Lagun

Contents:

  • Introduction
  • Main objects
  • Utility Functions
  • Shared
  • Prepare DOE
  • Menu Import
  • Surrogate
  • Menu Explore
  • Menu Optimize
    • Tutorials
    • Architecture
    • menuOptimize.R
      • UI and Server functions
        • menuOptimize.ui()
        • menuOptimize.server()
    • Unconstrained
      • unconstrained.R
        • UI and Server functions
        • Main functions
        • Plot functions
        • Secondary functions
    • Constrained
      • constrained.R
        • UI and Server functions
      • constrainedDefine.R
        • UI and Server functions
        • Main functions
      • constrainedSolve.R
        • UI and Server functions
        • Main functions
        • Plot functions
        • Secondary functions
      • constrainedExplore.R
        • UI and Server functions
        • Main functions
        • Plot functions
        • Secondary functions
    • Sequential
      • sequential.R
        • UI and Server functions
      • sequentialOptimizers.R
        • Main functions
      • sequentialSolve.R
        • UI and Server functions
        • Plot functions
        • Secondary functions
    • Robust
      • robust.R
        • UI and Server functions
        • Secondary functions
      • robustDefine.R
        • UI and Server functions
        • Main functions
        • Secondary functions
      • robustAnalysis.R
        • UI and Server functions
        • Main functions
        • Plot functions
        • Secondary functions
      • robustSolve.R
        • UI and Server functions
        • Main functions
        • Plot functions
        • Secondary functions
    • References
  • saveLoadStudy
Lagun
  • Menu Optimize
  • View page source

Menu Optimize

Tutorials

Optimization

pdf_1

Optimization under Uncertainty

pdf_2

Sequential Optimization

pdf_3

Architecture

../_images/menuOptimize_diag.svg

menuOptimize.R

source("modules/menuOptimize/unconstrained/unconstrained.R", local = TRUE) source("modules/menuOptimize/constrained/constrained.R", local = TRUE) source("modules/menuOptimize/sequential/sequential.R", local = TRUE) source("modules/menuOptimize/robust/robust.R", local = TRUE)

UI and Server functions

menuOptimize.ui(id)

This function adds the menu “Optimize” to the user interface, and creates the pages:

  • Page Optimization with Surrogate Model

    • Panel Unconstrained Optimization

    • Panel Constrained Optimization

  • Page Sequential Optimization with Surrogate Model

  • Page Robust Optimization with Surrogate Model

Parameters:

id (character) – namespace of the module

Main reactives:

  • Calls unconstrained.ui() with id unconstrained

  • Calls constrained.ui() with id constrained

  • Calls sequential.ui() with id sequential

  • Calls robust.ui() with id robust

menuOptimize.server(input, output, session, DOE, listmodels, advance.importDOE, settings, use_simulator)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • advance.importDOE (object) – stores the simulation information status (completed/waiting/running) when Lagun is connected to an external simulator

  • settings (list-like-object) – variables specified in settingsOptimization.R

  • use_simulator (logical) – informs if the user uses a simulator linked to Lagun

Returns:

extra points in the DOE to refine the model for a sequential optimization and to confirm constrained and unconstrained optimization results

Return type:

list

Main reactives:

  • Calls unconstrained.server() with id unconstrained

  • Calls constrained.server() with id constrained

  • Calls sequential.server() with id sequential

  • Calls robust.server() with id robust

Unconstrained

unconstrained.R

source("modules/shared/XinfosChange.R", local = TRUE) source("modules/shared/dynamicSelect.R", local = TRUE)

UI and Server functions

unconstrained.ui(id)

This function populates the Unconstrained Optimization panel

Parameters:

id (character) – namespace of the module

Main reactives:

  • chooseY1: objective 1 selection

  • chooseY2: objective 2 selection

  • sign1: optimization type selection for objective 1

  • sign2: optimization type selection for objective 2

  • goOptim: button to launch optimization

  • download: button to export optimization results

  • plotOptim: displays optimization results plot

  • tableOptim: displays optimization results data as a table

unconstrained.server(input, output, session, DOE, listmodels, settings, use_simulator)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • settings (list-like-object) – variables specified in settingsOptimizations.R

