eaopt

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Published: Nov 16, 2020 License: MIT

eaopt is an evolutionary optimization library

Changelog

• 11/11/18: a simple version of OpenAI's evolution strategy has been implemented, it's called `OES`.
• 02/08/18: gago has now become eaopt. You can still everything you could do before but the scope is now larger than genetic algorithms. The goal is to implement many more evolutionary optimization algorithms on top of the existing codebase.

Example

The following example attempts to minimize the Drop-Wave function using a genetic algorithm. The Drop-Wave function is known to have a minimum value of -1 when each of it's arguments is equal to 0.

``````package main

import (
"fmt"
m "math"
"math/rand"

"github.com/MaxHalford/eaopt"
)

// A Vector contains float64s.
type Vector []float64

// Evaluate a Vector with the Drop-Wave function which takes two variables as
// input and reaches a minimum of -1 in (0, 0). The function is simple so there
// isn't any error handling to do.
func (X Vector) Evaluate() (float64, error) {
var (
numerator   = 1 + m.Cos(12*m.Sqrt(m.Pow(X[0], 2)+m.Pow(X[1], 2)))
denominator = 0.5*(m.Pow(X[0], 2)+m.Pow(X[1], 2)) + 2
)
return -numerator / denominator, nil
}

// Mutate a Vector by resampling each element from a normal distribution with
// probability 0.8.
func (X Vector) Mutate(rng *rand.Rand) {
eaopt.MutNormalFloat64(X, 0.8, rng)
}

// Crossover a Vector with another Vector by applying uniform crossover.
func (X Vector) Crossover(Y eaopt.Genome, rng *rand.Rand) {
eaopt.CrossUniformFloat64(X, Y.(Vector), rng)
}

// Clone a Vector to produce a new one that points to a different slice.
func (X Vector) Clone() eaopt.Genome {
var Y = make(Vector, len(X))
copy(Y, X)
return Y
}

// VectorFactory returns a random vector by generating 2 values uniformally
// distributed between -10 and 10.
func VectorFactory(rng *rand.Rand) eaopt.Genome {
return Vector(eaopt.InitUnifFloat64(2, -10, 10, rng))
}

func main() {
// Instantiate a GA with a GAConfig
var ga, err = eaopt.NewDefaultGAConfig().NewGA()
if err != nil {
fmt.Println(err)
return
}

// Set the number of generations to run for
ga.NGenerations = 10

// Add a custom print function to track progress
ga.Callback = func(ga *eaopt.GA) {
fmt.Printf("Best fitness at generation %d: %f\n", ga.Generations, ga.HallOfFame[0].Fitness)
}

// Find the minimum
err = ga.Minimize(VectorFactory)
if err != nil {
fmt.Println(err)
return
}
}

``````
``````>>> Best fitness at generation 0: -0.550982
>>> Best fitness at generation 1: -0.924220
>>> Best fitness at generation 2: -0.987282
>>> Best fitness at generation 3: -0.987282
>>> Best fitness at generation 4: -0.987282
>>> Best fitness at generation 5: -0.987282
>>> Best fitness at generation 6: -0.987282
>>> Best fitness at generation 7: -0.997961
>>> Best fitness at generation 8: -0.999954
>>> Best fitness at generation 9: -0.999995
>>> Best fitness at generation 10: -0.999999
``````

All the examples can be found in this repository.

Background

Evolutionary optimization algorithms are a subdomain of evolutionary computation. Their goal is to minimize/maximize a function without using any gradient information (usually because there isn't any gradient available). They share the common property of exploring the search space by breeding, mutating, evaluating, and sorting so-called individuals. Most evolutionary algorithms are designed to handle real valued functions, however in practice they are commonly used for handling more exotic problems. For example genetic algorithms can be used to find the optimal structure of a neural network.

eaopt provides implementations for various evolutionary optimization algorithms. Implementation-wise, the idea is that most (if not all) of said algorithms can be written as special cases of a genetic algorithm. Indeed this is made possible by using a generic definition of a genetic algorithm by allowing the mutation, crossover, selection, and replacement procedures to be modified at will. The `GA` struct is thus the most flexible struct of eaopt, the other algorithms are written on top of it. If you don't find any algorithm that suits your need then you can easily write your own operators (as is done in most of the examples).

Features

• Different evolutionary algorithms are available with a consistent API
• You can practically do anything by using the `GA` struct
• Speciation and migration procedures are available
• Common genetic operators (mutation, crossover, selection, migration, speciation) are already implemented
• Function evaluation can be done in parallel if your function is costly

Usage

• Evolutionary algorithms are usually designed for solving specific kinds of problems. Take a look at the `Minimize` function of each method to get an idea of what type of function it can optimize.
• Use the associated constructor function of each method to initialize it. For example use the `NewPSO` function instead of instantiating the `PSO` struct yourself. Along with making your life easier, these functions provide the added benefit of checking for parameter input errors.
• If you're going to use the `GA` struct then be aware that some evolutionary operators are already implemented in eaopt (you don't necessarily have to reinvent the wheel).
• Don't feel overwhelmed by the fact that algorithms are implemented as special cases of genetic algorithms. It doesn't matter if you just want to get things done, it just makes things easier under the hood.

Genetic algorithms

Overview

Genetic algorithms are the backbone of eaopt. Most of the other algorithms available in eaopt are implemented as special cases of GAs. A GA isn't an algorithm per say, but rather a blueprint which can be used to optimize any kind of problem.

In a nutshell, a GA solves an optimization problem by doing the following:

1. Generate random solutions to a problem.
2. Assign a fitness to each solutions.
3. Check if a new best solution has been found.
4. Apply genetic operators following a given evolutionary model.
5. Repeat from step 2 until the stopping criterion is satisfied.

This description is voluntarily vague. It is up to the user to define the problem and the genetic operators to use. Different categories of genetic operators exist:

• Mutation operators modify an existing solution.
• Crossover operators generate a new solution by combining two or more existing ones.
• Selection operators selects individuals that are to be evolved.
• Migration swaps individuals between populations.
• Speciation clusters individuals into subpopulations.

Popular stopping criteria include

• a fixed number of generations,
• a fixed duration,
• an indicator that the population is stagnating.

Genetic algorithms can be used via the `GA` struct. The necessary steps for using the GA struct are

1. Implement the `Genome` interface to model your problem
2. Instantiate a `GA` struct (preferably via the `GAConfig` struct)
3. Call the GA's `Minimize` function and check the `HallOfFame` field
Implementing the Genome interface

To use the `GA` struct you first have to implement the `Genome` interface, which is used to define the logic that is specific to your problem (logic that eaopt doesn't know about). For example this is where you will define an `Evaluate()` method for evaluating a particular problem. The `GA` struct contains context-agnostic information. For example this is where you can choose the number of individuals in a population (which is a separate concern from your particular problem). Apart from a good design pattern, decoupling the problem definition from the optimization through the `Genome` interface means that eaopt can be used to optimize any kind of problem.

Let's have a look at the `Genome` interface.

``````type Genome interface {
Evaluate() (float64, error)
Mutate(rng *rand.Rand)
Crossover(genome Genome, rng *rand.Rand)
Clone() Genome
}
``````

The `Evaluate()` method returns the fitness of a genome. The sweet thing is that you can do whatever you want in this method. Your struct that implements the interface doesn't necessarily have to be a slice. The `Evaluate()` method is your problem to deal with. eaopt only needs it's output to be able to function. You can also return an `error` which eaopt will catch and return when calling `ga.Initialize()` and `ga.Evolve()`.

