Clarification on Constraints and Penalties

[yhamadi75]

Hi everyone,

I’m working on a mono-objective optimization problem with penalties based on constraint violations. Currently, the evaluate function calculates the objectives, then calls __evaluate_constraints, which sets penalties. The full penalty score is stored in solution.constraints[0].

However, this doesn’t seem to guide the search as expected. Would it help to declare one constraint for each variable (I have 5–30 variables) and update solution.constraints[i] based on violations for each associated variable? This might give more precise guidance than a single penalty score.

Also, I’ve found that treating penalties as a second objective works better, achieving a penalty of 0 while keeping good values for the first objective.

Thanks for your support!

[ajnebro]

Hi.
If you add a large number of constraints that could lead to many unfeasible solutions, which would make more difficult the search.

Have you defined the constraints as inequalities according to the scheme expression >= 0.0?

Antonio

[yhamadi75]

Hello Antonio,
In my settings, each constraint can be transformed as inequalities >=0.
I have done the following:

• the problem is mono objective with k constraints.
• evaluate() computes the current solution objective then calls __evaluate_constraints
• In __evaluate_constraints, an unsat constraint c gets a negative penalty: solution.constraints[c] = -penalty.

I am using NSGAII, with the dominance_comparator:
algorithm = NSGAII(
problem=problem,
population_size=100,
offspring_population_size=100,
mutation=PolynomialMutation(probability=1.0 / problem.number_of_variables(), distribution_index=20),
crossover=SBXCrossover(probability=1.0, distribution_index=20),
termination_criterion=StoppingByEvaluations(max_evaluations=max_evaluations),
dominance_comparator=DominanceWithConstraintsComparator(),
)
As a result, invalid solutions are filtered out, but in the end the objective value is not fantastic. This is compared against a bi-objective NSGAII which minimizes both penalties and objective.

How is the" solution.constraints[c]" exploited by the DominanceWithConstraintsComparator()? Is there a way to access other comparators with NSGAII or to parameterize this one? Any understanding of constraints handling would be helpful.

Last, would it be helpful to have unsat constraints get a negative penalty proportional to their unsat degree? For now they are just "counted" with "-1".

What would be the simplest way, maybe through an "observer" to know the proportion or non-viable solutions in each population?

Thanks for your support!