  • use_simulator (logical) – informs if the user uses a simulator linked to Lagun

Returns:

extra points in the DOE to confirm unconstrained optimization results

Return type:

list

Main reactives:

  • resoptim: stores optimization results and settings

  • choicesY1: output variable list

  • choicesY2: output variable list

  • output$tableOptim: displays optimization results data as a table

  • output$plotOptim: displays optimization results plot

  • output$download: downloadable CSV file containing optimization results data

Main functions

biObjectiveOptim(dimx, DOE, Xinfos, lb, ub, predfun, yname1, sign1, yname2, sign2)

Performs bi-objective optimization using NSGA-II genetic algorithm [1]

Parameters:

  • dimx (numeric) – input variable dimension

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • Xinfos (object) – input variable information

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • yname1 (character) – name of output variable for objective 1

  • sign1 (character) – optimization type for variable 1 (minimize or maximize)

  • yname2 (character) – name of output variable for objective 2

  • sign2 (character) – optimization type for variable 2 (minimize or maximize)

monoObjectiveOptimWithoutCat(dimx, id, lb, ub, predfun, yname1, sign1, callback, inc, nmultistart)

Performs mono-objective optimization using BFGS algorithm (without categorical variables)

Parameters:

  • dimx (numeric) – input variable dimension

  • id (integer) – output index of objective 1 (yname1)

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • yname1 (character) – name of output variable for objective 1

  • sign1 (character) – optimization type for variable 1 (minimize or maximize)

  • callback (function) – reports progress

  • inc (numeric) – iteration number for callback

  • nmultistart (numeric) – number of initialization for multistart optimization

monoObjectiveOptim(dimx, DOE, Xinfos, lb, ub, predfun, yname1, sign1, callback, nmultistart)

Performs mono-objective optimization using BFGS algorithm (brute force runs of monoObjectiveOptimWithoutCat for all combinations of categorical values)

Parameters:

  • dimx (numeric) – input variable dimension

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • Xinfos (object) – input variable information

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • yname1 (character) – name of output variable for objective 1

  • sign1 (character) – optimization type for variable 1 (minimize or maximize)

  • callback (function) – reports progress

  • nmultistart (numeric) – number of initialization for multistart optimization

Plot functions

plotMonoObjectiveOptim(resoptim)

Plots results for mono-objective optimization

Parameters:

resoptim (list) – optimization results

plotBiObjectiveOptim(resoptim)

Plots results for bi-objective optimization

Parameters:

resoptim (list) – optimization results

Secondary functions

callback(inc, nm)__

Reports progress of a task. Calls R Shiny incProgress

Parameters:

  • inc (numeric) – incth iteration

  • nm (numeric) – nmth initialization

Constrained

constrained.R

source("modules/menuOptimize/constrained/constrainedDefine.R", local = TRUE) source("modules/menuOptimize/constrained/constrainedSolve.R", local = TRUE) source("modules/menuOptimize/constrained/constrainedExplore.R", local = TRUE)

UI and Server functions

constrained.ui(id)

Populates the Constrained Optimization panel with three subpanels:

  • Define Optimization Problem

  • Solve Optimization Problem

  • Explore Solution(s)

Parameters:

id (character) – namespace of the module

Main reactives:

  • Calls constrainedDefine.ui() with id constrainedDefine

  • Calls constrainedSolve.ui() with id constrainedSolve

  • Calls constrainedExplore.ui() with id constrainedExplore

constrained.server(input, output, session, DOE, listmodels, settings, use_simulator)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • settings (list-like-object) – variables specified in settingsOptimizations.R

  • use_simulator (logical) – informs if the user uses a simulator linked to Lagun

Returns:

extra points in the DOE to confirm constrained optimization results

Return type:

list

Main reactives:

  • Calls constrainedDefine.server() with id constrainedDefine

  • Calls constrainedSolve.server() with id constrainedSolve

  • Calls constrainedExplore.server() with id constrainedExplore

constrainedDefine.R

source("modules/shared/XinfosChange.R", local = TRUE)

