SCPSolver

SCPSolver

Linear Programming in Java madeeasy

Overview

• What is Linear Programming?

• Why one would like to use it?

• What is SCPSolver (not)?

• Demo

– Modelling for Beginners

– Modelling for Advanced Users

Hannes Planatscher 2

Linear Optimization

• „Linear Programming is a technique for the optimization of a linear objective function subject to linear constraints.“


n

i

ii xc1

max

1

,1n

ij i j

i

a x b j m

subject to m linear constraints

n-dimensional linear objective function

Constraints define halfspaces


x1

x2

Feasible region


x1

x2

feasible region

Location of global optima


x1

x2

feasible regionpotential optimum

potential optimum

potential optimum

potential optimum

If the linear program is

feasible and not

unbounded, the

optimum can be found

at a vertex, in special

cases also at an

edge, of the polytope.



x1

x2

optimum


feasible and not

unbounded, the



cases also at an



9

x1

x2

optimum


feasible and not

unbounded, the



cases also at an


Simplex

10

x1

x2


optimum

potential optimum

potential optimum

The Simplex

Algorithm visits one

vertex after another

until the optimum is

found.

Interior Point

11

x1

x2


optimum

potential optimum

potential optimum

Interior point

algorithms try find to

optimum starting from

within the feasible

region.

Integer Variables

12

x1

x2

Why use Linear Programming?

• Even if the Simplex Algorithm has exponentialworst case complexity, it is very fast in mostreal world scenarios.

• Very efficient solvers, which can solve linear (integer) programs with several 100.000 variables and constraints, exist.

• If possible, always try to reformulate youroptimization problem as a Linear Program.


Linear Programming in Java

• Using existing Linear Programming Solvers in Java programs is a pain, because of:

– platform dependency (.dll, .so, .jnilib)

– bad API s

– difficult deployment (where to put the libraries)

• You have to stick with its (usually bad) API, once you have chosen a solver.


SCPSolver

• Main goals– make it easy to develop

– keep the API lean

– get „platformindependent“

– automate binary librarydeployment

– separate modelling fromthe solver

• Not a goal: Write a newSolver in Java!


„Low-level“-Modelling


LinearProgram lp = new LinearProgram(new double[]{5.0,10.0});

lp.setMinProblem(true);

lp.addConstraint(new LinearBiggerThanEqualsConstraint(new double[]{3.0,1.0}, 8.0, "c1"));

lp.addConstraint(new LinearBiggerThanEqualsConstraint(new double[]{0.0,4.0}, 4.0, "c2"));

lp.addConstraint(new LinearSmallerThanEqualsConstraint(new double[]{2.0,0.0}, 2.0, "c3"));

LinearProgramSolver solver = SolverFactory.newDefault();

double[] sol = solver.solve(lp);

1 2min5.0 10.0x x

1 23.0 1.0 8.0x x

24.0 4.0x

12.0 2.0x

„High-Level“-Modelling


LPWizard lpw = new LPWizard();

lpw.plus("x1",5.0).plus("x2",10.0);

lpw.addConstraint("c1",8,"<=").plus("x1",3.0).plus("x2",1.0);

lpw.addConstraint("c2",4,"<=").plus("x2",4.0);

lpw.addConstraint("c3", 2, ">=").plus("x1",2.0);

System.out.println(lpw.solve());

1 2min5.0 10.0x x

1 23.0 1.0 8.0x x

24.0 4.0x

12.0 2.0x

Solver Packs

• Solvers

– lpsolve (Open Source)

– GLPK (Open Source)

– CPLEX (closed

• Platforms

– Linux 32/64-bit (tested: Ubuntu, Scientific Linux)

– Mac Os X 64-bit (> 10.5)

– Windows 32-bit(tested: XP)


solver_x86.dll

solver_x86.so

solver_x64.jnilib

JNI Interface to solver

Solver Pack Jar

Solver Packs

• All libraries are asstatically linked aspossible

• Minimal dependencies on execution environment.

• Advantage– packs runs instantly on

many systems

• Disadvantage– the solver packs are pretty

large (lpsolve 1.3 MB, GLPK 2.3 MB, CPLEX 19 MB)


solver_x86.dll

solver_x86.so

solver_x86.jnilib

JNI Interface to solver

Solver Pack Jar

Farming

• Need to decide how much tons of wheat and/or rye toproduce.

• Rye earns 198 Euro/ton, wheat 226 Euro/ton• Rye needs 0.2 ha/ton, wheat 0.15 ha/ton• Rye needs 50 labour-units/ton, wheat 80 labour-

units/ton.• 50 ha and 5000 labour-units available• There are two barns, which can store up to 30 and 65

tons of one type of crop.• Because of EU-Regulations we have to produce exact

integer tons of both crops.


SCPSolver

Documents

Transcript of SCPSolver