GAMS: A POWERFUL OPTIMIZATION TOOL AND ITS INTERFACE TO MATLAB - - PowerPoint PPT Presentation

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
• ptimization 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 𝑂 networks with overlapped coverage and 𝑁 users
• Out of 𝑁 users, we have:

𝑁1 users can get service (bandwidth) using only single-network 𝑁2 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 + 𝑦𝑜𝑛𝑐𝑜𝑛 − 𝑞𝑜𝑛𝑦𝑜𝑛𝑐𝑜𝑛}

𝑛 𝑜

S.t. 𝐶𝑛𝑗𝑜,𝑛 ≤ 𝑦𝑜𝑛𝑐𝑜𝑛 ≤ 𝐶𝑛𝑏𝑦,𝑛

𝑜

∀𝑛 𝑦𝑜𝑛 = 1, 𝑦𝑜𝑛 = 0,1 , ∀𝑛 ∈ 𝑁1

𝑜

𝑦𝑜𝑛 = 1, ∀𝑛 ∈ 𝑁2 Assignment variable Binary Bandwidth allocation variable Positive Priority parameter Matrix  Table Total max. and

• min. required

BW Vector Problem  MINLP 𝑦𝑜𝑛𝑐𝑜𝑛 ≤ 𝐷𝑜

𝑜

∀𝑜 Capacity of each network Vector

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GAMS Input File

Sets Data Variables Equations Model & Call Solver 𝑂, 𝑁 𝑞𝑜𝑛 Table, 𝑔 Scalar 𝐷𝑜, 𝐶𝑛𝑏𝑦,𝑛, 𝐶𝑛𝑗𝑜,𝑛  parameters 𝑦𝑜𝑛  Binary 𝑐𝑜𝑛  Positive Objective function and constraints (equalities and inequalities) MINLP , solver = BARON

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𝑨  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.

• nly 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 𝐶 = 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

• n 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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