Genetic Algorithm in Metaheuristics: A Technical Guide

METAHEURISTICS
Genetic Algorithm

Population Based Techniques (PBT)
•A Population Based Technique (PBT)can be seen as an iterative process
starting with an initial population P0including Nfeasible solutions. x* is
the best solution of the population P0.
•At each iteration ( generation):
- During a collective process, the solutions of the current population are
compared and combined to generate new offspring-solutions inheriting the
prevaling characteristics of the parent-solutions.
- Then the new offspring-solutions evolve individually according to an
individual process.
- The best solution x* is updated.
- Finally a new population of size N is generated.
•The procedure continues until some stopping criterion is satisfied.

Problem used to illustrate
•General problem
min f(x)
x єX
•Assignment type problem: Assignment of resources j to activities i
min f(x)
Subject to ∑1≤ j≤ m xij = 1 1≤ i ≤ n
xij = 0 or 1 1≤ i ≤ n, 1≤ j ≤ m

Encoding the solution
•The phenotype form of the solution x є ℝnis encoded (represented) as a
genotype form vector z є ℝm(or chromozome) where m may be different
from n.
•For example in the assignment type problem:
let xbe the following solution: for each 1≤ i ≤ n,
xij(i)= 1
xij = 0 for all other j
x є ℝnxm can be encoded as z є ℝnwhere
zi = j(i)i= 1, 2, …, n
i.e., zi is the index of the resource j(i) assigned to activity i

Genetic Algorithm (GA)
•Population based algorithm
•At each iteration (generation) three different operators are first applied to
generate a set of new (offspring) solutions using the N solutions of the
current population:
selection operator: selecting from the current population parent-solutions
that reproduce themselves
crossover (reproduction) operator: producing offspring-solutions from each
pair of parent-solutions
mutation operator: modifying (improving) individual offspring-solution
•A fourth operator (culling operator) is applied to determine a new
population of size Nby selecting among the solutions of the current
population and the offspring-solutions according to some strategy