# Rmalschains-package

##### Getting started with the Rmalschains package

This package implements an algorithm family for continuous optimization called memetic algorithms with local search chains (MA-LS-Chains).

- Keywords
- optimization, MA-LS-Chains

##### Details

One of the main issues to optimize a real-coded function is the capability of the algorithm to realize a good exploration of the search space and, at the same time, to exploit the most promising region to obtain accurate solutions.

Memetic algorithms are hybridizations of genetic algorithms with local search methods. They are especially suited for continuous optimization, as they combine the power of evolutionary algorithms to explore the search space with a local search method to find the local optimum of a promising region. In these algorithms, it is recommended to increase the effort invested in the local search (measured in number of evaluations, called intensity) in the improvement of the most promising solution. However, it is not easy to decide the right intensity for each solution.

MA-LS-Chains is a steady-state memetic algorithm, which combines a steady-state genetic algorithm with various different local search methods. In contrast to the generational approach, where all individuals are substituted in an iteration, in the steady-state genetic algorithm in each iteration only one solution, the worst one, is subtituted in the population. This makes it possible to not lose the improvement obtained by the local search over the individuals.

For MA-LS-Chains, the current state of the local search algorithm is stored along with the individuals. So, it becomes possible to run the local search a fixed number of iterations, stop it, and possibly later continue the previous local search over the same individual. In this way, MA-LS-Chains controls the application of the local search to the most promising solutions.

The package implements various different local search strategies:

CMA-ES The Covariance Matrix Adaptation Evolution Strategy

SW A Solis Wets solver

SSW Subgrouping Solis Wets

Simplex

CMA-ES is a very effective local search strategy, but quite complicated, and it does not scale well if the amount of parameters to optimize is huge. The Solis Wets solver is pretty simple and therewith fast. The SSW strategy is an adapted version of the Solis Wets solver for high dimensional data, so that the algorithm with this type of local search scales well with the dimensionality of the data. It applies the Solis Wets solver to randomly chosen subgroups of variables (Subgrouping Solis Wets).

All the local search methods can also be used directly, without making use of the evolutionary algorithm.

The package contains some demos illustrating its use. To get a list of them, type:

`library(Rmalschains)`

`demo()`

The demos currently available are `claw`

, `rastrigin`

, `sphere`

, `rastrigin_highDim`

, and `rastrigin_inline`

. So in order to,
e.g., execute the `claw`

demo, type

`demo(claw)`

All algorithms are implemented in C++, and they run pretty fast. A usual processing to speed up optimization is to implement the objective function also in C/C++.
However, a bottleneck in this approach is that the function needs to be passed as an R function, so that the optimizer needs to go back from C++ to R to C/C++ in each call
of the target function. The package provides an interface which allows to pass the C/C++ target function directly as a pointer. See the `rastrigin_inline`

demo for how to do that. The demo also shows how an environment can in this approach be used to pass additional parameters to the target function.

For theoretical background of the algorithm, the reader may refer to the cited literature, where the algorithms where originally proposed.

##### References

Bergmeir, C., Molina, D., Ben<U+00ED>tez, J.M. Memetic Algorithms with Local Search Chains in R: The Rmalschains Package (2016) Journal of Statistical Software, 75(4), 1-33., doi:10.18637/jss.v075.i04

Molina, D., Lozano, M., S<U+00E1>nchez, A.M., Herrera, F. Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains (2011) Soft Computing, 15 (11), pp. 2201-2220.

Molina, D., Lozano, M., Herrera, F. MA-SW-Chains: Memetic algorithm based on local search chains for large scale continuous global optimization (2010) 2010 IEEE World Congress on Computational Intelligence, WCCI 2010 - 2010 IEEE Congress on Evolutionary Computation, CEC 2010.

Molina, D., Lozano, M., Garc<U+00ED>a-Mart<U+00ED>nez, C., Herrera, F. Memetic algorithms for continuous optimisation based on local search chains (2010) Evolutionary Computation, 18 (1), pp. 27-63.

##### See Also

##### Examples

```
# NOT RUN {
##############################################
#Example for maximization of the claw function
##############################################
claw <- function(xx) {
x <- xx[1]
y <- (0.46 * (dnorm(x, -1, 2/3) + dnorm(x, 1, 2/3)) +
(1/300) * (dnorm(x, -0.5, 0.01) + dnorm(x, -1,
0.01) + dnorm(x, -1.5, 0.01)) + (7/300) *
(dnorm(x, 0.5, 0.07) + dnorm(x, 1, 0.07) + dnorm(x,
1.5, 0.07)))
return(y)
}
#use MA-CMA-Chains
res.claw <- malschains(function(x) {-claw(x)}, lower=c(-3), upper=c(3),
maxEvals=50000, control=malschains.control(popsize=50,
istep=300, ls="cmaes", optimum=-5))
# }
# NOT RUN {
#use only the CMA-ES local search
res.claw2 <- malschains(function(x) {-claw(x)}, lower=c(-3), upper=c(3), verbosity=0,
maxEvals=50000, control=malschains.control(ls="cmaes",
lsOnly=TRUE, optimum=-5))
#use only the Simplex local search
res.claw3 <- malschains(function(x) {-claw(x)}, lower=c(-3), upper=c(3), verbosity=0,
maxEvals=50000, control=malschains.control(ls="simplex",
lsOnly=TRUE, optimum=-5))
x <- seq(-3, 3,length=1000)
claw_x <- NULL
for (i in 1:length(x)) claw_x[i] <- claw(x[i])
plot(x,claw_x, type="l")
points(res.claw$sol, -res.claw$fitness, col="red")
points(res.claw2$sol, pch=3, -res.claw2$fitness, col="blue")
points(res.claw3$sol, pch=3, -res.claw3$fitness, col="green")
##############################################
#Example for the rastrigin function
##############################################
rastrigin <- function(x) {
dimension <- length(x)
res <- 0.0
for (i in 1:dimension) {
res <- res + (x[i]*x[i] - 10.0*cos(2.0*pi*x[i]) + 10.0)
}
res
}
res.rastrigin1 <- malschains(rastrigin, lower=seq(-1.0, -1.0, length=30),
upper=seq(1.0, 1.0, length=30), maxEvals=50000,
control=malschains.control(effort=0.8, alpha=0.3,
popsize=20, istep=100, ls="simplex"))
res.rastrigin2 <- malschains(rastrigin, lower=seq(-1.0, -1.0, length=30),
upper=seq(1.0, 1.0, length=30), maxEvals=50000,
initialpop = seq(0.1, 0.1, length=30),
control=malschains.control(popsize=50,
istep=300, ls="cmaes"))
res.rastrigin1
res.rastrigin2
# }
```

*Documentation reproduced from package Rmalschains, version 0.2-6, License: GPL-3 | file LICENSE*