UI and Server functions

constrainedDefine.ui(id)

Populates the Define Optimization Problem subpanel

Parameters:

id (character) – namespace of the module

Main reactives:

  • optimdef: button to define the problem formulation, opens modal window containing:

    • file: file input to upload the problem formulation

    • obj1.ui, obj2.ui: objective selection (output variables)

    • signobj1.ui, signobj2.ui: optimization type selection

    • nbcons.ui: input for the number of constraints

    • listconstraints.ui: list of defined contraints

    • saveoptimdef: button to save and close

    • closeoptimdef: button to cancel problem formulation

  • downloadformulation: button to export problem formulation

  • XinfosChange.ui(ns(“bounds”)): button to change input information

  • XinfosChange.ui.preview(ns(“bounds”)): displays table to preview input information

  • thresholds: displays thresholds as a table

  • optimTypes: displays optimization types as a table

constrainedDefine.server(input, output, session, DOE, listmodels, nbcons.min = 1, nbobj = 1, simulations = NULL)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • nbcons.min (numeric) – minimum number of contraints (default=1)

  • nbobj (numeric) – number of objectives (default=1)

  • simulations (object) – simulations if a simulator is connected to Lagun (default=NULL)

Main reactives:

  • COformulation: contains constraint formulation

  • choicesY, choicesY2: contains output variables

  • output$obj1.ui, output$obj2.ui: selected optimization objectives

  • output$signobj1.ui, output$signobj2.ui: selected optimization types

  • output$nbcons.ui: number of constraints input

  • output$listconstraints.ui: UI containing the defined constraints

  • output$thresholds: table containing thresholds

  • output$optimTypes: table containing optimization types

  • output$downloadformulation: downloadable TXT file containing constraint formulation

Main functions

getCOformulationThresholds(COformulation, ynames)

Returns a matrix with the threshold for each output

Parameters:

  • COformulation (list) – constraint formulation

  • ynames (list) – output variable names

getCOformulationOptimTypes(COformulation, ynames)

Returns a matrix with optimization type for each output

Parameters:

  • COformulation (list) – constraint formulation

  • ynames (list) – output variable names

getCOformulation(dinit, ynames)

Returns constraint formulation with thresholds and optimization types. Calls getCOformulationThresholds and getCOformulationOptimTypes

Parameters:

  • dinit (list) – intial constraint formulation

  • ynames (list) – output variable names

check.CO.formulation(dinit, ynames, nbobj)

Checks if contraint formulation is valid

Parameters:

  • dinit (list) – intial constraint formulation

  • ynames (list) – output variable names

  • nbobj (numeric) – number of objectives

constrainedSolve.R

UI and Server functions

constrainedSolve.ui(id)

Populates the Solve Optimization Problem panel

Parameters:

id (character) – namespace of the module

Main reactives:

  • go: button to launch optimization

  • OptimFailed: display choice if no optimum satisfying all constraints is found

  • download: button to export optimization results

  • Graphical Representation:

    • plotObj: displays objective plot

    • plotConstr: displays constraint plot

  • Table Representation:

    • table: displays optimization results as a table

constrainedSolve.server(input, output, session, DOE, listmodels, Xinfos, COformulation, settings, use_simulator)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • Xinfos (object) – input variable information

  • COformulation (list) – constraint formulation

  • settings (list-like-object) – variables specified in settingsOptimizations.R

  • use_simulator (logical) – informs if the user uses a simulator linked to Lagun

Returns:

resCoptim & simulations

Return type:

list

Main reactives:

  • resCoptim: contains constrained optimization results

  • simulations: contains extra points in the DOE to confirm constrained optimization results

  • output$plotObj: displays objective plot

  • output$plotConstr: displays constraint plot

  • output$table: displays optimization results as a table

  • output$download: downloadable CSV file containing constrained optimization results

Main functions

computeConstrainedOptimWithoutCat(dimx, lb, ub, predfun, COformulation, COalgo, inc, nmultistart, callback)

Performs constrained optimization without categorical variables, using one of the following methods:

  • COBYLA [2]

  • ISRES [3]

