Cpo Presentation

IBM ILOG CP Optimizer
CP-AI-OR 2009 Masterclass
28/05/2009
Paul ShawConstraint Programming Group
paul.shaw@fr.ibm.com

28/05/2009 ILOG, All rights reserved 2
What is CP Optimizer?
A Constraint Programming engine with an emphasis on modelling and automatic search
General feeling that CP toolkits were becoming too complicated, and the audience more limited
Models quickly became very hard to maintain
Simplify learning and use of the productIncrease model development speedQuickly evaluate CP technology on the problemYou can still program the search in the native engine
language (C++) if you wish

What kinds of problems?
CP Optimizer has a large emphasis on scheduling problems
However, we will not have time to cover interval-based modelling today
Look at examples beginning with sched_
Also addresses more traditional combinatorial problems
What we will do today

Getting at CP Optimizer
Available as a toolkit in C++, Java, .NETC++ is the native language and allows more
possibilities, like writing incremental custom constraints, and fully controlling the search process
Available as an engine inside OPLWhat we will use todayHigher level modelling and data manipulationCustom visualisation and scenarios via ODM

Getting Started with OPL Development Studio

Import Existing OPL 6.x projects

Browse projects

A project = - a set of model files (.mod) - a set of data files (.dat) - a set of settings files (.ops) - other files (e.g. .xls files ) - a set of rrrrrruuuuuunnnnnn ccccccoooooonnnnnnffffffiiiiiigggggguuuuuurrrrrraaaaaatitititititioooooonnnnnnssssss

Model edition: - data manipulation - expression - objective - constraint - script for pre- and post-processing - use Help-> Dynamic Help for information on keywords

Model navigation

Data file: - explicit data - connection to: * databases * Excel worksheets

Double-click for full-size window

Overview of an OPL Model
TopData manipulation and pre-processing
declarative (expressions) and/or imperative (script)
Variable declarations

CP Optimizer model

DDDDDDaaaaaattttttaaaaaa ssssssttttttrrrrrruuuuuuccccccttttttuuuuuurrrrrreeeeeessssss aaaaaannnnnndddddd dadadadadadattttttaaaaaa rrrrrreeeeeeaaaaaaddddddininininininggggggHere, read input grid

PrPrPrPrPrPrepreprepreprepreprococococococeeeeeessssssssssssiiiiiinnnnnnggggggHere: display grid

VVVVVVaaaaaarrrrrriiiiiiaaaaaabbbbbblllllle e e e e e DDDDDDeeeeeeccccccllllllaaaaaararararararattttttiiiiiionononononon

Some OPL Syntax: declarations
CP Optimizer has integer variables only (dvar int)No set variables, no floating point variables
BUT, floating point expressions are allowede.g. 0.3 * x + y / 13

Some OPL Syntax: declarations
CP Optimizer has integer variables only (dvar int) No set variables, no floating point variables
BUT, floating point expressions are allowede.g. 0.3 * x + y / 13

Some OPL Syntax: data preparation
int n = ...; // From data file
range R = 1..n;
int area[i in R] = width[i] * height[i];
int totalArea = sum(i in R) area[i];
{int} bigOnes = {i | i in R : area[i] >= 100};
tuple Pair { int p1; int p2; };
{Pair} sumTo100 = {
| ordered a,b in R : area[a] + area[b] >= 100
};

int n = ...; // From data file
range R = 1..n;
int area[i in R] = width[i] * height[i];
int totalArea = sum(i in R) area[i];
{int} bigOnes = {i | i in R : area[i] >= 100};
tuple Pair { int p1; int p2; };
{Pair} sumTo100 = {
| ordered a,b in R : area[a] + area[b] >= 100
};

An initial execution block can be useful for debugging and displaying input data
execute { writeln(sumTo100);}
gives...
{, , , , , , ...

TopData manipulation and pre-processing
declarative (expressions) and/or imperative (script)
Variable declarationsMiddle
Declarative modelobjective (optional) and constraints

MMMMMModelodelodelodelodelodel::::::-VVVVVVaaaaaarrrrrriaiaiaiaiaiablblblblblbleeeeeessssss-EEEEEExxxxxxpppppprerererereressssssssssssionionionionionionssssss-OOOOOObjecbjecbjecbjecbjecbjecttttttiiiiiivvvvvveeeeee-CCCCCCononononononssssssttttttrrrrrraaaaaaiiiiiinnnnnnttttttssssss

Basic structure of middle section
[ minimize/maximize ]
subject to / constraints { ; ; ...}

For allffffffoooooorrrrrraaaaaallllllllllll (i in {1,3,5})
x[i]

x[i]

Expressions and Constraints
Arithmetic constraints x + y, x y, x * y, x / y, x div y, x % y min, max, abs, log, exp etc. Piecewise linear functions
Relational constraints x == y, x != y, x

Reification Relational or logical constraints can be used in a value
context, where they evaluate to 0 or 1
Examples Arithmetic: max(0, abs(load[i] - cap)) Relational: wid * hei * depth * density

Count expression count(dvar int[] x, int c) Evaluates the number of variables in x with value c e.g. Count the number of nurses allocated to ward 5
count(wardAllocation, 5) >= 3
Element expression (int[] a)[dvar int x] OR (dvar int[] a)[dvar int x] Evaluates to the xth member of a e.g. travel == 2 * distFromPittsburgh[holidayTown] travel and holidayTown are variables

Count expression count(dvar int[] x, int c) Evaluates the number of variables in x with value c e.g. Count the number of nurses allocated to ward 5
count(wardAllocation, 5) >= 3
Element expression (int[] a)[dvar int x] OR (int var[] a)[dvar int x] Evaluates to the xth member of a e.g. travel == 2 * distFromPittsburgh[holidayTown] travel and holidayTown are variables

All Different allDifferent(dvar int[] x) All variables in x must take diff

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