A Survey and Analysis of Evolutionary Operators for Permutations

Overview of Evolutionary Operators for Permutations

The research paper performs a comprehensive analysis of evolutionary operators used in the context of permutation-based problems, such as the Traveling Salesperson Problem (TSP) and various scheduling problems. While some evolutionary algorithms use genetic algorithms with bit string representations, solutions for these types of optimization problems often directly apply permutations. To evolve these permutations effectively, specialized crossover and mutation operators are utilized, taking into account the permutation features they preserve or change.

Crossover Operators

Crossover operators combine the information from parent solutions to generate new offspring solutions that may possess combined traits of parents. Various crossover operators prioritize different permutation features:

• Elements at specific positions can be preserved across generations, ensuring that certain items maintain their positions.
• If the permutation is seen as a sequence of (undirected or directed) edges, some operators aim to keep edges persistent in offspring.
• Precedences, where the relative order of elements is significant, can be considered by certain crossover operators, such that if x precedes y in a parent, it will do the same in the child.

Mutation Operators

Mutation operators introduce small random changes into permutations to explore new solution spaces and avoid premature convergence. They are designed to manipulate permutations in various ways:

• Swaps interchange the positions of two elements.
• Insertion mutations remove and reintroduce an element at a different position, affecting relatively few edges.
• Scramble mutations randomize a block of elements, which might be disruptive but are considered when maintenance of relative orderings is essential.

Analysis and Empirical Findings

The authors have implemented the crossover and mutation operators in the open-source Java library, Chips-n-Salsa, and empirically analyzed their performance. They carried out this empirical analysis through the creation of artificial fitness landscapes, which isolated different features of permutations. The findings indicate which operators are effective for specific permutation features.

Concluding Insights

The paper's analysis concludes that selection of the right evolutionary operator largely depends on the permutation feature that most greatly influences the fitness function of the optimization problem at hand. It provides a catalog of evolutionary operators and insights into which operators are worth considering for problems with specific characteristics. The results accentuate the importance of operator selection in evolutionary algorithms and the potential need to balance the behavior of these operators to optimize multiple permutation features concurrently.

This study serves as a foundational step for further exploration, particularly with regards to operators that might need careful tuning and those that are dependent on problem-specific heuristics. The outcomes of the research facilitate better understanding and use of evolutionary operators in permutation-based optimization challenges.