Adaptive Nature-inspired Algorithms for Hybrid Genetic Optimization

Description

The package adana provides the functions related to the hyrid adaptive genetic algorithms for solving optimization problems.

Details

The Genetic Algorithm (GA) is a type of optimization method of Evolutionary Algorithms. It uses the biologically inspired operators such as mutation, crossover, selection and replacement.Because of their global search and robustness abilities, GAs have been widely utilized in machine learning, expert systems, data science, engineering, life sciences and many other areas of research and business. However, the regular GAs need the techniques to improve their efficiences in computing time and performance in finding global optimum using some adaptation and hybridization strategies. The adaptive GAs (AGA) increase the convergence speed and success of regular GAs by setting the parameters crossover and mutation probabilities dynamically. The hybrid GAs combine the exploration strength of a stochastic GAs with the exact convergence ability of any type of deterministic local search algorithms such as simulated-annealing, in addition to other nature-inspired algorithms such as ant colony optimization, particle swarm optimization etc. The package 'adana' includes a rich working environment with its many functions that make possible to build and work regular GA, adaptive GA, hybrid GA and hybrid adaptive GA for any kind of optimization problems.

Author(s)

Zeynel Cebeci, Erkut Tekeli

References

Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari [Genetic Algorithms and Optimization Applications with R], 535 p. Nobel Academic Publishing. Ankara

See Also

adana

Adaptive Nature-inspired Algorithms for Hybrid Genetic Optimization

Description

The adana function is a GA function that can be used for any single-objective optimization problem.

Usage

adana(gatype = "gga", objective = "max", maxiter = 100, initfunc = initbin, fitfunc,
      selfunc = seltour, crossfunc = px1, mutfunc = bitmut, replace = elitism,
      adapfunc = NULL, hgafunc = NULL, monitorfunc = NULL, n = 100, m = 8,
      lb = rep(0, 8), ub = rep(1, 8), nmode = "real", type = 1, permset = 0:9,
      prevpop = NULL, selt = 2, selbc = 0.5, selc = 2, selk = 1.005, sells = 1.5,
      selns = 0.5, selps = 0.5, sels = 1.5, selt0 = 50, selw = 2, reptype = FALSE,
      cxpc = 0.9, cxpc2 = 0.8, cxon = 2, cxk = 2, cxps = 0.5, cxa = 0, cxb = 0.15,
      cxealfa = 1, cxalfa = 0.5, mutpm = 0.05, mutpm2 = 0.2, mutb = 2, mutpow = 2,
      mutq = 0.5, mutmy = c(), mutsdy = c(), adapa = 0.75, adapb = 0.5, adapc = 0.1,
      adapd = 0.1, hgastep = 10, hgans = 1, hgaftype = "w", reps = 1, repk = 10,
      lambda = 1, tercrit = c(1), abdif = 1e-06, bestdif = 1e-06, objval = 0,
      optdif = 1e-06, rmcnt = 10, rmdif = 1e-06, phidif = 1e-06, rangedif = 1e-06,
      meandif = 1e-06, sddif = 1e-06, mincv = 0.001, simlev = 0.95, maxtime = 60,
      keepbest = TRUE, parfile = NULL, verbose = FALSE, ...)

Arguments

Details

adana function is a genetic algorithm function that can be used for all kinds of single-objective optimization problems. The adana function, unlike other GA packages, not only has adaptive GA functions, but also offers specially developed deterministic and self-adaptive techniques called adana1, adana2, and adana3, and is easily hybridized with other optimization methods inspired by nature. Besides, the adana function supports the use of monitors to monitor the progress of the GA run. In addition to containing many crossover and mutation operators, it is coded with a plug-and-play approach so that the user can add custom operator functions that he has developed.

The initialization population is created by using the name of the initialization function and other parameters passed to initfunc with the initialize function. The fit values of individuals in the population are calculated using fitfunc, which is passed to the evaluate function before each iteration. Then, the termination conditions are checked according to the criteria specified in the termination criteria (tercrit) argument via the terminate function. When the termination condition is not met, adana GA continues to run and searches for the best solution. If the keepbest argument is TRUE, the best solution value, chromosome, and generation number are saved in the list named bestsol.

Since the adana function allows adaptive GA studies, from which it is named, it runs a function that is passed with the adapfunc argument and contains the code of the adaptation algorithm. This adaptation function returns the crossover and mutation rates by recalculating. Thus, it strengthens the GA with its exploitation and exploration adaptations.

In order to determine the individuals to be selected for the mating pool, the selection process is done with the selfunc selection function transferred to the select function.

The crossover of selected individuals is executed with the crossover operator in the crossfunc argument passed to the cross function.

Mutation operations are performed with the mutation operator function assigned to mutfunc by the mutate function.

Finally, for GA, replacement is performed by passing the parent population and the offspring population to the replace function.

Hybridization with other optimization techniques can also be done before an iteration of the GA is complete. For this, the hybridization function passed to the hgafunc argument is used. Other parameters that need the optimization technique called in the hybridization function call, are also passed.

Progress made in each GA generation can be monitored visually with a monitor function. For this, the monitor function passed to the monitorfunc argument is used.

In GA implementations, if the required parameters for R functions that perform selection, crossover, mutation, renewal, and other operations are not entered in the function call, their default values are used. The user can change these parameters during the function call to suit the problem. However, there are many parameters used by the adana function and the functions it calls. It may be more practical to use the parameters by saving them to a file. The parfile argument can be used for this purpose.

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.

See Also

GA Operators: initialize, evaluate, terminate, select, cross, mutate

Initialize Functions: initbin, initval, initperm, initnorm

Selection Functions: selrand, selrswrp, selrws, selrws2, selrss, selsus, seldet, selwscale, selsscale, selsscale2, sellscale, selrscale, selrscale2, selpscale, selescale, seltour, seltour2, selboltour, sellrs, sellrs2, sellrs3, selnlrs, selers, seltrunc

Crossover Functions: px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Mutation Functions: bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Replacement Functions: grdelall, elitism, grmuplambda, grmuplambda2, grmuplambda3, grmuplambda4, grmuvlambda, grrobin, ssrmup1, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Adaptation Functions: fixpcmut, ilmdhc, adana1, adana2, adana3, leitingzhi

Hybridization Functions: hgaoptim, hgaoptimx, hgaroi

Examples

# Preparing data
material = c("knife", "tin", "potato", "coffee", "sleeping bag", "rope", "compass")
weigth = c(1, 5, 10, 1, 7, 5, 1)
point = c(10, 20, 15, 2, 30, 10, 30)
kspdata = data.frame(material, weigth, point)
capacity = 100

# Fitness Function
kspfit2 = function(x, ...) {
  tpoint = x %*% kspdata$point
  tweigth = x %*% kspdata$weigth
  G1 = tweigth-capacity 
  fitval = tpoint-max(0,G1)^2     
  return(fitval)
}

# Run GA
n = 20
m = nrow(kspdata)
niter = 100
kspGGA = adana(n=n, m=m, maxiter=niter, objective="max", gatype="gga",
  initfunc=initbin, fitfunc=kspfit2, selfunc=seltour, 
  crossfunc=kpx, mutfunc=bitmut, replace=elitism,
  selt=2, reps=4, repk=5, cxon=2, cxk=3, cxpc=0.8, 
  mutpm=0.05, tercrit=c(1), keepbest=TRUE,
  verbose=TRUE, monitorfunc=monprogress)
  
head(kspGGA$finalpop)        # Display Final Population
head(kspGGA$genfits)         # Display Fitness Values According to Generations
bestsol(kspGGA)              # Display Best Solution  
kspdata[kspGGA$bestsol$chromosome == 1, ]    # Display Best Chromosome

Adaptive Dynamic Algorithm (Adana 1)

Description

Adana-1 is an adaptation function that calculates the mutation rates to be applied in generations by sine wave modeling (Cebeci, 2021).

