crossover.go

package eaopt

import (
	"math/rand"
	"sort"
)

// Type specific mutations for slices

// 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 CrossUniformFloat64(p1 []float64, p2 []float64, rng *rand.Rand) {
	for i := range p1 {
		var p = rng.Float64()
		var o1 = p*p1[i] + (1-p)*p2[i]
		var o2 = (1-p)*p1[i] + p*p2[i]
		p1[i] = o1
		p2[i] = o2
	}
}

// Generic mutations for slices

// Contains the deterministic part of the GNX method for testing purposes.
func gnx(p1, p2 Slice, indexes []int) {
	var (
		n      = p1.Len()
		o1     = p1.Copy()
		o2     = p2.Copy()
		toggle = true
	)
	// Add the first and last indexes
	indexes = append([]int{0}, indexes...)
	indexes = append(indexes, n)
	for i := 0; i < len(indexes)-1; i++ {
		if toggle {
			o1.Slice(indexes[i], indexes[i+1]).Replace(p1.Slice(indexes[i], indexes[i+1]))
			o2.Slice(indexes[i], indexes[i+1]).Replace(p2.Slice(indexes[i], indexes[i+1]))
		} else {
			o1.Slice(indexes[i], indexes[i+1]).Replace(p2.Slice(indexes[i], indexes[i+1]))
			o2.Slice(indexes[i], indexes[i+1]).Replace(p1.Slice(indexes[i], indexes[i+1]))
		}
		toggle = !toggle // Alternate for the new copying
	}
	p1.Replace(o1)
	p2.Replace(o2)
}

// 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 CrossGNX(p1 Slice, p2 Slice, n uint, rng *rand.Rand) {
	var indexes = randomInts(n, 1, p1.Len(), rng)
	sort.Ints(indexes)
	gnx(p1, p2, indexes)
}

// CrossGNXInt calls CrossGNX on two int slices.
func CrossGNXInt(s1 []int, s2 []int, n uint, rng *rand.Rand) {
	CrossGNX(IntSlice(s1), IntSlice(s2), n, rng)
}

// CrossGNXFloat64 calls CrossGNX on two float64 slices.
func CrossGNXFloat64(s1 []float64, s2 []float64, n uint, rng *rand.Rand) {
	CrossGNX(Float64Slice(s1), Float64Slice(s2), n, rng)
}

// CrossGNXString calls CrossGNX on two string slices.
func CrossGNXString(s1 []string, s2 []string, n uint, rng *rand.Rand) {
	CrossGNX(StringSlice(s1), StringSlice(s2), n, rng)
}

// Contains the deterministic part of the PMX method for testing purposes.
func pmx(p1, p2 Slice, a, b int) {
	var (
		n  = p1.Len()
		o1 = p1.Copy()
		o2 = p2.Copy()
	)
	// Create lookup maps to quickly see if a gene has been visited
	var (
		p1Visited, p2Visited = make(set), make(set)
		o1Visited, o2Visited = make(set), make(set)
	)
	for i := a; i < b; i++ {
		p1Visited[p1.At(i)] = true
		p2Visited[p2.At(i)] = true
		o1Visited[i] = true
		o2Visited[i] = true
	}
	for i := a; i < b; i++ {
		// Find the element in the second parent that has not been copied in the first offspring
		if !p1Visited[p2.At(i)] {
			var j = i
			for o1Visited[j] {
				j, _ = search(o1.At(j), p2)
			}
			o1.Set(j, p2.At(i))
			o1Visited[j] = true
		}
		// Find the element in the first parent that has not been copied in the second offspring
		if !p2Visited[p1.At(i)] {
			var j = i
			for o2Visited[j] {
				j, _ = search(o2.At(j), p1)
			}
			o2.Set(j, p1.At(i))
			o2Visited[j] = true
		}
	}
	// Fill in the offspring's missing values with the opposite parent's values
	for i := 0; i < n; i++ {
		if !o1Visited[i] {
			o1.Set(i, p2.At(i))
		}
		if !o2Visited[i] {
			o2.Set(i, p1.At(i))
		}
	}
	p1.Replace(o1)
	p2.Replace(o2)
}

// 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 CrossPMX(p1 Slice, p2 Slice, rng *rand.Rand) {
	var indexes = randomInts(2, 1, p1.Len(), rng)
	sort.Ints(indexes)
	pmx(p1, p2, indexes[0], indexes[1])
}

// CrossPMXInt calls CrossPMX on an int slice.
func CrossPMXInt(s1 []int, s2 []int, rng *rand.Rand) {
	CrossPMX(IntSlice(s1), IntSlice(s2), rng)
}

// CrossPMXFloat64 calls CrossPMX on a float64 slice.
func CrossPMXFloat64(s1 []float64, s2 []float64, rng *rand.Rand) {
	CrossPMX(Float64Slice(s1), Float64Slice(s2), rng)
}

// CrossPMXString calls CrossPMX on a string slice.
func CrossPMXString(s1 []string, s2 []string, rng *rand.Rand) {
	CrossPMX(StringSlice(s1), StringSlice(s2), rng)
}

