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).




                                                                                                            6
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.




                                                                                                              9
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?




                                                                                                            11
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.




                                                                                      13
14
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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