Usage

adana1(g, gmax, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.

See Also

fixpcmut, ilmdhc, adana2, leitingzhi, adana3

Examples

gmax <- 1000
g <- c(1, 10, 50, 100, 250, 500, 750, gmax)
adana1(g=g, gmax=gmax)

Adaptive Dynamic Algorithm (Adana 2)

Description

Adana-2 is an adaptation function that calculates the mutation rates to be applied in generations by square root modeling (Cebeci, 2021).

Usage

adana2(g, gmax, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.

See Also

fixpcmut, ilmdhc, adana1, leitingzhi, adana3

Examples

gmax <- 1000
g <- c(1, 10, 50, 100, 250, 500, 750, gmax)
adana1(g=g, gmax=gmax)

Dynamic mutation and crossover function (Adana 3)

Description

This adaptation function proposed by Cebeci (2021) is an adaptation function that takes into account the cooperation of individuals.

Usage

adana3(fitvals, g, gmax, cxpc, mutpm,
                  adapc, adapd, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.

See Also

fixpcmut, ilmdhc, adana1, adana2, leitingzhi

Asymmetric Two-Point Crossover (ATC)

Description

The Asymmetric Two-Point Crossover (ATC) operator relies on the two-point crossover being implemented differently for Parent1 and Parent2 (Yuan, 2002). Offspring2 is generated by a standard two-point crossover. However, in the generation of Offspring1, the part between the cut points is taken from Parent2, while the other parts are completed from Parent1.

Usage

atc(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Yuan B. (2002). Deterministic crowding, recombination and self-similarity. In Proc. of the 2002 Cong. on Evolutionary Computation (Cat. No. 02TH8600) (Vol. 2, pp. 1516-1521). IEEE.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 0, 1, 0, 1, 1, 1, 0)
parent2 = c(1, 1, 1, 0, 1, 0, 0, 1)
atc(parent1, parent2)

Avarage Crossover

Description

The AX operator calculates the simple arithmetic mean of the parental chromosomes. Therefore, it is a single-output operator and generates a single offspring (Gwiazda, 2006).

Usage

ax(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Gwiazda T.D. (2006). Genetic Algorithms Reference. Vol. I: Crossover for Single-Objective Numerical Optimization Problems. Tomaszgwiadze E-books, Poland.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
ax(parent1, parent2, cxon=1)

Best solution monitoring function

Description

Display best solution from result of GA

Usage

bestsol(garesult)

Arguments

Value

Display chromosome, fitness value and generation number of best solution.

Author(s)

Zeynel Cebeci & Erkut Tekeli

Convert from binary to gray code integer

Description

The function bin2gray converts a binary coded number to gray coded integer.

Usage

bin2gray(bin)

Arguments

Details

The bin2gray function works as a compliment of the gray2bin function.

Value

Returns the gray coded integer equivalent of the input number.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

gray2bin

Examples

  bin = c(1,0,1,1)
  bin2gray(bin)     # returns 1110
  
  bin = c(1,0,1,0)
  bin2gray(bin)     # returns 1111

Convert Binary Numbers to Integers

Description

The function bin2int converts a binary coded number to integer.

Usage

bin2int(bin)

Arguments

Details

The bin2int function works as a compliment of the int2bin function.

Value

Returns the integer equivalent of the input number.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

int2bin

Examples

x <- c(1,1,1,1,1,0,1,0,0)
bin2int(x)  # returns 500

Bit Flip Mutation

Description

The Bit Flip Mutation operator converts the bit at a randomly selected point to its allele.

This operator is used on binary encoded chromosomes.

Usage

bitmut(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

offspring = c(1,1,0,1,0,1,0,1,0,0)
bitmut(offspring)

Blended Crossover (BLX-\alpha)

Description

Eshelman and Schaffer (1993) proposed an algorithm called Blended-\alpha Crossover (BLX-\alpha) by introducing the concept of interval scheme to be applied in real-valued problems (Takahashi & Kita, 2001).

Usage

blxa(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Eshelman, L.J. and Schaffer, J.D. (1993). Real-coded genetic algorithms and interval schemata. In Foundations of Genetic Algorithms, Vol. 2, pp. 187-202, Elsevier.

Takahashi, M. and Kita, H. (2001). A crossover operator using independent component analysis for real-coded genetic algorithms. In Proc. of the 2001 Cong. on Evolutionary Computation (IEEE Cat.No. 01TH8546), Vol. 1, pp. 643-649. IEEE.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

ebeveyn1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
ebeveyn2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
blxa(ebeveyn1, ebeveyn2, cxon=3)

Blended crossover-\alpha\beta (BLX-\alpha\beta)

Description

Blended crossover-\alpha\beta is another version of the Blended crossover-\alpha operator.

Usage

blxab(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
blxab(parent1, parent2)

Boundary Mutation

Description

The Boundary Mutation operator is a mutation operator that changes the value of a randomly selected gene in the chromosome with the upper or lower limit value for that gene.

This operator is used for value encoded (integer or real number) chromosomes.

Usage

boundmut(y, lb, ub, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

lb = c(2, 1, 3, 1, 0, 4)
ub = c(10, 15, 8, 5, 6, 9)
offspring = c(8, 6, 4, 1, 3, 7)
boundmut(offspring, lb=lb, ub=ub)

Boundary Search Mutation 1

Description

Boundary Search Mutation-1 is an algorithm based on probing the boundaries of the convenience region in constraint processing for NLP optimization (Michalewicz & Schoenauer, 1996). Two genes are randomly selected from the chromosome and one of them is multiplied by a random factor at the q value, while the other gene is multiplied by 1/q.

This operator is used for value encoded (integer or real number) chromosomes.

Usage

bsearchmut1(y, mutq, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Michalewicz, Z. and Schoenauer, M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(1), 1-32.

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

offspring = c(8, 6, 4, 1, 3)
#set.seed(12)
bsearchmut1(offspring)
mutq = 0.5
#set.seed(12)
bsearchmut1(offspring, mutq=mutq)

Boundary Search Mutation 2

Description

Boundary Search Mutation-2 is an algorithm based on searching the convenience region boundaries in constraint processing for NLP optimization (Michalewicz & Schoenauer, 1996). Two genes are randomly selected from the chromosome and one is multiplied by the random value p, while the other gene is multiplied by the q value calculated using p.

This operator is used for value encoded (integer or real number) chromosomes.

Usage

bsearchmut2(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Michalewicz, Z. and Schoenauer, M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(1), 1-32.

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

offspring = c(8, 6, 4, 1, 3)
bsearchmut2(offspring)

Box Crossover / Flat Crossover

Description

In the parent chromosomes, the randomly selected value between the minimum and maximum values of each gene is assigned as the value of that gene in the offspring chromosome (Herrera et.al, 1998).

Usage

bx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Herrera, F., Lozano, M. and Verdegay J.L. (1998). Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis. Artificial Intelligence Review, 12(4), 265-319.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
bx(parent1, parent2)

Calculate the number of bits in the binary representation of the integer vector

Description

The function CalcM calculates the number of bits in the binary representation of the integer vector

Usage

calcM(ub, ...)

Arguments

Details

This function uses the upper bounds of the integer vector to calculate the number of bits in the binary representation of an integer vector.