The `Mutate(rng *rand.Rand)` method is where you can modify an existing solution by tinkering with it's variables. The way in which you should mutate a solution essentially boils down to your particular problem. eaopt provides some common mutation methods that you can use instead of reinventing the wheel -- this is what is being done in most of the examples.

The `Crossover(genome Genome, rng *rand.Rand)` method combines two individuals. The important thing to notice is that the type of first argument differs from the struct calling the method. Indeed the first argument is a `Genome` that has to be casted into your struct before being able to apply a crossover operator. This is due to the fact that Go doesn't provide generics out of the box; it's easier to convince yourself by checking out the examples.

The `Clone()` method is there to produce independent copies of the struct you want to evolve. This is necessary for internal reasons and ensures that pointer fields are not pointing to identical memory addresses. Usually this is not too difficult implement; you just have to make sure that the clones you produce are not shallow copies of the genome that is being cloned. This is also fairly easy to unit test.

Once you have implemented the `Genome` interface you have provided eaopt with all the information it couldn't guess for you.

Instantiate the GA struct

You can now instantiate a `GA` and use it to find an optimal solution to your problem. The `GA` struct has a lot of fields, hence the recommended way is to use the `GAConfig` struct and call it's `NewGA` method.

Let's have a look at the `GAConfig` struct.

``````type GAConfig struct {
NPops        uint
PopSize      uint
NGenerations uint
HofSize      uint
Model        Model

// Optional fields
ParallelEval bool // Whether to evaluate Individuals in parallel or not
Migrator     Migrator
MigFrequency uint // Frequency at which migrations occur
Speciator    Speciator
Logger       *log.Logger
Callback     func(ga *GA)
EarlyStop    func(ga *GA) bool
RNG          *rand.Rand
}
``````
• `NPops` determines the number of populations that will be used.
• `PopSize` determines the number of individuals inside each population.
• `NGenerations` determines for many generations the populations will be evolved.
• `HofSize` determines how many of the best individuals should be recorded.
• `Model` is a struct that determines how to evolve each population of individuals.
• Optional fields
• `ParallelEval` determines if a population is evaluated in parallel. The rule of thumb is to set this to `true` if your `Evaluate` method is expensive, if not it won't be worth the overhead. Refer to the section on parallelism for a more comprehensive explanation.
• `Migrator` and `MigFrequency` should be provided if you want to exchange individuals between populations in case of a multi-population GA. If not the populations will be run independently. Again this is an advanced concept in the genetic algorithms field that you shouldn't deal with at first.
• `Speciator` will split each population in distinct species at each generation. Each specie will be evolved separately from the others, after all the species has been evolved they are regrouped.
• `Logger` can be used to record basic population statistics, you can read more about it in the logging section.
• `Callback` will execute any piece of code you wish every time `ga.Evolve()` is called. `Callback` will also be called when `ga.Initialize()` is. Using a callback can be useful for many things:
• Calculating specific population statistics that are not provided by the logger
• Changing parameters of the GA after a certain number of generations
• Monitoring convergence
• `EarlyStop` will be called before each generation to check if the evolution should be stopped early.
• `RNG` can be set to make results reproducible. If it is not provided then a default `rand.New(rand.NewSource(time.Now().UnixNano()))` will be used. If you want to make your results reproducible use a constant source, e.g. `rand.New(rand.NewSource(42))`.

Once you have instantiated a `GAConfig` you can call it's `NewGA` method to obtain a `GA`. The `GA` struct has the following definition:

``````type GA struct {
GAConfig

Populations Populations
HallOfFame  Individuals
Age         time.Duration
Generations uint
}
``````

Naturally a `GA` stores a copy of the `GAConfig` that was used to instantiate it. Apart from this the following fields are available:

• `Populations` is where all the current populations and individuals are kept.
• `HallOfFame` contains the `HofSize` best individuals ever encountered. This slice is always sorted, meaning that the first element of the slice will be the best individual ever encountered.
• `Age` indicates the duration the GA has spent evolving.
• `Generations` indicates how many how many generations have gone by.

You could bypass the `NewGA` method instantiate a `GA` with a `GAConfig` but this would leave the `GAConfig`'s fields unchecked for input errors.

Calling the Minimize method

You are now all set to find an optimal solution to your problem. To do so you have to call the GA's `Minimize` function which has the following signature:

``````func (ga *GA) Minimize(newGenome func(rng *rand.Rand) Genome) error
``````

You have to provide the `Minimize` a function which returns a `Genome`. It is recommended that the `Genome` thus produced contains random values. This is where the connection between the `Genome` interface and the `GA` struct is made.

The `Minimize` function will return an error (`nil` if everything went okay) once it is done. You can done access the first entry in the `HallOfFame` field to retrieve the best encountered solution.

Using the Slice interface

Classically GAs are used to optimize problems where the genome has a slice representation - eg. a vector or a sequence of DNA code. Almost all the mutation and crossover algorithms available in eaopt are based on the `Slice` interface which has the following definition.

``````type Slice interface {
At(i int) interface{}
Set(i int, v interface{})
Len() int
Swap(i, j int)
Slice(a, b int) Slice
Split(k int) (Slice, Slice)
Append(Slice) Slice
Replace(Slice)
Copy() Slice
}
``````

Internally `IntSlice`, `Float64Slice` and `StringSlice` implement this interface so that you can use the available operators for most use cases. If however you wish to use the operators with slices of a different type you will have to implement the `Slice` interface. Although there are many methods to implement, they are all trivial (have a look at `slice.go` and the TSP example.

Models

eaopt makes it easy to use different so called models. Simply put, a models defines how a GA evolves a population of individuals through a sequence of genetic operators. It does so without considering whatsoever the intrinsics of the underlying operators. In a nutshell, an evolution model attempts to mimic evolution in the real world. It's extremely important to choose a good model because it is usually the highest influence on the performance of a GA.

Generational model

The generational model is one the, if not the most, popular models. Simply put it generates n offsprings from a population of size n and replaces the population with the offsprings. The offsprings are generated by selecting 2 individuals from the population and applying a crossover method to the selected individuals until the n offsprings have been generated. The newly generated offsprings are then optionally mutated before replacing the original population. Crossover generates two new individuals, thus if the population size isn't an even number then the second individual from the last crossover (individual n+1) won't be included in the new population.

The steady state model differs from the generational model in that the entire population isn't replaced between each generations. Instead of adding the children of the selected parents into the next generation, the 2 best individuals out of the two parents and two children are added back into the population so that the population size remains constant. However, one may also replace the parents with the children regardless of their fitness. This method has the advantage of not having to evaluate the newly generated offsprings. Whats more, crossover often generates individuals who are sub-par but who have a lot of potential; giving individuals generated from crossover a chance can be beneficial on the long run.

Select down to size model

The select down to size model uses two selection rounds. The first one is similar to the one used in the generational model. Parents are selected to generate new individuals through crossover. However, the offsprings are then merged with the original population and a second selection round occurs to determine which individuals will survive to the next generation. Formally m offsprings are generated from a population of n, the n+m individuals are then "selected down to size" so that there only remains n individuals.

Ring model

In the ring model, crossovers are applied to neighbours in a one-directional ring topology. Two by the two neighbours generate 2 offsprings. The best out of the 4 individuals (2 parents + 2 offsprings) replaces the first neighbour.

