# Genetic Algorithms by yaofenji

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IEEM 5119           Genetic Algorithms
Final Exam (January 12, 2006)
close books, close neighborhood, and open mind                       Total:

ID:                                    Name:

1.              (40%)     2.              (5%)      3.              (5%)     4.                 (5%)

5.              (5%)     6.               (10%),    7.             (10%),     8.            (10%),

40%
1. Answer the following questions: (3% each)
(1-1) How to handle the infeasibility (violation of constraints) in genetic algorithms?

(1-2) Mixed sampling.

1
(1-3) Arithmetic operators (for nonlinear programming problem).

(1-4) Selection pressure. Why do we consider selection pressure in genetic algorithms?

2
(1-5) Scaling method. Why do we consider scaling methods in genetic algorithms?

(1-6) Give the solution procedure of simulated annealing? Why can it escape from local optimum?

3
(1-7) Give the solution procedure of Tabu search? Why can it escape from local optimum?

(1-8) What is the crowding strategy? What is the purpose? Give two strategies.

4
(1-9) Find the spanning tree with Prüfer number (6, 3, 3, 5, 2).

(1-10) Roulette wheel selection.
What is the purpose of roulette wheel selection?
What is the disadvantage of roulette wheel selection?

5
5%
2. Consider the following bin packing problem.
object           1       2       3       4      5       6            7   8      9      10      11      12
weight wj        7       5       6       6      2       5            3   4      3       3       7      3
capacity                                                    c = 10

(2-1)    Find a solution by using Best-Fit heuristic algorithm.
(2-2)    Give a suitable fitness function and evaluate the fitness value of the solution given in (2-1).

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5%
3. Consider the following undirected traveling salesman problem with the following network weights.

For chromosomes 4573216 and 3764512, perform heuristic crossovers. (If there is a tie, chose the
edge with the lowest index.)

7
5%
4. Encode the following two-dimensional bin packing solution.

8
7
5
1
6
3
2                   4

8
5%
5. For the three-row machine layout problem, the distance matrix and the clearance between machines is

0   1   1   1   2   1   2                  2                  2
                                                                
1   0   1   1   1   1   1 ,                2 ,                2 .
                                                                
1   1   0   1   1   1   2                  2                  2
[d ij ]  1   1   1   0   3   1   2     [d 10 ]     2     [d 60 ]     2
                                                                
2   1   1   3   0   2   2                  2                  2
                                                                
1   1   1   1   2   0   1                  2                  2
                                                                
2   1   2   2   2   1   0                  2                  2

Machine Sizes
Machine i       Dimension (li  bi)
1                  12
2                  22
3                  32
4                  22
5                  31
6                  32
7                  33

Give a chromosome representation and its machine layout.

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10
10%
6. Consider the following network.

7           d       9
b               5                    f
8
1                                        4
a                       c
3       2               6                    g
10
h                       e
5

(6-1) Explain the ant cycle algorithm for solving the traveling salesman problem.
(6-2) Let the initial pheromone be c0. Find the transition probability Pcd(t), Pce(t) for the arcs (c, d), and
(c, e) for t = 7 and t = 12.
(6-3)   What is the MMAS (Max-min Ant System)? How to implement MMAS in Traveling Salesman
Problem? Why do we use MMAS?

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12
10%
7. Design a genetic algorithm for the Quadratic assignment problem. For example,

Explain the chromosome representation, crossover operation, mutation and selection.
(7-1) chromosome representation.
(7-2) crossover operation.
(7-3) mutation.
(7-4) evaluation of chromosome selection rule.

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10%
8. Consider the following nonlinear programming problem.

min    f ( x1 , x 2 )  ( x1  2) 3  ( x 2  5) 2
s.t.    g1 ( x1 , x 2 )  1000 x1  2350 x 2  1  0
x12  x2
g 2 ( x1 , x 2 )          2 1 0
100 45
g 3 ( x1 , x 2 )  5 x1 x 2  x12  3x 2  7
3

Design a hybrid genetic algorithm with directional-based operators. You should explain
(8-1) chromosome representation;
(8-2) fitness function and selection rule;
(8-3) crossover operation, mutation operation;
(8-4) control parameters.

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