# Distribution estimation algorithm with empirical cumulative distribution function (ECDF). Implements an EDA with ECDF. ```r EDA.ecdf(fun, lower, upper, n = 30, maxiter, k = 2, k0 = 10, tolerance = 0.01, ...) ``` ## Arguments - `fun`: A function to be minimized, with first argument the vector of parameters over which minimization is to take place. - `lower`: Lower limits of the parameters. - `upper`: Upper bounds on the parameters. - `n`: Number of individuals per generation - `maxiter`: Maximum number of iterations. - `k`: The minimum number of consecutive generations using the same search distribution. - `k0`: The minimum number of consecutive generations using the uniform distribution. - `tolerance`: Criterion for determining whether the distribution has changed. - `...`: Additional arguments of the objective function. ## Details Implements an EDA with ecdf that uses the proposal presented in Salinas-Gutiérrez and Zavala, 2023 before changing the model. ## Returns Returns a list with the following entries: - **`sol`**: The best solution found. - **`par`**: The n best individuals generated by the last model. - **`value`**: The best value of the objective function. - **`historical`**: The best fitness value in each generatio. ## Examples ```r #Example happy cat fun <- function(X){ D <- length(X) f <- abs(sum(X^2) - D)^(1/4) + (0.5 * sum(X^2) + sum(X))/D + 0.5 return(f) } n <- 30 k <- 2 tolerance <- 0.01 lower <- rep(-5,2) upper <- rep(5,2) res <- EDA.ecdf(fun, lower = lower, upper = upper,n = n, k = k, tolerance = tolerance, maxiter = 200) z <- outer(X = seq(-5, 5, 0.05), Y = seq(-5, 5, 0.05), FUN = Vectorize(function(X, Y) { fun(c(X, Y)) })) contour(seq(-5, 5, 0.05),seq(-5, 5, 0.05),z, nlevels = 20, cex.axis = .8) points(res$sol[1],res$sol[2], col = "blue", pch = 19) #Multiple regression example set.seed(pi) x1 <- rnorm(n = 100, mean = 10, sd = 5) x2 <- rnorm(n = 100, mean = 8, sd = 2) y <- 7 + 4 * x1 - 6 * x2 + rnorm(n = 100, mean = 0, sd = 3) ec <- function(par,y,x1,x2){ b0 <- par[1] b1 <- par[2] b2 <- par[3] y_hat <- b0 + b1 * x1 + b2 * x2 value <- sum((y - y_hat)^2) return(value) } opt <- EDA.ecdf(fun = ec, lower = c(-20,-20,-20), upper = c(20,20,20), maxiter = 150, y = y, x1 = x1, x2 = x2) opt$sol ``` ## References Salinas-Gutiérrez, R., & Zavala, A. E. M. (2023).An explicit exploration strategy for evolutionary algorithms. Applied Soft Computing, 140. https://doi.org/10.1016/j.asoc.2023.110230 ## See Also `EDA.hist`, `EDA.mnorm`, `EDA.norm`, `ExplicitExploration`

EDA.ecdf function