Seminar: Embedding Optimization in Applications with MPL OptiMax - April 2012

1Copyright © 2012 Maximal Software, Inc. All rights reserved

Optimization Seminar - OptiMax

Embedding Optimization in Applications

with MPL OptiMax

Presented by

Bjarni Kristjansson

Maximal Software, Inc.


Presentation Overview

• Tools and Methods for embedding optimization in Applications• Introduction to MPL OptiMax for Visual Basic, CSharp, Python,

and Matlab• Using the Python Command Language Interface (IDLE)• Using the Numpy, Scipy, and MatPlotLib with MPL for Python• Writing GUI Optimization Applications in Python and CSharp• Multi-Threaded support for MPL OptiMax on Servers• Connecting MPL OptiMax with Web API’s and Web Services• Deploying Optimization on Mobile/Tablet Computers


Building Optimization Applications Development/Deployment Issues

Phase I - Development• Model Development Environment • Formulating the Model• Connecting to External Data• Solver Testing and Tuning

Phase II - Deployment• End-User Applications• Run-times / Component Libraries • Embedding Optimization into Application• Packaging/Distribution


SolverSolver

ProgramProgram

Callable Libraries for Solvers


SolverSolver

ModLangModLang

SolverSolver

ProgramProgram

Algebraic Modeling Languages


SolverSolverDBDB

ModLangModLang

SolverSolverDBDB

ProgramProgram

Connecting to Databases


SolverSolverDBDB

ProgramModLang

ProgramModLang

Merging Program with Model


Application Programming• Programming Languages (Procedural)• Application/User-Interface• Database Programming• Most programmers tend to know rather little about

optimization and formulating models

Optimization Modeling• Modeling Languages (Declarative)• Optimization Packages• Most model builders tend to know rather little about

application/GUI and database programming

Programming vs. Optimization Modeling


DBDBProgramProgram

SolverSolver

ModLangModLang

Application

Optimization

Program Running Model


DBDB

ProgramProgram

SolverSolver

ModLangModLang

OptiMaxOptiMax

Application

Optimization

Optimization Component Library


OptiMax Component Library Seamless Integration of Technologies

• Modeling Language• Solver/Optimizers• Database/Data Sources• Programming Languages (COM/ActiveX)

• Visual Basic/VBA• C/C++• Java• Delphi• Web scripting


Solvers Database

OptiMax

VB C++ Delphi Java

MPLWIN MPLX

MPL Modeling Language

MPL Library (C++)

MPL/OptiMax Design Overview


Models (Model)

OptiMax

Solvers (Solver)

Matrix

Solution

SolverOptions (SolverOption)

Symbols (Symbol)

Variables (Variable)

Constraints (Constraint)

Variables (Variable)

Constraints (Constraint)

StatusWindow

MplOptions (MplOption)

OptiMax Component Library Object Model Hierarchy


Models (Model)

OptiMax

DataConstants (DataConstant)

Symbols (Symbol)

DataVectors (DataVector)

Subscripts (Subscript)

VariableVectors (VariableVector)


ConstraintVectors (ConstraintVector)


Macros (Macro)

PlainVariables (Variable)

PlainConstraints (Constraint)

IndexSets (IndexSet)

OptiMax Component Library Object Model - Symbols


OptiMax Component Library Application Building Features

• General Model Handling • Model Parsing• Model Querying• Modifying Models / Solving Models• Write Standard Output Files• Database Import/Export• Multiple Models in Memory• Multiple Model Runs / Iterations over models• Use Solution Values as Input• Callbacks/User Exits• Access to MPL Internal Indexing Data Structures


MPL OptiMax for .Net

MPL Release 4.2n:

• Supports both CSharp and Visual Basic (2008/2010 - 32/64 bit)

• Multiple new objects, methods and properties

• Seamless integration with native .Net data structures

• Array

• ArrayList

• Generic List

• ICollection

• IEnumerable

• Iterators for all collection classes to support foreach loops

• ToString() implementation for all classes

• Exception handling with detailed error messages

• Extensive code samples showing the new OptiMax features

• Server version with full multi-threaded support


MPL OptiMax for Python

MPL Release 4.2n:

• Supports Python 2.6, 2.7, 3.1, and 3.2 in both 32-bit and 64-bit mode• Distributed as compiled PYD files for increased speed• Multiple new objects, methods and properties• Seamless integration with native python data structures

