crs (version 0.15-33)

snomadr: R interface to NOMAD


snomadr is an R interface to NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search, Abramson, Audet, Couture and Le Digabel (2011)), an open source software C++ implementation of the Mesh Adaptive Direct Search (MADS, Le Digabel (2011)) algorithm designed for constrained optimization of blackbox functions.

NOMAD is designed to find (local) solutions of mathematical optimization problems of the form

   min     f(x)
x in R^n

s.t. g(x) <= 0 x_L <= x <= x_U

where \(f(x)\colon R^n \to R^k\) is the objective function, and \(g(x)\colon R^n \to R^m\) are the constraint functions. The vectors \(x_L\) and \(x_U\) are the bounds on the variables \(x\). The functions \(f(x)\) and \(g(x)\) can be nonlinear and nonconvex. The variables can be integer, continuous real number, binary, and categorical.

Kindly see and the references below for details.


        bbin = NULL,  
        bbout = NULL, 
        x0 = NULL, 
        lb = NULL, 
        ub = NULL, 
        nmulti = 0,
        random.seed = 0,
        opts = list(),
        print.output = TRUE, 
        information = list(), 
        snomadr.environment = new.env(), 
        ... )



function that returns the value of the objective function


the number of variables


types of variables. Variable types are 0 (CONTINUOUS), 1 (INTEGER), 2 (CATEGORICAL), 3 (BINARY)


types of output of eval.f. See the NOMAD User Guide


vector with starting values for the optimization. If it is provided and nmulti is bigger than 1, x0 will be the first initial point for multiple initial points


vector with lower bounds of the controls (use -1.0e19 for controls without lower bound)


vector with upper bounds of the controls (use 1.0e19 for controls without upper bound)


when it is missing, or it is equal to 0 and x0 is provided, snomadRSolve will be called to solve the problem. Otherwise, smultinomadRSolve will be called


when it is not missing and not equal to 0, the initial points will be generated using this seed when nmulti > 0


list of options for NOMAD, see the NOMAD user guide Options can also be set by nomad.opt which should be in the folder where R (snomadr) is executed. Options that affect the solution and their defaults and some potential values are





Note that the "r..." denotes relative measurement (relative to lb and ub)

Note that decreasing the maximum number of black box evaluations ("MAX_BB_EVAL") will terminate search sooner and may result in a less accurate solution. For complicated problems you may want to increase this value. When experimenting it is desirable to set "DISPLAY_DEGREE"=1 (or a larger integer) to get some sense for how the algorithm is progressing


when FALSE, no output from snomadr is displayed on the screen. If the NOMAD option "DISPLAY_DEGREE"=0, is set, there will also be no output from NOMAD. Higher integer values for "DISPLAY_DEGREE"= provide successively more detail


is a list. snomadr will call snomadRInfo to return the information about NOMAD according to the values of "info", "version" and "help".

"info"="-i": display the usage and copyright of NOMAD

"version"="-v": display the version of NOMAD you are using

"help"="-h": display all options

You also can display a specific option, for example, "help"="-h x0", this will tell you how to set x0


environment that is used to evaluate the functions. Use this to pass additional data or parameters to a function


arguments that will be passed to the user-defined objective and constraints functions. See the examples below


The return value contains a list with the inputs, and additional elements


the call that was made to solve


integer value with the status of the optimization


more informative message with the status of the optimization


number of iterations that were executed, if multiple initial points are set, this number will be the sum for each initial point.


value if the objective function in the solution


optimal value of the controls


snomadr is used in the crs package to numerically minimize an objective function with respect to the spline degree, number of knots, and optionally the kernel bandwidths when using crs with the option cv="nomad" (default). This is a constrained mixed integer combinatoric problem and is known to be computationally ‘hard’. See frscvNOMAD and krscvNOMAD for the functions called when cv="nomad" while using crs.

However, the user should note that for simple problems involving one predictor exhaustive search may be faster and potentially more accurate, so please bear in mind that cv="exhaustive" can be useful when using crs.

Naturally, exhaustive search is also useful for verifying solutions returned by snomadr. See frscv and krscv for the functions called when cv="exhaustive" while using crs.


Abramson, M.A. and C. Audet and G. Couture and J.E. Dennis Jr. and S. Le Digabel (2011), “The NOMAD project”. Software available at

Le Digabel, S. (2011), “Algorithm 909: NOMAD: Nonlinear Optimization With The MADS Algorithm”. ACM Transactions on Mathematical Software, 37(4):44:1-44:15.

