Search results for "Optimization problem"
showing 10 items of 281 documents
A Random Extension for Discriminative Dimensionality Reduction and Metric Learning
2009
A recently proposed metric learning algorithm which enforces the optimal discrimination of the different classes is extended and empirically assessed using different kinds of publicly available data. The optimization problem is posed in terms of landmark points and then, a stochastic approach is followed in order to bypass some of the problems of the original algorithm. According to the results, both computational burden and generalization ability are improved while absolute performance results remain almost unchanged.
Explicit Algorithms for a New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal
2000
In this paper we formulate a time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin and Osher [ Total variation based image restoration with free local constraints, in Proceedings IEEE Internat. Conf. Imag. Proc., IEEE Press, Piscataway, NJ, (1994), pp. 31--35] and Rudin, Osher, and Fatemi [ Phys. D, 60 (1992), pp. 259--268], respectively. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on Roe's scheme [ J. Comput. Phys., 43 (1981), pp. 357--372], used in fluid dynamics. We show numerical evidence of the speed of resolution…
Fast Decentralized Linear Functions via Successive Graph Shift Operators
2019
Decentralized signal processing performs learning tasks on data distributed over a multi-node network which can be represented by a graph. Implementing linear transformations emerges as a key task in a number of applications of decentralized signal processing. Recently, some decentralized methods have been proposed to accomplish that task by leveraging the notion of graph shift operator, which captures the local structure of the graph. However, existing approaches have some drawbacks such as considering special instances of linear transformations, or reducing the family of transformations by assuming that a shift matrix is given such that a subset of its eigenvectors spans the subspace of i…
Sparse Dynamic Programming for Longest Common Subsequence from Fragments
2002
Sparse Dynamic Programming has emerged as an essential tool for the design of efficient algorithms for optimization problems coming from such diverse areas as computer science, computational biology, and speech recognition. We provide a new sparse dynamic programming technique that extends the Hunt?Szymanski paradigm for the computation of the longest common subsequence (LCS) and apply it to solve the LCS from Fragments problem: given a pair of strings X and Y (of length n and m, respectively) and a set M of matching substrings of X and Y, find the longest common subsequence based only on the symbol correspondences induced by the substrings. This problem arises in an application to analysis…
Accelerated Proximal Gradient Descent in Metric Learning for Kernel Regression
2018
The purpose of this paper is to learn a specific distance function for the Nadayara Watson estimator to be applied as a non-linear classifier. The idea of transforming the predictor variables and learning a kernel function based on Mahalanobis pseudo distance througth an low rank structure in the distance function will help us to lead the development of this problem. In context of metric learning for kernel regression, we introduce an Accelerated Proximal Gradient to solve the non-convex optimization problem with better convergence rate than gradient descent. An extensive experiment and the corresponding discussion tries to show that our strategie its a competitive solution in relation to p…
Tabu search for a multi-objective routing problem
2006
Multi-objective optimization problems deal with the presence of different conflicting objectives. Given that it is not possible to obtain a single solution by optimizing all the objectives simultaneously, a common way to face these problems is to obtain a set of efficient solutions called the non-dominated frontier. In this paper, we address the problem of routing school buses with two objectives: minimize the number of buses, and minimize the longest time a student would have to stay in the bus. The trade-off in this problem is between service level, which is represented by the maximum route length, and operational cost, which is represented by the number of buses in the solution. We prese…
GRASP with path relinking for the orienteering problem
2014
In this paper, we address an optimization problem resulting from the combination of the well-known travelling salesman and knapsack problems. In particular, we target the orienteering problem, originated in the context of sport, which consists of maximizing the total score associated with the vertices visited in a path within the available time. The problem, also known as the selective travelling salesman problem, is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in routing and tourism. We propose a heuristic method—based on the Greedy Randomized Adapt…
Constructing a Pareto front approximation for decision making
2011
An approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed. The approximation is constructed as a sub-complex of a Delaunay triangulation of a finite set of Pareto optimal outcomes to the problem. The approach is based on the concept of inherent nondominance. Rules for checking the inherent nondominance of complexes are developed and applying the rules is demonstrated with examples. The quality of the approximation is quantified with error estimates. Due to its properties, the Pareto front approximation works as a surrogate to the original problem for decision making with interactive methods. Qc 20120127
Interactive multiobjective optimization for anatomy-based three-dimensional HDR brachytherapy.
2010
In this paper, we present an anatomy-based three-dimensional dose optimization approach for HDR brachytherapy using interactive multiobjective optimization (IMOO). In brachytherapy, the goals are to irradiate a tumor without causing damage to healthy tissue. These goals are often conflicting, i.e. when one target is optimized the other will suffer, and the solution is a compromise between them. IMOO is capable of handling multiple and strongly conflicting objectives in a convenient way. With the IMOO approach, a treatment planner’s knowledge is used to direct the optimization process. Thus, the weaknesses of widely used optimization techniques (e.g. defining weights, computational burden an…
Interface Models for the Analysis of Time-Dependent Effects in Masonry Structures
2001
The present paper is devoted to the theoretical formulation and numerical implementation of an interface model suitable to simulate the behavior of cementitious joints at long term. The interface laws are formulated in the framework of viscoplasticity for non standard materials in order to simulate the time-dependent softening response which occurs along the decohesion process in presence of shear and tension tractions. The interface model parameters identification is discussed on the base of experimental data reported in the literature. The optimization problem related to the parameters evaluation is approached by a heuristic algorithm. Finally some examples show the capabilities of the pr…