Mutation only

It's possible to run a GA without crossover simply by mutating individuals. This can be done with the `ModMutationOnly` struct. At each generation each individual is mutated. `ModMutationOnly` has a `strict` field to determine if the mutant should replace the initial individual only if it's fitness is lower.

Speciation

Clusters, also called species in the literature, are a partitioning of individuals into smaller groups of similar individuals. Programmatically a cluster is a list of lists that each contain individuals. Individuals inside each species are supposed to be similar. The similarity depends on a metric, for example it could be based on the fitness of the individuals. In the literature, speciation is also called speciation.

The purpose of a partitioning individuals is to apply genetic operators to similar individuals. In biological terms this encourages "incest" and maintains isolated species. For example in nature animals usually breed with local mates and don't breed with different animal species.

Using speciation/speciation with genetic algorithms became "popular" when they were first applied to the optimization of neural network topologies. By mixing two neural networks during crossover, the resulting neural networks were often useless because the inherited weights were not optimized for the new topology. This meant that newly generated neural networks were not performing well and would likely disappear during the selection phase. Thus speciation was introduced so that neural networks evolved in similar groups in order for new neural networks wouldn't disappear immediately. Instead the similar neural networks would evolve between each other until they were good enough to mixed with the other neural networks.

With eaopt it's possible to use speciation on top of all the rest. To do so the `Speciator` field of the `GA` struct has to specified.

Multiple populations and migration

Multi-populations GAs run independent populations in parallel. They are not frequently used, however they are very easy to understand and to implement. In eaopt a `GA` struct contains a `Populations` field which stores each population in a slice. The number of populations is specified in the `GAConfig`'s `NPops` field.

If `Migrator` and `MigFrequency` are not provided the populations will be run independently in parallel. However, if they are provided then at each generation number that is divisible by `MigFrequency` (for example 5 divides generation number 25) individuals will be exchanged between the populations following the `Migrator`.

Using multi-populations can be an easy way to gain in diversity. Moreover, not using multi-populations on a multi-core architecture is a waste of resources.

With eaopt you can use multi-populations and speciation at the same time. The following flowchart shows what that would look like.

Logging population statistics

It's possible to log statistics for each population at every generation. To do so you simply have to provide the `GA` struct a `Logger` from the Go standard library. This is quite convenient because it allows you to decide where to write the log output, whether it be in a file or directly in the standard output.

``````ga.Logger = log.New(os.Stdout, "", log.Ldate|log.Ltime)
``````

If a logger is provided, each row in the log output will include

• the population ID,
• the population minimum fitness,
• the population maximum fitness,
• the population average fitness,
• the population's fitness standard deviation.

Particle swarm optimization

Description

Particle swarm optimization (PSO) can be used to optimize real valued functions. It maintains a population of candidate solutions called particles. The particles move around the search-space according to a mathematical formula that takes as input the particle's position and it's velocity. Each particle's movement is influenced by its's local best encountered position, as well as the best overall position in the search-space (these values are updated after each generation). This is expected to move the swarm toward the best solutions.

As can be expected there are many variants of PSO. The `SPSO` struct implements the SPSO-2011 standard.

Example

In this example we're going to minimize th Styblinski-Tang function with two dimensions. The global minimum is about -39.16599 times the number of dimensions.

``````package main

import (
"fmt"
m "math"
"math/rand"

"github.com/MaxHalford/eaopt"
)

func StyblinskiTang(X []float64) (y float64) {
for _, x := range X {
y += m.Pow(x, 4) - 16*m.Pow(x, 2) + 5*x
}
return 0.5 * y
}

func main() {
// Instantiate SPSO
var spso, err = eaopt.NewDefaultSPSO()
if err != nil {
fmt.Println(err)
return
}

// Fix random number generation
spso.GA.RNG = rand.New(rand.NewSource(42))

// Run minimization
_, y, err := spso.Minimize(StyblinskiTang, 2)
if err != nil {
fmt.Println(err)
return
}

// Output best encountered solution
fmt.Printf("Found minimum of %.5f, the global minimum is %.5f\n", y, -39.16599*2)
}
``````

This should produce the following output.

``````>>> Found minimum of -78.23783, the global minimum is -78.33198
``````
Parameters

You can (and should) instantiate an `SPSO` with the `NewSPSO` method. You can also use the `NewDefaultSPSO` method as is done in the previous example.

``````func NewSPSO(nParticles, nSteps uint, min, max, w float64, parallel bool, rng *rand.Rand) (*SPSO, error)
``````
• `nParticles` is the number of particles to use
• `nSteps` is the number of steps during which evolution occurs
• `min` and `max` are the boundaries from which the initial values are sampled from
• `w` is the velocity amplifier
• `parallel` determines if the particles are evaluated in parallel or not
• `rng` is a random number generator, you can set it to `nil` if you want it to be random

Differential evolution

Description

Differential evolution (DE) somewhat resembles PSO and is also used for optimizing real-valued functions. At each generation, each so-called agent is moved according to the position of 3 randomly sampled agents. If the new position is not better than the current one then it is discarded.

As can be expected there are many variants of PSO. The `SPSO` struct implements the SPSO-2011 standard.

Example

In this example we're going to minimize th Ackley function with two dimensions. The global minimum is 0.

``````package main

import (
"fmt"
m "math"
"math/rand"

"github.com/MaxHalford/eaopt"
)

func Ackley(x []float64) float64 {
var (
a, b, c = 20.0, 0.2, 2 * m.Pi
s1, s2  float64
d       = float64(len(x))
)
for _, xi := range x {
s1 += xi * xi
s2 += m.Cos(c * xi)
}
return -a*m.Exp(-b*m.Sqrt(s1/d)) - m.Exp(s2/d) + a + m.Exp(1)
}

func main() {
// Instantiate DiffEvo
var de, err = eaopt.NewDefaultDiffEvo()
if err != nil {
fmt.Println(err)
return
}

// Fix random number generation
de.GA.RNG = rand.New(rand.NewSource(42))

// Run minimization
_, y, err := de.Minimize(Ackley, 2)
if err != nil {
fmt.Println(err)
return
}

// Output best encountered solution
fmt.Printf("Found minimum of %.5f, the global minimum is 0\n", y)
}
``````

This should produce the following output.

``````>>> Found minimum of 0.00137, the global minimum is 0
``````
Parameters

You can (and should) instantiate an `DiffEvo` with the `NewDiffEvo` method. You can also use the `NewDefaultDiffEvo` method as is done in the previous example.

``````func NewDiffEvo(nAgents, nSteps uint, min, max, cRate, dWeight float64, parallel bool, rng *rand.Rand) (*DiffEvo, error)
``````
• `nAgents` is the number of agents to use (it has to be at least 4)
• `nSteps` is the number of steps during which evolution occurs
• `min` and `max` are the boundaries from which the initial values are sampled from
• `cRate` is the crossover rate
• `dWeight` is the differential weight
• `parallel` determines if the agents are evaluated in parallel or not
• `rng` is a random number generator, you can set it to `nil` if you want it to be random

OpenAI evolution strategy

Description

OpenAI proposed a simple evolution strategy based on the use of natural gradients. The algorithm is dead simple:

1. Choose a center `mu` at random
2. Sample points around `mu` using a normal distribution
3. Evaluate each point and obtain the natural gradient `g`
4. Move `mu` along the natural gradient `g` using a learning rate
5. Repeat from step 2 until satisfied
Example

