Optimization Problem with Equal and Inequal constraints

[a3725...@gmail.com]

Hi there,
I'm a beginner of Inspyred, had very limited knowledge about GA(use MATLAB before) and want to use this lovely lib to construct an enginnering numerical optimization problem which may be described as follows:

Variables: x[0], x[1], x[2] .... x[n] (n > 10)

Object Funcion: [Single Objective Problem]
Min_Func(x):
'Seems like a black box function'
return Magic_Value

Inequal Constraint:
I_Constraint1(x):
'Seems like a black box function'
return Magic_value_which_must_larger_than_1

I_Constraint2(x):
'Seems like a black box function'
return Magic_value_which_must_larger_than_2
....Some similar Function...

Equal Constraint:
E_Constraint1(x):
'Seems like a black box function'
return Magic_value_which_must_equal_zero

I'm a little bit confused by the code structure of Inspyred, I see that there are some benchmarks like Rastrigin and Branin Hoo Class to be an example of Optimization and run them successfully, but I haven't seen any method to build equal or inequal constraint. What is the right way to build such a problem ?

Many Thanks

[Aaron Garrett]

Without knowing the specifics, I would guess you'd want to use penalties for those constraints. Here's a goofy example:

import inspyred

import random

import time

def Min_Func(x):

    'Seems like a black box function'

    Magic_Value = sum(x)

    return Magic_Value

def I_Constraint1(x):

    'Seems like a black box function'

    Magic_value_which_must_larger_than_1 = sum([even for even in x[0::2]])

    return Magic_value_which_must_larger_than_1

def I_Constraint2(x):

    'Seems like a black box function'

    Magic_value_which_must_larger_than_2 = x[-1]

    return Magic_value_which_must_larger_than_2

def E_Constraint1(x):

    'Seems like a black box function'

    Magic_value_which_must_equal_zero = x[-1] - x[0]

    return Magic_value_which_must_equal_zero

def my_generator(random, args):

    n = args.get('n', 11)

    return [random.uniform(0, 3) for _ in range(n)]

    

@inspyred.ec.evaluators.evaluator

def my_evaluator(candidate, args):

    penalty = [10, 15, 50]

    minfun = Min_Func(candidate)

    i1 = I_Constraint1(candidate)

    i1 = 0 if i1 > 1 else abs(1 - i1)

    i2 = I_Constraint2(candidate)

    i2 = 0 if i2 > 2 else abs(2 - i2)

    e1 = abs(E_Constraint1(candidate))

    return sum([c * v for c, v in zip([1] + penalty, [minfun, i1, i2, e1])])

    

prng = random.Random()

prng.seed(time.time())

ec = inspyred.ec.EvolutionaryComputation(prng)

ec.selector = inspyred.ec.selectors.tournament_selection

ec.variator = inspyred.ec.variators.gaussian_mutation

ec.replacer = inspyred.ec.replacers.generational_replacement

ec.terminator = inspyred.ec.terminators.evaluation_termination

final_pop = ec.evolve(generator=my_generator,

                      evaluator=my_evaluator,

                      pop_size=100,

                      maximize=False,

                      n=11,

                      bounder=inspyred.ec.Bounder(0, 3),

                      max_evaluations=20000,

                      mutation_rate=0.1,

                      num_elites=1)

                      

# Sort and print the best individual, who will be at index 0.

final_pop.sort(reverse=True)

print(final_pop[0])

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--

Aaron Garrett, Ph.D.

Associate Professor

Computer Science

131 Ayers Hall

Jacksonville State University

Jacksonville, AL  36265

agar...@jsu.edu

256-782-5364

[Will Tsing]

Really thanks Garrett,

    Very detailed and helpful example.

    So here's one more kind of stupid question:

        How to make an exist parameters (baseline reference of an opt problem) be an individual at start ?

[Aaron Garrett]

Pass it in as a seed.

baseline_candidate = [8, 6, 7, 5, 3, 0, 9]

...

ec.evolve(my_generator,

          my_evaluator,

          pop_size=100,

          seeds=[baseline_candidate],

          ...) 

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