Selection determines the number of offspring that an individual will produce. In
our model, the parents were selected by the tournament selection method, which
works by running several tournaments, i.e. selecting a number of individuals from
the current population at random and then selecting only the best of those individuals (with the best fitness).
Recombination is the process by which chromosomes selected from a current
population are recombined to form members of the next population. The crossover
operator is applied to two individuals, randomly paired with a user-definable
probability, cp. To avoid having violations of the equality constraints in (38.7),
we used the arithmetic crossover with the user-defined parameter α, that randomly
selects two parents, P 1 , P 2 , and breeds two children, C 1 , C 2 , which replaces the
parents in the next population.
C 1 ¼ P 1 α þ 1 À α
ð
ÞP 2
C 2 ¼ P 1 1 À α
ð
ÞþP 2 α
Mutation is used to maintain genetic diversity from one generation of a population to the next: it alters one or more gene values in a randomly chosen chromosome with a user-definable probability, mp, and produces a new genetic individual.
We used the swap mutation operator to change the sequence of genes for some
randomly chosen chromosomes. This operator works by generating two different
random numbers within the length of the chromosome that will specify the places of
the genes that will be swapped. To keep the chromosome a feasible one, the swap is
performed only between the genes that contribute to the same equality constraint
from (38.7).
Evaluation, selection, crossover and mutation forms one generation in the
execution of a GA, and after several generations, the best individual is obtained.
In cases where the problem to be solved does not have one individual solution, as is
the case in multi-objective optimization, the GA is useful for providing a number of
potential solutions at once, letting the user to choose the best one.
38.4 Numerical Experiments
In our numerical experiments we were essentially concerned with the unbalanced
inconsistent transportation problem described in Table 38.2 (called P2), but we also
considered the unbalanced consistent transport problem described in Table 38.3
(called P1), for calibration of the genetic algorithm from Sect. 38.3 and for
comparison with the Simplex-type Matlab implementation.
38 Genetic Versus Han-Type Algorithms for Maritime Transportation Problems
637
our model, the parents were selected by the tournament selection method, which
works by running several tournaments, i.e. selecting a number of individuals from
the current population at random and then selecting only the best of those individuals (with the best fitness).
Recombination is the process by which chromosomes selected from a current
population are recombined to form members of the next population. The crossover
operator is applied to two individuals, randomly paired with a user-definable
probability, cp. To avoid having violations of the equality constraints in (38.7),
we used the arithmetic crossover with the user-defined parameter α, that randomly
selects two parents, P 1 , P 2 , and breeds two children, C 1 , C 2 , which replaces the
parents in the next population.
C 1 ¼ P 1 α þ 1 À α
ð
ÞP 2
C 2 ¼ P 1 1 À α
ð
ÞþP 2 α
Mutation is used to maintain genetic diversity from one generation of a population to the next: it alters one or more gene values in a randomly chosen chromosome with a user-definable probability, mp, and produces a new genetic individual.
We used the swap mutation operator to change the sequence of genes for some
randomly chosen chromosomes. This operator works by generating two different
random numbers within the length of the chromosome that will specify the places of
the genes that will be swapped. To keep the chromosome a feasible one, the swap is
performed only between the genes that contribute to the same equality constraint
from (38.7).
Evaluation, selection, crossover and mutation forms one generation in the
execution of a GA, and after several generations, the best individual is obtained.
In cases where the problem to be solved does not have one individual solution, as is
the case in multi-objective optimization, the GA is useful for providing a number of
potential solutions at once, letting the user to choose the best one.
38.4 Numerical Experiments
In our numerical experiments we were essentially concerned with the unbalanced
inconsistent transportation problem described in Table 38.2 (called P2), but we also
considered the unbalanced consistent transport problem described in Table 38.3
(called P1), for calibration of the genetic algorithm from Sect. 38.3 and for
comparison with the Simplex-type Matlab implementation.
38 Genetic Versus Han-Type Algorithms for Maritime Transportation Problems
637