Constructing a custom problem in Pymoo (Picking a subset of Vehicles from a Bag)

[usmanustc]

I am trying to follow this [method (https://pymoo.org/customization/custom.html) to solve an optimization problem. I have a bag of N=100 vehicles which have certain properties. For example cost, rank, and mpg. I am looking to find k=5 subsets of vehicles that have higher mpg and rank than others. N and k can take any values.

Following the (pymoo)[https://pymoo.org/customization/custom.html], the evaluation function looks like this:

def _evaluate(self, x, out, *args, **kwargs):
    out["F"] = np.array([x["rank"], x["mpg"]], dtype=float)

Here, x has as many dimensions as many columns for vehicles. In this case, I am using rank and mpg as I want to maximize these.

The guide says to create methods including:

Sampling Crossover Mutation

I want to know how can I formulate the above problem in these functions.

Sampling: refer the link above, should I create a method that takes 5 random vehicles from bag and return these?
Crossover: I am blind to this. What should I be doing in my case?
Mutation: I don't know what to implement here.
If somebody has used pymoo, give me some hints on the above so that I can do my implementation.

Many Thanks

[cyrilpic]

You are trying to solve a subset selection problem. That means that you are looking for k indices from N. As such, your decision vector x is a list with k integers (ideally you would like to use a set instead of a list but I'm not sure that pymoo can do that), e.g. x=[10, 32, 55, 97, 98]. From that, you need to think about methods that can make changes to this list.

Sampling: randomly choose k from N.
Mutation: randomly replace one element with an index that is not yet in the list.
Crossover: given two lists, swap some elements between the lists.

I also want to point out that your evaluate method should be a bit different:

def _evaluate(self, x, out, *args, **kwargs):
    out["F"] = np.array([self.metrics["rank"][x], self.metrics["mpg"][x]], dtype=float)

where metrics is the full list from which you want to pick your subset x.

[usmanustc]

So as per theory "sort the solutions according to the Pareto dominance principle" ? Which parts of the above example need to be removed in that case or modified?

[blankjul]

You don't call an optimizer at all but use NonDominatedSorting. It is basically a totally different code compared to the above (but will give you the guaranteed optimum). If you are not familiar with the domination principle and how finding a non-dominated set of solutions works, I highly recommend: https://www.wiley.com/en-us/Multi+Objective+Optimization+using+Evolutionary+Algorithms-p-9780471873396

[usmanustc]

I get you. I understand that I need to find non-dominated solutions and then select the best ones.

Could I use Pymoo for this purpose? https://pymoo.org/algorithms/moo/nsga2.html

[usmanustc]

thanks for the book suggestion. I will check it out.

[blankjul]

You can directly use NonDominatedSorting (https://github.com/anyoptimization/pymoo/blob/main/pymoo/util/nds/non_dominated_sorting.py).
NonDominatedSorting().do(F, only_non_dominated_front=True)