How to define a multi-objective problem for nsga2/3?

[Alan Zandie]

Hello,

I have been reading through the tutorials available for DEAP package, there are examples for nsga 2/3 where an already defined problem (named zdt1..zdt4), but I am looking for a way to define my problem instead of the code below:

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PROBLEM = "dtlz2"
NOBJ = 3
K = 10
NDIM = NOBJ + K - 1
P = 12
H = factorial(NOBJ + P - 1) / (factorial(P) * factorial(NOBJ - 1))
BOUND_LOW, BOUND_UP = 0.0, 1.0
problem = pymop.factory.get_problem(PROBLEM, n_var=NDIM, n_obj=NOBJ)

------------

I have created this below:

def MIMO(data):

    Q = data[0]

    ....my calculations here....

    return Visibility, Temperature, Velocity, Pressure, Q
     
PROBLEM = "MIMO"
NOBJ = 1
K = 10
NDIM = NOBJ + K - 1
P = 12
H = factorial(NOBJ + P - 1) / (factorial(P) * factorial(NOBJ - 1))
BOUND_LOW, BOUND_UP = 0.0, 1.0
problem = pymop.factory.get_problem(PROBLEM, n_var=NDIM, n_obj=NOBJ)
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but it says my problem "mimo" is not defined.

I am wondering if you could help me with this issue, thank you

[François-Michel De Rainville]

This part is just for the toy problems, you should remove the pymop line.

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[Alan Zandie]

Could you please expand a bit more? thank you

[François-Michel De Rainville]

pymop is a multi objective framework that provides toy problems. This line only serve to create the problem within pymop. That's where your objective function should be.

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[Warriors Defence Academy]

Sure! Here's how to define a multi-objective problem for NSGA-II/NSGA-III in short:

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✅ Steps to Define a Multi-Objective Problem:

1. Decision Variables:
   Define variables with type and bounds.
   Example: x ∈ [0, 1], y ∈ [0, 1]

2. Objective Functions:
   Define 2 or more conflicting objectives.
   Example:

   • f1(x, y) = x² + y² (minimize)

   • f2(x, y) = (x - 1)² + (y - 1)² (minimize)

3. Constraints (Optional):
   Define any rules the solution must follow.
   Example: x + y ≤ 1

4. Encoding & Evaluation:
   Represent the problem in code (e.g., DEAP, pymoo, Platypus).
   Evaluation function should return a tuple: (f1, f2)

5. Choose Algorithm:

   • Use NSGA-II for 2–3 objectives

   • Use NSGA-III for 4+ objectives (requires reference points)

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Thank You
Warriors