Linear Programming Motivation
CS 149 Sta September 11, 2007
The slides dene a combinatorial optimization problem as: Given a set of variables, each associated with a value domain, and given constraint
Least Discrepancy Search
CS 149 Sta
November 17, 2009
When performing a branch and bound search, imagine we had a heuristic that
could tell us the probability p > 0.5 of nding the optimal node by sear
CS149
Introduction to Combinatorial Optimization
Homework 1
Problem 1
Formulate the Knapsack Problem mathematically.
Problem 2
The company "Olivander, Inc." produces several lengths of wands. Wands ar
CS149
Introduction to Combinatorial Optimization
Homework 4
Problem 1
Provide all the solutions (in the vector
Ax = b, when
3 0 2
6 0 1
A=
5 1 0
4 0 0
form that we did in class and recitation) of the
CS149
Introduction to Combinatorial Optimization
Homework 3
Problem 1
Your good amigo, who has a small business creating sauce for Tortillas, asks for your advice. He
has 300 pounds of tomatoes and 10
CS149
Introduction to Combinatorial Optimization
Problem 1
a) Show how the LP
cT x
min
s.t.
Ax = b
x 0.
can be written as
min
s.t.
T
c x
A x b
x 0.
for the matrices
14
1 77 41 3 27 4
18
8 2 9 8 29
CS149
Introduction to Combinatorial Optimization
Homework 5
Problem 1
Here we will see an example where Blands rule is needed to avoid cycles. We are given the tableau:
3/4 20 1/2 6 0 0
1/4
8
1 9 1 0
CS149
Introduction to Combinatorial Optimization
Homework 6
Problem 1
We want to buy some quantity of meat and bread, in order to satisfy some dietary needs. A kg of
meat contains 100g of carbs, 100g
CS149
Introduction to Combinatorial Optimization
Homework 7
Problem 1
We are given the following linear program:
max
s.t.
x1 4x2 3x3 3x4
x1 x2
+x4
x1 x2 x3 x4
x1 +x2
x4
x1 +x2 +x3 +x4
x1 , x2 , x3 , x
Sudoku
1
In this assignment, you will be writing a program that can solve Sudoku puzzles, using the
ILOG constraint programming library. Sudoku puzzles consist of a 9x9 grid with a few cells lled
in w
Mastermind
1
In this assignment, you will be writing a computer player for the game of Mastermind, using the
ILOG constraint programming library. Mastermind is traditionally a board game for two playe
CS149
Introduction to Combinatorial Optimization
Homework 10
Problem 1
There are 5 girls in a long row in math class.1 Each girl has a favourite chocolate bar, colour, pet,
hobby, and would like to go
Test Cover
1
In this project you are going to deal with the Test Cover Problem. A possible domain of the
problem is the following: Assume that you want to be able to distinguish between a number of
di