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Exact and heuristics algorithms

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Exercice1

• Model charging station deployement problem.

• Program the Genetic algorithm to solve it.

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Genetic algorithm: Chromosomes

• Chromosomes are used to code information.

• Example: 3 warehouses, 5 clients

W1 W2 W3 C1 C2 C3 C4 C5

1 0 1 3 2 1 1 2

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Genetic algorithm: OperatorsPopulationPopulation

SelectSelect

CrossoverCrossover

MutationMutation

Recombination

Recombination

Best solution

Best solution

Final iterati

on

Final iterati

on

Yes

No

5

Genetic algorithm: OperatorsPopulationPopulation

SelectSelect

1- Randomly generate an initial population (random chromosomes)

3-Select some chromosomes from the population as an offspring individual:

-Randomly - using stochastic method

2 -Compute and save the fitness (Objective function F) for each individual (chromosomes) in the current population

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Genetic algorithm: Operators• The crossover is done on a selected part of

population (offspring) to create the basis of the next generation (exchange information).

• This operator is applied with propability Pc

CrossoverCrossover

W1 W2 W3 C1 C2 C3 C4 C5

1 0 1 3 2 1 1 2

W1 W2 W3 C1 C2 C3 C4 C5

1 0 1 3 2 1 1 2

Father

Mother

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Genetic algorithm: Operators

CrossoverCrossover

Child 1

Child 2

W1

W2

W3

C1 C2 C3 C4 C5

1 0 1 3 2 1 1 2

W1

W2

W3

C1 C2 C3 C4 C5

1 0 1 3 3 1 2 2

W1

W2

W3

C1 C2 C3 C4 C5

1 0 1 3 3 1 1 2

W1

W2

W3

C1 C2 C3 C4 C5

1 0 1 3 2 1 2 2

Father

Mother

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Genetic algorithm: Operators• This operation is a random change in

the population. It modifies one or• more gene values in a chromosome to

have a new chromosom value in the pool.

• This operator is applied with propability Pm

MutationMutation

W1 W2 W3 C1 C2 C3 C4 C5

1 0 1 3 2 1 1 2

W1 W2 W3 C1 C2 C3 C4 C5

0 0 1 3 2 1 1 2

Current

New

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Genetic algorithm: Operators• Recombination combines the

chromosomes from the initial population and the new offspring chromosomes.

Recombination

Recombination

Final iterati

on

Final iterati

on

• Repeat a fixed number of iteration or until the solution converge to one solution (always with the best fitness) .