Advance operator and technique in Genetic algorithm

JMHM JayamahaSEU/IS/10/PS/104

PS0372

Content The low-level operators

Diploidy, Dominance Inversion and Reordering

Partially Matched Crossover (PMX). Order corssover

Multi-Objective Optimization Knowledge Based Techniques Summary References

Diploidy, Dominance When nature wants to construct a more complex or animal life to rely

upon, a more complex underlying chromosome structure is needed and this is achieved by the diploid or double stranded chromosomes

In the diploid form, a genotype carries one or more pairs of chromosomes, each containing information for the same function.

Consider a diploid chromosome structure where different letters represent different alleles (different gene function values)

Allele represents the property of a particular gene

Diploidy, Dominance (continue) Each locus of a letter represents one allele.

The uppercase and the lowercase letters mentioned above represent the alternative alleles at that position.

Originally, in nature each allele may represent different phenotypic properties. For example Q may represent gray haired gene and q may be black haired gene.

a pair of genes exists describing each function; there should be some aspect to decide which of the two values to choose because, for example, the phenotype may not have both gray haired and black

haired at the same time.

Diploidy, Dominance(continue) The basic approach for eliminating this conflict of redundancy is

through a genetic called dominance.

At a locus, it has been noted that one allele (called the dominant allele) will take the precedence over the other alternative allele (called the recessive allele).

In the above example, if it is assumed that all uppercase letters are dominant and all lowercase letters are recessive, the phenotype expressed by the example chromosome is written as,

Diploidy, Dominance(continue) The dominant gene is expressed when heterozygote (mixed, Pp→P) or

homozygote (SS→S) and the recessive genes expressed only when homozygote (tt→t).

Diploidy, Dominance(continue) Advantages

Diploid chromosomes lend advantages to individuals where the environment may change over a period of time

Disadvantages Currently harmful, but potentially useful alleles can still be maintained, but

in a recessive position

In a GA, diploidy might be useful in an on-line application where the system could switch between different states.

Inversion and Reordering Inversion operator is a primary natural mechanism to recode a

problem. In inversion operator, two points are selected along the length of the

chromosome, the chromosome is cut at those points and the end points of the section cut, gets reversed (switched, swapped).

To make it clear, consider a chromosome of length 8 where two inverse points are selected random (the points are 2 and 6 denoted by ˆ character)

On using inversion operator, the string becomes,

Inversion and Reordering(continue) The features of inversion and crossover are combined together to

produce a single operator, which lead to the development of other reordering operators. On combining inversion and crossover, the reordering operators formulated are 1. Partially Matched Crossover (PMX). 2. Order Crossover (OX). 3. Cycle Crossover (CX).

Partially Matched Crossover (PMX). In Partially Matched Crossover, two strings are aligned, and two

crossover points are selected uniformly at random along the length of the strings.

The two crossover points give a matching selection, which is used to affect a cross through position by-position exchange operations.

Consider two strings

Two crossover points were selected at random, and PMX proceeds by position wise exchanges.

Partially Matched Crossover (PMX).(continue)

In-between the crossover points the genes get exchanged i.e., the 3 and the 2, the 6 and the 7, the 5 and the 9 exchange places. This is by mapping parent B to parent A. Now mapping parent A to parent B, the 7 and the 6, the 9 and the 5, the 2 and the 3 exchange places.

Thus after PMX, the offspring produced as follows

Order Crossover (OX) The order crossover begins in a manner similar to PMX. But instead of

using point by- point exchanges as PMX does, order crossover applies sliding motion to fill the left out holes by transferring the mapped positions.

Consider the parent chromosomes,

On mapping parent B with parent A, the places 3,6 and 5 are left with holes.

Order Crossover (OX)(continue) These holes are now filled with a sliding motion that starts with the

second crossover point.

The holes are then filled with the matching section taken from the parent A. Thus performing this operation, the offspring produced using order crossover is as given below.

Multi-Objective Optimization Multi-objective optimization problems have received interest form

researches since early 1960s

In a multi-objective optimization problem, multiple objective functions need to be optimized simultaneously.

In the case of multiple objectives, there does not necessarily exist a solution that is best with respect to all objectives because of differentiation between objectives. A solution may be best in one objective but worst in another.

Therefore, there usually exist a set of solutions for the multiple-objective

case, which cannot simply be compared with each other.

Multi-Objective Optimization(continue)

For such solutions, called Pareto optimal solutions or non-dominated solutions, no improvement is possible in any objective function without sacrificing at least one of the other objective functions.

Thus by using the concept of Pareto-optimality we can find a set of solutions that are all optimal compromises between the conflicting objectives. Pareto-optimality is a concept used economics, game theory, etc.

In the past few years, there has been a wide development in applying genetic algorithms to solve the multi-objective optimization problem, known as evolutionary multi-objective optimization or genetic multi-objective optimization.

Multi-Objective Optimization(continue)

The population-to-population approach is beneficial in the exploration of Pareto-optimal solutions.

The main issue in solving multi-objective optimization problems by use of genetic algorithms is how to determine the fitness value of individuals according to multiple objectives.

Knowledge Based Techniques While most research has gone into GAs using the traditional crossover

and mutation operators, some have advocated designing new operators for each task, using domain knowledge.

This makes each GA more task specific (less robust), but may improve performance significantly.

GA is being designed to tackle a real world problem, and has to compete with other search and optimization techniques, the incorporation of domain knowledge often makes sense.

Domain knowledge may be used to prevent obviously unfit chromosomes,or those, which would violate problem constraints, from being produced in the first place.

Knowledge Based Techniques(continue)

This avoids wasting time evaluating such individuals, and avoids introducing poor performers into the population.

For example, a researcher designed analogous crossover for his task in robotic trajectory generation. This used local information in the chromosome (i.e., the values of just a few

genes) to decide which crossover sites would be certain to yield unfit offspring.

Domain knowledge can also be used to design local improvement operators, which allow more efficient exploration of the search space around good point

It can also be used to perform heuristic initialization of the population, so that search begins with some reasonably good points, rather than a random set.

Knowledge Based Techniques(continue)

The various methods for combining problem specific information with genetic algorithm are as follows: Hybrid schemes Parallel computers.

Hybrid Schemes

In hybrid schemes GAs are used to get close to optimum value, then conventional optimization schemes like greedy search, gradient search or stochastic hill climbing may be used to become closer to optimum value.

The hybrid scheme can be represented using scheme as shown in Figure

Hybrid Schemes (continue) Thus from Figure , it can be noted that the genetic algorithm sorts out

peak and the local search techniques are used for hill climbing. Considering greedy heuristic crossover for Traveling salesman problem, if chromosomes are permutations of city numbers, then normal crossover may produce infeasible chromosomes. This is done by, Start at a random city X and go to the closest city to X using the parent’s

tours;repeat.

Parallel Computers Using parallel computers in Genetic Algorithms, master/slave

operation is performed. Master does selection and mating and slaves evaluated fitness of new

chromosomes. Master waits for all the slaves to finish or master can hand out new

work as each slave finishes. Thus on a parallel machine the conventional optimization can be

done on each species on its own CPU. This is shown in next figure.

Summary The low-level operators

Diploidy, Dominance Multi-Objective Optimization Knowledge Based Techniques

References

Introduction to Genetic Algorithms by S.N.Sivanandam · S.N.Deepa (page 83 – 104)