Genetic Algorithms  Advanced Topics
Tutorial on genetic algorithms
20201120 01:06:05
Genetic Algorithms  Advanced Topics
In this section, we present some advanced topics on genetic algorithms. A reader looking for a simple introduction to GA may choose to skip this section.
Constrained optimization problems
Constrained optimization problems are the optimization problems in which we must maximize or minimize an objective function value subject to certain constraints . Therefore, not all results in the solution space are achievable, and the solution space contains achievable regions as shown in the following image.
In such a scenario, the crossing and mutation operators could give us some unachievable solutions. Therefore, additional mechanisms must be used in the GA to traiter constrained optimization problems.
Some of the more common methods are 

Use penalty functions which reduce the Matching unrealistic solutions, preferably such that the match is reduced in proportion to the number of constraints violated or the distance from the feasible region.

Use repair functions that take an unworkable solution and modify it so that the violated constraints are satisfied.

Do not let impossible solutions at all enter the population.

Use a special representation or decoder functions which ensure the feasibility of the solutions.
Basic Theoretical Background
In this section, we will discuss the scheme and theorem of the NFL as well as the block hypothesis of construction.
Theorem ofschema
Researchers have tried to understand the basic problem behind how genetic algorithms work, and Holland's schema theorem is a step in that direction. During the year,
In this section, we will not delve into the mathematics of the Schema Theorem, rather we try to develop a basic understanding of what the Schema Theorem is. The basic terminology to know is as follows 

A Schema is a "template ". Formally it is a string over the alphabet = {0,1, *},
where * doesn't care and can take any value.
Therefore, * 10 * 1 could mean 01001, 01011, 11001 or 11011
Geometrically, a diagram is a hyperplane in the solution search space.

The order of a pattern is the number of fixed positions specified in a gene.
Schema theorem states that this schema with above average physical form, short definition length and lower order is more likely to survive crossing and mutation.
Building Blocks Assumption
Building Blocks are low order, short length schematics of definition wi e the average physical form given above The building blocks hypothesis says that these building blocks serve as the basis for the success and adaptation of GA in GA as it grows.ogression by successively identifying and recombining these "building blocks".
No Free Lunch Theorem (NFL)
Wolpert and Macready published an article in 1997 called "No Free Lunch Theorems for Optimization. " He basically states that if we do the averaged over the space of all possible problems, then all nonrevisiting black box algorithms will exhibit the same performance.
This means that the more we understand a problem, our GA becomes more specific to the problem and performs better, but it compensates for this by performing poorly for other problems.
GAbased machine learning
Genetic algorithms also find application in machine learning. Classification Systems are a form of GeneticBased Machine Learning (GBML) system that is frequently used in the field of selflearningmatic. GBML methods are a niche approach to machine learning.
There are two categories of GBML systems 

The Pittsburg Approach  In this approach, a chromosome encoded a solution, and therefore the physical form is assigned to the solutions.

The Michigan Approach  one solution is usually represented by many chromosomes and therefore physical form is assigned to partial solutions.
It should be borne in mind that the standard problem like crossbreeding, mutation, Lamarckian or Darwinian, etc. are also present in GBML systems.