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 constraints over the variables, nd an assignment of values to var
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 searching the
left branch as opposed to the right branch. G
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 are cut from ten inch long mahogany staffs that Mr. Oliva
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 system
1
0
0
0
0 2 0
1 7 0
,
0 4 0
0 0 1
4
2
b = .
2
5
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 100 pounds of hot peppers. He produces two types of sauce
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 9
,b = .
A=
19
23 9 98 9
3 8
2
8 6 39 3
1 8
.
b) Show h
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
1/2 12 1/2 3 0 1
0
0
1
0 0 0
0
0
0
1
3
0
0
1
Perform th
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 of fat and 175g of proteins. A kg of bread contains 250
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 with number 1-9. You must ll in the rest of the grid to
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 players.
The goal of the game is for the code-breaker, which
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 on a certain holiday. All the girls like dierent thing
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
diseases, given a set of tests. Each test will give a pos