1. Yu-Chi Ho Jonathan T. Lee Harvard University Sep. 7, 2000
Genetic Algorithm
Yu-Chi Ho
Jonathan T. Lee
Harvard University
Sep. 7, 2000
Version: 3.1
Date:

2. Outline
Intuition
The Algorithm
Issues
References

3. First Genetic Algorithm

4. Intuition
Based on the theory of evolution: survival of the fittest, “good” parents produce “good” children
First introduced by John Holland (1975)

5. Brief Description Code the designs as chromosomes
A population-based model that produces new designs through “reproduction”
A simulated “evolution”
First, a coding scheme need to be decided to encode the designs as chromosomes. Then, a population of designs are produced and a simulated “evolution” is run. N

6. Example Traveling Salesman Problem
A design/chromosome, the traveling order of the cities: [a b c d f e] a b
Assume for the moment, we have a traveling salesman problem with 6 cities. One possible route of traveling of all cities is [a b c d f e]. f c e d N

7. The Algorithm Step 0: Randomly generate an initial population.
Step 1: Select parents and “reproduce” the next generation
Step 2: Evaluate the fitness of the new generation
Step 3: Replace the old generation with the new generation
Step 4: Repeat step 1 though 3 till iteration T
T is predefined by the user. N

8. Selection
Designs with a better fitness value have a better chance to be chosen as a parent
To insure that the good “information” from the good parents is being passed onto the next generation
The literature, sometimes, makes a distinction between performance value and fitness value. Performance value is the output value from the performance criterion of a particular design in a problem. The performance criterion is a given in the optimization problem at hand. The fitness value, often, is a transformation of the performance value. For example, the fitness value of a particular design could be the performance value of that design normalized by the average performance values of the designs in that generation. If we are minimizing, all the designs with a fitness value that is less than 1, better than the average, will have a better chance of being selected as a parent for the next generation. N

9. Reproduction Cross-over
Pick the parents [a b c d e f] and [b c d a f e]
Pick the cross-over point [a b c d | e f] and [b c d a | f e]
Reproduce [a b c d e f]  [b c d a e f] [b c d a f e]  [a b c d f e]
Correction if necessary
Sometimes, the reproduction by cross-over would result in a designs that is infeasible. Thus, a correction step is necessary. In this example, the offspring are feasible, e.g., all the city appears once and only once. Therefore, it is not necessary. N

10. Reproduction (cont.) Mutation Pick the parent [a b c d e f]
Pick the mutation point and value [a b c d e f]: e  c
Reproduce [a b c d e f]  [a b c d c f]
Correction if necessary [a b c d c f]  [a b e d c f]
Sometimes, the reproduction by mutation would result in a designs that is infeasible. Thus, a correction step is necessary. In this example, the offspring is not feasible, e.g., the city c appeared twice. In order to correct that, the originate c was changed into e. N

11. Issues Pros: Cons: Requirement: Robust
What is the best way to encode the designs?
Requirement:
Evaluation function must be relatively fast
Once the original problem is encoded, the process of GA seldom depends on
the structure of the problem. Thus it is robust to the structure.
But different codes vary the efficiency of the calculation sharply.

12. References
Whitley, D., “A Genetic Algorithm Tutorial,” Statistics and Computing, Volume 4, pp , 1994.
Holland, J., Adaptation in Natural and Artificial Systems, University of Michigan Press, 1975.
Heitkötter, J. and D. Beasley (Eds.), The Hitch-Hiker's Guide to Evolutionary Computation, <