  • AUGLAG [4] + COBYLA [2]

  • SQP [5]

Parameters:

  • dimx (numeric) – input variable dimension

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • COformulation (list) – constraint formulation

  • COalgo (character) – constrained optimization algorithm

  • inc (numeric) – iteration number

  • nmultistart (numeric) – number of initialization for multistart optimization

  • callback (function) – reports progress

computeConstrainedBiOptimWithoutCat(dimx, lb, ub, predfun, COformulation)

Performs constrained bi-objective optimization without categorical variables using NSGA-II genetic algorithm [1]

Parameters:

  • dimx (numeric) – input variable dimension

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • COformulation (list) – constraint formulation

computeConstrainedOptim(dimx, DOE, Xinfos, lb, ub, predfun, COformulation, COalgo, nmultistart, callback)

Performs constrained optimization calling computeConstrainedOptimWithoutCat (iteratively if some inputs are categorical to explore all combinations)

Parameters:

  • dimx (numeric) – input variable dimension

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • Xinfos (object) – input variable information

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • COformulation (list) – constraint formulation

  • COalgo (character) – constrained optimization algorithm

  • nmultistart (numeric) – number of initialization for multistart optimization

  • callback (function) – reports progress

computeConstrainedBiOptim(dimx, DOE, Xinfos, lb, ub, predfun, COformulation, callback)

Performs constrained bi-objective optimization calling computeConstrainedBiOptimWithoutCat (iteratively if some inputs are categorical to explore all combinations)

Parameters:

  • dimx (numeric) – input variable dimension

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • Xinfos (object) – input variable information

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • COformulation (list) – constraint formulation

  • callback (function) – reports progress

Plot functions

plotConstrainedOptimBiObj(DOE, COformulation, resCoptim)

Plots bi-objective optimization results

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • COformulation (list) – constraint formulation

  • resCoptim (list) – constrained optimization results

plotConstrainedOptimObj(DOE, COformulation, resCoptim)

Plots optimization results

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • COformulation (list) – constraint formulation

  • resCoptim (list) – constrained optimization results

plotConstrainedOptimConstr(DOE, COformulation, resCoptim)

Plots optimization constraint satisfaction

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • COformulation (list) – constraint formulation

  • resCoptim (list) – constrained optimization results

Secondary functions

get.resCoptim.table(DOE, COformulation, resCoptim, choiceOptimFailed)

Shapes optimization results as a data.frame

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • COformulation (list) – constraint formulation

  • resCoptim (list) – constrained optimization results

  • choiceOptimFailed (character) – choice to display if no optimum satisfying all constraints was found

get.resCoptim.export(DOE, COformulation, resCoptim, choiceOptimFailed)

Shapes optimization results as a data.frame for file export

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • COformulation (list) – constraint formulation

  • resCoptim (list) – constrained optimization results

  • choiceOptimFailed (character) – choice to display if no optimum satisfying all constraints was found

callback(inc, i)__

Reports progress of a task. Calls R Shiny incProgress

Parameters:

  • inc (numeric) – incth iteration

  • i (numeric) – ith initialization (multistart)

constrainedExplore.R

UI and Server functions

constrainedExplore.ui(id)

Populates the Explore Solution(s) panel

Parameters:

id (character) – namespace of the module

Main reactives:

  • parcoords: parallel plot

constrainedExplore.server(input, output, session, DOE, listmodels, COformulation, resCoptim, settings)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • COformulation (list) – constraint formulation

  • resCoptim (list) – constrained optimization results

  • settings (list-like-object) – variables specified in settingsOptimizations.R

Main reactives:

  • Yinfos: contains the output variable information

  • output$parcoords: displays the parallel plot

Main functions

Plot functions

Secondary functions

getParcoordsCOExplo(DOE, predfun, lb, ub, COformulation, resCoptim, Yinfos, nobsparcoords)

Builds a parallel plot of the constrained optimization

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • predfun (function) – predict function of the selected metamodel

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • COformulation (list) – constraint formulation