Value

A vector of the numbers of bits for binary representation of an integer vector.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

encode4int

Examples

ub = c(10, 10, 10)
calcM(ub)

Count-preserving Crossover (CPC)

Description

Count-preserving Crossover (CPC) is an operator that assumes the same number of chromosomes equal to 1 in each chromosome in the initial population and tries to preserve this number (Hartley & Konstam, 1993; Gwiazda 2006).

Usage

cpc(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Hartley S.J. and Konstam A.H. (1993). Using genetic algorithms to generates Steiner triple systems. In Proc. of the 1993 ACM Conf. on Computer Science (pp. 366-371).

Gwiazda T.D. (2006). Genetic Algorithms Reference. Vol. I: Crossover for Single-Objective Numerical Optimization Problems. Tomaszgwiadze E-books, Poland.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 0, 1, 0, 1, 1, 1, 0)
parent2 = c(1, 1, 1, 0, 1, 0, 0, 1)
cpc(parent1, parent2)

Crossover

Description

It is a wrapper function that calls crossover operators from a single function.

Usage

cross(crossfunc, matpool, cxon, cxpc, gatype, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.

See Also

px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

genpop = initbin(12,8)                             #Initial population
m = ncol(genpop)-2                                 #Number of Gene
sumx = function(x, ...) (sum(x))                   #Fitness Function
fitvals = evaluate(fitfunc=sumx, genpop[,1:m])     #Fitness Values
genpop[,"fitval"] = fitvals
selidx = select(selfunc=selrws, fitvals)           #Selection of Parents
matpool = genpop[selidx,]                          #Mating Pool
offsprings = cross(crossfunc=px1, matpool=matpool, #Crossing
 cxon=2, cxpc=0.8, gatype="gga")
offsprings
offsprings = cross(crossfunc=kpx, matpool=matpool,
  cxon=2, cxpc=0.8, gatype="ssga", cxps=0.5, cxk=2)
offsprings

Cycle Crossover (CX)

Description

The Cycle Crossover (CX) is an algorithm that considers the gene order in the parental chromosomes (Oliver et.al., 1987).

Usage

cx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Oliver, I.M., Smith, D. and Holland J.R. (1987). Study of the permutation crossover operators on the traveler salesman problem. In Grefenstette, J.J. (ed). Genetic Algorithms and Their Applications, Proc. of the 2nd Int. Conf. Hillsdale, New Jersey: Lawrence Erlbaum, pp. 224-230.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, icx, smc

Examples

parent1 =c(9, 8, 2, 1, 7, 4, 5, 0, 6, 3)
parent2 =c(1, 2, 3, 4, 5, 6, 7, 8, 9, 0)
cx(parent1, parent2)

Discrete Crossover

Description

The Discrete Crossover (DC) operator is an operator that swaps parent genes if a randomly selected value in the range [0,1] for each gene in the chromosome is greater than or equal to a given threshold value, and does not change if it is less than the threshold value.

Usage

dc(x1, x2, cxon, cxps, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
dc(parent1, parent2, cxps=0.6)

Convert from binary number to real number

Description

The function decode converts a binary number with m digits to a real number between the lower and upper bound.

Usage

decode(bin, lb, ub, m)

Arguments

Details

This function converts a binary number with m digits to its real equivalent expressed in the range [lb, ub].

Value

Returns the real equivalent of the input number.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

encode

Examples

x = c(0,1,0,0,0,0,1,1)
decode(x, lb=50, ub=250, m=8)

Convert binary vectors to integer vectors

Description

The function decode4int converts each element in a given binary vector to a integer number.

Usage

decode4int(x, M, ...)

Arguments

Details

This function converts each element in the binary vector passed with the x argument to an integer. The M argument refers to the number of bits of each binary in the x vector.

Value

A vector of integer for input binary vector

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

encode4int

Examples

binmat = c(0,0,1,1,1,0,0,1,0,0,1,0)
M = c(4,4,4)
intmat = decode4int(binmat, M=M)
intmat

Convert binary number matrix to real number matrix

Description

The decodepop function generates a real-valued population from a population encoded with binary representation.

Usage

decodepop(x, lb, ub, m,  ...)

Arguments

Value

A real-valued matrix

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

encodepop

Examples

lb = c(2.5, -2, 0)
ub = c(4.3, 2, 1.5)
eps = c(0.1, 1, 0.01)
#d = nchar(sub('^+','',sub("\.",'',eps)))-1

d = grep('.', strsplit(as.character(eps), '')[[1]])-1
x = round(runif(5, lb[1],ub[1]),d[1])
y = round(runif(5, lb[2],ub[2]),d[2])
w = round(runif(5, lb[3],ub[3]),d[3])
pop = cbind(x, y, w)
pop    
encpop = encodepop(pop, lb=lb, ub=ub, eps=eps)
pop = encpop$binmat 
m = encpop$m
decpop = decodepop(pop, lb=lb, ub=ub, m=m)
decpop
for(j in 1:ncol(decpop)) decpop[,j]=round(decpop[,j], d[j])
decpop

Disrespectful Crossover (DISC)

Description

Disrespectful Crossover (DISC) is an operator that breaks down similarities or reinforces differences in parental chromosomes (Watson & Pollack, 2000).

Usage

disc(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Watson R.A. and Pollack J.B. (2000). Recombination without respect: Schema combination and disruption in genetic algorithm crossover. In Proc. of the 2nd Annual Conf. on Genetic and Evolutionary Computation (pp. 112-119).

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 0, 1, 0, 1, 1, 1, 0)
parent2 = c(1, 1, 1, 0, 1, 0, 0, 1)
disc(parent1, parent2)

Displacement mutation

Description

The Displacement mutation cuts the genes between two randomly determined cut-points from the chromosome as a subset and then inserts them, starting from a randomly selected location (Michalewicz, 1992).

This operator is used in problems with permutation encoding.

Usage

dismut(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Michalewicz, Z. (1992). Genetic Algorithms + Data Structures = Evolution Programs. Berlin-Heidelberg: Springer Verlag.

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, invswapmut, insswapmut, invdismut

Examples

offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9)
dismut(offspring)

Extended Box Crossover

Description

Extended Box Crossover (EBX) was proposed by Yoon and Kim (2012) as the more advanced form of Box Crossover (BX). In the EBX operator, the minimum and maximum values are weighted by an alpha factor.

Usage

ebx(x1, x2, lb, ub, cxon, cxalfa, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Yoon, Y. and Kim, Y.H. (2012). The roles of crossover and mutation in real-coded genetic algorithms. In Bioinspired Computational Algorithms anf Their Applications (ed. S. Gao), London: INTECH Open Acces Publisher. pp. 65-82.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

lb = c(0, 0, 0, 0, 0, 0)
ub = c(2, 3, 1, 2, 4, 3)
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
ebx(parent1, parent2, lb, ub)

Exchange/Linkage Crossover (EC,LC)

Description

Linkage Crossover (LC) is an operator based on the repositioning of a randomly selected fragment from one of the parents, starting from a randomly selected location in the offspring chromosome (Harik & Goldberg, 1997). It is also called Exchange Crossover (EC).

Usage

eclc(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Harik, G.D. and Goldberg, D.E. (1997). Learning linkage. Foundation of Genetic Algorithms Ch. 4, Morgan-Kaufmann. pp. 247-262.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 0, 1, 0, 1, 1, 1, 0)
parent2 = c(1, 1, 1, 0, 1, 0, 0, 1)
eclc(parent1, parent2)

Elistist Replacement (Elitism) Function

Description

The reproduction of individuals with the highest fitness is called elitism. The elitism operator copies a certain number of individuals into the new population. Other individuals are selected from among the offspring in proportion to their fitness values.

