Discrete Optimization - Genetic Algorithms

In summary, the conversation is about someone struggling with two courseworks on Genetic Algorithms and a specific question about coding a chromosome for five variables. The person is advised to read up on the subject and do some research before attempting to answer the question.
  • #1
kikitard
6
0

Homework Statement


I have a whole two courseworks on Genetic Algorithms, but we have been shown no examples. I am stumped!

1. A function f is set to depend on five variables x1, . . . , x5 where x1 can take 2 different
values, x2 can take 8 different values and x3, x4, x5 each take 4 different values. Design
a minimal binary coding for x1, . . . , x5, i.e. what would a chromosome look like which
encodes these five numbers? What is the maximal number of settings represented by
chromosomes coded this way? What is the number of schemata in this encoding?

This is the very first question.

Homework Equations


Nothing, sorry!

The Attempt at a Solution


I wish I knew where to begin!
 
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  • #2
Welcome to PF!

These are very basic questions in genetic algorithms, so my guess is that you are supposed to read up on the subject matter before you can understand what is being asked. Surely you must have been given some textbooks or similar that explains this? And even without such, a quick search for "genetic algorithm" on the net should provide you with enough clues and examples. Have you made such (re-) search?
 

What is discrete optimization?

Discrete optimization is a branch of mathematics that deals with finding the best possible solution to a problem with a limited set of options. This is in contrast to continuous optimization, where the solution can take on any value within a range.

What are genetic algorithms?

Genetic algorithms are a type of optimization algorithm that is inspired by the process of natural selection in biological evolution. They use techniques such as mutation, crossover, and selection to iteratively improve a population of potential solutions to a problem.

How do genetic algorithms work?

Genetic algorithms work by starting with a population of random solutions to a problem. These solutions then undergo genetic operations such as mutation and crossover to create new, potentially better solutions. The new solutions are then evaluated and the process repeats until a satisfactory solution is found.

What are the advantages of using genetic algorithms for discrete optimization?

Genetic algorithms have several advantages for discrete optimization problems. They can handle a large number of variables and constraints, as well as non-linear and multi-modal objective functions. They are also able to find good solutions in a relatively short amount of time.

What are the limitations of genetic algorithms in discrete optimization?

While genetic algorithms have many strengths, they also have some limitations. They may not always find the optimal solution to a problem, and the quality of the solution can depend on the initial population and genetic operators used. They can also be computationally expensive for very large and complex problems.

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