• Lists, List of Lists• Tuples, Tuples of Tuples

• Iterators for all collection classes to support for loops• Implementation of magic methods for all classes

__init__(), __len__(), __iter__(), __getitem__(), __str__()• Dynamic object attributes for model identifiers• Exception handling with detailed error messages• Extensive code samples showing the new OptiMax features• Server version with full multi-threaded support


MPL OptiMax for Matlab

MPL Release 4.2n:

• Supports Matlab in both 32-bit and 64-bit mode

• Distributed as compiled MEX files

• Utilizes the new C-API Mpllib42.dll library

• Based on the standard interface of Matlab Optimization Toolbox

• mpl_initlibrary()

• mpl_linprog()

• mpl_bintprog()

• mpl_mintprog()

• mpl_freelibrary()

• MPL can be kept in memory through the hmpl library handle

• Solver can be specified through the solverName argument

• Solver options can be set through the option list argument


MPLLib C-API DLL Library

MPL Release 4.2n:

• Full C-Api library interface with over 600 functions

• Available in both 32-bit and 64-bit versions

• Utilized by MPL OptiMax Component Libraries

• MPL OptiMax for .Net

• MPL OptiMax for Python

• MPL OptiMax for Matlab

• Supports all functionality of MPL OptiMax from the C language


Simple MPL OptiMax Example in Python

from mplpy import *

def RunModel(modelName):

modelFile = mpl.HomeDir + modelName + ".mpl"

print("MPL file: " + modelFile)

mod.ReadModel(modelFile)

print("Variables = " + str(mod.Matrix.Variables.Count))

print("Constraints = " + str(mod.Matrix.Constraints.Count))

print("")

print("Solving " + modelName + " with " + mpl.Solver.Name + " solver:")

mod.Solve(mpl.coinmp)

print("")

print(mod.Solution.ResultString)

print("ObjectValue = " + str(mod.Solution.ObjectValue))

for var in mod.Solution.Variables:

print(var.Name + " = " + str(var.Activity))


Planning Example in CSharp

OptiMax mpl = new OptiMax();

mpl.UseExceptions = false;

Solver solver = mpl.Solvers.Add("CPLEX");

Model model = mpl.Models.Add("Planning");

string modelFile = mpl.HomeDirectory + modelName + ".mpl";

Console.WriteLine("Reading MPL file: " + modelFile);

ResultType result = model.ReadModel(modelFile);

if (result != ResultType.Success)

{

Console.WriteLine(model.Error.ToString());

}

Console.WriteLine("Solving " + modelName + " with " + solver.Name + " solver");

result = model.Solve(solver);

foreach (Variable var in model.Solution.Nonzeros)

{

Console.WriteLine(var.Name + " " + var.Activity.ToString());

}

Console.WriteLine(model.Solution.ResultString + " ObjectValue = " + model.Solution.ObjectValue);

Console.WriteLine("Nonzeros = " + model.Solution.Nonzeros.Count.ToString());


Portfolio Example - Dynamic Attributes

from mplpy import mplfrom numpy import arange, float32from matplotlib import pyplot as plot

modelFilename = mpl.HomeDir + "Portfolio.mpl"result = mpl.model.SolveModel(modelFilename, mpl.cplex)

investVect = mpl.model.InvestinvestVect.ZeroTol = 0.001

count = investVect.Nonzeros.CountinvestAmount = arange(count, dtype=float32)stockNames = range(count)

for i, var in enumerate(investVect.Nonzeros): investAmount[i] = var.Activity stockNames[i] = investVect.stock.ValueStr print((stockNames[i] + ":").ljust(8) + ("%1.1f%%" % (investAmount[i] * 100.0)).rjust(6))


EFrontier Example - Changing RHS

iterCount = 100deltaPercent = 0.02CPLEX_OPTIMAL = 1targetReturnData = model.TargetReturnvarianceMacro = model.Variance meetTargetCon = model.MeetTargetTargetArray = arange(iterCount, dtype=float32)VarianceArray = arange(iterCount, dtype=float32)

for i in range(iterCount): target = targetReturnData.Value * (1 + i * deltaPercent) meetTargetCon.RHSValue = target model.Solve(mpl.cplex) print(str(i) + ") " + str(target) + ", " + str(varianceMacro.Value)) if model.Solution.ResultCode == CPLEX_OPTIMAL: TargetArray[i] = target VarianceArray[i] = varianceMacro.Value else: solCount = i print(str(solCount + 1) + ") " + model.Solution.ResultString + " (" + str(model.Solution.ResultCode) + ")") break