Usage

elitism(parpop, offpop, reps, ...)

Arguments

Value

A matrix. Population of the new generation.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

grdelall, grmuplambda, grmuplambda2, grmuplambda3, grmuplambda4, grmuvlambda, grrobin, ssrmup1, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Extended-Line Crossover (ELX)

Description

With the Extended-Line Crossover (ELX) operator, offspring are generated on a line determined by the variable values in the parental chromosomes. ELX identifies the possible line from which offspring can be generated.

Usage

elx(x1, x2, lb, ub, cxon, cxealfa, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

lb = c(0, 0, 0, 0, 0, 0)
ub = c(2, 3, 1, 2, 4, 3)
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
elx(parent1, parent2, lb, ub, cxealfa=1000)

Convert from real number to binary number

Description

The function encode converts a real number to a binary number with m digits between the given lower bound and upper bound.

Usage

encode(real, lb, ub, m)

Arguments

Details

This function converts a real number to its binary equivalent expressed in m digits in the range [lb, ub].

Value

Returns the binary equivalent of the input number.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

decode

Examples

x = 102.5
encode(x, lb=50, ub=250, m=8)

Convert integer vectors to binary vectors

Description

The function encode4int converts each element in a given integer vector to a binary number.

Usage

encode4int(x, M, ...)

Arguments

Details

This function converts each element in the integer vector passed with the x argument to a binary number. The M argument refers to the number of bits in the binary representation of each integer variable.

Value

A vector of binary representation of input vector

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

decode4int, calcM

Examples

n = 5
lb = c(0, 0, 0)
ub = c(10, 10, 10)
set.seed(1)
intmat = matrix(round(runif(3*n, lb, ub)), nr=n, nc=3) 
colnames(intmat) = paste0("v",1:3)
head(intmat)
M = calcM(ub)
M
binmat = matrix(NA, nrow=n, ncol=sum(M))
for(i in 1:n)
  binmat[i,] = encode4int(intmat[i,], M=M)
head(binmat)

Binary encoding of real number matrix

Description

The encodepop function generates a population encoded with binary representation from a real-valued population given as a matrix.

Usage

encodepop(x, lb, ub, eps, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

decodepop

Examples

lb = c(2.5, -2, 0)
ub = c(4.3, 2, 1.5)
eps = c(0.1, 1, 0.01)
#d = nchar(sub('^+','',sub("\.",'',eps)))-1
d = grep('.', strsplit(as.character(eps), '')[[1]])-1
x = round(runif(5, lb[1],ub[1]),d[1])
y = round(runif(5, lb[2],ub[2]),d[2])
w = round(runif(5, lb[3],ub[3]),d[3])
pop = cbind(x, y, w)
pop
encpop = encodepop(pop, lb, ub, eps)
head(encpop$binmat[,1:10])
m = encpop$m
m

Edge Recombination Crossover (ERX)

Description

The Edge Recombination Crossover (ERX) operator ignores outbound directions, that is, it evaluates a chromosome with an undirected edge loop (Whitley et.al., 1989). This operator is based on the concept of neighborhood, as the main idea is to prioritize the edges common to both parents when creating offspring.

Usage

erx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Whitley, L.D., Starkweather, T. and D'Ann, F. (1989). Scheduling problems and traveling salesman: the genetic edge recombination operator. In Proc. of ICGA, Vol. 89, pp. 133-40.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 3, 5, 6, 4, 2, 8, 7)
parent2 = c(1, 4, 2, 3, 6, 5, 7, 8)
erx(parent1, parent2, cxon=2)

Calculate the fitness values of population

Description

Calculates the fitness value of a population using the fitness function given with the fitfunc argument.

Usage

evaluate(fitfunc, population, objective, ...)

Arguments

Value

A vector of fitness values for each induvidual in population.

Author(s)

Zeynel Cebeci & Erkut Tekeli

Examples

population = initbin()
head(population, 5)
m = ncol(population)-2
fitvals = evaluate(maxone, population[,1:m], objective="max")
head(fitvals, 5)

Finds peaks and valleys on the curve of a function with single variable

Description

This function finds the peaks and valleys on the curve of user-defined functions with one variable. The function also plots the function curve that can be used to demonstrate the points for local optima and global optimum in a optimization problem.

Usage

findoptima(x, type="max", pflag=TRUE)

Arguments

Details

The findoptima function finds all the peaks and valleys in a given function curve. The points can be colorized with different colors. See the example below.

Value

Returns a vector of indices of the peaks or valleys on the function curve.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Cebeci Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari. Ankara:Nobel Akademik Yayincilik

Examples

fx <- function(x) -sin(x)-sin(2*x)-cos(3*x) + 3
x <- seq(-2*pi, 2*pi, by=0.001)
curve(fx, x)
cr <- curve(fx, x, lwd=2)
xy <- cbind(cr$x, cr$y)
peaks <- findoptima(cr$y, type = "max")
valleys <- findoptima(cr$y, type = "min")

## Finds peaks and valleys
peaks <- findoptima(cr$y, type="max")
valleys <-  findoptima(cr$y, type="min")

## Plotting the function curve and local optima and global optimum
points(xy[peaks,], pch=19, cex=1.2, col=2)
points(xy[valleys,], pch=18, cex=1.2, col=4)
gmin <- valleys[which.min(xy[valleys,2])]
gmax <- peaks[which.min(xy[valleys,2])]
points(xy[gmax,1], xy[gmax,2], pch=19, cex=2, col=2)
points(xy[gmin,1], xy[gmin,2], pch=18, cex=2, col=4)
text(xy[gmax,1], xy[gmax,2], labels="Glob.Max", pos=2, cex=0.8, col=1)
text(xy[gmin,1], xy[gmin,2], labels="Glob.Min", pos=2, cex=0.8, col=1)

Static crossover and mutation rate

Description

The function is used when the crossover and mutation rates are not changed throughout the GA run.

Usage

fixpcmut(cxpc, mutpm, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

ilmdhc, adana1, adana2, leitingzhi, adana3

Gauss Mutation

Description

Gauss Mutation is an operator made by adding randomly selected values from a normal distribution with a mean of 0 and a standard deviation of sigma to a randomly selected gene in the chromosome (Michalewicz, 1995; Back et.al., 1991; Fogel, 1995).

This operator is used for value encoded (integer or real number) chromosomes.

Usage

gaussmut(y, mutsdy, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Michalewicz, Z. (1995). Genetic algorithms, numerical optimizations and constraints. In Proc. of the 6th. Int. Conf. on Genetic Algorithms, pp. 151-158. Morgan Kaufmann.

Back, T., Hoffmeister, F. and Schwefel, H.F. (1991). A survey of elolution strategies. In Proc. of the 4th. Int. Conf. on Genetic Algorithms (eds. R.K. Belew and L.B. Booker), pp. 2-9. Morgan Kaufmann.

Fogel D.B. (1995). Evolutionary computation. Toward a new philosophy of machine intellegence. Piscataway, NJ: IEEE Press.

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

mutsdy = c(1, 1.5, 1.01, 0.4, 1.5, 1.2)
offspring = c(8, 6, 4, 1, 3, 7)
set.seed(12)
gaussmut(offspring)

Gauss Mutation 2

Description

Gauss Mutation-2 is an operator by adding a randomly selected value from the standard normal distribution to a randomly selected gene in the chromosome.

This operator is used for value encoded (integer or real number) chromosomes.

