1. Overview
In this tutorial, we’ll discuss a crossover operator used in genetic algorithms: order one crossover. We’ll present the process to apply this operator with an example.
Finally, we’ll highlight the advantages and disadvantages of this operator.
2. Introduction
Genetic algorithms (GAs) are optimization algorithms based on the principles of natural selection and genetics. Additionally, we utilize them to solve complex optimization problems.
Among all the operations, a crossover is a crucial step in genetic algorithms. Once we select the parents, the GA performs a crossover operation that combines the genetic material of two parent chromosomes to create new offspring chromosomes. Additionally, there’re various crossover operators such as order one crossover, uniform crossover, and two-point crossover.
We use the order one crossover (OX1) in genetic algorithms to generate new candidate solutions from parents’ solutions. Specifically, it’s a useful operator for problems that have a permutation representation.
In OX1, we randomly select a crossover point along with the chromosomes of two parents. Furthermore, we copy the elements between the two points in the first parent to the offspring, preserving their relative order. Additionally, the remaining elements in the offspring are then filled in by the second parent in the order that they appear in the second parent, without repeating any elements already included in the offspring.
We mainly use the order one crossover operator in evolutionary algorithms for combining two parent individuals to generate offspring. Another common application of order one crossover is in solving optimization problems where the goal is to find the values of a set of parameters that optimize some objective function.
3. Working Process
Now let’s discuss how an order one crossover operator works. It has three major steps:
The first step is to select two parent chromosomes from the current population. As soon as we initialize the parent chromosomes, we need to choose a crossover point. Furthermore, we generally pick a random crossover point for simplicity.
The crossover point divides the parent chromosomes into two parts. Now it’s time to generate the new chromosome. The length of the new offspring chromosome is the same as the two parent chromosomes. Additionally, the new offspring chromosome contains two parts in the same way we divide the parent chromosomes.
Now, we copy the first section of one parent chromosome into the corresponding section of the offspring chromosome. Additionally, if there’re any remaining positions in the offspring chromosome, we need to fill them, as the length of the offspring should be the same as the parent chromosomes.
Hence, we fill in the remaining positions in the offspring chromosome with the remaining elements from the other parent chromosome without duplicating any elements that have already been included in the offspring chromosome. However, if the parent chromosomes contain identical elements, the offspring chromosome will have duplicate elements.
Finally, we add the resulting offspring chromosome to the next generation population. By using OX1, the offspring chromosome contains genetic material from both parent chromosomes, allowing for the creation of new candidate solutions that may not have been present in the initial population.
4. Example
Now let’s take an example to illustrate how OX1 works. First, we’re taking two parent chromosomes to apply one order crossover operator on them:
Now, we need to choose a random crossover point. In our example, we pick index 2 as a crossover point. The crossover point divides the parent chromosomes into two sections:
Moving forward, we copy the first section of Parent 1 into the first section of the offspring. Similarly, we fill the second part of the offspring with the first part of Parent 2.
Finally, we fill the remaining positions from the parent’s chromosomes. While filling the remaining elements in the offspring, it’s important to remember that no duplicate element is allowed if each parent contains unique elements. Hence, we fill the remaining part in our example with element 5. Finally, we generate a new population:
However, if the parent chromosomes contain identical elements, the offspring chromosome will have duplicate elements. Let’s take a look at an example where parent chromosomes contain identical repetitive elements:
Additionally, the newly generated population isn’t unique. Based on the crossover point and the elements needed to be preserved, we can generate multiple new populations from parent chromosomes.
5. Advantages
There are several advantages of using order one crossover (OX1) in genetic algorithms (GAs). Some of the vital benefits are the maintenance of the diversity of chromosomes, simplicity, and preservation of important elements in chromosomes.
OX1 allows the creation of offspring chromosomes containing genetic material from both parent chromosomes. It helps to maintain diversity in the population and prevents the GA from getting stuck in local optima.
Additionally, OX1 is a simple and easy-to-implement crossover operator. It only requires the selection of a single crossover point and doesn’t require complex calculations or operations.
Finally, it ensures that important elements in the parent chromosomes are preserved in the offspring chromosomes. This is because the first section of one parent chromosome is always copied into the offspring chromosome, ensuring that at least some of the genetic material from that parent is preserved.
Overall, OX1 is a simple and effective crossover operator that can help to maintain diversity in the population and produce high-quality candidate solutions.
6. Disadvantages
OX1 is a popular and effective crossover operator in genetic algorithms (GAs). However, there’re also some disadvantages and limitations associated with its use. Some of the drawbacks of the OX1 operator are limited exploration, leading to premature convergence, and ineffective for non-permutation problems.
OX1 can be limited in its ability to explore the search space. This is because it only creates offspring chromosomes by exchanging genetic material between two parent chromosomes. Furthermore, it doesn’t introduce new genetic material from outside the current population, which could be useful in exploring new regions of the search space.
Additionally, it can sometimes lead to premature convergence, where the GA converges to a suboptimal solution too quickly. This can happen when the initial population contains a large number of similar or identical chromosomes. In such cases, OX1 may simply recombine genetic material between similar chromosomes, leading to a lack of diversity in the population.
Finally, OX1 is designed specifically for problems that have a permutation representation. It may not be suitable for problems that have a different representation, such as real-valued or binary-coded variables.
7. Conclusion
In this tutorial, we discussed a crossover operator in genetic algorithms: order one crossover. We explored how to apply this operator in order to generate new offspring chromosomes with an example.
Finally, we highlighted the advantages and disadvantages of this operator.