  • resCoptim (list) – constrained optimization results

  • Yinfos (object) – output variable information

  • nobsparcoords (numeric) – number of observations

Sequential

sequential.R

source("modules/menuOptimize/constrained/constrainedDefine.R", local = TRUE) source("modules/menuOptimize/sequential/sequentialSolve.R", local = TRUE)

UI and Server functions

sequential.ui(id)

Builds the Sequential Optimization with Surrogate Model page with two panels:

  • Define Optimization Problem

  • Solve Optimization Problem

Parameters:

id (character) – namespace of the module

Details

  • calls constrainedDefine.ui() with id sequentialDefine

  • calls sequentialSolve.ui() with id sequentialSolve

sequential.server(input, output, session, DOE, listmodels, advance.importDOE, settings)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • advance.importDOE (object) – stores the simulation information status (completed/waiting/running) when Lagun is connected to an external simulator

  • settings (list-like-object) – variables specified in settingsOptimizations.R

Details

  • calls constrainedDefine.server() with id sequentialDefine

  • calls sequentialSolve.server() with id sequentialSolve

sequentialOptimizers.R

Main functions

available.seq.optimizers()

Returns available sequential optimizers

acquisition.function(dimx, objs, minimize, idconstr, boundsO, boundsC, sdreweightedloo=FALSE)

Builds function to compute a criterion according to the constraints and the optimization type

Parameters:

  • dimx (numeric) – input variable dimension

  • objs (object) – trained metamodels and their information

  • minimize (logical) – informs whether the optimization type is a minimization

  • idconstr (character) – variables on which a constraint is applied, if any

  • boundsO (list) – objective bounds

  • boundsC (list) – constraint bounds

  • sdreweightedloo (logical) – indicates whether the standard deviation should be weighted by the error (default=FALSE)

acquisition.function.MO(dimx, objs, minimize, idconstr, boundsO, boundsC, sdreweightedloo=FALSE)

Same as acquisition.function() but for MO algorithm

Parameters:

  • dimx (numeric) – input variable dimension

  • objs (object) – trained metamodels and their information

  • minimize (logical) – informs whether the optimization type is “minimize”

  • idconstr (character) – variables on which a constraint is applied, if any

  • boundsO (list) – objective bounds

  • boundsC (list) – constraint bounds

  • sdreweightedloo (logical) – indicates whether the standard deviation should be weighted by the error (default=FALSE)

EGO.seq.optimize(models, Xinfos, DOE, npts = 1, idobj = 1, minimize=TRUE, idconstr=NULL, boundsO, boundsC, settings)

Performs EGO sequential optimization

Parameters:

  • models (list) – list of trained metamodels

  • Xinfos (object) – input variable information

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • npts (numeric) – number of points / observations (default=1)

  • idobj (numeric) – model ID (default=1)

  • minimize (logical) – informs whether the optimization type is “minimize” (default=TRUE)

  • idconstr (character) – variables on which a constraint is applied, if any (default=NULL)

  • boundsO (list) – objective bounds

  • boundsC (list) – constraint bounds

  • settings (list-like-object) – variables specified in settingsOptimizations.R

EGO.seq.settings()

Retruns EGO optimizer settings

RS.seq.optimize(models, Xinfos, DOE, npts=1, idobj=1, minimize=TRUE, idconstr=NULL, boundsO=NULL, boundsC=NULL, settings=NULL)

Performs RS sequential optimization

Parameters:

  • models (list) – list of trained metamodels

  • Xinfos (object) – input variable information

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • npts (numeric) – number of points / observations (default=1)

  • idobj (numeric) – model ID (default=1)

  • minimize (logical) – informs whether the optimization type is “minimize” (default=TRUE)

  • idconstr (character) – variables on which a constraint is applied, if any (default=NULL)

  • boundsO (list) – objective bounds (default=NULL)

  • boundsC (list) – constraint bounds (default=NULL)

  • settings (list-like-object) – variables specified in settingsOptimizations.R (default=NULL)

RS.seq.settings()

Retruns RS optimizer settings

sequentialSolve.R

source("modules/shared/XinfosChange.R", local = TRUE) source("modules/shared/dynamicSelect.R", local = TRUE) source("modules/menuOptimize/sequential/sequentialOptimizers.R", local = TRUE)