Usage

gaussmut2(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

offspring = c(8, 6, 4, 1, 3, 7)
set.seed(12)
gaussmut2(offspring)

Gauss Mutation 3

Description

GM is an operator made by adding randomly selected values from a normal distribution with mean and standard deviation of MU and SIGMA, respectively, to a randomly selected gene in the chromosome.

This operator is used for value encoded (integer or real number) chromosomes.

Usage

gaussmut3(y, mutmy, mutsdy, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

mutmy = c(5, 5, 2, 4, 3, 4)
mutsdy = c(1, 1.5, 1.01, 0.4, 1.5, 1.2)
offspring = c(8, 6, 4, 1, 3, 7)
set.seed(12)
gaussmut(offspring, mutmy=mutmy, mutsdy=mutsdy)

Geometric Crossover

Description

Geometric Crossover is used to search for applicable region boundaries in constraint processing in NLP problems (Michalewicz & Schoenauer, 1996). It generates one offspring per each cross.

Usage

geomx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Michalewicz, Z. and Schoenauer, M. (1996). Evolutionary Algorithms for constrained parameter optimization problems. Evoltionary Computation, 4(1), 1-32.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
geomx(parent1, parent2)

Convert gray code to binary integer #1

Description

The function gray2bin converts gray coded integer to a binary coded number.

Usage

gray2bin(gray)

Arguments

Details

The gray2bin function works as a compliment of the bin2gray function.

Value

Returns the binary coded integer equivalent of the input number.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

bin2gray, gray2bin2

Examples

gray = c(1,1,1,0)
gray2bin(gray)       # returns 1011
gray = c(1,1,1,1)
gray2bin(gray)       # returns 1010

Convert gray code to binary integer #2

Description

The function gray2bin2 converts a gray-coded integer to a binary-coded number. The conversion function is performed according to the algorithm given by Chakraborty and Janikov (2003).

Usage

gray2bin2(gray)

Arguments

Details

To convert gray coded numbers to binary numbers, a conversion function is defined using the algorithm given by Chakraborty and Janikov (2003). This function is a generic function that does not use the xor operator.

Value

Returns the binary coded integer equivalent of the input number.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Chakraborty, U.K., and Janikow C.Z. (2003). An analysis of Gray versus binary encoding in genetic search. Information Sciences, 156 (3-4), 253-269.

See Also

bin2gray, gray2bin

Examples

gray = c(1,1,1,0) 
gray2bin2(gray)       # returns 1011

gray = c(1,1,1,1)
gray2bin2(gray)       # returns 1010

Delete-All Replacement

Description

All members of the current population are deleted, the new population is created entirely from offspring.

Usage

grdelall(parpop, offpop)

Arguments

Value

A matrix. Population of the new generation.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

elitism, grmuplambda, grmuplambda2, grmuplambda3, grmuplambda4, grmuvlambda, grrobin, ssrmup1, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Mu+Lambda replacement function 1

Description

The Mu+Lamda replacement is based on the selection of the fittest parents and offspring as individuals of the new generation population (Smith et.al., 1999; Jenkins et.al., 2019).

Usage

grmuplambda(parpop, offpop, ...)

Arguments

Value

A matrix. Population of the new generation.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Smith, A.E. and Vavak F. (1999). Replacement strategies in steady state genetic algorithms: Static environments. Foundations of Genetic Algorithms. pp. 499-505.

Jenkins, A., Gupta, V., Myrick, A. and Lenoir, M. (2019). Variations of Genetic Algorithms. arXiv preprint arXiv:1911.00490.

See Also

grdelall, elitism, grmuplambda2, grmuplambda3, grmuplambda4, grmuvlambda, grrobin, ssrmup1, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Mu+Lambda replacement function 2 (delete the worst \lambda)

Description

Parents and offspring are ranked separately according to their compatibility among themselves. Then \lambda offspring with the best fitness value is replaced by \lambda parent with the worst fitness value.

Usage

grmuplambda2(parpop, offpop, lambda, ...)

Arguments

Value

A matrix. Population of the new generation.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

grdelall, elitism, grmuplambda, grmuplambda3, grmuplambda4, grmuvlambda, grrobin, ssrmup1, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Mu+Lambda replacement function 3

Description

After the offspring are ranked according to their fitness values, the \lambda best fit offspring are replaced by \lambda parents randomly selected from the current parent population.

Usage

grmuplambda3(parpop, offpop, lambda, ...)

Arguments

Value

A matrix. Population of the new generation.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

grdelall, elitism, grmuplambda, grmuplambda2, grmuplambda4, grmuvlambda, grrobin, ssrmup1, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Mu+Lambda replacement function 4

Description

In the current population, randomly selected \lambda parents are replaced by randomly selected \lambda offspring.

Usage

grmuplambda4(parpop, offpop, lambda, ...)

Arguments

Value

A matrix. Population of the new generation.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

grdelall, elitism, grmuplambda, grmuplambda2, grmuplambda3, grmuvlambda, grrobin, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Mu & Lambda Replacement Function

Description

In this renewal strategy, after the offspring are ranked according to their fitness values, the number of the population of the offspring with the best fitness value is replaced by the parents (Schwefel, 1981). To use this renewal algorithm, it is necessary to produce many more offspring than the population count.

Usage

grmuvlambda(parpop, offpop, ...)

Arguments

Value

A matrix. Population of the new generation.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

grdelall, elitism, grmuplambda, grmuplambda2, grmuplambda3, grmuplambda4, grrobin, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Round Robin Replacement Function

Description

The parent and offspring populations are combined. Then, each individual in the combined population is compared with k randomly selected individuals. In these double tournaments, if an individual has higher fitness than the individual they are compared to, +1 point is obtained. The new population is created from the individuals with the highest score.

Usage

grrobin(parpop, offpop, repk, ...)

Arguments

Value

A matrix. Population of the new generation.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

grdelall, elitism, grmuplambda, grmuplambda2, grmuplambda3, grmuplambda4, grmuvlambda, ssrmup1, ssrgenitor, ssrfamtour, ssrx

Heuristic Crossover

Description

The Heuristic Crossover (HC) operator is a conditional operator (Herrera et.al, 1998; Umbarkar & Sheth, 2005). A random r value is generated in the range [0,1]. Then if Parent2's fitness value is greater than or equal to Parent1's fitness value, the difference between them is weighted by r and added to Parent2. It is subtracted in minimization problems. This operator produces a single offspring, but due to the random value of r, repeated offspring may result in different offspring.

Usage

hc(x1, x2, fitfunc, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Herrera, F., Lozano, M. and Verdegay, J.L. (1998). Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis. Artificial Intellegence Review, 12(4), 265-319 Umbarkar, A.J. and Sheth P.D. (2015). Crossover operators in genetic algorithms: A riview, ICTACT Journal on Soft Computing, 6(1), 1083-1092.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
hc(parent1, parent2, fitfunc)

GA + optim hybridization function

Description

This function allows GA to hybridize with methods in the optim general-purpose optimization function for n-variable problems in R's basic stats package (R Core Team, 2021).

Usage

hgaoptim(genpop, fitfunc, hgaparams,
                    hgaftype, hgans, ...)

