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

Optimization Seminar - OptiMax

Embedding Optimization in Applications
with MPL OptiMax

Presented by
Bjarni Kristjansson
Maximal Software, Inc.

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

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

2

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

3

Callable Libraries for Solvers

Program
Program

Solver
Solver

4

Algebraic Modeling Languages

ModLang
ModLang Program
Program

Solver
Solver Solver
Solver

5

Connecting to Databases

ModLang
ModLang Program
Program

Solver
Solver DB Solver
Solver DB
DB DB

6

Merging Program with Model

Program
Program
ModLang
ModLang

Solver
Solver DB
DB

7

Programming vs. Optimization Modeling

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

8

Program Running Model

Program
Program DB
DB

Application
Optimization

ModLang
ModLang

Solver
Solver

9

Optimization Component Library

Program
Program

OptiMax
OptiMax DB
DB

Application
Optimization

ModLang
ModLang

Solver
Solver

10

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

11

MPL/OptiMax Design Overview

VB C++ Delphi Java

MPLWIN MPLX OptiMax

MPL Library (C++)

MPL Modeling Language

Solvers Database

12

Object Model Hierarchy

OptiMax

Solvers (Solver)

SolverOptions (SolverOption)

MplOptions (MplOption)

StatusWindow

Models (Model)

Matrix

Variables (Variable)

Constraints (Constraint)

Solution

Variables (Variable)

Constraints (Constraint)

Symbols (Symbol)

13

Object Model - Symbols

OptiMax

Models (Model)

Symbols (Symbol)

IndexSets (IndexSet)

DataConstants (DataConstant)

DataVectors (DataVector)

Subscripts (Subscript)

Macros (Macro)

VariableVectors (VariableVector)


ConstraintVectors (ConstraintVector)


PlainVariables (Variable)

PlainConstraints (Constraint)

14

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

15

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
16

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

17

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

18

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

19

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))

20

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());

21

Portfolio Example - Dynamic Attributes

from mplpy import mpl
from numpy import arange, float32
from matplotlib import pyplot as plot

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

investVect = mpl.model.Invest
investVect.ZeroTol = 0.001

count = investVect.Nonzeros.Count
investAmount = 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))

22

EFrontier Example - Changing RHS

iterCount = 100
deltaPercent = 0.02
CPLEX_OPTIMAL = 1
targetReturnData = model.TargetReturn
varianceMacro = model.Variance
meetTargetCon = model.MeetTarget
TargetArray = 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
23

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

24

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)

25

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:MplWin4OptiMaxPythonCutStock
Line: (line=1, col=43)

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

26

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.

27

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
28

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

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