In this example we're going to minimize th Rastrigin function with three dimensions. The global minimum is 0.

``````package main

import (
"fmt"
m "math"
"math/rand"

"github.com/MaxHalford/eaopt"
)

func Rastrigin(x []float64) (y float64) {
y = 10 * float64(len(x))
for _, xi := range x {
y += m.Pow(xi, 2) - 10*m.Cos(2*m.Pi*xi)
}
return y
}

func main() {
// Instantiate DiffEvo
var oes, err = eaopt.NewDefaultOES()
if err != nil {
fmt.Println(err)
return
}

// Fix random number generation
oes.GA.RNG = rand.New(rand.NewSource(42))

// Run minimization
_, y, err := oes.Minimize(Rastrigin, 2)
if err != nil {
fmt.Println(err)
return
}

// Output best encountered solution
fmt.Printf("Found minimum of %.5f, the global minimum is 0\n", y)
}
``````

This should produce the following output.

``````>>> Found minimum of 0.02270, the global minimum is 0
``````
Parameters

You can (and should) instantiate an `OES` with the `NewOES` method. You can also use the `NewDefaultOES` method as is done in the previous example.

``````func NewOES(nPoints, nSteps uint, sigma, lr float64, parallel bool, rng *rand.Rand) (*OES, error)
``````
• `nPoints` is the number of points to use (it has to be at least 3)
• `nSteps` is the number of steps during which evolution occurs
• `sigma` determines the shape of the normal distribution used to sample new points
• `lr` is the learning rate
• `parallel` determines if the agents are evaluated in parallel or not
• `rng` is a random number generator, you can set it to `nil` if you want it to be random

A note on parallelism

Evolutionary algorithms are famous for being embarrassingly parallel. Most of the operations can be run independently each one from another. For example individuals can be mutated in parallel because mutation doesn't have any side effects.

The Go language provides nice mechanisms to run stuff in parallel, provided you have more than one core available. However, parallelism is only worth it when the functions you want to run in parallel are heavy. If the functions are cheap then the overhead of spawning routines will be too high and not worth it. It's simply not worth using a routine for each individual because operations at an individual level are often not time consuming enough.

By default eaopt will evolve populations in parallel. This is because evolving one population implies a lot of operations and parallelism is worth it. If your `Evaluate` method is heavy then it might be worth evaluating individuals in parallel, which can done by setting the `GA`'s `ParallelEval` field to `true`. Evaluating individuals in parallel can be done regardless of the fact that you are using more than one population.

FAQ

What if I don't want to use crossover?

Alas you still have to implement the `Genome` interface. You can however provide a blank `Crossover` method just to satisfy the interface.

``````type Vector []float64

func (X Vector) Crossover(Y eaopt.Genome, rng *rand.Rand) {}
``````

Why aren't my `Mutate` and `Crossover` methods modifying my `Genome`s?

The `Mutate` and `Crossover` methods have to modify the values of the `Genome` in-place. The following code will work because the `Vector` is a slice; slices in Go are references to underlying data, hence modifying a slice modifies them in-place.

``````type Vector []float64

func (X Vector) Mutate(rng *rand.Rand) {
eaopt.MutNormal(X, rng, 0.5)
}
``````

On the contrary, mutating other kind of structs will require the `*` symbol to access the struct's pointer. Notice the `*Name` in the following example.

``````type Name string

func (n *Name) Mutate(rng *rand.Rand) {
n = randomName()
}
``````

Are evolutionary optimization algorithms any good?

For real-valued, differentiable functions, evolutionary optimization algorithms will probably not fair well against methods based on gradient descent. Intuitively this is because evolutionary optimization algorithms ignore the shape and slope of the function. However gradient descent algorithms usually get stuck in local optimas, whereas evolutionary optimization algorithms don't.

As mentioned earlier, some problems can simply not be written down as closed-form expressions. In this case methods based on gradient information can't be used whilst evolutionary optimization algorithms can still be used. For example tuning the number of layers and of neurons per layer in a neural network is an open problem that doesn't yet have a reliable solution. Neural networks architectures used in production are usually designed by human experts. The field of neuroevolution aims to train neural networks with evolutionary algorithms.

How can I contribute?

Feel free to implement your own operators or to make suggestions! Check out the CONTRIBUTING file for some guidelines. This repository has a long list of existing evolutionary algorithms.

Dependencies

You can see the list of dependencies here and the graph view here. Here is the list of external dependencies:

Documentation ¶

Constants ¶

This section is empty.

Variables ¶

This section is empty.

Functions ¶

func CrossCX ¶

`func CrossCX(p1, p2 Slice)`

CrossCX (Cycle Crossover). Cycles between the parents are indentified, they are then copied alternatively onto the offsprings. The CX method is deterministic and preserves gene uniqueness.

func CrossCXFloat64 ¶

`func CrossCXFloat64(s1 []float64, s2 []float64)`

CrossCXFloat64 calls CrossCX on a float64 slice.

func CrossCXInt ¶

`func CrossCXInt(s1 []int, s2 []int)`

CrossCXInt calls CrossCX on an int slice.

func CrossCXString ¶

`func CrossCXString(s1 []string, s2 []string)`

CrossCXString calls CrossCX on a string slice.

func CrossERX ¶

`func CrossERX(p1, p2 Slice)`

CrossERX (Edge Recombination Crossover).

func CrossERXFloat64 ¶

`func CrossERXFloat64(s1 []float64, s2 []float64)`

CrossERXFloat64 callsCrossERX on a float64 slice.

func CrossERXInt ¶

`func CrossERXInt(s1 []int, s2 []int)`

CrossERXInt calls CrossERX on an int slice.

func CrossERXString ¶

`func CrossERXString(s1 []string, s2 []string)`

CrossERXString calls CrossERX on a string slice.

func CrossGNX ¶

`func CrossGNX(p1 Slice, p2 Slice, n uint, rng *rand.Rand)`

CrossGNX (Generalized N-point Crossover). An identical point is chosen on each parent's genome and the mirroring segments are switched. n determines the number of crossovers (aka mirroring segments) to perform. n has to be equal or lower than the number of genes in each parent.

func CrossGNXFloat64 ¶

`func CrossGNXFloat64(s1 []float64, s2 []float64, n uint, rng *rand.Rand)`

CrossGNXFloat64 calls CrossGNX on two float64 slices.

func CrossGNXInt ¶

`func CrossGNXInt(s1 []int, s2 []int, n uint, rng *rand.Rand)`

CrossGNXInt calls CrossGNX on two int slices.

func CrossGNXString ¶

`func CrossGNXString(s1 []string, s2 []string, n uint, rng *rand.Rand)`

CrossGNXString calls CrossGNX on two string slices.

func CrossOX ¶

`func CrossOX(p1 Slice, p2 Slice, rng *rand.Rand)`

CrossOX (Ordered Crossover). Part of the first parent's genome is copied onto the first offspring's genome. Then the second parent's genome is iterated over, starting on the right of the part that was copied. Each gene of the second parent's genome is copied onto the next blank gene of the first offspring's genome if it wasn't already copied from the first parent. The OX method preserves gene uniqueness.

func CrossOXFloat64 ¶

`func CrossOXFloat64(s1 []float64, s2 []float64, rng *rand.Rand)`

CrossOXFloat64 calls CrossOX on a float64 slice.