Arguments

Value

A matrix containing the updated population.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

R Core Team. (2021). R: A language and environmental for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

See Also

hgaoptimx, hgaroi

Examples

hgaparams = list(method="Nelder-Mead", poptim=0.05, pressel=0.5,
  control = list(fnscale=1, maxit=100))
n = 5                   # Size of population 
m = 2                   # Number of variables
lb = c(-5.12, -5.12)    # Lower bounds for sample data
ub = c(5.12, 5.12)      # Upper bounds for sample data
genpop = initval(n, m, lb=lb, ub=ub) # Sample population
fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10
fitvals = evaluate(fitfunc, genpop[,1:m])
genpop[,"fitval"]=fitvals
genpop
newpop = hgaoptim(genpop, fitfunc, hgaparams, hgaftype="r", hgans=3)
newpop

GA + optimx hybridization function

Description

This function allows GA to hybridize with methods in the optimx package (Nash & Varadhan, 2011; Nash, 2014).

Usage

hgaoptimx(genpop, fitfunc, hgaparams,
                     hgaftype, hgans, ...)

Arguments

Value

A matrix containing the updated population.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Nash, J.C. and Varadhan, R. (2011). Unified optimization algorithms to aid software system users: optimx for R. Journal of Statistical Software, 43(9), 1-14. URL http://www.jstatsoft.org/v43/i09. Nash, J.C. (2014). On best practice optimization methods in R. Journal of Statistical Software, 60(2), 1-14. URL http://www.jstatsoft.org/v60/i02.

See Also

hgaoptim, hgaroi

Examples

n = 5                                # Size of population 
m = 2                                # Number of Variables
lb = c(-5.12, -5.12)                 # Lower bounds of sample data
ub = c(5.12, 5.12)                   # Upper bounds of sample data
hgaparams = list(method="L-BFGS-B", 
  poptim=0.05, pressel=0.5,
  lower=lb, upper=ub,
  control=list(maximize=FALSE, maxit=100))
genpop = initval(n, m, lb=lb, ub=ub) # Sample population
fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10
fitvals = evaluate(fitfunc, genpop[,1:m])
genpop[,"fitval"]=fitvals
genpop
genpop = hgaoptimx(genpop, fitfunc, hgaparams, hgaftype="r", hgans=3)
genpop

GA + ROI hybridization function

Description

This function allows GA to hybridize with methods in the ROI package (Theussl et.al., 2020).

Usage

hgaroi(genpop, fitfunc, hgaparams,
                  hgaftype, hgans, ...)

Arguments

Value

A matrix containing the updated population.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Theussl, S., Schwendinger, F. and Hornik, K. (2020). ROI: An extensible R optimization infrastructure. Journal of Statistical Software, 94(15), 1-64.

See Also

hgaoptim, hgaoptimx

Examples

n = 5                                 # Size of population 
m = 2                                 # Number of variable
lb = c(-5.12, -5.12)                  # Lower bounds of sample data
ub = c(5.12, 5.12)                    # Upper bounds of sample data
hgaparams = list(method="L-BFGS-B", 
  poptim=0.05, pressel=0.5,
  lower=lb, upper=ub,
  control=list(maxit=100))
genpop = initval(n, m, lb=lb, ub=ub)  # Sample population
fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10
fitvals = evaluate(fitfunc, genpop[,1:m])
genpop[,"fitval"]=fitvals
genpop
genpop = hgaroi(genpop, fitfunc, hgaparams, 
  hgaftype="r", hgans=3)
genpop

Heuristic Uniform Crossover

Description

"Heuristic Uniform Crossover" is an algorithm that works by detecting genes that differ to control the level of disruption in Parental chromosomes (De Jong & Spears, 1991).

Usage

hux(x1, x2, cxon, cxps, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

De Jong, K.A. and Spears, W. (1991). On the virtues of parameterized uniform crossover. In Proc. of the 4th Int. Conf. on Genetic Algorithms. Morgan Kaufman Publishers.

See Also

cross, px1, kpx, sc, rsc, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 0, 1, 0, 1, 1, 1, 0)
parent2 = c(1, 1, 1, 0, 1, 0, 0, 1)
hux(parent1, parent2)

Improved Cycle Crossover (ICX)

Description

ICX is based on a deterministic algorithm that can produce up to 2 offspring (Hussain et.al., 2018).

Usage

icx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Hussain, A., Muhammad, Y.S. and Sajid, M.N. (2018). An improved genetic algorithm crossover operator for traveling salesman problem. Turkish Journal of Mathematics and Computer Science, 9, 1-13.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, smc

Examples

parent1 = c(3, 4, 8, 2, 7, 1, 6, 5)
parent2 = c(4, 2, 5, 1, 6, 8, 3, 7)
icx(parent1, parent2)

ILM/DHC adaptation function

Description

ILM/DHC is an adaptive function with an increasing low mutation rate (ILM) and a decreasing high crossover rate (DHC) as the generation progresses (Hassanat et.al., 2019).

Usage

ilmdhc(g, gmax, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Hassanat, A., Almohammadi, K., Alkafaween, E., Abunawas, E., Hammouri, A. and Prasath, V.B. (2019). Choosing mutation and crossover ratios for genetic algorithm: A review with a new dynamic approach. Information, 10(12), 390.

See Also

fixpcmut, adana1, adana2, leitingzhi, adana3

Examples

N = 50
gmax = 1000
g = c(1, 10, 50, 100, 250, 500, 750, gmax)
pc = ilmdhc(g=g, gmax=gmax)$pc
pc
nc = round(pc*N)
nc
pm = ilmdhc(g=g, gmax=gmax)$pm
pm
nm = round(pm*N)
nm
nm = ifelse (!nm, 1, nm)
nm
plot(pm, type="l", col=4, lwd=2, lty=1, xaxt="n", ylab="Ratio", xlab="Generation")
lines(pc, type="l", col=2, lwd=2, lty=2)
legend("top", inset=.02, c("pm","pc"), col=c(4,2), lty=c(1,2), horiz=TRUE, cex=0.8)
axis(1, at=1:length(g),labels=g, col.axis="red", las=2)

Initialize the population with binary encoding

Description

The initbin function is an initialization function that can be used for binary encoding. It generates an initial population of population size n and chromosome length m.

Usage

initbin(n, m, prevpop, type, ...)

Arguments

Value

The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes chromosomes of initial population and additional two empty columns for generation number and fitness values.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

initval, initperm, initnorm, initialize

Examples

n = 20  #Population size (number of chromosemes)
m = 5   #Number of gene (chromosome length)
population = initbin(n, m)
head(population, 4)
tail(population, 4)

Initialize function

Description

The initialize function is a function that wraps various initialization functions.

Usage

initialize(initfunc, n, m, type, ...)

Arguments

Value

The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes chromosomes of initial population and additional two empty columns for generation number and fitness values.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

initbin, initval, initperm, initnorm

Examples

initpop = initialize(initfunc=initbin, n=6, m=4) 
initpop

Normal distribution based initialization

Description

The pmean and psd arguments of this function represent the mean and standard deviation of a normally distributed population, respectively. Using these parameters, the function generates a random initial population with n individuals and m variables.~

Usage

initnorm(n, m, pmean, psd, type, ...)

Arguments

Value

The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes chromosomes of initial population and additional two empty columns for generation number and fitness values.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

initbin, initval, initperm, initialize

Examples

initpop = initialize(initfunc=initnorm, n=20, m=5, 
  pmean=50, psd=5, type=2) 
head(initpop,3)

Permutation coded initialization

Description

This function generates an initial population when each variable of the chromosomes is desired to be encoded on a rank scale or permutation.

Usage

initperm(n, permset, prevpop, type, ...)

Arguments

Details

Unlike other initialization function inputs, the initperm function has an argument called permset. This argument is a vector containing permutation set values. The permutation set can contain numbers or letters. In the initial population, each variable randomly takes any value from this set, but there cannot be two of the same value in a chromosome.

