Permutation-based Recombination Operator to Node-depth Encoding

AbstractThe node-depth encoding is a representation for evolutionary algorithms applied to tree problems. Its represents trees by storing the nodes and their depth in a proper ordered list. The original formulation of the node-depth encoding has only mutation operators as the search mechanism. Although the representation has this restriction, it has obtained good results with low convergence. Then, this work proposes a specific recombination operator to improve the convergence of the node-depth encoding representation. These operators are based on recombination for permutation representations. An investigation into the bias and heritability of the proposed recombination operator shows that it has a bias towards stars and low heritability. The performance of node-depth encoding with the proposed operator is investigated for the optimal communication spanning tree problem. The results are presented for benchmark instances in the literature. The use of the recombination operator results in a faster convergence than with only mutation operators

The Implementation of Genetic Algorithm in Path Optimization

Traveling Salesman Problem (TSP) is a classical problem in Artificial Intelligence (AI) field. Since 1800s when first mathematical problems related to TSP was treated, it became an interesting topic of optimization problem to be studied. In this project, TSP will be used to model and easy visualize the path optimization problem and Genetic Algorithm (GA) was chosen to be implemented in resolving the problem. This project will focus on the static variable referring to the length of distance as the fitness function of optimization. The idea of resolving TSP study is to come out with the shortest path among all possible solutions of tour to be taken. However, the major concern here is how to ensure that the optimum result is obtained. Therefore, the operators and parameters of GA itself were studied in depth particularly the mutation operator. Experiments were conducted to measure the effectiveness of two different types of mutation method namely swapping method and inversion method. The comparison of both performances in achieving optimum result had been analyzed in detail. Therefore, the implementation ofGA in path optimization can be ascertained offering a compelling result

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Sampling of min-entropy relative to quantum knowledge

Let X_1, ..., X_n be a sequence of n classical random variables and consider a sample of r positions selected at random. Then, except with (exponentially in r) small probability, the min-entropy of the sample is not smaller than, roughly, a fraction r/n of the total min-entropy of all positions X_1, ..., X_n, which is optimal. Here, we show that this statement, originally proven by Vadhan [LNCS, vol. 2729, Springer, 2003] for the purely classical case, is still true if the min-entropy is measured relative to a quantum system. Because min-entropy quantifies the amount of randomness that can be extracted from a given random variable, our result can be used to prove the soundness of locally computable extractors in a context where side information might be quantum-mechanical. In particular, it implies that key agreement in the bounded-storage model (using a standard sample-and-hash protocol) is fully secure against quantum adversaries, thus solving a long-standing open problem.Comment: 48 pages, late