GAMS: A POWERFUL

OPTIMIZATION TOOL AND ITS

INTERFACE TO MATLAB

Muhammad Ismail

Outline

Introduction

GAMS Input File

GAMS Output

MATLAB Interface

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Introduction

- GAMS = General Algebraic Modeling System

- Model linear, nonlinear, and mixed integer

optimization problems

- GAMS can be downloaded from its home page:

http://www.gams.com/

- Without a valid GAMS license, GAMS will operate as

a free demo with limitations on number of constraints

and variables [GAMS license is placed, when

available, in the GAMS directory]

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GAMS Structure and MATLAB Interface

GAMS Input File

(name.gms)

GAMS Output File

(name.lst)

GAMS

Compilation

Optimization

Solver

MATLAB

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Outline

Introduction

GAMS Input File

GAMS Output

MATLAB Interface

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GAMS Input File Structure

Sets

Data

Variables

Equations

Model & Call Solver

Correspond to indices in you

problem

Can be: parameters, tables,

and scalar

Can be: free (-∞,+∞), +ve, -ve,

binary, integer

Equalities and inequalities

LP, NLP, MIP, MINLP

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Problem Example

- Consider 𝑁 networks with overlapped coverage and 𝑀 users

- Out of 𝑀 users, we have:

𝑀1 users can get service (bandwidth) using only single-network

𝑀2 users can get service (bandwidth) using all available networks,

i.e. multi-homing

- Obj.: Find network assignment for single-network users and

bandwidth allocation for both single-network and multi-homing

users which maximizes some utility function

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Mathematical Formulation

Max {log 1 + 𝑥𝑛𝑚𝑏𝑛𝑚 − 𝑝𝑛𝑚𝑥𝑛𝑚𝑏𝑛𝑚}𝑚𝑛

S.t. 𝐵𝑚𝑖𝑛,𝑚 ≤ 𝑥𝑛𝑚𝑏𝑛𝑚 ≤ 𝐵𝑚𝑎𝑥,𝑚𝑛 ∀𝑚

𝑥𝑛𝑚 = 1, 𝑥𝑛𝑚 = 0,1 , ∀𝑚 ∈ 𝑀1𝑛

𝑥𝑛𝑚 = 1, ∀𝑚 ∈ 𝑀2

Assignment variable

Binary

Bandwidth allocation variable

Positive

Priority parameter

Matrix Table

Total max. and

min. required

BW

Vector Problem MINLP

𝑥𝑛𝑚𝑏𝑛𝑚 ≤ 𝐶𝑛𝑛 ∀𝑛

Capacity of each network

Vector

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GAMS Input File

Sets

Data

Variables

Equations

Model & Call Solver

𝑁,𝑀

𝑝𝑛𝑚 Table, 𝑓 Scalar

𝐶𝑛, 𝐵𝑚𝑎𝑥,𝑚, 𝐵𝑚𝑖𝑛,𝑚 parameters

𝑥𝑛𝑚 Binary

𝑏𝑛𝑚 Positive

Objective function and constraints

(equalities and inequalities)

MINLP, solver = BARON

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𝑧 free

GAMS Input File Cont.

Set declaration

End Set declaration

Sets names

Comments

Sets members

1. Sets:

2. Data:

Table declaration Table name Domains = rows and columns

Columns = same as M

Rows = same as N Data End Table

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GAMS Input File Cont.

2. Data Cont.: Parameters

Declaration

Parameters

Names

And

Domain

Data

End

Parameters

Declaration

Scalar

Declaration

Scalar Name

Scalar Value End

3. Variables:

Declare

Variables Obj. fn. Value BW & Assign.

Variables types

z = free by default

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GAMS Input File Cont.

4. Equations:

Declare Equations

End Equations

Equations

Names and

Domain =

≤

≥

Condition:

Apply this only

for M = 1:3, i.e.

only for multi-

homing users

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GAMS Input File Cont.

4. Model & Call Solver:

Problem Type Solver Name

Problem Modeling

Maximize obj. fn.

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GAMS Input File Cont.

Problem type

& Solver Sets

Data

Variables

Equations

Model & Solve

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Outline

Introduction

GAMS Input File

GAMS Output

MATLAB Interface

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GAMS Outputs

Run your Model

Name of

my GAMS

input file

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GAMS Outputs Cont.

Listing file

Check the

results of your

variables

B is a Matrix

𝐵 =0.101 … .0.411 … .

Rows =

Networks

Columns = Users

Add bounds

Necessary for BARON to guarantee global optimality

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GAMS Outputs Cont.

Double click on error gives you

its location in your code

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Outline

Introduction

GAMS Input File

GAMS Output

MATLAB Interface

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MATLAB Interface

Why?

- Test how performance changes with some parameters, e.g.

how does bandwidth allocation changes with number of users?

- If you have a simulation on MATLAB and part of your MATLAB

code needs to solve a complex optimization problem

- Better view of your results Matrix form, or a plot

GDX Utilities GAMS Data Exchange

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MATLAB Interface Cont.

Step 1: Update MATLAB Path to Include GAMS Directory:

MATLAB: File > Set path > Add folder

Browse

Add

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MATLAB Interface Cont.

Step 2: Update System Variables to Include GAMS Directory:

Computer: Right click > Properties > Advanced system settings

Environment Variables Edit and Type GAMS Path

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MATLAB Interface Cont.

Step 3: Modify your GAMS Input File:

No members

No Values

Comes from MATLAB

1. Open a file tstdat.gdx: “gdxin

filename” tstdat created by MATLAB

2. Load set members and parameters

values from this file

3. Close the file: “gdxin”

Put the variables you want to read

on MATLAB in file tstsol.gdx ;

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MATLAB Interface Cont.

Step 4: MATLAB File:

A. Create MATLAB function: inputs = set members and parameters

data, outputs: problem variables

B. Define Sets

Same as in my GAMS input file

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MATLAB Interface Cont.

C. Define Parameters

Vector

Scalar Table

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MATLAB Interface Cont.

D. Write Values in tstdat.gdx

Write function

E. Run the GAMS Input File

Avoid crash

with loops

Function: Run

GAMS input file

Name of my

GAMS input file

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MATLAB Interface Cont.

F. Read GAMS Results on MATLAB

My GAMS Variables

Read function

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MATLAB Interface Cont.

Define sets

Define

Parameters

Write set members and

parameters values Run GAMS input file

Read GAMS results

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MATLAB Interface Cont.

G. Save GAMS Input File and MATLAB function on Same Directory

H. On MATLAB Command Window

Input

Data Run GAMS and Read Results

Results

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MATLAB Interface Cont.

Also, I can make a for loop in MATLAB on one of the parameters and

fix other parameters to study some performance and plot results on

MATLAB

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Summary

Introduction

GAMS Input File

GAMS Output

MATLAB Interface

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