Value

The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes chromosomes of initial population and additional two empty columns for generation number and fitness values.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

initbin, initval, initnorm, initialize

Examples

n = 20   #Population size (number of chromosemes)
m = 6    #number of Variables
lb = c(10, 2, 5, 100, 50, 25)
ub = c(40, 8, 20, 500, 250, 90)
population = initval(n, m, lb=lb, ub=ub, nmode="integer")
tail(population, 3)

Value encoded initialization

Description

Initialize the population with integer or real numbers

Usage

initval(n, m, prevpop, lb, ub, nmode="real", type, ...)

Arguments

Details

With this function, populations are initialized with integer and/or real numbers depending on the GA problem. In this case, the value type must be known. Furthermore, the lower and upper bound values for each variable must be known. If desired, heuristic or mixed initialization can be done with the prevpop argument.

Value

The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes chromosomes of initial population and additional two empty columns for generation number and fitness values.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

initbin, initperm, initnorm, initialize

Examples

n = 15  #Population size (number of chromosemes)
m = 4   #number of Variables
population = initval(n, m)
head(population, 3)
tail(population, 3)

Insertation Mutation

Description

SM is inserted back in a different place into the chromosome by removing a randomly selected gene from the chromosome.

This operator is used in problems with permutation encoding.

Usage

insmut(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, dismut, invswapmut, insswapmut, invdismut

Examples

offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9)
insmut(offspring)

Insertion + Inversion Mutation

Description

It is a mutation operator that combines insertion and inversion mutation.

This operator is used in problems with permutation encoding.

Usage

insswapmut(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, invdismut

Examples

offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9)
insswapmut(offspring)

Convert an integer to binary coded number

Description

The function int2bin converts integers to binary coded numbers.

Usage

int2bin(int, m)

Arguments

Value

Returns the binary coded number of the integer number given in the input.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

int2bin

Examples

int2bin(250)      # returns 11111010
int2bin(250, 9)   # returns 011111010

Displacement + Inversion Mutation

Description

It is a mutation operator that combines displacement and inversion mutation.

This operator is used in problems with permutation encoding.

Usage

invdismut(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut

Examples

offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9)
invdismut(offspring)

Inversion Mutation

Description

Inversion Mutation selects a subset of genes and inverses the genes in the subset (Hollad, 1975; Fogel, 1990).

This operator is used in problems with permutation or binary encoding.

Usage

invmut(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Holland, J. (1975). Adaptation in Naturel and Articial Systems, Ann Arbor: University of Michigan Press.

Fogel D.B. (1995). Evolutionary computation. Toward a new philosophy of machine intellegence. Piscataway, NJ: IEEE Press.

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9)
invmut(offspring)

Swap + Inversion Mutation

Description

It is a mutation operator that combines swap and inversion mutation.

This operator is used in problems with permutation encoding.

Usage

invswapmut(y, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, insswapmut, invdismut

Examples

offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9)
invswapmut(offspring)

k-point Crossover

Description

In the k-PX cross, the parent chromosomes are cut from two or more points and transferred to the offspring, providing more diversity.

Usage

kpx(x1, x2, cxon, cxk, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

cross, px1, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 0, 1, 0, 1, 1, 1, 0)
parent2 = c(1, 1, 1, 0, 1, 0, 0, 1)
kpx(parent1, parent2)

Laplace Crossover

Description

Laplace Crossover (LAPX) is a crossover operator that uses a location parameter and a scaling parameter (Krishnamoorthy, 2006; Deep et.al., 2009).

Usage

lapx(x1, x2, cxon, cxa, cxb, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC

Deep, K., Singh, K.P., Kansal, M.L. and Mohan, C. (2009). A real-coded genetic algorithm for solving integer and mixed integer optimization problems. Applied Mathematics and Computation, 212(2): 505-518.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
lapx(parent1, parent2, cxon=3)

Local Arithmetic Crossover

Description

New offspring are generated by applying an arithmetic mean on the parents' chromosomes with a different random weight for each gene.

Usage

lax(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2)
parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4)
lax(parent1, parent2, cxon=3)

Lei & Tingzhi Adaptation Function

Description

This adaptation function proposed by Lei & Tingzhi (1994) is an adaptation function that takes into account the cooperation of individuals.

Usage

leitingzhi(fitvals, cxpc, cxpc2, 
                      mutpm, mutpm2, adapa, adapb, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Lei, W. and Tingzhi, S. (2004). An improved adaptive genetic algorithm and its application to image segmentation. In Proc. of 5th Int. Conf. on Artificial Neural Network and Genetic Algorithms, pp. 112-119.

See Also

fixpcmut, ilmdhc, adana1, adana2, adana3

MAXONE fitness function

Description

Fitness function that calculates the number of 1s in each individual

Usage

maxone(x, ...)

Arguments

Value

Number of 1s

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

maxone1, maxone2, minone

Examples

C2 = c(1, 1, 1, 0, 1, 0, 0, 0)
maxone(C2)
C3 = c(1, 1, 1, 1, 1, 1, 1, 1)
maxone(C3)

MAXONE1 fitness function

Description

Fitness function that calculates the number of 1s in each individual

Usage

maxone1(x, ...)

Arguments

Value

Number of 1s

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

maxone, maxone2, minone

Examples

C2 = c(1, 1, 1, 0, 1, 0, 0, 0)
maxone1(C2)
C3 = c(1, 1, 1, 1, 1, 1, 1, 1)
maxone1(C3)

maxone2 fitness function

Description

Calculates the sum of each row of a matrix or data frame.

Usage

maxone2(x, ...)

Arguments

Value

A vector includes sum of each row in a matrix or data frame

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

maxone1, maxone, minone

Examples

binmat = matrix(nrow=5, ncol=8, byrow=TRUE, c(
1, 0, 1, 0, 1, 1, 1, 0,
1, 1, 1, 0, 1, 0, 0, 0,
1, 1, 1, 1, 1, 1, 1, 1,
0, 1, 0, 1, 0, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0
))
rownames(binmat) = paste0("C",1:5)
maxone2(binmat)

minone fitness function

Description

Calculates the inverse of the sum of each row of a matrix or data frame.

Usage

minone(x, ...)

Arguments

Value

A vector includes the inverse of the sum of each row in a matrix or data frame

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

maxone, maxone1, maxone2

Examples

binmat = matrix(nrow=5, ncol=8, byrow=TRUE, c(
1, 0, 1, 0, 1, 1, 1, 0,
1, 1, 1, 0, 1, 0, 0, 0,
1, 1, 1, 1, 1, 1, 1, 1,
0, 1, 0, 1, 0, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0
))
rownames(binmat) = paste0("C",1:5)
minone(binmat)

Monitor Fitness Value Progress

Description

Monprogress function performs by creating a line plot of the best fitness value found across generations.

Usage

monprogress(g, genfits, objective, ...)

Arguments

Value

No return value, called for the side effect of drawing a plot.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

show

Examples

n = 100
genfits = matrix(NA, nrow=n, ncol=5)
genfits[1,3] = 50
objective = "max"
for(i in 1:(n-1)){
  g=i
  monprogress(g=g, genfits=genfits, objective=objective)
  genfits[g+1, 3] = genfits[g, 3] + runif(1, -2, 5)
}

Modified Partially Mapped Crossover

Description

Modified Partially Mapped Crossover (MPMX) is a crossover operator for permutation encoded chromosomes. Each of the offspring uses sequencing information partially determined by each of their parents. Two different cut points are randomly determined. The part outside of the two cut points is replaced. Pieces between the two cut points are complemented from the original parental genes. However, if the same genes are found among the copied genes, they are changed.

