatter Search
Tabu Search
Reactive Tabu Search

Evolutionary Algorithms

Genetic Algorithm
Genetic Programming
Evolution Strategies
Differential Evolution
Evolutionary Programming
Grammatical Evolution
Gene Expression Programming
Learning Classifier System
Non-dominated Sorting Genetic Algorithm
Strength Pareto Evolutionary Algorithm

Physical Algorithms

Simulated Annealing
Extremal Optimization
Harmony Search
Cultural Algorithm
Memetic Algorithm

Probabilistic Algorithms

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

Swarm Algorithms

Particle Swarm Optimization
Ant System
Ant Colony System
Bees Algorithm
Bacterial Foraging Optimization Algorithm

Immune Algorithms

Clonal Selection Algorithm
Negative Selection Algorithm
Artificial Immune Recognition System
Immune Network Algorithm
Dendritic Cell Algorithm

Neural Algorithms

Perceptron
Back-propagation
Hopfield Network
Learning Vector Quantization
Self-Organizing Map

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!

Files

README.md

Latest commit

History

README.md

File metadata and controls

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