basic job-shop problem using genetic algorithm with a simple example

1. Presented by :
Bhavya Singh
(9917102266)
Mentor:
Dr. Varsha Garg
(Electronics & Communications dept.)
A GENETIC ALGORITHM FOR JOB-SHOP
SCHEDULING

2. GENETIC ALGORITHM
 Based on the phenomena of natural selection/evolution.
 Works on producing a set of random solutions (population).
 Each solution in the set corresponds to a chromosome.
 Produced compete in a space where only the fittest solution survive.
 Used for optimization

3. Operators
 Reproduction- Evolves the next generation.
 Crossover- Swaps the portions of two selected chromosomes.
 Mutation- Invert/change a randomly selected gene in the chromosome.
Fitness Function
 Evaluates the fitness (profit) of a solution.

4. JOB SHOP PROBLEM
 Three Manufacturing units M1,M2 and M3.
 Each unit manufactures a different product.
 1 represents that the unit is ON (manufacturing) and 0 represents that the unit is OFF (not
manufacturing).
 The set/chromosome {1,0,1} represents that M1 and M3 are ON while M3 is OFF.
 We need to find an optimal solution which yields maximum profit, i.e.,{1,1,1}.

5. Define a fitness function.
Select a population of the solution and calculate their fitness values.
APPLYING GENETIC ALGORITHM

6. Applying Reproduction :-
 Suppose we randomly generate 500 sets of such solutions.
 Resulting population will have 2000 chromosomes.
 Among the 2000 chromosomes, the one having the maximum fitness value will be having the maximum
appearance like as follows: {0,0,1}, {0,1,0}, {1,1,0}, {1,0,1},{1,1,0}, {0,1,0},{1,1,0}, {1,0,1},…,{1,0,1},
{0,1,0},{1,1,0},{0,1,0},{0,0,1},{1,1,0},{1,1,0},{0,1,0},…,{1,0,1},{1,1,0},……. up to 2000th chromosome.

7. Applying Crossover :-
 Let’s select two solutions randomly from 2000 chromosomes
a) {1,10} and {0,1,0}
b) {1,0,1} and {1,1,0}
 Randomly choose a crossing site
a) 1st bit for pair a
b) 0th bit for pair b

8. Applying Mutation :-
 Let’s select a chromosome {0,1,0} to be mutated.
 After flipping either of the three bits, we can have the following possible chromosomes:
{0,1,1}
{0,0,0}
{1,1,0}

9. CONCLUSION
 In the end we can say that by the application of
Crossover we have reached an optimal solution for the
job shop problem.

10. REFERENCES
 Nakano, Ryohei & Yamada, Takeshi. (1991). Conventional Genetic Algorithm for Job Shop Problems.. 91.
474-479.
 Elaine Rich and Kevin Knight, 1991, Artificial Intelligence, 2nd Edition, Tata McGraw-Hill, New Delhi.

11. THANK YOU