A knowledge-based evolution strategy for the multi-objective minimum spanning tree problem

A fast Knowledge-based Evolution Strategy, KES, for the multi-objective minimum spanning tree, is presented. The proposed algorithm is validated, for the bi-objective case, with an exhaustive search for small problems (4-10 nodes), and compared with a deterministic algorithm, EPDA and NSGA-II for larger problems (up to 100 nodes) using benchmark hard instances. Experimental results show that KES finds the true Pareto fronts for small instances of the problem and calculates good approximation Pareto sets for larger instances tested. It is shown that the fronts calculated by YES are superior to NSGA-II fronts and almost as good as those established by EPDA. KES is designed to be scalable to multi-objective problems and fast due to its small complexity.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Mixed initial-boundary value problem in particle modeling of microelectronic devices

The Boltzmann equation in presence of boundary and initial conditions, which describes the general case of carrier transport in microelectronic devices is analysed in terms of Monte Carlo theory. The classical Ensemble Monte Carlo algorithm which has been devised by merely phenomenological considerations of the initial and boundary carrier contributions is now derived in a formal way. The approach allows to suggest a set of event-biasing algorithms for statistical enhancement as an alternative of the population control technique, which is virtually the only algorithm currently used in particle simulators. The scheme of the self-consistent coupling of Boltzmann and Poisson equation is considered for the case of weighted particles. It is shown that particles survive the successive iteration steps.

A similarity solution for a shock reflection problem in isentropic gas dynamics

A one-dimensional shock-reflection test problem in the case of slab, cylindrical, or spherical symmetry is discussed. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankie-Hugoniot shock relations.

Solutions of a two-dimensional dam-break problem

Solutions of a two-dimensional dam break problem are presented for two tailwater/reservoir height ratios. The numerical scheme used is an extension of one previously given by the author [J. Hyd. Res. 26(3), 293–306 (1988)], and is based on numerical characteristic decomposition. Thus approximate solutions are obtained via linearised problems, and the method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations.

Mining gene networks with application to GAW15 problem 1

The genetic analysis workshop 15 (GAW15) problem 1 contained baseline expression levels of 8793 genes in immortalised B cells from 194 individuals in 14 Centre d’Etude du Polymorphisme Humane (CEPH) Utah pedigrees. Previous analysis of the data showed linkage and association and evidence of substantial individual variations. In particular, correlation was examined on expression levels of 31 genes and 25 target genes corresponding to two master regulatory regions. In this analysis, we apply Bayesian network analysis to gain further insight into these findings. We identify strong dependences and therefore provide additional insight into the underlying relationships between the genes involved. More generally, the approach is expected to be applicable for integrated analysis of genes on biological pathways.