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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (âefficientâ) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find âquicklyâ (reasonable run-times), with âhighâ probability, provable âgoodâ solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
On the design of state-of-the-art pseudorandom number generators by means of genetic programming
Congress on Evolutionary Computation. Portland, EEUU, 19-23 June 2004The design of pseudorandom number generators by means of evolutionary computation is a classical problem. Today, it has been mostly and better accomplished by means of cellular automata and not many proposals, inside or outside this paradigm could claim to be both robust (passing all the statistical tests, including the most demanding ones) and fast, as is the case of the proposal we present here. Furthermore, for obtaining these generators, we use a radical approach, where our fitness function is not at all based in any measure of randomness, as is frequently the case in the literature, but of nonlinearity. Efficiency is assured by using only very efficient operators (both in hardware and software) and by limiting the number of terminals in the genetic programming implementation
Parallel Implementation of Efficient Search Schemes for the Inference of Cancer Progression Models
The emergence and development of cancer is a consequence of the accumulation
over time of genomic mutations involving a specific set of genes, which
provides the cancer clones with a functional selective advantage. In this work,
we model the order of accumulation of such mutations during the progression,
which eventually leads to the disease, by means of probabilistic graphic
models, i.e., Bayesian Networks (BNs). We investigate how to perform the task
of learning the structure of such BNs, according to experimental evidence,
adopting a global optimization meta-heuristics. In particular, in this work we
rely on Genetic Algorithms, and to strongly reduce the execution time of the
inference -- which can also involve multiple repetitions to collect
statistically significant assessments of the data -- we distribute the
calculations using both multi-threading and a multi-node architecture. The
results show that our approach is characterized by good accuracy and
specificity; we also demonstrate its feasibility, thanks to a 84x reduction of
the overall execution time with respect to a traditional sequential
implementation
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