UI and Server functions

sequentialSolve.ui(id)

Populates the panel Solve Optimization Problem

Parameters:

id (character) – namespace of the module

Details

  • chooseOptimAlgo: optimization algorithm selection

  • nitermax: input to define the number max of iteration

  • nptsiter: input to define the number of points per iteration

  • optimsettings: button to display advanced settings

    • settings.dynui: displays advanced settings

  • launchButtonUI: button to launch optimization

  • stopOptim: button to stop optimization

  • restartOptim: button to restart optimization

  • settings.dynui: button to display advanced optimizer settings

  • studyIter: button to display iteration analysis

    • sliderIter.dynui: slider to choose iteration to analyze

    • plotRadar: Constraint Visualization: DOE quantiles, thresholds and current iteration

    • Xaddcontents: displays input variables selected iterations as a table

  • rowvisu.dynui: displays optimization results plot, constraints heatplot, Q2 plot

sequentialSolve.server(input, output, session, DOE, listmodels, Xinfos, COformulation, advance.importDOE, settings)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • Xinfos (object) – input variable information

  • COformulation (list) – constraint formulation

  • advance.importDOE (object) – stores the simulation information status (completed/waiting/running) when Lagun is connected to an external simulator

  • settings (list-like-object) – variables specified in settingsOptimizations.R

Details

  • choicesOptimAlgo: optimization algorithm selection

  • output$launchButtonUI: button to launch optimization

  • output$sliderIter.dynui: slider input fir iteration number selection

  • output$plotRadar: displays radar plot

  • output$Xaddcontents: builds table with input variables selected iterations

  • output$rowvisu.dynui: displays optimization results plot, constraints heatplot, Q2 plot

    • output$plotObj: builds optimization results plot

    • output$plotConstr: builds constraints heatplot

    • output$plotQ2: builds Q2 plot

Plot functions

update.plots.pred(DOE, COformulation, seq, simulations, nitermax, session, npts)

Updates plots with outputs that are compliant with the contraints when a simulator is used

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • COformulation (list) – constraint formulation

  • seq (object) – contains sequential optimization data and results

  • simulations (object) – simulations if a simulator is connected to Lagun

  • nitermax (numeric) – number max of iterations

  • session (object) – environment that can be used to access information and functionality related to the session

  • npts (numeric) – number of points per iteration

update.plots(DOE, COformulation, seq, simulations, nitermax, session, npts)

Updates plots with outputs that are compliant with the contraints

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • COformulation (list) – constraint formulation

  • seq (object) – contains sequential optimization data and results

  • simulations (object) – simulations if a simulator is connected to Lagun

  • nitermax (numeric) – number max of iterations

  • session (object) – environment that can be used to access information and functionality related to the session

  • npts (numeric) – number of points per iteration

Secondary functions

respect.constraints(Y, signconstr, thconstr)

Checks if the outputs are compliant with the contraints

Parameters:

  • Y (list) – output variable list

  • signconstr (numeric) – optimization type / sign (-1 or 1)

  • thconstr (numeric) – constraint threshold

getlbub(signs, thresholds)

Returns lower-bounds and upper-bounds of the threshold vector

Parameters:

  • signs (numeric) – optimization type / sign (-1 or 1)

  • thconstr (numeric) – constraint threshold

Robust

robust.R

source("modules/menuOptimize/robust/robustDefine.R", local = TRUE) source("modules/menuOptimize/robust/robustAnalysis.R", local = TRUE) source("modules/menuOptimize/robust/robustSolve.R", local = TRUE)

UI and Server functions

robust.ui(id)

Builds the Robust Optimization with Surrogate Model page with two panels:

  • Define Optimization Problem

  • Preliminary Analysis

  • Solve Problem

Parameters:

id (character) – namespace of the module

Details

  • calls robustDefine.ui() with id robustDefine

  • calls robustAnalysis.ui() with id robustAnalysis

  • calls robustSolve.ui() with id robustSolve

robust.server(input, output, session, DOE, listmodels, settings)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • settings (list-like-object) – variables specified in settingsOptimizations.R

