Dependency Algorithm - find a minimum set of packages to install

Question

I\'m working on an algorithm which goal is to find a minimum set of packages to install package \"X\".

I\'ll explain better with an example:

Answer 1

Another (fun) way to solved this issue is to use a genetic algorithm.

Genetic Algorithm is powerful but you have to use a lot of parameters and find the better one.

Genetic Step are the following one :

a . Creation : a number of random individual, the first generation (for instance : 100)

b. mutation : mutate of low percent of them (for instance : 0,5%)

c. Rate : rate (also call fitness) all the individual.

d. Reproduction : select (using rates) pair of them and create child (for instance : 2 child)

e. Selection : select Parent and Child to create a new generation (for instance : keep 100 individual by generation)

f. Loop : Go back to step "a" and repeat all the process a number of time (for instance : 400 generation)

g. Pick : Select an individual of the last generation with a max rate. Individual will be your solution.

Here is what you have to decide :

1. Find a genetic code for your individual

You have to represent a possible solution (call individual) of your problem as a genetic code.

In your case, it could be a group of letter representing the node which respect constraint OR and NOT.

For instance :

[ A E B Y ], [ A C K H ], [A E Z B Y] ...

2. Find a way to rate individual

To know if an individual is a good solution, you have to rate it, in order to compare it to other individual.

In your case, it could be pretty easy : individual rate = number of node - number of individual node

For instance :

[ A E B Y ] = 8 - 4 = 4

[ A E Z B Y] = 8 - 5 = 3

[ A E B Y ] as a better rate than [ A E Z B Y ]

3. Selection

Thanks to individual's rate, we can select Pair of them for reproduction.

For instance by using Genetic Algorithm roulette wheel selection

4. Reproduction

Take a pair of individual an create some (for instance 2) child (other individual) from them.

For instance :

Take a node from the first one and swap it with a node of the second one.

Make some adjustment to fit "or, and" constraint.

[ A E B Y ], [ A C K H ] => [ A C E H B Y ], [ A E C K B Y]

Note : that this is not the good way to reproduct it because the child are worth than the parent. Maybe we can swap a range of node.

5. Mutation

You have just to change genetic code of select individual.

For instance :

• Delete a node

• Make some adjustment to fit "or, and" constraint.

As you can see, it's not hard to implements but a lot of choice has to be done for designing it with a specific issue and to control the different parameters (percent of mutation, rate system, reproduction system, number of individual, number of generation, ...)