func CrossOXInt ¶

`func CrossOXInt(s1 []int, s2 []int, rng *rand.Rand)`

CrossOXInt calls CrossOX on a int slice.

func CrossOXString ¶

`func CrossOXString(s1 []string, s2 []string, rng *rand.Rand)`

CrossOXString calls CrossOX on a string slice.

func CrossPMX ¶

`func CrossPMX(p1 Slice, p2 Slice, rng *rand.Rand)`

CrossPMX (Partially Mapped Crossover). The offsprings are generated by copying one of the parents and then copying the other parent's values up to a randomly chosen crossover point. Each gene that is replaced is permuted with the gene that is copied in the first parent's genome. Two offsprings are generated in such a way (because there are two parents). The PMX method preserves gene uniqueness.

func CrossPMXFloat64 ¶

`func CrossPMXFloat64(s1 []float64, s2 []float64, rng *rand.Rand)`

CrossPMXFloat64 calls CrossPMX on a float64 slice.

func CrossPMXInt ¶

`func CrossPMXInt(s1 []int, s2 []int, rng *rand.Rand)`

CrossPMXInt calls CrossPMX on an int slice.

func CrossPMXString ¶

`func CrossPMXString(s1 []string, s2 []string, rng *rand.Rand)`

CrossPMXString calls CrossPMX on a string slice.

func CrossUniformFloat64 ¶

`func CrossUniformFloat64(p1 []float64, p2 []float64, rng *rand.Rand)`

CrossUniformFloat64 crossover combines two individuals (the parents) into one (the offspring). Each parent's contribution to the Genome is determined by the value of a probability p. Each offspring receives a proportion of both of it's parents genomes. The new values are located in the hyper-rectangle defined between both parent's position in Cartesian space.

func InitJaggFloat64 ¶

`func InitJaggFloat64(n uint, lower, upper []float64, rng *rand.Rand) (floats []float64)`

InitJaggFloat64 generates random float64s x such that lower < x < upper with jagged bounds

func InitNormFloat64 ¶

`func InitNormFloat64(n uint, mean, std float64, rng *rand.Rand) (floats []float64)`

InitNormFloat64 generates random float64s sampled from a normal distribution.

func InitUnifFloat64 ¶

`func InitUnifFloat64(n uint, lower, upper float64, rng *rand.Rand) (floats []float64)`

InitUnifFloat64 generates random float64s x such that lower < x < upper.

func InitUnifString ¶

`func InitUnifString(n uint, corpus []string, rng *rand.Rand) (strings []string)`

InitUnifString generates random strings based on a given corpus. The strings are not necessarily distinct.

func InitUniqueString ¶

`func InitUniqueString(n uint, corpus []string, rng *rand.Rand) (strings []string)`

InitUniqueString generates random string slices based on a given corpus, each element from the corpus is only represented once in each slice. The method starts by shuffling, it then assigns the elements of the corpus in increasing index order to an individual.

func MutNormalFloat64 ¶

`func MutNormalFloat64(genome []float64, rate float64, rng *rand.Rand)`

MutNormalFloat64 modifies a float64 gene if a coin toss is under a defined mutation rate. The new gene value is a random value sampled from a normal distribution centered on the gene's current value and with a standard deviation proportional to the current value. It does so for each gene.

func MutPermute ¶

`func MutPermute(genome Slice, n int, rng *rand.Rand)`

MutPermute permutes two genes at random n times.

func MutPermuteFloat64 ¶

`func MutPermuteFloat64(s []float64, n int, rng *rand.Rand)`

MutPermuteFloat64 calls MutPermute on a float64 slice.

func MutPermuteInt ¶

`func MutPermuteInt(s []int, n int, rng *rand.Rand)`

MutPermuteInt calls MutPermute on an int slice.

func MutPermuteString ¶

`func MutPermuteString(s []string, n int, rng *rand.Rand)`

MutPermuteString callsMutPermute on a string slice.

func MutSplice ¶

`func MutSplice(genome Slice, rng *rand.Rand)`

MutSplice splits a genome in 2 and glues the pieces back together in reverse order.

func MutSpliceFloat64 ¶

`func MutSpliceFloat64(s []float64, rng *rand.Rand)`

MutSpliceFloat64 calls MutSplice on a float64 slice.

func MutSpliceInt ¶

`func MutSpliceInt(s []int, rng *rand.Rand)`

MutSpliceInt calls MutSplice on an int slice.

func MutSpliceString ¶

`func MutSpliceString(s []string, rng *rand.Rand)`

MutSpliceString calls MutSplice on a string slice.

func MutUniformString ¶

`func MutUniformString(genome []string, corpus []string, n int, rng *rand.Rand)`

MutUniformString picks a gene at random and replaces it with a random from a provided corpus. It repeats this n times.

Types ¶

type Agent ¶ added in v0.4.2

```type Agent struct {
DE *DiffEvo
// contains filtered or unexported fields
}```

An Agent is a candidate solution to a problem.

func (Agent) Clone ¶ added in v0.4.2

`func (a Agent) Clone() Genome`

Clone returns a deep copy of an Agent.

func (*Agent) Crossover ¶ added in v0.4.2

`func (a *Agent) Crossover(q Genome, rng *rand.Rand)`

Crossover doesn't do anything.

func (Agent) Evaluate ¶ added in v0.4.2

`func (a Agent) Evaluate() (float64, error)`

Evaluate the Agent by computing the value of the function at the current position.

func (*Agent) Mutate ¶ added in v0.4.2

`func (a *Agent) Mutate(rng *rand.Rand)`

Mutate the Agent.

type DiffEvo ¶ added in v0.4.2

```type DiffEvo struct {
Min, Max float64 // Boundaries for initial values
CRate    float64 // Crossover rate
DWeight  float64 // Differential weight
NDims    uint
F        func(x []float64) float64
GA       *GA
}```

DiffEvo implements differential evolution.

Example
```// Instantiate DiffEvo
var de, err = NewDefaultDiffEvo()
if err != nil {
fmt.Println(err)
return
}

// Fix random number generation
de.GA.RNG = rand.New(rand.NewSource(42))

// Define function to minimize
var ackley = func(x []float64) float64 {
var (
a, b, c = 20.0, 0.2, 2 * math.Pi
s1, s2  float64
d       = float64(len(x))
)
for _, xi := range x {
s1 += xi * xi
s2 += math.Cos(c * xi)
}
return -a*math.Exp(-b*math.Sqrt(s1/d)) - math.Exp(s2/d) + a + math.Exp(1)
}

// Run minimization
x, y, err := de.Minimize(ackley, 2)
if err != nil {
fmt.Println(err)
return
}

// Output best encountered solution
fmt.Printf("Found minimum of %.5f in %v\n", y, x)
```
```Output:

Found minimum of 0.00137 in [0.0004420129693826938 0.000195924625132926]
```

func NewDefaultDiffEvo ¶ added in v0.4.2

`func NewDefaultDiffEvo() (*DiffEvo, error)`

NewDefaultDiffEvo calls NewDiffEvo with default values.

func NewDiffEvo ¶ added in v0.4.2

```func NewDiffEvo(nAgents, nSteps uint, min, max, cRate, dWeight float64,
parallel bool, rng *rand.Rand) (*DiffEvo, error)```

NewDiffEvo instantiates and returns a DiffEvo instance after having checked for input errors.

func (*DiffEvo) Minimize ¶ added in v0.4.2

`func (de *DiffEvo) Minimize(f func([]float64) float64, nDims uint) ([]float64, float64, error)`

Minimize finds the minimum of a given real-valued function.

type DistanceMemoizer ¶