Details

  • calls robustDefine.server() with id robustDefine

  • calls robustAnalysis.server() with id robustAnalysis

  • calls robustSolve.server() with id robustSolve

Secondary functions

q10(v)

Returns 10% quantile

Parameters:

v (vector) – data vector of numerical values

q90(v)

Returns 90% quantile

Parameters:

v (vector) – data vector of numerical values

robustDefine.R

UI and Server functions

robustDefine.ui(id)

Populates the panel Define Optimization Problem

Parameters:

id (character) – namespace of the module

Details

  • design: table containing formulation design

  • thresholds: table containing formulation thresholds

  • optimTypes: table containing formulation optimization types

robustDefine.server(input, output, session, DOE)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

Details

  • ROformulation: contains formulation information

  • output$error.file: errors returned by check.RO.formulation() if any

  • output$design: builds table containing formulation design

  • output$thresholds: builds table containing formulation thresholds

  • output$optimTypes: builds table containing formulation optimization types

Main functions

getROformulationDesign(DOE, ROformulation)

Returns formulation design (variable type, mean, standard deviation) as a data.frame

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

getROformulationThresholds(DOE, ROformulation)

Returns formulation thresholds

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

getROformulationOptimTypes(DOE, ROformulation)

Returns formulation optimization types

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

getROformulation(dinit, DOE)

Returns the complete formulation using the functions above.

Parameters:

  • dinit (object) – content of the input file

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

Secondary functions

check.RO.formulation(dinit, nX, nY)

Checks if content of the input file is valid

Parameters:

  • dinit (object) – content of the input file

  • nX (numeric) – number of inputs

  • nY (numeric) – number of outputs

robustAnalysis.R

source("modules/shared/dynamicSelect.R", local = TRUE)

UI and Server functions

robustAnalysis.ui(id)

Populates the panel Preliminary Analysis

Parameters:

id (character) – namespace of the module

Details

  • chooseY: output variable selection

  • contentC: displays estimation of problem complexity

  • plotpairPrelimIndiv: pairplot to check the probability of respecting the selected constraint

  • plotpairPrelimJoint: pairplot to check the probability of respecting all constraints simultaneously

  • plotPrelimC: plots constraint satisfaction probability

robustAnalysis.server(input, output, session, DOE, listmodels, ROformulation)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • ROformulation (list) – Robust Optimization formulation

Main reactives:

  • choicesY: output variable selection

  • resPrelimC: preliminary constraint evaluation

  • output$contentC: estimation of problem complexity as a table

  • output$plotPrelimC: plots constraint satisfaction probability

  • output$plotpairPrelimIndiv: plots probability of respecting the selected constraint

  • output$plotpairPrelimJoint: plots probability of respecting all constraint

Main functions

getResPrelimC.proba(DOE, ROformulation, resPrelimC)

Computes percentage of tested points whose probability to respect the constraint is greater than a control level of 0.9, 0.95 and 0.99.

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

  • resPrelimC (list) – preliminary constraint evaluation

evaluateConstraints(DOE, lb, ub, predfun, ROformulation, nlhs, callback)

Generates a Monte Carlo random sample and evaluates which points satisfy the defined constraints

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • ROformulation (list) – Robust Optimization formulation

  • nlhs (numeric) – number of points

  • callback (function) – reports progress

Plot functions

plotPrelimC(DOE, ROformulation, resPrelimC, yname)

Plots constraint satisfaction probability

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

  • resPrelimC (list) – preliminary constraint evaluation

  • yname (character) – output variable name

plotpairPrelimIndiv(DOE, ROformulation, resPrelimC, yname)

Plots a pairplot to check the probability of respecting the selected constraint

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

  • resPrelimC (list) – preliminary constraint evaluation

  • yname (character) – output variable name

plotpairPrelimJoint(DOE, ROformulation, resPrelimC, yname)

Plots a pairplot to check the probability of respecting all constraints simultaneously

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

  • resPrelimC (list) – preliminary constraint evaluation

  • yname (character) – output variable name

Secondary functions

callback(i)__

Reports progress of a task. Calls R Shiny incProgress

Parameters:

i (numeric) – ith iteration

robustSolve.R

UI and Server functions

robustSolve.ui(id)

Populates the panel Solve Problem

Parameters:

id (character) – namespace of the module

Details

  • go: button to launch robust optimization

  • ROcrit: robust optimization criterion selection

  • threshproba: constraint probability selection

  • download: button to export optimization results

robustSolve.server(input, output, session, DOE, listmodels, ROformulation, settings)
Parameters:

  • input (list-like-object) – stores the widgets’ values.