Usage

mpmx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(0, 8, 4, 5, 6, 7, 1, 2, 3, 9)
parent2 = c(6, 7, 1, 2, 4, 8, 3, 5, 9, 0)
mpmx(parent1, parent2)

Maximal Preservative Crossover (MPX)

Description

The Maximal Preservative Crossover (MPX) operator is an operator that tries to preserve good edges but ensure adequate gene exchange between parents (Muhlenbein et.al., 1988).

Usage

mpx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Muhlenbein, H., Gorges-Schleuter, M. and Kramer, O. (1988). Evolution algorithms in combinatorial optimization. Parallel Computing, 7(1), 65-85.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(0, 8, 4, 5, 6, 7, 1, 2, 3, 9)
parent2 = c(6, 7, 1, 2, 4, 8, 3, 5, 9, 0)
mpx(parent1, parent2)

Function of Mutation Application

Description

With mutation, the chromosomes of individuals are randomly changed and sent to the next generation.

Usage

mutate(mutfunc, population, mutpm, gatype, ...)

Arguments

Value

A matrix. Population of the mutated offsprings

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.

See Also

bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

offsprings=initbin(25,5)
offsprings[,"fitval"] = evaluate(maxone, offsprings[,1:(ncol(offsprings)-2)])
head(offsprings, 4)          # mutant individual may be further ahead.
mutatedpop = mutate(mutfunc=bitmut, population=offsprings, mutpm=0.1, gatype="gga")
mutatedpop[,"fitval"] = evaluate(maxone, mutatedpop[,1:(ncol(mutatedpop)-2)])
head(mutatedpop, 4)

Mask crossover

Description

This crossover function copies parent1 and parent2 to offspring1 and offspring2, respectively. A vector of length m is then randomly generated for each parent, containing the values 0 and 1. Elements in this vector are then compared for each gene location. If the element at the ith position of the first vector is equal to that of the second vector, no change is made. However, if the first is 0 and the second is 1, the ith gene of Parent2 is copied as the ith gene of Offspring1. If the ith elements of the vectors are 1 and 0, the i th gene of Parent1 is copied as the i th gene of Offspring2 (Louis & Rawlins, 1991).

Usage

mx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Louis S.J. and Rawlins G.J. (1991). Designer Genetic Algorithms: Genetic Algorithms in Structure Design. In 4th Int. Conf. on Genetic Algorithms. (pp. 53-60)

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 0, 1, 0, 1, 1, 1, 0)
parent2 = c(1, 1, 1, 0, 1, 0, 0, 1)
mx(parent1, parent2, cxon=3)

Non-uniform Mutation

Description

The nunimut operator is a mutation operator that adjusts for generations by reducing the mutation severity according to genetic progression (Michalewicz, 1994).

This operator is used for value encoded (integer or real number) chromosomes.

Usage

nunimut(y, lb, ub, g, gmax, mutb, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Michalewicz, . (1994).

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut2, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

lb = c(2, 1, 3, 1, 0, 4)
ub = c(10, 15, 8, 5, 6, 9)
offspring = c(8, 6, 4, 1, 3, 7)
set.seed(12)
nunimut(offspring, lb=lb, ub=ub, g=1, gmax=100, mutb=0.5)
set.seed(12)
nunimut(offspring, lb=lb, ub=ub, g=50, gmax=100, mutb=0.5)

Adaptive Non-uniform mutation

Description

This operator is an adaptive mutation operator that increases the probability of the mutation severity approaching 0 as the number of generations increases.

This operator is used for value encoded (integer or real number) chromosomes.

Usage

nunimut2(y, lb, ub, g, gmax, mutb, ...)

Arguments

Value

Author(s)

Zeynel Cebeci & Erkut Tekeli

See Also

mutate, bitmut, randmut, randmut2, randmut3, randmut4, unimut, boundmut, nunimut, powmut, powmut2, gaussmut, gaussmut2, gaussmut3, bsearchmut1, bsearchmut2, swapmut, invmut, shufmut, insmut, dismut, invswapmut, insswapmut, invdismut

Examples

lb = c(2, 1, 3, 1, 0, 4)
ub = c(10, 15, 8, 5, 6, 9)
offspring = c(8, 6, 4, 1, 3, 7)
set.seed(12)
nunimut2(offspring, lb=lb, ub=ub, g=1, gmax=100, mutb=0.5)
set.seed(12)
nunimut2(offspring, lb=lb, ub=ub, g=50, gmax=100, mutb=0.5)

Order Crossover (OX)

Description

Order Crossover (OX) is a crossover operator for permutation encoded chromosomes. It is a different variant of PMX and it receives a part of the offspring chromosome from Parent1 and the remaining part from Parent2 in a certain sequence (Davis, 1985).

Usage

ox(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Davis, L. (1985). Appliying adaptive algorithms to epistatic domains. In Proc. of the Int. Joint Conf. on Artificial Intellegence, Vol. 85, pp. 162-164.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox2, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(3, 4, 8, 2, 7, 1, 6, 5)
parent2 = c(4, 2, 5, 1, 6, 8, 3, 7)
ox(parent1, parent2)

Order-based crossover (OX2)

Description

Order-based crossover (OX2) is a crossover operator for permutation encoded chromosomes. It is an operator that forces the order of several randomly selected positions in one parent to the other parent (Syswerda, 1991).

Usage

ox2(x1, x2, cxon, cxoxk, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Sysweda, G. (1991). Schedule optimization using genetic algorithms. Handbook of Genetic Algorithms.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, mpx, erx, pbx, pbx2, cx, icx, smc

Examples

parent1 = c(1, 2, 3, 4, 5, 6, 7, 8)
parent2 = c(4, 2, 5, 1, 6, 8, 3, 7)
ox2(parent1, parent2)

Position-Based Crossover (PBX)

Description

The Position-Based Crossover (PBX) operator inserts a different number of randomly selected genes in one parent into the same position in Offspring1, then rounds off the other genes in sequence according to their positions in the other parent (Syswerda, 1991). Other offspring are generated similarly if desired or necessary. PBX is an operator that tries to ensure diversity in recombination while taking care to preserve position.

Usage

pbx(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Syswerda, G. (1991). Schedule optimization using genetic algorithms. Handbook of Genetic Algorithms.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx2, cx, icx, smc

Examples

parent1 = c(3, 4, 8, 2, 7, 1, 6, 5)
parent2 = c(4, 2, 5, 1, 6, 8, 3, 7)
pbx(parent1, parent2, cxon=2)

Position-Based Crossover 2 (PBX2)

Description

The Position-Based Crossover (PBX) operator inserts a different number of randomly selected genes in one parent into the same position in Offspring1, then rounds off the other genes in sequence according to their positions in the other parent (Syswerda, 1991). Other offspring are generated similarly if desired or necessary. PBX is an operator that tries to ensure diversity in recombination while taking care to preserve position.

Usage

pbx2(x1, x2, cxon, ...)

Arguments

Value

A matrix containing the generated offsprings.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Syswerda, G. (1991). Schedule optimization using genetic algorithms. Handbook of Genetic Algorithms.

See Also

cross, px1, kpx, sc, rsc, hux, ux, ux2, mx, rrc, disc, atc, cpc, eclc, raoc, dc, ax, hc, sax, wax, lax, bx, ebx, blxa, blxab, lapx, elx, geomx, spherex, pmx, mpmx, upmx, ox, ox2, mpx, erx, pbx, cx, icx, smc