// Contains the deterministic part of the OX method for testing purposes.
func ox(p1, p2 Slice, a, b int) {
	var (
		n  = p1.Len()
		o1 = p1.Copy()
		o2 = p2.Copy()
	)
	// Create lookup maps to quickly see if a gene has been copied from a parent or not
	var p1Occurences, p2Occurences = make(setInt), make(setInt)
	for i := b; i < a+n; i++ {
		var k = i % n
		p1Occurences[p1.At(k)]++
		p2Occurences[p2.At(k)]++
	}
	// Keep two indicators to know where to fill the offsprings
	var j1, j2 = b, b
	for i := b; i < b+n; i++ {
		var k = i % n
		if p1Occurences[p2.At(k)] > 0 {
			p1Occurences[p2.At(k)]--
			o1.Set(j1%n, p2.At(k))
			j1++
		}
		if p2Occurences[p1.At(k)] > 0 {
			p2Occurences[p1.At(k)]--
			o2.Set(j2%n, p1.At(k))
			j2++
		}
	}
	p1.Replace(o1)
	p2.Replace(o2)
}

// 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 CrossOX(p1 Slice, p2 Slice, rng *rand.Rand) {
	var indexes = randomInts(2, 1, p1.Len(), rng)
	sort.Ints(indexes)
	ox(p1, p2, indexes[0], indexes[1])
}

// CrossOXInt calls CrossOX on a int slice.
func CrossOXInt(s1 []int, s2 []int, rng *rand.Rand) {
	CrossOX(IntSlice(s1), IntSlice(s2), rng)
}

// CrossOXFloat64 calls CrossOX on a float64 slice.
func CrossOXFloat64(s1 []float64, s2 []float64, rng *rand.Rand) {
	CrossOX(Float64Slice(s1), Float64Slice(s2), rng)
}

// CrossOXString calls CrossOX on a string slice.
func CrossOXString(s1 []string, s2 []string, rng *rand.Rand) {
	CrossOX(StringSlice(s1), StringSlice(s2), rng)
}

// 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 CrossCX(p1, p2 Slice) {
	var (
		o1     = p1.Copy()
		o2     = p2.Copy()
		cycles = getCycles(p1, p2)
		toggle = true
	)
	for i := 0; i < len(cycles); i++ {
		for _, j := range cycles[i] {
			if toggle {
				o1.Set(j, p1.At(j))
				o2.Set(j, p2.At(j))
			} else {
				o2.Set(j, p1.At(j))
				o1.Set(j, p2.At(j))
			}
		}
		toggle = !toggle
	}
	p1.Replace(o1)
	p2.Replace(o2)
}

// CrossCXInt calls CrossCX on an int slice.
func CrossCXInt(s1 []int, s2 []int) {
	CrossCX(IntSlice(s1), IntSlice(s2))
}

// CrossCXFloat64 calls CrossCX on a float64 slice.
func CrossCXFloat64(s1 []float64, s2 []float64) {
	CrossCX(Float64Slice(s1), Float64Slice(s2))
}

// CrossCXString calls CrossCX on a string slice.
func CrossCXString(s1 []string, s2 []string) {
	CrossCX(StringSlice(s1), StringSlice(s2))
}

// CrossERX (Edge Recombination Crossover).
func CrossERX(p1, p2 Slice) {
	var (
		n            = p1.Len()
		o1           = p1.Copy()
		o2           = p2.Copy()
		parents      = []Slice{p1, p2}
		offsprings   = []Slice{o1, o2}
		p1Neighbours = getNeighbours(p1)
		p2Neighbours = getNeighbours(p2)
		pNeighbours  = make(map[interface{}]set)
	)
	// Merge the neighbours of each parent whilst ignoring duplicates
	for i := range p1Neighbours {
		pNeighbours[i] = union(p1Neighbours[i], p2Neighbours[i])
	}
	// Hold two copies of the parent neighbours (one for each offspring)
	var neighbours = []map[interface{}]set{pNeighbours, nil}
	neighbours[1] = make(map[interface{}]set)
	for k, v := range pNeighbours {
		neighbours[1][k] = v
	}
	// Set the first element of each offspring to be the one of the
	// corresponding parent
	o1.Set(0, p1.At(0))
	o2.Set(0, p2.At(0))
	// Delete the neighbour from the adjacency set
	for i := range neighbours {
		delete(neighbours[i], parents[i].At(0))
		for j := range neighbours[i] {
			if neighbours[i][j][parents[i].At(0)] {
				delete(neighbours[i][j], parents[i].At(0))
			}
		}
	}
	for o := range offsprings {
		for i := 1; i < n; i++ {
			// Find the gene with the least neighbours
			var (
				j   interface{}
				min = 5 // There can't be more than 5 neighbours between 2 parents
			)
			for k, v := range neighbours[o] {
				if len(v) < min {
					j = k
					min = len(v)
				}
			}
			offsprings[o].Set(i, j)
			delete(neighbours[o], j)
			for k := range neighbours[o] {
				if neighbours[o][k][j] {
					delete(neighbours[o][k], j)
				}
			}
		}
	}
	p1.Replace(o1)
	p2.Replace(o2)
}

// CrossERXInt calls CrossERX on an int slice.
func CrossERXInt(s1 []int, s2 []int) {
	CrossERX(IntSlice(s1), IntSlice(s2))
}

// CrossERXFloat64 callsCrossERX on a float64 slice.
func CrossERXFloat64(s1 []float64, s2 []float64) {
	CrossERX(Float64Slice(s1), Float64Slice(s2))
}

// CrossERXString calls CrossERX on a string slice.
func CrossERXString(s1 []string, s2 []string) {
	CrossERX(StringSlice(s1), StringSlice(s2))
}