```type DistanceMemoizer struct {
Metric    Metric
Distances map[string]map[string]float64
// contains filtered or unexported fields
}```

A DistanceMemoizer computes and stores Metric calculations.

func (*DistanceMemoizer) GetDistance ¶

`func (dm *DistanceMemoizer) GetDistance(a, b Individual) float64`

GetDistance returns the distance between two Individuals based on the DistanceMemoizer's Metric field. If the two individuals share the same ID then GetDistance returns 0. DistanceMemoizer stores the calculated distances so that if GetDistance is called twice with the two same Individuals then the second call will return the stored distance instead of recomputing it.

type Float64Slice ¶

`type Float64Slice []float64`

Float64Slice attaches the methods of Slice to []float64

func (Float64Slice) Append ¶

`func (s Float64Slice) Append(t Slice) Slice`

Append method from Slice

func (Float64Slice) At ¶

`func (s Float64Slice) At(i int) interface{}`

At method from Slice

func (Float64Slice) Copy ¶

`func (s Float64Slice) Copy() Slice`

Copy method from Slice

func (Float64Slice) Len ¶

`func (s Float64Slice) Len() int`

Len method from Slice

func (Float64Slice) Replace ¶

`func (s Float64Slice) Replace(t Slice)`

Replace method from Slice

func (Float64Slice) Set ¶

`func (s Float64Slice) Set(i int, v interface{})`

Set method from Slice

func (Float64Slice) Slice ¶

`func (s Float64Slice) Slice(a, b int) Slice`

Slice method from Slice

func (Float64Slice) Split ¶

`func (s Float64Slice) Split(k int) (Slice, Slice)`

Split method from Slice

func (Float64Slice) Swap ¶

`func (s Float64Slice) Swap(i, j int)`

Swap method from Slice

type GA ¶

```type GA struct {
GAConfig `json:"-"`

// Fields generated at runtime
Populations Populations   `json:"populations"`
HallOfFame  Individuals   `json:"hall_of_fame"` // Sorted best Individuals ever encountered
Age         time.Duration `json:"duration"`     // Duration during which the GA has been evolved
Generations uint          `json:"generations"`  // Number of generations the GA has been evolved
}```

A GA contains populations which themselves contain individuals.

func (*GA) Minimize ¶ added in v0.4.2

`func (ga *GA) Minimize(newGenome func(rng *rand.Rand) Genome) error`

Minimize evolves the GA's Populations following the given evolutionary method. The GA's hall of fame is updated after each generation.

type GAConfig ¶ added in v0.4.2

```type GAConfig struct {
NPops        uint
PopSize      uint
NGenerations uint
HofSize      uint
Model        Model

// Optional fields
ParallelEval bool // Whether to evaluate Individuals in parallel or not
Migrator     Migrator
MigFrequency uint // Frequency at which migrations occur
Speciator    Speciator
Logger       *log.Logger
Callback     func(ga *GA)
EarlyStop    func(ga *GA) bool
RNG          *rand.Rand
}```

GAConfig contains fields that are necessary to instantiate a GA.

func NewDefaultGAConfig ¶ added in v0.4.2

`func NewDefaultGAConfig() GAConfig`

NewDefaultGAConfig returns a valid GAConfig with default values.

func (GAConfig) NewGA ¶ added in v0.4.2

`func (conf GAConfig) NewGA() (*GA, error)`

NewGA returns a pointer to a GA instance and checks for configuration errors.

type Genome ¶

```type Genome interface {
Evaluate() (float64, error)
Mutate(rng *rand.Rand)
Crossover(genome Genome, rng *rand.Rand)
Clone() Genome
}```

A Genome is an entity that can have any number and kinds of properties. It can be evolved as long as it can be evaluated, mutated, crossedover, and cloned then it can.

type Individual ¶

```type Individual struct {
Genome    Genome  `json:"genome"`
Fitness   float64 `json:"fitness"`
Evaluated bool    `json:"-"`
ID        string  `json:"id"`
}```

An Individual wraps a Genome and contains the fitness assigned to the Genome.

func NewIndividual ¶

`func NewIndividual(genome Genome, rng *rand.Rand) Individual`

NewIndividual returns a fresh individual.

func (Individual) Clone ¶

`func (indi Individual) Clone(rng *rand.Rand) Individual`

Clone an individual to produce a new individual with a different pointer and a different ID.

func (*Individual) Crossover ¶

`func (indi *Individual) Crossover(mate Individual, rng *rand.Rand)`

Crossover an individual by calling the Crossover method of it's Genome.

func (*Individual) Evaluate ¶

`func (indi *Individual) Evaluate() error`

Evaluate the fitness of an individual. Don't evaluate individuals that have already been evaluated.

func (*Individual) GetFitness ¶

`func (indi *Individual) GetFitness() float64`

GetFitness returns the fitness of an Individual after making sure it has been evaluated.

func (Individual) IdxOfClosest ¶

`func (indi Individual) IdxOfClosest(indis Individuals, dm DistanceMemoizer) (i int)`

IdxOfClosest returns the index of the closest individual from a slice of individuals based on the Metric field of a DistanceMemoizer.

func (*Individual) Mutate ¶

`func (indi *Individual) Mutate(rng *rand.Rand)`

Mutate an individual by calling the Mutate method of it's Genome.

func (Individual) String ¶ added in v0.4.2

`func (indi Individual) String() string`

String representation of an Individual. A tick (✔) or cross (✘) marker is added at the end to indicate if the Individual has been evaluated or not.

type Individuals ¶

`type Individuals []Individual`

Individuals is a convenience type, methods that belong to an Individual can be called declaratively.

func (Individuals) Clone ¶

`func (indis Individuals) Clone(rng *rand.Rand) Individuals`

Clone returns the same exact same slice of individuals but with different pointers and ID fields.

func (Individuals) Evaluate ¶

`func (indis Individuals) Evaluate(parallel bool) error`

Evaluate each Individual in a slice.

func (Individuals) FitAvg ¶

`func (indis Individuals) FitAvg() float64`

FitAvg returns the average fitness of a slice of individuals.

func (Individuals) FitMax ¶

`func (indis Individuals) FitMax() float64`

FitMax returns the worst fitness of a slice of individuals.

func (Individuals) FitMin ¶

`func (indis Individuals) FitMin() float64`

FitMin returns the best fitness of a slice of individuals.

func (Individuals) FitStd ¶

`func (indis Individuals) FitStd() float64`

FitStd returns the standard deviation of the fitness of a slice of individuals.

func (Individuals) IsSortedByFitness ¶

`func (indis Individuals) IsSortedByFitness() bool`

IsSortedByFitness checks if individuals are ascendingly sorted by fitness.

func (Individuals) Mutate ¶

`func (indis Individuals) Mutate(mutRate float64, rng *rand.Rand)`

Mutate each individual.

func (Individuals) SortByDistanceToMedoid ¶

`func (indis Individuals) SortByDistanceToMedoid(dm DistanceMemoizer)`

SortByDistanceToMedoid sorts Individuals according to their distance to the medoid. The medoid is the Individual that has the lowest average distance to the rest of the Individuals.

