María Victoria Luzón

Modeling the performance of evolutionary algorithms on the root identification problem: A case study with pbil and chc algorithms

The availability of a model to measure the performance of evolutionary algorithms is very important, especially when these algorithms are applied to solve problems with high computational requirements. That model would compute an index of the quality of the solution reached by the algorithm as a function of run-time. Conversely, if we fix an index of quality for the solution, the model would give the number of iterations to be expected. In this work, we develop a statistical model to describe the performance of PBIL and CHC evolutionary algorithms applied to solve the root identification problem. This problem is basic in constraint-based, geometric parametric modeling, as an instance of general constraint-satisfaction problems. The performance model is empirically validated over a benchmark with very large search spaces.

Parameter tuning of PBIL and CHC evolutionary algorithms applied to solve the Root Identification Problem

Evolutionary algorithms are among the most successful approaches for solving a number of problems where systematic searches in huge domains must be performed. One problem of practical interest that falls into this category is known as The Root Identification Problem in Geometric Constraint Solving, where one solution to the geometric problem must be selected among a number of possible solutions bounded by an exponential number. In previous works we have shown that applying genetic algorithms, a category of evolutionary algorithms, to solve the Root Identification Problem is both feasible and effective. In this work, we report on an empirical statistical study conducted to establish the influence of the driving parameters in the PBIL and CHC evolutionary algorithms when they are used to solve the Root Identification Problem. We identify a set of values that optimize algorithms performance. The driving parameters considered for the PBIL algorithm are population size, mutation probability, mutation shift and learning rate. For the CHC algorithm we studied population size, divergence rate, differential threshold and the set of best individuals. In both cases we applied unifactorial and multifactorial analysis, post hoc tests and best parameter level selection. Experimental results show that CHC outperforms PBIL when applied to solve the Root Identification Problem.

Automatic parameter tuning for Evolutionary Algorithms using a Bayesian Case-Based Reasoning system

The widespread use and applicability of Evolutionary Algorithms is due in part to the ability to adapt them to a particular problem-solving context by tuning their parameters. This is one of the problems that a user faces when applying an Evolutionary Algorithm to solve a given problem. Before running the algorithm, the user typically has to specify values for a number of parameters, such as population size, selection rate, and probability operators. This paper empirically assesses the performance of an automatic parameter tuning system in order to avoid the problems of time requirements and the interaction of parameters. The system, based on Bayesian Networks and Case-Based Reasoning methodology, estimates the best parameter setting for maximizing the performance of Evolutionary Algorithms. The algorithms are applied to solve a basic problem in constraint-based, geometric parametric modeling, as an instance of general constraint-satisfaction problems. The experimental results demonstrate the validity of the proposed system and its potential effectiveness for configuring algorithms.

A stochastic approach to simulate artists behaviour for automatic felt-tipped stippling

Nowadays, non-photorealistic rendering is an area in computer graphics that tries to simulate what artists do and the tools they use. Stippling illustrations with felt-tipped colour pen is not a commonly used technique by artists due to its complexity. In this paper we present a new method to simulate stippling illustrations with felt-tipped colour pen from a photograph or an image. This method infers a probability function with an expert system from some rules given by the artist and then simulates the behaviour of the artist when placing the dots on the illustration by means of a stochastic algorithm.