CutStock Example – Add() Statements

def LoadModel(self, model, cutNames, patternNames, priceSheet, sheetsAvail, cutDemand, cutsInPattern):

try: model.IndexSets.AddNameSet("cuts", cutNames) model.IndexSets.AddNameSet("patterns", patternNames) model.DataConstants.Add("PriceSheet", priceSheet) model.DataConstants.Add("SheetsAvail", sheetsAvail) model.DataVectors.AddDense("CutDemand[cuts]", cutDemand) model.DataVectors.Add("CutsInPattern[patterns, cuts]", cutsInPattern) model.PlainVariables.Add("SheetsCut", "-> T1") model.PlainVariables.Add("TotalCost", "-> TC") model.VariableVectors.Add("PatternCount[patterns]", "-> \"\"") model.VariableVectors.Add("ExcessCuts[cuts]", "-> X") model.Objectives.Add("TotalCost", ObjectSense.Minimize) model.PlainConstraints.Add("TotCost", "TotalCost = PriceSheet*SheetsCut") model.PlainConstraints.Add("RawAvail", "SheetsCut < SheetsAvail") model.PlainConstraints.Add("Sheets", "SheetsCut = SUM(patterns: PatternCount[patterns])") model.ConstraintVectors.Add("CutReq[cuts]", "SUM(patterns: CutsInPattern[patterns, cuts] * PatternCount[patterns]) CutDemand[cuts] + ExcessCuts[cuts]") except Exception as ex: print(str(ex)) result = model.LastResult return result


Add Statements - IndexSet / DataVectors

Adding IndexSet:

cutNames = ['w1', 'w2', 'w3', 'w4', 'w5', 'w6', 'w7', 'w8']

model.IndexSets.AddNameSet("cuts", cutNames)

Adding DataVectors:

cutDemand = [500, 400, 300, 450, 350, 200, 800, 200]

model.DataVectors.AddDense("CutDemand[cuts]", cutDemand)

cutsInPattern = ['p1', 'w1', 1, 'p1', 'w8', 1, 'p2', 'w2', 1, 'p2', 'w7', 1, . . . 'p28', 'w8', 5, 'p29', 'w8', 7]

model.DataVectors.Add("CutsInPattern[patterns, cuts]", cutsInPattern)


Exceptions with Detailed Syntax Error Messages

Syntax Error:

model.PlainConstraints.Add("TotCost", "TotalCost = PriceSheet */ SheetsCut")

Exception Output:

The PlainConstraints.Add('TotCost', expr='TotalCost = PriceSheet */ SheetsCut') method

returned 'SyntaxError' (2) with the following error message:

**** A minor mistake was found in line 1:

6. I expected to see either a number or a variable, but found instead '/'.

File: C:\MplWin4\OptiMax\Python\CutStock Line: (line=1, col=43)

SUBJECT TO TotCost: TotalCost = PriceSheet */ SheetsCut; ^


Exceptions with Wrong Data Types

Syntax Error:

cutNames = ['w1', 'w2', 'w3', 'w4', 'w5', 'w6', 'w7', 'w8']

model.DataConstants.Add("SheetsAvail", cutNames)

Exception Output:

The argument 'dataValue' for the 'DataConstants.Add('SheetsAvail', dataValue, dataAttr)' method

cannot be assigned the value '['w1', 'w2', 'w3', 'w4', 'w5', 'w6', 'w7', 'w8']' of type 'list'.

Quick fix: Please enter either a numeric or string value.


Applications with MPL OptiMax

• Model written in MPL• Data transferred to/from MPL through

• Excel Ranges

• Database Connection

• Text files

• End-User Application Building• User-Interface done in VB/CSharp/C-API/C++/Java/Phyton

• Process Input from User

• Control Solver Runs

• Process Output from Model

• Display graphs

• Model solved with any supported solver

No limits on size, speed, or robustness

Technology

Seminar: Embedding Optimization in Applications with MPL OptiMax - April 2012