Practice homework for Differential Evolution for Theory Students
1. Differential Evolution
You are trying to minimize a three dimensional function f(x1,x2,x3) with Differential
Evolution with a population of size 20. Let
The parent vector is
(3,5,7). Assu
HW#10 Solutions 2010
Points possible: 20
Problem 1: DES (not graded)
The derivation of this equation is as follows:
Problem 2: Symbolic Regression (not graded)
(a) The parse tree can be represented mathematically as follows:
Performing simple algebra, you
Points possible: 20
Problem 1: (5 points)
Part (a) (2 points)
There are 7 non-dominated solutions
Tradeoff curve is non-convex.
Part (b) (3 points)
A student is considering four schools for graduate studies:
Objective is to minimize f(A), f(B), f(C) and f
HW 9 Solutions Fall 2010
Points possible: 20
1. SA Theory
We will use the theory of Markov chain to analyze the Metropolis algorithm as defined
below. Metropolis is the name for simulated annealing algorithm running at a fixed
temperature. Please not e th
Points possible: 10
1.
Consider the problem given in the figure below.
Let N(Si) = Si plus all nodes connected by an edge; therefore N(S1) =cfw_ S1, S2, S3.
Your objective is to minimize the cost, which is given inside the circles for each S j.
For each o
HW #7 Solutions Fall 2010
Total points possible: 20
1. Relative performances of SA, DDS and GA on the bump function.
Recall the bump function from HW 5 with n = 20:
(a) (4 points) Implement the SA algorithm to maximize the 20-variable bump function. In
th
HW 6 Solutions Fall 2010
Points possible: 10
Statistical Comparisons: The table below shows the objective function value for the
best solution in each trial for three different algorithms applied to the same problem:
Trial
1
2
3
4
5
6
7
8
9
10
Mean
Std. D
HW 5 Solutions 2010
Points possible: 20
1. A 5-bit binary GA with a population size of 4 is used to solve a maximization
problem. At generation zero the following information is available to you:
Member
String
Fitness
1
10001
20
2
11001
10
3
00101
5
4
011
HW 4 Solution Fall 2010
Total points possible: 20
1. Satisfiability Formulation:
Ann, Brad, Cindy, Dan, Eugene and Frank have to get back to their apartment from a
club. They have exactly one car, and not all can fit into the car. Anyone not in the car wi
HW3 solutions Fall 2010
Points possible: 20
1. Maximize the following function:
F(s1,s2) = 10^9-(625-(s1-25)^2) *(1600-(s2-10)^2)*sin(s1)*pi/10)*sin(s2)*pi/10)
The global maximum is F(125,115) = 1088359375.
a. (6 points, 1 for each algorithm) Write a MATL
HW2 Solutions Fall 2010
Total points possible: 20
1. SA Parameter Selection when cost function range = (MaxCost and MinCost) are known:
a) (1 pt) If Mincost is taken as a lower bound on Cost in the search space, and MaxCost the upper
bound, assume you kno
HW1 Solutions
Total points possible: 20
Simple optimization algorithms: We wish to minimize the following simple onedimensional cost function:
Costs(s) = (400 (s 21)2) * sin(s*pi/6)
Constraints: s integer-valued, 0 s 500
Part(a): (2 points)
Write a MATLAB
Name: _
Heuristic Methods for Optimization Final 2010 (Non-theory section)
Read and sign the pledge before beginning the exam:
Academic integrity is expected of all students of Cornell University at all times, whether in the
presence or absence of members
Name: _
Signature: _
Theory
CEE 5290/COM S 5722/ORIE 5340
Heuristic Methods for Optimization Fall 2009
Final 12/10/2009
(Show your work so the grader can read and understand what you have done. Clearly state any
assumptions you make and give any equations