The project will focus on the study, imple … The project will focus on the study, implementation, comparison and
analysis of different algorithms for the optimization of pseudo-Boolean
functions, i.e., functions defined over binary variables with values in
R. These functions have been studied a lot in the mathematical
programming literature, and different algorithms have been proposed (1).
More recently, the same problems have been faced in evolutionary
computations, with the use of genetic algorithms, and in particular
estimation of distribution algorithms (2,3). Estimation of distribution
algorithms are a recent meta-heuristic, where classical crossover and
mutation operators used in genetic algorithms are replaced with
operators that come from statistics, such as sampling and estimation.
The focus will be on the implementation of a new algorithm able to
combine different approaches (estimation and sampling, from one side,
and exploitation of prior knowledge about the structure of problem, on
the other), together with the comparison of the results with existing
techniques that historically appear in different (and often separated)
communities. Good coding (C/C++) abilities are required. Since the
approach will be based on statistical models, the student is supposed to
be comfortable with notions that come from probability and statistics
courses. The project could require some extra effort in order to build
and consolidate some background in math, especially in Bayesian
statistics and MCMC techniques, such as Gibbs and Metropolis samplers (4).
The project can be extended to master thesis, according to interesting
and novel directions of research that will emerge in the first part of
the work. Possible ideas may concern the proposal of new algorithms able
to learn existing dependencies among the variables in the function to be
optimized, and exploit them in order to increase the probability to
converge to the global optimum.
Picture taken from http://www.ra.cs.uni-tuebingen.de/
# Boros, Endre and Boros, Endre and Hammer, Peter L. (2002) Pseudo-boolean optimization. Discrete Applied Mathematics.
# Pelikan, Martin; Goldberg, David; Lobo, Fernando (1999), A Survey of Optimization by Building and Using Probabilistic Models, Illinois: Illinois Genetic Algorithms Laboratory (IlliGAL), University of Illinois at Urbana-Champaign.
# Larrañga, Pedro; & Lozano, Jose A. (Eds.). Estimation of distribution algorithms: A new tool for evolutionary computation. Kluwer Academic Publishers, Boston, 2002.
# Image Analysis, Random Fields Markov Chain Monte Carlo Methods om Fields Markov Chain Monte Carlo Methods