A comparison of simulated annealing and genetic algorithms for the genome mapping problems

The data used for the construction of genome maps is imperfect, therefore the mapping of a physically linear structure must take place in a very uneven feature space. As the number of genes to be ordered grows, it appears to be impractical to use exhaustive search techniques to find the optimal mapping. In this paper we compare genetic algorithms and simulated annealing, two methods that are widely believed to be well-suited to non-smooth feature spaces, and find that the genetic algorithm approach yields superior results. Here we present performance profiles of comparable implementations of both genetic algorithms and simulated annealing. We have translated the problem to a form comparable to the shortest-path problem and found that the ability of a genetic algorithm to combine different partial solutions seems to be responsible for its superiority over the simulated annealing method. This is because in the genome mapping problem, as in the Traveling Salesman Problem, good solutions tend to be rather sparse and because optimal subtours tend to be components of nearly optimal tours

Developing linear algebra algorithms: A collection of class projects

Abstract In this document we present a new approach to developing sequential and parallel dense linear algebra libraries. Given a linear algebra operation, we demonstrate how formal techniques can be used to derive a family of algorithms. Due to the systematic approach used, correctness of the algorithms can be asserted. Next, we introduce a library of routines that hides the manipulation of indices and allows the code to mirror the algorithms as they are naturally presented. The idea is that by having the code mirror the algorithm, the opportunity for introducing indexing errors is minimized. Thus, the correctness assertions regarding the algorithms carry over to the implementations. The philosophy behind the approach is that one should start by systematically deriving the algorithms. The recipe for derivation is given in Chapter 2. Moreover, this derivation should be carefully documented. To facilitate this, we provide a set of LATEX macros, given in an appendix. Once one or more algorithms have been developed, they are translated to implementations using a library of C routines, as part of the Formal Linear Algebra Methods Environment (FLAME). This library allows the code to look much like the algorithms as written using LATEX. For all examples in the report we demonstrate that high performance can be attained on an Intel Pentium (R) III processor. We illustrate the techniques with a large number of case studies, most of which were carried out by teams of computer science undergraduate students as part of a class taught in Spring 2001 at UT-Austin titled High-Performance Parallel Algorithms. The names of the members of the teams are given as the authors of the chapter on the operation assigned to that team. Thus we show that the approach makes the development and implementation of high-performance sequential and parallel algorithms for dense linear algebra operations accessible to novices