Re: Support for constrained multiobjective optimization

[Aaron Garrett]

It supports constraints, yes, and NSGA-II is implemented already. Depending on the types of constraints you have, it may take a little extra code to get it to do exactly what you want, but it should work. I'm happy to answer specific questions about that, though.

On Thursday, November 8, 2012 2:35:15 AM UTC-6, Olumide wrote:

I'm considering learning inspyred with a view to using it to solve a constrained multiobjective optimization problem. Does inspyred support such problems?

Also, does inspyred implement NSGA-II?

Thanks,

- Olumide

[Olumide]

Sorry about that. I mean to ask if SPEA2 is implemented.

I am currently working my way though the tutorial and will get back to you with specific questions, should they arise.

[Aaron Garrett]

SPEA2 is not implemented. It's on my roadmap of things to add, but I haven't done that yet (and cannot give a timeline on it). 

Aaron Garrett, Ph.D.
Assistant Professor
Computer Science
Jacksonville State University
Jacksonville, AL  36265
agar...@jsu.edu
256-782-5364
http://mcis.jsu.edu/faculty/agarrett

On Sun, Nov 11, 2012 at 1:34 PM, Olumide <50...@web.de> wrote:

Sorry about that. I mean to ask if SPEA2 is implemented.

I am currently working my way though the tutorial and will get back to you with specific questions, should they arise.

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[Eason Chen]

Hi Aaron Garrett, 

 do you have some examples of constrained optimization problem, such as constrained linear programming problem? or some hints?

Thanks, 

在 2012年11月8日星期四UTC+8下午10时58分31秒，Aaron Garrett写道：

[Aaron Garrett]

I don't have any examples, but if you have a specific problem, I can help you make it work. And then it would become an example. :-)

Aaron Garrett, Ph.D.
Assistant Professor
Computer Science

131 Ayers Hall

Jacksonville State University
Jacksonville, AL  36265
agar...@jsu.edu
256-782-5364

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[Eason Chen]

Hi Aaron Garrett, 

 I really appreciate for your help. I have a complicated constrained  linear programming problem, and I extract a simple example as:

 

Min z=8*x1+2*x2+ 4*x3+7*x4 + 5*x5

  subject to

  -3*x1-3*x2+x3+2*x4+3*x5 <= -2

  -5*x1-3*x2-2*x3-x4+x5 <= -4

  xj =0 or 1

could you give me some codes to solve it using some tools in the Inspyred package?

Thanks in advance! 

在 2013年7月3日星期三UTC+8下午8时16分19秒，Aaron Garrett写道：

[Aaron Garrett]

OK. Here is one way to handle constraints. You can set a penalty for the individual proportional to the number of constraints that it violates (or the degree of the violation, if you prefer, but I didn't do that here).

That's what this code does. If that doesn't suit your purposes, let me know what you would rather see.

import inspyred

import random

import time

def my_generator(random, args):

    size = args.get('num_inputs', 3)

    return [random.choice([0, 1]) for i in range(size)]

@inspyred.ec.evaluators.evaluator

def my_evaluator(candidate, args):

    # Check the constraints.

    constraint_bounds = [-2, -4]

    constraint_coefficients = [[-3, -3, 1, 2, 3], [-5, -3, -2, -1, 1]]

    constraints = [sum([c * v for c, v in zip(coeff, candidate)]) for coeff in constraint_coefficients]

    failed_constraints = 0

    for constraint, bound in zip(constraints, constraint_bounds):

        if constraint > bound:

            failed_constraints += 1

            

    # Now calculate the fitness. Depending on the computational time, 

    # failed constraints may cause us to just skip this part.

    coefficients = [8, 2, 4, 7, 5]

    fitness = 0

    for c, v in zip(coefficients, candidate):

        fitness += c * v

    

    # Now, punish the candidate for any failed constraints. For the current

    # problem, the largest (i.e., worst) value for any candidate is 26, so

    # we'll make sure that our constraint penalty is larger than that.

    # (We'll make it an order of magnitude larger at 100.)

    return failed_constraints * 100 + fitness

prng_seed = int(time.time())

prng = random.Random()

prng.seed(prng_seed)

optimizer = inspyred.ec.GA(prng)

optimizer.selector = inspyred.ec.selectors.tournament_selection

#optimizer.selector = inspyred.ec.selectors.rank_selection   # <--- This is the GA's default selection scheme.

optimizer.terminator = inspyred.ec.terminators.evaluation_termination

optimizer.observer = inspyred.ec.observers.stats_observer

final_pop = optimizer.evolve(generator=my_generator,

                             evaluator=my_evaluator,

                             pop_size=2,

                             maximize=False,

                             bounder=inspyred.ec.DiscreteBounder([0, 1]),

                             max_evaluations=10,

                             tournament_size=2,

                             mutation_rate=0.1,

                             num_elites=1,

                             num_inputs=5)

final_pop.sort(reverse=True)

print(final_pop[0])

Aaron Garrett, Ph.D.
Assistant Professor
Computer Science

131 Ayers Hall
Jacksonville State University
Jacksonville, AL  36265
agar...@jsu.edu
256-782-5364

[Eason Chen]

Aaron Garrett,

  I appreciate you so much for the perfect works. You give me a good way to solve my problems, I hope I can keep touch with you for talking some issues about inspyred package. Thank you once again!

Bests,

在 2013年7月8日星期一UTC+8下午9时21分50秒，Aaron Garrett写道：

[Will Tsing]

Aaron Garrett, 

  Many thanks for your code and detailed explanations, I just wounder if we could make a step further: are there anyways to handle mixed integer nonlinear programming problems with constraints using Inspyred?

  like:

  Min z=8*x1+2*x2+ 4*x3+7*x4 + 5*x5 + (x6+ x4)**3

  subject to

  -3*x1-3*x2+x3+2*x4+3*x5 <= -2

  -5*x1-3*x2-2*x3-x4+x5 <= -4

   x6 * (3* x1 + x2+1) + 10(x4 + x5) >= 0

  xj =0 or 1(exclude x6)

  -10< x6 < 10 (float)

not sure if the is a proper question, I just modified the above examples to looks like a  mixed integer nonlinear programming problem and it is OK if some other  MINLP benchmark problems are used.

Many Thanks!

在 2013年7月8日星期一 UTC+8下午9:21:50，Aaron Garrett写道：

[Aaron Garrett]

I think you should be able to adapt the previous answer to do what you want, yes. I don't see any clear reason why that wouldn't work.

Visit this group at https://groups.google.com/group/inspyred.
For more options, visit https://groups.google.com/d/optout.

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Aaron Garrett, Ph.D.

Assistant Professor

Computer Science

Wofford College

429 North Church Street

Spartanburg, SC 29303

garr...@wofford.edu

(864) 597-4529