func (Individuals) SortByFitness ¶

`func (indis Individuals) SortByFitness()`

SortByFitness ascendingly sorts individuals by fitness.

func (Individuals) String ¶ added in v0.4.2

`func (indis Individuals) String() string`

String representation of a slice of Individuals.

type IntSlice ¶

`type IntSlice []int`

IntSlice attaches the methods of Slice to []float64

func (IntSlice) Append ¶

`func (s IntSlice) Append(t Slice) Slice`

Append method from Slice

func (IntSlice) At ¶

`func (s IntSlice) At(i int) interface{}`

At method from Slice

func (IntSlice) Copy ¶

`func (s IntSlice) Copy() Slice`

Copy method from Slice

func (IntSlice) Len ¶

`func (s IntSlice) Len() int`

Len method from Slice

func (IntSlice) Replace ¶

`func (s IntSlice) Replace(t Slice)`

Replace method from Slice

func (IntSlice) Set ¶

`func (s IntSlice) Set(i int, v interface{})`

Set method from Slice

func (IntSlice) Slice ¶

`func (s IntSlice) Slice(a, b int) Slice`

Slice method from Slice

func (IntSlice) Split ¶

`func (s IntSlice) Split(k int) (Slice, Slice)`

Split method from Slice

func (IntSlice) Swap ¶

`func (s IntSlice) Swap(i, j int)`

Swap method from Slice

type Metric ¶

`type Metric func(a, b Individual) float64`

A Metric returns the distance between two genomes.

type MigRing ¶

```type MigRing struct {
NMigrants uint // Number of migrants per exchange between Populations
}```

MigRing migration exchanges individuals between consecutive Populations in a random fashion. One by one, each population exchanges NMigrants individuals at random with the next population. NMigrants should be not higher than the number of individuals in each population, else all the individuals will migrate and it will be as if nothing happened.

func (MigRing) Apply ¶

`func (mig MigRing) Apply(pops Populations, rng *rand.Rand)`

Apply MigRing.

func (MigRing) Validate ¶

`func (mig MigRing) Validate() error`

Validate MigRing fields.

type Migrator ¶

```type Migrator interface {
Apply(pops Populations, rng *rand.Rand)
Validate() error
}```

Migrator applies crossover to the GA level, as such it doesn't require an independent random number generator and can use the global one.

type ModDownToSize ¶

```type ModDownToSize struct {
NOffsprings uint
SelectorA   Selector
SelectorB   Selector
MutRate     float64
CrossRate   float64
}```

ModDownToSize implements the select down to size model.

func (ModDownToSize) Apply ¶

`func (mod ModDownToSize) Apply(pop *Population) error`

Apply ModDownToSize.

func (ModDownToSize) Validate ¶

`func (mod ModDownToSize) Validate() error`

Validate ModDownToSize fields.

type ModGenerational ¶

```type ModGenerational struct {
Selector  Selector
MutRate   float64
CrossRate float64
}```

ModGenerational implements the generational model.

func (ModGenerational) Apply ¶

`func (mod ModGenerational) Apply(pop *Population) error`

Apply ModGenerational.

func (ModGenerational) Validate ¶

`func (mod ModGenerational) Validate() error`

Validate ModGenerational fields.

type ModMutationOnly ¶

```type ModMutationOnly struct {
Strict bool
}```

ModMutationOnly implements the mutation only model. Each generation, all the Individuals are mutated. If Strict is true then the individuals are only replaced if the mutation is favorable.

func (ModMutationOnly) Apply ¶

`func (mod ModMutationOnly) Apply(pop *Population) error`

Apply ModMutationOnly.

func (ModMutationOnly) Validate ¶

`func (mod ModMutationOnly) Validate() error`

Validate ModMutationOnly fields.

type ModRing ¶

```type ModRing struct {
Selector Selector
MutRate  float64
}```

ModRing implements the island ring model.

func (ModRing) Apply ¶

`func (mod ModRing) Apply(pop *Population) error`

Apply ModRing.

func (ModRing) Validate ¶

`func (mod ModRing) Validate() error`

Validate ModRing fields.

```type ModSteadyState struct {
Selector  Selector
KeepBest  bool
MutRate   float64
CrossRate float64
}```

`func (mod ModSteadyState) Apply(pop *Population) error`

`func (mod ModSteadyState) Validate() error`

type Model ¶

```type Model interface {
Apply(pop *Population) error
Validate() error
}```

A Model specifies a protocol for applying genetic operators to a population at generation i in order for it obtain better individuals at generation i+1.

type OES ¶ added in v0.4.2

```type OES struct {
Sigma        float64
LearningRate float64
Mu           []float64
F            func([]float64) float64
GA           *GA
}```

OES implements a simple version of the evolution strategy proposed by OpenAI. Reference: https://arxiv.org/abs/1703.03864

Example
```// Instantiate DiffEvo
var oes, err = NewDefaultOES()
if err != nil {
fmt.Println(err)
return
}

// Fix random number generation
oes.GA.RNG = rand.New(rand.NewSource(42))

// Define function to minimize
var rastrigin = func(x []float64) (y float64) {
y = 10 * float64(len(x))
for _, xi := range x {
y += math.Pow(xi, 2) - 10*math.Cos(2*math.Pi*xi)
}
return y
}

// Run minimization
X, y, err := oes.Minimize(rastrigin, []float64{0, 0})
if err != nil {
fmt.Println(err)
return
}

// Output best encountered solution
fmt.Printf("Found minimum of %.5f in %v\n", y, X)
```
```Output:

Found minimum of 0.02270 in [0.006807861794722094 -0.008251984117745246]
```

func NewDefaultOES ¶ added in v0.4.2

`func NewDefaultOES() (*OES, error)`

NewDefaultOES calls NewOES with default values.

func NewOES ¶ added in v0.4.2

`func NewOES(nPoints, nSteps uint, sigma, lr float64, parallel bool, rng *rand.Rand) (*OES, error)`

NewOES instantiates and returns a OES instance after having checked for input errors.

func (*OES) Minimize ¶ added in v0.4.2

`func (oes *OES) Minimize(f func([]float64) float64, x []float64) ([]float64, float64, error)`

Minimize finds the minimum of a given real-valued function.

type Particle ¶ added in v0.4.2

```type Particle struct {
CurrentX []float64
CurrentY float64
BestX    []float64
BestY    float64
Velocity []float64
SPSO     *SPSO
}```

A Particle is an element of a Swarm. It tracks it's current position, the best position it has encountered, and a velocity vector. It also has a pointer to the SPSO which generated it so that it can access the function to minimize and the global best position.

func (Particle) Clone ¶ added in v0.4.2

`func (p Particle) Clone() Genome`

Clone returns a deep copy of the Particle.

func (*Particle) Crossover ¶ added in v0.4.2

`func (p *Particle) Crossover(q Genome, rng *rand.Rand)`

Crossover doesn't do anything.

func (*Particle) Evaluate ¶ added in v0.4.2

`func (p *Particle) Evaluate() (float64, error)`

Evaluate the Particle by computing the value of the function at the current position. If the position is better than the best position encountered by the Particle then it replaces it. Likewhise, the global best position is replaced if the current position is better.

func (*Particle) Mutate ¶ added in v0.4.2

`func (p *Particle) Mutate(rng *rand.Rand)`

Mutate the Particle by modifying it's velocity and it's current position.

