Polytechnic University,
Department of CIS
Computer Simulation
Spring 2003, CS 909 (1025), Tue., 6:00 - 8:15 pm, RH 702
Instructor: K. Ming Leung
In many areas of science and engineering, computer simulation and
other computational methods now have a role
equal in importance to the traditional theoretical and experimental approaches.
Even in disciplines, such as finance, management, and social sciences,
which traditionally have not been considered as highly computational in nature,
the use of simulation and other numerical methods have been steadily
growing.
The ability to compute by simulation has now become a part of the
essential repertoire of many researchers in these areas.
The course CS 909 deals with basic computer simulation techniques,
such as Monte Carlo, genetic algorithms and artificial life,
random walks and diffusion, cellular automata, neural networks, and
molecular dynamics.
Students must have at least taken the complete sequence of
introductory level mathematics courses, and have the ability
to
write computer programs in a high level computer language.
Prior knowledge in numerical analysis is not required.
Although there is no
required textbook for this course, you will find the following 2 books useful.
They have been placed on course reserve in our library.
- Simulation Modeling and Analysis, 3rd edition,
Averill M. Law and W. David Kelton (McGraw-Hill, 2000).
- A Primer for the Monte Carlo Method, by Ilya
M. Sobol (CRC Press, 1994).
The following is a tentative schedule:.
-
Portable Pseudorandom Number Generators (2 weeks)
- Linear Congruential Method
- Generalized Feedback Shift Register Method
- Mersenne Twister
- Usage of Random Numbers in Simulation - A Simple
Hit-Or-Miss Monte Carlo Method
-
Discrete Random Variables (1 week)
-
Continuous Random Variables (1 week)
-
Monte Carlo Simulations (3 weeks)
- The Hit-Or-Miss Method with Error Analysis
- The Sample Mean Method
- Nonuniform Probability Distributions
- Importance Sampling & Other Variance Reduction Techniques
- Application: Neutron Transport through Materials
-
Quasi-Monte Carlo Simulations (1 week)
- The van der Corput sequence
- The Hammersley point set
- The Halton sequence
- The skipped Halton sequence
- The random-start Halton sequence
- Genetic Algorithms & Artificial Life (2 weeks)
- Reproduction, Crossover, and Mutation
- Similarity Templates - Schemata
- Optimization via Simulation - Use of Hilbert and other
Space-Filling Curves in GA
-
Cellular Automata (2 weeks)
- One-Dimensional CA
- Modeling Traffic Flow
- High-Dimensional CA, Game of Life
-
Discrete-Event System Simulation (2 weeks)
- Simulation of Queueing Systems
- Simulation of Inventory Systems
Homework Assignments
-
Assignment 1
-
Assignment 2
-
Assignment 3
-
Assignment 4
-
Assignment 5
-
Assignment 6
25 numbers from the Halton sequence in s=5 dimensions
Lecture Notes
-
Pseudorandom Number Generators and Introduction to Computer Simulation
-
Discrete and Continuous Random Variables
-
Basic Monte Carlo Method
-
Generating Non-uniformly Distributed Random Numbers
-
Use of Variance Reduction and Importance Sampling techniques in Monte Carlo Simulation
-
Metropolis Rule in Monte Carlo Simulation
-
Use of Quasi-Random (Low Discrepancy) Sequences in Simulation
-
Cellular Automata
-
One Dimensional Cellular Automata
-
Two Dimensional Celluar Automata
-
Genetic Algorithm
Matlab program
-
Sample-Mean Monte Carlo Method to Evaluate a 5-Dimensional Integral (Assignment #4)