An accelerated and robust algorithm for ant colony optimization in continuous functions

There is a wide variety of computational methods used for solving optimization problems. Among these, there are various strategies that are derived from the concept of ant colony optimization (ACO). However, the great majority of these methods are limited-range-search algorithms, that is, they find the optimal solution, as long as the domain provided contains this solution. This becomes a limitation, due to the fact that it does not allow these algorithms to be applied successfully to real-world problems, as in the real world, it is not always possible to determine with certainty the correct domain. The article proposes the use of a broad-range search algorithm, that is, that seeks the optimal solution, with success most of the time, even if the initial domain provided does not contain this solution, as the initial domain provided will be adjusted until it finds a domain that contains the solution. This algorithm called ARACO, derived from RACO, makes for the obtaining of better results possible, through strategies that accelerate the parameters responsible for adjusting the supplied domain at opportune moments and, in case there is a stagnation of the algorithm, expansion of the domain around the best solution found to prevent the algorithm becoming trapped in a local minimum. Through these strategies, ARACO obtains better results than its predecessors, in relation to the number of function evaluations necessary to find the optimal solution, in addition to its 100% success rate in practically all the tested functions, thus demonstrating itself as being a high performance and reliable algorithm. The algorithm has been tested on some classic benchmark functions and also on the benchmark functions of the IEEE Congress of Evolutionary Computation Benchmark Test Functions (CEC 2019 100-Digit Challenge).

On the Evolution of Compressible and Incompressible Viscous Fluids with a Sharp Interface

In this paper, we consider some two phase problems of compressible and incompressible viscous fluids’ flow without surface tension under the assumption that the initial domain is a uniform Wq2−1/q domain in RN (N≥2). We prove the local in the time unique existence theorem for our problem in the Lp in time and Lq in space framework with 2<p<∞ and N<q<∞ under our assumption. In our proof, we first transform an unknown time-dependent domain into the initial domain by using the Lagrangian transformation. Secondly, we solve the problem by the contraction mapping theorem with the maximal Lp-Lq regularity of the generalized Stokes operator for the compressible and incompressible viscous fluids’ flow with the free boundary condition. The key step of our proof is to prove the existence of an R-bounded solution operator to resolve the corresponding linearized problem. The Weis operator-valued Fourier multiplier theorem with R-boundedness implies the generation of a continuous analytic semigroup and the maximal Lp-Lq regularity theorem.

Learning from Both Experts and Data

In this work, we study the problem of inferring a discrete probability distribution using both expert knowledge and empirical data. This is an important issue for many applications where the scarcity of data prevents a purely empirical approach. In this context, it is common to rely first on an a priori from initial domain knowledge before proceeding to an online data acquisition. We are particularly interested in the intermediate regime, where we do not have enough data to do without the initial a priori of the experts, but enough to correct it if necessary. We present here a novel way to tackle this issue, with a method providing an objective way to choose the weight to be given to experts compared to data. We show, both empirically and theoretically, that our proposed estimator is always more efficient than the best of the two models (expert or data) within a constant.

Estimation of the regions of attraction for autonomous nonlinear systems

A methodology for estimating the region of attraction for autonomous nonlinear systems is developed. The methodology is based on a proof that the region of attraction can be estimated accurately by the zero sublevel set of an implicit function which is the viscosity solution of a time-dependent Hamilton–Jacobi equation. The methodology starts with a given initial domain and yields a sequence of region of attraction estimates by tracking the evolution of the implicit function. The resulting sequence is contained in and converges to the exact region of attraction. While alternative iterative methods for estimating the region of attraction have been proposed, the methodology proposed in this paper can compute the region of attraction to achieve any desired accuracy in a dimensionally independent and efficient way. An implementation of the proposed methodology has been developed in the Matlab environment. The correctness and efficiency of the methodology are verified through a few examples.

A new approach to modelling the two way coupling for momentum transfer in a hollow-cone spray

A new approach to modelling the interaction between droplets and the carrier phase is suggested. The new model isapplied to the analysis of a spray injected into a chamber of quiescent air, using an Eulerian-Lagrangian approach. The conservative formulation of the equations for mass, momentum and energy transport is used for the analysis of the carrier phase. The dispersed phase is modelled using the Lagrangian approach with droplets represented by individual parcels.The implementation of the Discontinuous Galerkin method (ForestDG), based on a topological representation of the computational mesh by a hierarchical structure consisting of oct- quad- and binary trees, is used in our analysis. Adaptive mesh refinement (h-refinement) enables us to increase the spatial resolution for the computational mesh in the vicinity of the points of interest such as interfaces, geometrical features, or flow discontinuities. The local increase in the expansion order (p-refinement) at areas of high strain rates or vorticity magnitude results in an increase of the order of the accuracy of discretisation of shear layers and vortices.The initial domain consists of a graph of unitarian-trees representing hexahedral, prismatic and tetrahedral elements. The ancestral elements of the mesh can be split into self-similar elements allowing each tree to grow branches to an arbitrary level of refinement. The connectivity of the elements, their genealogy and their partitioning are described by linked lists of pointers. These are attached to the tree data structure which facilitates the on-the-fly splitting, merging and repartitioning of the computational mesh by rearranging the links of each node of the tree. This enables us to refine the computational mesh in the vicinity of the droplet parcels aiming to accurately resolve the coupling betweenthe two phases.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4671