Nareli Cruz-Cortés

Handling constraints in global optimization using an artificial immune system

In this paper, we present a study of the use of an artificial immune system (CLONALG) for solving constrained global optimization problems. As part of this study, we evaluate the performance of the algorithm both with binary encoding and with real-numbers encoding. Additionally, we also evaluate the impact of the mutation operator in the performance of the approach by comparing Cauchy and Gaussian mutations. Finally, we propose a new mutation operator which significantly improves the performance of CLONALG in constrained optimization.

An Artificial Immune System Heuristic for Generating Short Addition Chains

This paper deals with the optimal computation of finite field exponentiation, which is a well-studied problem with many important applications in the areas of error-correcting codes and cryptography. It has been shown that the optimal computation of finite field exponentiation is a problem which is closely related to finding a suitable addition chain with the shortest possible length. However, it is also known that obtaining the shortest addition chain for a given arbitrary exponent is an NP-hard problem. As a consequence, heuristics are an obvious choice to compute field exponentiation with a semi-optimal number of underlying arithmetic operations. In this paper, we propose the use of an artificial immune system to tackle this problem. Particularly, we study the problem of finding both the shortest addition chains for exponents e with moderate size (i.e., with a length of less than 20 bits), and for the huge exponents typically adopted in cryptographic applications, (i.e., in the range from 128 to 2048 bits).

A fast implementation of multiplicative inversion over GF(2/sup m/)

In this paper, an efficient architecture for multiplicative inversion in GF(2/sup m/) using addition chains is presented. The approach followed was based on the Itoh-Tsujii algorithm targeting a fast implementation on reconfigurable hardware devices. We give the design details of the proposed architecture whose main building blocks are a field multi-squarer block, a field polynomial multiplier and a BRAM two-port memory. Our design is able to compute multiplicative inversion in GF(2/sup 193/) in about 1.33/spl mu/S using only 27 clock cycles.

Finding optimal addition chains using a genetic algorithm approach

Since most public key cryptosystem primitives require the computation of modular exponentiation as their main building block, the problem of performing modular exponentiation efficiently has received considerable attention over the years. It is known that optimal (shortest) addition chains are the key mathematical concept for accomplishing modular exponentiations optimally. However, finding an optimal addition chain of length r is an NP-hard problem whose search space size is comparable to r !. In this contribution we explore the usage of a Genetic Algorithm (GA) approach for the problem of finding optimal (shortest) addition chains. We explain our GA strategy in detail reporting several promising experimental results that suggest that evolutionary algorithms may be a viable alternative to solve this illustrious problem in a quasi optimal fashion.

Finding Minimal Addition Chains with a Particle Swarm Optimization Algorithm

The addition chains with minimal length are the basic block to the optimal computation of finite field exponentiations. It has very important applications in the areas of error-correcting codes and cryptography. However, obtaining the shortest addition chains for a given exponent is a NP-hard problem. In this work we propose the adaptation of a Particle Swarm Optimization algorithm to deal with this problem. Our proposal is tested on several exponents whose addition chains are considered hard to find. We obtained very promising results.

Optimal Triangulation in 3D Computer Vision Using a Multi-objective Evolutionary Algorithm

The triangulationis a process by which the 3D point position can be calculated from two images where that point is visible. This process requires the intersection of two known lines in the space. However, in the presence of noise this intersection does not occur, then it is necessary to estimate the best approximation. One option towards achieving this goal is the usage of evolutionary algorithms. In general, evolutionary algorithms are very robust optimization techniques, however in some cases, they could have some troubles finding the global optimum getting trapped in a local optimum. To overcome this situation some authors suggested removing the local optima in the search space by means of a single-objective problem to a multi-objective transformation. This process is called multi-objectivization. In this paper we successfully apply this multi-objectivizationto the triangulation problem.

A Genetic Algorithm with repair and local search mechanisms able to find minimal length addition chains for small exponents

In this paper, we present an improved Genetic Algorithm (GA) that is able to find the shortest addition chains for a given exponent e. Two new variation operators (special two-point crossover and a local-search-like mutation) are proposed as a means to improve the GA search capabilities. Furthermore, the usage of an improved repair mechanism is applied to the process of generating the initial population of the algorithm. The proposed approach is compared on a set of test problems with two state-of-the-art evolutionary heuristic-based approaches recently published. Finally, the modified GA is used to find the optimal addition chain length for a small collection of “hard” exponents. The results obtained are competitive and even better in the more difficult instances of the exponentiation problem that were considered here.

Hardware implementation of the elitist compact Genetic Algorithm using Cellular Automata pseudo-random number generator ☆

Abstract In this paper the design and implementation of two versions of the compact Genetic Algorithm (cGA), with and without mutation and elitism, and a Cellular Automata-based pseudo-random number generator on a Field Programmable Gate Arrays (FPGAs) are accomplished. The design is made using a Hardware Description Language, called VHDL. Accordingly, the obtained results show that it is viable to have this searching algorithm in hardware to be used in real time applications.

Euclidean Distance Fit of Ellipses with a Genetic Algorithm

We use a genetic algorithm to solve the problem, widely treated in the specialized literature, of fitting an ellipse to a set of given points. Our proposal uses as the objective function the minimization of the sum of orthogonal Euclidean distances from the given points to the curve; this is a non-linear problem which is usually solved using the minimization of the quadratic distances that allows to use the gradient and the numerical methods based on it, such as Gauss-Newton. The novelty of the proposed approach is that as we are using a GA, our algorithm does not need initialization, and uses the Euclidean distance as the objective function. We will also show that in our experiments, we are able to obtain better results than those previously reported. Additionally our solutions have a very low variance, which indicates the robustness of our approach.

Routing algorithms for wireless sensor networks using ant colony optimization

Wireless Sensor Networks have become an active research topic in the last years. The routing problem is a very important part in this kind of networks that need to be considered in order to maximize the network life time. As the size of the network increases, routing becomes more complex due the amount of sensor nodes in the network. Sensor nodes in Wireless Sensor Networks are very constrained in memory capabilities, processing power and batteries. Ant Colony Optimization based routing algorithms have been proposed to solve the routing problem trying to deal with these constrains. We present a comparison of two Ant Colony-based routing algorithms, taking into account current amounts of energy consumption under different scenarios and reporting the usual metrics for routing in wireless sensor networks.