caRamel: MAIN FUNCTION: multi-objective optimizer

Description

Multi-objective optimizer. It requires to define a multi-objective function (func) to calibrate the model and bounds on the parameters to optimize.

Usage

caRamel(
  nobj,
  nvar,
  minmax,
  bounds,
  func,
  popsize,
  archsize,
  maxrun,
  prec,
  repart_gene = c(5, 5, 5, 5),
  gpp = NULL,
  blocks = NULL,
  pop = NULL,
  funcinit = NULL,
  objnames = NULL,
  listsave = NULL,
  write_gen = FALSE,
  carallel = 1,
  numcores = NULL,
  graph = TRUE,
  sensitivity = FALSE,
  verbose = TRUE,
  worklist = NULL
)

Value

List of seven elements:

success: return value (logical, length = 1) : TRUE if successfull
parameters: Pareto front (matrix, nrow = archsize, ncol = nvar)
objectives: objectives of the Pareto front (matrix, nrow = archsize, ncol = nobj+nadditional)
derivatives: list of the Jacobian matrices of the Pareto front if the sensitivity parameter is TRUE or NA otherwise
save_crit: evolution of the optimal objectives
total_pop: total population (matrix, nrow = popsize+archsize, ncol = nvar+nobj+nadditional)
gpp: the calling period for the third generation rule (independent sampling with a priori parameters variance)

Arguments

nobj: : (integer, length = 1) the number of objectives to optimize (nobj >= 2)
nvar: : (integer, length = 1) the number of variables
minmax: : (logical, length = nobj) the objective is either a minimization (FALSE value) or a maximization (TRUE value)
bounds: : (matrix, nrow = nvar, ncol = 2) lower and upper bounds for the variables
func: : (function) the objective function to optimize. Input argument is the number of parameter set (integer) in the x matrix. The function has to return a vector of at least 'nobj' values (Objectives 1 to nobj are used for optimization, values after nobj are recorded for information.).
popsize: : (integer, length = 1) the population size for the genetic algorithm
archsize: : (integer, length = 1) the size of the Pareto front
maxrun: : (integer, length = 1) the max. number of simulations allowed
prec: : (double, length = nobj) the desired accuracy for the optimization of the objectives
repart_gene: : (integer, length = 4) optional, number of new parameter sets for each rule and per generation
gpp: : (integer, length = 1) optional, calling frequency for the rule "Fireworks"
blocks: (optional): groups for parameters
pop: : (matrix, nrow = nset, ncol = nvar or nvar+nobj ) optional, initial population (used to restart an optimization)
funcinit: (function, optional): the initialization function applied on each node of cluster when parallel computation. The arguments are cl and numcores
objnames: (optional): names of the objectives
listsave: (optional): names of the listing files. Default: None (no output). If exists, fields to be defined: "pmt" (file of parameters on the Pareto Front), "obj" (file of corresponding objective values), "evol" (evolution of maximum objectives by generation). Optional field: "totalpop" (total population and corresponding objectives, useful to restart a computation)
write_gen: : (logical, length = 1) optional, if TRUE, save files 'pmt' and 'obj' at each generation (FALSE by default)
carallel: : (integer, length = 1) optional, do parallel computations? (0: sequential, 1:parallel (default) , 2:user-defined choice)
numcores: : (integer, length = 1) optional, the number of cores for the parallel computations (all cores by default)
graph: : (logical, length = 1) optional, plot graphical output at each generation (TRUE by default)
sensitivity: : (logical, length = 1) optional, compute the first order derivatives of the pareto front (FALSE by default)
verbose: : (logical, length = 1) optional, verbosity mode (TRUE by default)
worklist: : optional values to be transmitted to the user's function (not used)

Author

Fabrice Zaoui - Celine Monteil

Details

The optimizer was originally written for Scilab by Nicolas Le Moine. The algorithm is a hybrid of the MEAS algorithm (Efstratiadis and Koutsoyiannis (2005) <doi:10.13140/RG.2.2.32963.81446>) by using the directional search method based on the simplexes of the objective space and the epsilon-NGSA-II algorithm with the method of classification of the parameter vectors archiving management by epsilon-dominance (Reed and Devireddy <doi:10.1142/9789812567796_0004>). Reference : "Multi-objective calibration by combination of stochastic and gradient-like parameter generation rules – the caRamel algorithm" Celine Monteil (EDF), Fabrice Zaoui (EDF), Nicolas Le Moine (UPMC) and Frederic Hendrickx (EDF) June 2020 Hydrology and Earth System Sciences 24(6):3189-3209 DOI: 10.5194/hess-24-3189-2020 Documentation : "Principe de l'optimiseur CaRaMEL et illustration au travers d'exemples de parametres dans le cadre de la modelisation hydrologique conceptuelle" Frederic Hendrickx (EDF) and Nicolas Le Moine (UPMC) Report EDF H-P73-2014-09038-FR

Examples

Run this code

# Definition of the test function
viennet <- function(i) {
  val1 <- 0.5*(x[i,1]*x[i,1]+x[i,2]*x[i,2])+sin(x[i,1]*x[i,1]+x[i,2]*x[i,2])
  val2 <- 15+(x[i,1]-x[i,2]+1)*(x[i,1]-x[i,2]+1)/27+(3*x[i,1]-2*x[i,2]+4)*(3*x[i,1]-2*x[i,2]+4)/8
  val3 <- 1/(x[i,1]*x[i,1]+x[i,2]*x[i,2]+1) -1.1*exp(-(x[i,1]*x[i,1]+x[i,2]*x[i,2]))
  return(c(val1,val2,val3))
}
# Number of objectives
nobj <- 3
# Number of variables
nvar <- 2
# All the objectives are to be minimized
minmax <- c(FALSE, FALSE, FALSE)
# Define the bound constraints
bounds <- matrix(data = 1, nrow = nvar, ncol = 2)
bounds[, 1] <- -3 * bounds[, 1]
bounds[, 2] <- 3 * bounds[, 2]

# Caramel optimization
results <-
  caRamel(nobj = nobj,
          nvar = nvar,
          minmax =  minmax,
          bounds = bounds,
          func = viennet,
          popsize = 100,
          archsize = 100,
          maxrun = 500,
          prec = matrix(1.e-3, nrow = 1, ncol = nobj),
          carallel = 0)

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