Computing a Finite Size Representation of the Set of Approximate Solutions of an MOP

Recently, a framework for the approximation of the entire set of $\epsilon$-efficient solutions (denote by $E_\epsilon$) of a multi-objective optimization problem with stochastic search algorithms has been proposed. It was proven that such an algorithm produces -- under mild assumptions on the process to generate new candidate solutions --a sequence of archives which converges to $E_{\epsilon}$ in the limit and in the probabilistic sense. The result, though satisfactory for most discrete MOPs, is at least from the practical viewpoint not sufficient for continuous models: in this case, the set of approximate solutions typically forms an $n$-dimensional object, where $n$ denotes the dimension of the parameter space, and thus, it may come to perfomance problems since in practise one has to cope with a finite archive. Here we focus on obtaining finite and tight approximations of $E_\epsilon$, the latter measured by the Hausdorff distance. We propose and investigate a novel archiving strategy theoretically and empirically. For this, we analyze the convergence behavior of the algorithm, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting approximation, and present some numerical results

Homology modeling and molecular dynamics simulations of MUC1-9/H-2Kb complex suggest novel binding interactions

International audienceHuman MUC1 is over-expressed in human adenocarcinomas and has been used as a target for immunotherapy studies. The 9-mer MUC1-9 peptide has been identified as one of the peptides which binds to murine MHC class I H-2K. The structure of MUC1-9 in complex with H-2K has been modeled and simulated with classical molecular dynamics, based on the x-ray structure of the SEV9 peptide/H-2K complex. Two independent trajectories with the solvated complex (10 ns in length) were produced. Approximately 12 hydrogen bonds were identified during both trajectories to contribute to peptide/MHC complex, as well as 1-2 water mediated hydrogen bonds. Stability of the complex was also confirmed by buried surface area analysis, although the corresponding values were about 20% lower than those of the original x-ray structure. Interestingly, a bulged conformation of the peptide's central region, partially characterized as a -turn, was found exposed form the binding groove. In addition, P1 and P9 residues remained bound in the A and F binding pockets, even though there was a suggestion that P9 was more flexible. The complex lacked numerous water mediated hydrogen bonds that were present in the reference peptide x-ray structure. Moreover, local displacements of residues Asp4, Thr5 and Pro9 resulted in loss of some key interactions with the MHC molecule. This might explain the reduced affinity of the MUC1-9 peptide, relatively to SEV9, for the MHC class I H-2K

EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation III

XVIII, 261 p. 114 illus., 15 illus. in color.onli

EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II

XXIV, 508 p. 152 illus.online resource

EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IVInternational Conference held at Leiden University, July 10-13, 2013 /

XIV, 324 p. 140 illus.online resource