greedySearch function

Greedy Search

greedySearch(OF, algo, ...)

Arguments

• OF: The objective function, to be minimised. Its first argument needs to be a solution; ...

  arguments are also passed.

• algo: List of settings. See Details.

• ...: Other variables to be passed to the objective function and to the neighbourhood function. See Details.

Details

A greedy search works starts at a provided initial solution (called the current solution) and searches a defined neighbourhood for the best possible solution. If this best neighbour is not better than the current solution, the search stops. Otherwise, the best neighbour becomes the current solution, and the search is repeated.

Returns

A list:

• xbest: best solution found.

• OFvalue: objective function value associated with best solution.

• Fmat: a matrix with two columns. Fmat[ ,1L] contains the proposed solution over all iterations; Fmat[ ,2L]

  contains the accepted solutions.

• xlist: a list

• initial.state: the value of .Random.seed when the function was called.

• x0: the initial solution

• iterations: the number of iterations after which the search stopped

References

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. tools:::Rd_expr_doi("10.1016/C2017-0-01621-X")

Schumann, E. (2023) Financial Optimisation with R (NMOF Manual). https://enricoschumann.net/NMOF.htm#NMOFmanual

Author(s)

Enrico Schumann

See Also

LSopt

Examples

na <- 100
inc <- 5
R <- randomReturns(na = na,
                   ns = 1000,
                   sd = seq(0.01, 0.02, length.out = 100),
                   rho = 0.5)
S <- cov(R)
OF <- function(x, S, ...) {
    w <- 1/sum(x)
    sum(w * w * S[x, x])
}

x <- logical(na)
x[1:inc] <- TRUE

all.neighbours <- function(x, ...) {
    true  <- which( x)
    false <- which(!x)
    ans <- list()
    for (i in true) {
        for (j in false) {
            ans1 <- x
            ans1[i] <- !x[i]
            ans1[j] <- !x[j]
            ans <- c(ans, list(ans1))
        }
    }
    ans
}

algo <- list(loopOF = TRUE,
             maxit = 1000,
             all.neighbours = all.neighbours,
             x0 = x)

system.time(sol.gs <- greedySearch(OF, algo = algo, S = S))
sqrt(sol.gs$OFvalue)