  • output (list-like-object) – stores the instructions to build R objects in the app.

  • session (object) – environment that can be used to access information and functionality relating to the session.

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • listmodels (list) – list of trained models

  • ROformulation (list) – Robust Optimization formulation

  • settings (list-like-object) – variables specified in settingsOptimizations.R

Details

  • resRoptim: contains optimization information and results

  • output$plot: displays plot of optimization results

  • output$table: displays table of optimization results

  • output$download: downloadble CSV file containing optimization results

Main functions

get.resRoptim.table(DOE, ROformulation, resRoptim, ROcrit)

Shapes optimization results as a data.frame

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

  • resRoptim (object) – optimization results

  • ROcrit (character) – robust optimization criterion

get.resRoptim.export(DOE, ROformulation, resRoptim)

Shapes optimization results as a data.frame for file export

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

  • resRoptim (object) – optimization results

computeRobustOptim(DOE, lb, ub, predfun, ROformulation, threshold, ROalgo, ROcrit, nmultistart, callback)

Performs robust optimization using one of the following methods:

  • COBYLA [2]

  • ISRES [3]

  • AUGLAG [4] + COBYLA [2]

  • SQP [5]

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • lb (numeric) – lower bound

  • ub (numeric) – upper bound

  • predfun (function) – predict function of the selected metamodel

  • ROformulation (list) – Robust Optimization formulation

  • threshold (numeric) – threshold, constraint probability

  • ROalgo (character) – optimization algorithm

  • ROcrit (character) – optimization criterion (mean, quantile 10%, quantile 90%)

  • nmultistart (numeric) – number of initialization for multistart optimization

  • callback (function) – reports progress

Plot functions

plotRobustOptim(DOE, ROformulation, resRoptim)

Plots robust optimization results

Parameters:

  • DOE (object) – stores the point values and the DOE information (e.g. bounds…)

  • ROformulation (list) – Robust Optimization formulation

  • resRoptim (object) – optimization results

Secondary functions

callback(i)__

Reports progress of a task. Calls R Shiny incProgress

Parameters:

i (numeric) – ith iteration

References

[1] (1,2)

NSGA-II Genetic Algorithm

Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T. (2012) A fast and elitist multiobjective genetic algorithm: NSGA-II, in IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197

[2] (1,2,3,4)

Constrained Optimization by Linear Approximations

Powell, M. J. D. (1994) A direct search optimization method that models the objective and constraint functions by linear interpolation, in Advances in Optimization and Numerical Analysis, eds. S. Gomez and J.-P. Hennart

R function documentation | R Package: nloptr

[3] (1,2)

Improved Stochastic Ranking Evolution Strategy

Thomas Philip Runarsson and Xin Yao (2005) Search biases in constrained evolutionary optimization, IEEE Trans. on Systems, Man, and Cybernetics Part C: Applications and Reviews, vol. 35 (no. 2), pp. 233-243

R function documentation | R Package: nloptr

[4] (1,2)

Augmented Lagrangian Algorithm

Andrew R. Conn, Nicholas I. M. Gould, and Philippe L. Toint (1991) A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal. vol. 28, no. 2, p. 545-572

Birgin, E. G. and Martinez, J. M. (2008) Improving ultimate convergence of an augmented Lagrangian method, Optimization Methods and Software vol. 23, no. 2, p. 177-195

R function documentation | R Package: nloptr

[5] (1,2)

Sequential Quadratic Programming

Nocedal, Jorge, and Stephen Wright (2006) Numerical optimization. Springer Science & Business Media

R function documentation | R Package: NlcOptim

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