EURO Journal on Computational Optimization最新文献

This study addresses the scheduling problem where every job requires several types of resources. At every point in time, the capacity of resources is limited. When necessary, the capacity can be increased at a cost. Each job has a due date, and the processing times of jobs are random variables with a known probability distribution. The considered problem is to determine a schedule that minimises the total cost, which consists of the cost incurred due to the violation of resource limits and the total tardiness of jobs. A genetic algorithm enhanced by local search is proposed. The sample average approximation method is used to construct a confidence interval for the optimality gap of the obtained solutions. Computational study on the application of the sample average approximation method and genetic algorithm is presented. It is revealed that the proposed method is capable of providing high-quality solutions to large instances in a reasonable time.

Typically, nonlinear Support Vector Machines (SVMs) produce significantly higher classification quality when compared to linear ones but, at the same time, their computational complexity is prohibitive for large-scale datasets: this drawback is essentially related to the necessity to store and manipulate large, dense and unstructured kernel matrices. Despite the fact that at the core of training an SVM there is a simple convex optimization problem, the presence of kernel matrices is responsible for dramatic performance reduction, making SVMs unworkably slow for large problems. Aiming at an efficient solution of large-scale nonlinear SVM problems, we propose the use of the Alternating Direction Method of Multipliers coupled with Hierarchically Semi-Separable (HSS) kernel approximations. As shown in this work, the detailed analysis of the interaction among their algorithmic components unveils a particularly efficient framework and indeed, the presented experimental results demonstrate, in the case of Radial Basis Kernels, a significant speed-up when compared to the state-of-the-art nonlinear SVM libraries (without significantly affecting the classification accuracy).

Robot Dance is a computational optimization platform developed in response to the COVID-19 outbreak, to support the decision-making on public policies at a regional level. The tool is suitable for understanding and suggesting levels of intervention needed to contain the spread of infectious diseases when the mobility of inhabitants through a regional network is a concern. Such is the case for the SARS-CoV-2 virus that is highly contagious and, therefore, makes it crucial to incorporate the circulation of people in the epidemiological compartmental models. Robot Dance anticipates the spread of an epidemic in a complex regional network, helping to identify fragile links where applying differentiated measures of containment, testing, and vaccination is important. Based on stochastic optimization, the model determines efficient strategies on the basis of commuting of individuals and the situation of hospitals in each district. Uncertainty in the capacity of intensive care beds is handled by a chance-constraint approach. Some functionalities of Robot Dance are illustrated in the state of São Paulo in Brazil, using real data for a region with more than forty million inhabitants.

We consider the Minimum Interference Frequency Assignment Problem and we propose a novel Simulated Annealing approach that makes use of a portfolio of different neighborhoods, specifically designed for this problem.

We undertake at once the two versions of the problem proposed by Correia (2001) and by Montemanni et al. (2001), respectively, and the corresponding benchmark instances. With the aim of determining the best configuration of the solver for the specific version of the problem we perform a comprehensive and statistically-principled tuning procedure.

Even tough a totally precise comparison is not possible, the experimental analysis show that we outperform all previous results on most instances for the first version of the problem, and we are at the same level of the best ones for the second version.

As a byproduct of this research, we designed a new robust file format for instances and solutions, and a data repository for validating and maintaining the available solutions.

We consider a variant of inexact Newton Method [20], [40], called Newton-MR, in which the least-squares sub-problems are solved approximately using Minimum Residual method [79]. By construction, Newton-MR can be readily applied for unconstrained optimization of a class of non-convex problems known as invex, which subsumes convexity as a sub-class. For invex optimization, instead of the classical Lipschitz continuity assumptions on gradient and Hessian, Newton-MR's global convergence can be guaranteed under a weaker notion of joint regularity of Hessian and gradient. We also obtain Newton-MR's problem-independent local convergence to the set of minima. We show that fast local/global convergence can be guaranteed under a novel inexactness condition, which, to our knowledge, is much weaker than the prior related works. Numerical results demonstrate the performance of Newton-MR as compared with several other Newton-type alternatives on a few machine learning problems.

This study investigates the progress made in lp and milp solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving lp/milp, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for lp and around 50 for milp, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time.

B-coloring is a problem in graph theory. It can model some real applications, as well as being used to enhance solution methods for the classical graph coloring problem. In turn, improved solutions for the classical coloring problem would impact a larger pool of practical applications in several different fields such as scheduling, timetabling and telecommunications. Given a graph $G=(V,E)$, the b-coloring problem aims to maximize the number of colors used while assigning a color to every vertex in V, preventing adjacent vertices from receiving the same color, with every color represented by a special vertex, called a b-vertex. A vertex can be a b-vertex only if the set of colors assigned to its adjacent vertices includes all the colors, apart from the one assigned to the vertex itself.

This work employs methods based on Linear Programming to derive new upper and lower bounds for the problem. In particular, starting from a Mixed Integer Linear Programming model recently presented, upper bounds are obtained through partial linear relaxations of this model, while lower bounds are derived by considering different variations of the original model, modified to target a specific number of colors provided as input. The experimental campaign documented in the paper led to several improvements to the state-of-the-art results.

Nonlinear conjugate gradients are among the most popular techniques for solving continuous optimization problems. Although these schemes have long been studied from a global convergence standpoint, their worst-case complexity properties have yet to be fully understood, especially in the nonconvex setting. In particular, it is unclear whether nonlinear conjugate gradient methods possess better guarantees than first-order methods such as gradient descent. Meanwhile, recent experiments have shown impressive performance of standard nonlinear conjugate gradient techniques on certain nonconvex problems, even when compared with methods endowed with the best known complexity guarantees.

In this paper, we propose a nonlinear conjugate gradient scheme based on a simple line-search paradigm and a modified restart condition. These two ingredients allow for monitoring the properties of the search directions, which is instrumental in obtaining complexity guarantees. Our complexity results illustrate the possible discrepancy between nonlinear conjugate gradient methods and classical gradient descent. A numerical investigation on nonconvex robust regression problems as well as a standard benchmark illustrate that the restarting condition can track the behavior of a standard implementation.