type Population ¶

```type Population struct {
Individuals Individuals   `json:"indis"`
Age         time.Duration `json:"age"`
Generations uint          `json:"generations"`
ID          string        `json:"id"`
RNG         *rand.Rand
}```

A Population contains individuals. Individuals mate within a population. Individuals can migrate from one population to another. Each population has a random number generator to bypass the global rand mutex.

func (Population) Log ¶

`func (pop Population) Log(logger *log.Logger)`

Log a Population's current statistics with a provided log.Logger.

type Populations ¶

`type Populations []Population`

Populations type is necessary for migration and speciation purposes.

func (Populations) Apply ¶ added in v0.4.2

`func (pops Populations) Apply(f func(pop *Population) error) error`

Apply a function to a slice of Populations.

type SPSO ¶ added in v0.4.2

```type SPSO struct {
Min, Max float64 // Boundaries for initial values
W        float64
NDims    uint
BestX    []float64
BestY    float64
F        func([]float64) float64
GA       *GA
// contains filtered or unexported fields
}```

SPSO implements the 2011 version of Standard Particle Swarm Optimization. It can optimize single-output real-valued functions. Reference: http://clerc.maurice.free.fr/pso/SPSO_descriptions.pdf

Example
```// Instantiate SPSO
var spso, err = NewDefaultSPSO()
if err != nil {
fmt.Println(err)
return
}

// Fix random number generation
spso.GA.RNG = rand.New(rand.NewSource(42))

// Define function to minimize
var styblinskiTang = func(x []float64) (y float64) {
for _, xi := range x {
y += math.Pow(xi, 4) - 16*math.Pow(xi, 2) + 5*xi
}
return 0.5 * y
}

// Run minimization
x, y, err := spso.Minimize(styblinskiTang, 2)
if err != nil {
fmt.Println(err)
return
}

// Output best encountered solution
fmt.Printf("Found minimum of %.5f in %v\n", y, x)
```
```Output:

Found minimum of -78.23783 in [-2.8586916496046983 -2.9619895273744623]
```

func NewDefaultSPSO ¶ added in v0.4.2

`func NewDefaultSPSO() (*SPSO, error)`

NewDefaultSPSO calls NewSPSO with default values.

func NewSPSO ¶ added in v0.4.2

`func NewSPSO(nParticles, nSteps uint, min, max, w float64, parallel bool, rng *rand.Rand) (*SPSO, error)`

NewSPSO instantiates and returns a SPSO instance after having checked for input errors.

func (*SPSO) Minimize ¶ added in v0.4.2

`func (pso *SPSO) Minimize(f func([]float64) float64, nDims uint) ([]float64, float64, error)`

Minimize finds the minimum of a given real-valued function.

type SelElitism ¶

`type SelElitism struct{}`

SelElitism selection returns the n best individuals of a group.

func (SelElitism) Apply ¶

`func (sel SelElitism) Apply(n uint, indis Individuals, rng *rand.Rand) (Individuals, []int, error)`

Apply SelElitism.

func (SelElitism) Validate ¶

`func (sel SelElitism) Validate() error`

Validate SelElitism fields.

type SelRoulette ¶

`type SelRoulette struct{}`

SelRoulette samples individuals through roulette wheel selection (also known as fitness proportionate selection).

func (SelRoulette) Apply ¶

`func (sel SelRoulette) Apply(n uint, indis Individuals, rng *rand.Rand) (Individuals, []int, error)`

Apply SelRoulette.

func (SelRoulette) Validate ¶

`func (sel SelRoulette) Validate() error`

Validate SelRoulette fields.

type SelTournament ¶

```type SelTournament struct {
NContestants uint
}```

SelTournament samples individuals through tournament selection. The tournament is composed of randomly chosen individuals. The winner of the tournament is the chosen individual with the lowest fitness. The obtained individuals are all distinct, in other words there are no repetitions.

func (SelTournament) Apply ¶

`func (sel SelTournament) Apply(n uint, indis Individuals, rng *rand.Rand) (Individuals, []int, error)`

Apply SelTournament.

func (SelTournament) Validate ¶

`func (sel SelTournament) Validate() error`

Validate SelTournament fields.

type Selector ¶

```type Selector interface {
Apply(n uint, indis Individuals, rng *rand.Rand) (selected Individuals, indexes []int, err error)
Validate() error
}```

Selector chooses a subset of size n from a group of individuals. The group of individuals a Selector is applied to is expected to be sorted.

type Slice ¶

```type Slice interface {
At(i int) interface{}
Set(i int, v interface{})
Len() int
Swap(i, j int)
Slice(a, b int) Slice
Split(k int) (Slice, Slice)
Append(Slice) Slice
Replace(Slice)
Copy() Slice
}```

A Slice is a genome with a list-like structure.

type SpecFitnessInterval ¶

```type SpecFitnessInterval struct {
K uint // Number of intervals
}```

SpecFitnessInterval speciates a population based on the fitness of each individual where each species contains m = n/k (rounded to the closest upper integer) individuals with similar fitnesses. For example, with 4 species, 30 individuals would be split into 3 groups of 8 individuals and 1 group of 6 individuals (3*8 + 1*6 = 30). More generally each group is of size min(n-i, m) where i is a multiple of m.

func (SpecFitnessInterval) Apply ¶

`func (spec SpecFitnessInterval) Apply(indis Individuals, rng *rand.Rand) ([]Individuals, error)`

Apply SpecFitnessInterval.

func (SpecFitnessInterval) Validate ¶

`func (spec SpecFitnessInterval) Validate() error`

Validate SpecFitnessInterval fields.

type SpecKMedoids ¶

```type SpecKMedoids struct {
K             uint // Number of medoids
MinPerCluster uint
Metric        Metric // Dissimimilarity measure
MaxIterations uint
}```

SpecKMedoids (k-medoid clustering).

func (SpecKMedoids) Apply ¶

`func (spec SpecKMedoids) Apply(indis Individuals, rng *rand.Rand) ([]Individuals, error)`

Apply SpecKMedoids.

func (SpecKMedoids) Validate ¶

`func (spec SpecKMedoids) Validate() error`

Validate SpecKMedoids fields.

type Speciator ¶

```type Speciator interface {
Apply(indis Individuals, rng *rand.Rand) ([]Individuals, error)
Validate() error
}```

A Speciator partitions a population into n smaller subpopulations. Each subpopulation shares the same random number generator inherited from the initial population.

type StringSlice ¶

`type StringSlice []string`

StringSlice attaches the methods of Slice to []float64

func (StringSlice) Append ¶

`func (s StringSlice) Append(t Slice) Slice`

Append method from Slice

func (StringSlice) At ¶

`func (s StringSlice) At(i int) interface{}`

At method from Slice

func (StringSlice) Copy ¶

`func (s StringSlice) Copy() Slice`

Copy method from Slice

func (StringSlice) Len ¶

`func (s StringSlice) Len() int`

Len method from Slice

func (StringSlice) Replace ¶

`func (s StringSlice) Replace(t Slice)`

Replace method from Slice

func (StringSlice) Set ¶

`func (s StringSlice) Set(i int, v interface{})`

Set method from Slice

func (StringSlice) Slice ¶

`func (s StringSlice) Slice(a, b int) Slice`

Slice method from Slice

func (StringSlice) Split ¶

`func (s StringSlice) Split(k int) (Slice, Slice)`

Split method from Slice

func (StringSlice) Swap ¶

`func (s StringSlice) Swap(i, j int)`

Swap method from Slice

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