GRASP heuristic with path-relinking for the multi-plant capacitated lot sizing problem

This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a path-relinking intensification procedure to find cost-effective solutions for this problem. In addition, the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines. The results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature. The results are confirmed by statistical tests. (C) 2009 Elsevier B.V. All rights reserved.

Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

Optimal subdivision of land in agrarian reform projects: an analysis using genetic algorithms

J.A. Ferreira Neto, E.C. Santos Junior, U. Fra Paleo, D. Miranda Barros, and M.C.O. Moreira. 2011. Optimal subdivision of land in agrarian reform projects: an analysis using genetic algorithms. Cien. Inv. Agr. 38(2): 169-178. The objective of this manuscript is to develop a new procedure to achieve optimal land subdivision using genetic algorithms (GA). The genetic algorithm was tested in the rural settlement of Veredas, located in Minas Gerais, Brazil. This implementation was based on the land aptitude and its productivity index. The sequence of tests in the study was carried out in two areas with eight different agricultural aptitude classes, including one area of 391.88 ha subdivided into 12 lots and another of 404.1763 ha subdivided into 14 lots. The effectiveness of the method was measured using the shunting line standard value of a parceled area lot`s productivity index. To evaluate each parameter, a sequence of 15 calculations was performed to record the best individual fitness average (MMI) found for each parameter variation. The best parameter combination found in testing and used to generate the new parceling with the GA was the following: 320 as the generation number, a population of 40 individuals, 0.8 mutation tax, and a 0.3 renewal tax. The solution generated rather homogeneous lots in terms of productive capacity.

Entropy-Based Approach to Analyze and Classify Mineral Aggregates

This paper presents an automatic method to detect and classify weathered aggregates by assessing changes of colors and textures. The method allows the extraction of aggregate features from images and the automatic classification of them based on surface characteristics. The concept of entropy is used to extract features from digital images. An analysis of the use of this concept is presented and two classification approaches, based on neural networks architectures, are proposed. The classification performance of the proposed approaches is compared to the results obtained by other algorithms (commonly considered for classification purposes). The obtained results confirm that the presented method strongly supports the detection of weathered aggregates.

Inference From Aging Information

For many learning tasks the duration of the data collection can be greater than the time scale for changes of the underlying data distribution. The question we ask is how to include the information that data are aging. Ad hoc methods to achieve this include the use of validity windows that prevent the learning machine from making inferences based on old data. This introduces the problem of how to define the size of validity windows. In this brief, a new adaptive Bayesian inspired algorithm is presented for learning drifting concepts. It uses the analogy of validity windows in an adaptive Bayesian way to incorporate changes in the data distribution over time. We apply a theoretical approach based on information geometry to the classification problem and measure its performance in simulations. The uncertainty about the appropriate size of the memory windows is dealt with in a Bayesian manner by integrating over the distribution of the adaptive window size. Thus, the posterior distribution of the weights may develop algebraic tails. The learning algorithm results from tracking the mean and variance of the posterior distribution of the weights. It was found that the algebraic tails of this posterior distribution give the learning algorithm the ability to cope with an evolving environment by permitting the escape from local traps.

Extending the use of canonical and microcanonical Monte Carlo algorithms to spin models

We describe the canonical and microcanonical Monte Carlo algorithms for different systems that can be described by spin models. Sites of the lattice, chosen at random, interchange their spin values, provided they are different. The canonical ensemble is generated by performing exchanges according to the Metropolis prescription whereas in the microcanonical ensemble, exchanges are performed as long as the total energy remains constant. A systematic finite size analysis of intensive quantities and a comparison with results obtained from distinct ensembles are performed and the quality of results reveal that the present approach may be an useful tool for the study of phase transitions, specially first-order transitions. (C) 2009 Elsevier B.V. All rights reserved.

A novel MAP-MRF approach for multispectral image contextual classification using combination of suboptimal iterative algorithms

In this paper we present a novel approach for multispectral image contextual classification by combining iterative combinatorial optimization algorithms. The pixel-wise decision rule is defined using a Bayesian approach to combine two MRF models: a Gaussian Markov Random Field (GMRF) for the observations (likelihood) and a Potts model for the a priori knowledge, to regularize the solution in the presence of noisy data. Hence, the classification problem is stated according to a Maximum a Posteriori (MAP) framework. In order to approximate the MAP solution we apply several combinatorial optimization methods using multiple simultaneous initializations, making the solution less sensitive to the initial conditions and reducing both computational cost and time in comparison to Simulated Annealing, often unfeasible in many real image processing applications. Markov Random Field model parameters are estimated by Maximum Pseudo-Likelihood (MPL) approach, avoiding manual adjustments in the choice of the regularization parameters. Asymptotic evaluations assess the accuracy of the proposed parameter estimation procedure. To test and evaluate the proposed classification method, we adopt metrics for quantitative performance assessment (Cohen`s Kappa coefficient), allowing a robust and accurate statistical analysis. The obtained results clearly show that combining sub-optimal contextual algorithms significantly improves the classification performance, indicating the effectiveness of the proposed methodology. (C) 2010 Elsevier B.V. All rights reserved.

PARALLEL ALGORITHMS FOR MAXIMAL CLIQUES IN CIRCLE GRAPHS AND UNRESTRICTED DEPTH SEARCH

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.

Approximation algorithms and hardness results for the clique packing problem

For a fixed family F of graphs, an F-packing in a graph G is a set of pairwise vertex-disjoint subgraphs of G, each isomorphic to an element of F. Finding an F-packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K(2)}. In this paper we provide new approximation algorithms and hardness results for the K(r)-packing problem where K(r) = {K(2), K(3,) . . . , K(r)}. We show that already for r = 3 the K(r)-packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed r. For r = 3, 4, 5 we obtain better approximations. For r = 3 we obtain a simple 3/2-approximation, achieving a known ratio that follows from a more involved algorithm of Halldorsson. For r = 4, we obtain a (3/2 + epsilon)-approximation, and for r = 5 we obtain a (25/14 + epsilon)-approximation. (C) 2008 Elsevier B.V. All rights reserved.

Algorithms for Maximum Independent Set in Convex Bipartite Graphs

A bipartite graph G = (V, W, E) is convex if there exists an ordering of the vertices of W such that, for each v. V, the neighbors of v are consecutive in W. We describe both a sequential and a BSP/CGM algorithm to find a maximum independent set in a convex bipartite graph. The sequential algorithm improves over the running time of the previously known algorithm and the BSP/CGM algorithm is a parallel version of the sequential one. The complexity of the algorithms does not depend on |W|.

Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

Three-dimensional, fully adaptive simulations of phase-field fluid models

We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.