See Also

optim, nlm, nlminb


## List all options

## Print given option,  for example,  MESH_SIZE
snomadr(information=list("help"="-h MESH_SIZE"))

## Print the version of NOMAD

## Print usage and copyright

## This is the example found in
## NOMAD/examples/basic/library/single_obj/basic_lib.cpp

eval.f <- function ( x ) {

    f <- c(Inf, Inf, Inf);
    n <- length (x);

    if ( n == 5 && ( is.double(x) || is.integer(x) ) ) {
        f[1] <- x[5];
        f[2] <- sum ( (x-1)^2 ) - 25;
        f[3] <- 25 - sum ( (x+1)^2 );

    return ( as.double(f) );

## Initial values
x0 <- rep(0.0, 5 )

bbin <-c(1, 1, 1, 1, 1)
## Bounds
lb <- rep(-6.0,5 )
ub <- c(5.0, 6.0, 7.0, 1000000, 100000)

bbout <-c(0, 2, 1)
## Options
opts <-list("MAX_BB_EVAL"=500,

snomadr(eval.f=eval.f,n=5,  x0=x0, bbin=bbin, bbout=bbout, lb=lb, ub=ub, opts=opts)

## How to transfer other parameters into eval.f
## First example: supply additional arguments in user-defined functions

## objective function and gradient in terms of parameters
eval.f.ex1 <- function(x, params) { 
    return( params[1]*x^2 + params[2]*x + params[3] ) 

## Define parameters that we want to use
params <- c(1,2,3)

## Define initial value of the optimization problem
x0 <- 0

## solve using snomadr 
snomadr( n          =1, 
        x0          = x0, 
        eval.f      = eval.f.ex1, 
        params      = params )

## Second example: define an environment that contains extra parameters

## Objective function and gradient in terms of parameters
## without supplying params as an argument
eval.f.ex2 <- function(x) { 
    return( params[1]*x^2 + params[2]*x + params[3] ) 

## Define initial value of the optimization problem
x0 <- 0

## Define a new environment that contains params
auxdata        <- new.env()
auxdata$params <- c(1,2,3)

## pass The environment that should be used to evaluate functions to snomadr 
snomadr(n                  =1, 
        x0                 = x0, 
        eval.f             = eval.f.ex2, 
        snomadr.environment = auxdata )

## Solve using algebra
cat( paste( "Minimizing f(x) = ax^2 + bx + c\n" ) )
cat( paste( "Optimal value of control is -b/(2a) = ", -params[2]/(2*params[1]), "\n" ) )
cat( paste( "With value of the objective function f(-b/(2a)) = ",
           eval.f.ex1( -params[2]/(2*params[1]), params ), "\n" ) )

## The following example is NOMAD/examples/advanced/multi_start/multi.cpp
## This will call smultinomadRSolve to resolve the problem.  
eval.f.ex1 <- function(x, params) { 

    f<-rep(0, M+1)

    x1 <- rep(0.0, NBC)
    y1 <- rep(0.0, NBC)


    epi <- 6
    for(i in 5:NBC){
        epi <- epi+1
    constraint <- 0.0
    ic <- 1
    ic <- ic+1

    constraint <- as.numeric(1.0)
    distmax <- as.numeric(0.0)
    avg_dist <- as.numeric(0.0)

    for(i in 1:(NBC-1)){
        for (j in (i+1):NBC){
            dist1 <- as.numeric((x1[i]-x1[j])*(x1[i]-x1[j])+(y1[i]-y1[j])*(y1[i]-y1[j]))
            if((dist1 > distmax)) {distmax <- as.numeric(dist1)}
            if((dist1[1]) < 1) {constraint <- constraint*sqrt(dist1)}
            else if((dist1) > 14) {avg_dist <- avg_dist+sqrt(dist1)}

    if(constraint < 0.9999) constraint <- 1001.0-constraint
    else constraint = sqrt(distmax)+avg_dist/(10.0*NBC)

    f[2] <- 0.0
    f[M+1] <- constraint 

    return(as.numeric(f) ) 

## Define parameters that we want to use
NBC <- 5
M <- 2

x0<-rep(0.1, n)
lb<-rep(0, n)
ub<-rep(4.5, n)

eval.f.ex1(x0, params)

bbout<-c(2, 2, 0)
bbin<-rep(0, n)
## Define initial value of the optimization problem

## Solve using snomadRSolve
snomadr(n            = as.integer(n), 
        x0           = x0, 
        eval.f       = eval.f.ex1, 
        bbin         = bbin, 
        bbout        = bbout, 
        lb           = lb, 
        ub           = ub, 
        params       = params )

## Solve using smultinomadRSolve, if x0 is provided,  x0 will
## be the first initial point,  otherwise,  the program will
## check best_x.txt,  if it exists,  it will be read in as
## the first initial point. Other initial points will be
## generated by uniform distribution.
## nmulti represents the number of mads will run.
snomadr(n            = as.integer(n), 
        eval.f       = eval.f.ex1, 
        bbin         = bbin, 
        bbout        = bbout, 
        lb           = lb, 
        ub           = ub, 
        nmulti = as.integer(nmulti), 
        print.output = TRUE, 
        params       = params )
# }
# }
<!-- %% End dontrun -->
# }