EURO Journal on Computational Optimization最新文献

In this paper, we study the behavior of feasible rounding approaches for mixed-integer optimization problems when integrated into branch-and-bound methods. Our research addresses two important aspects. First, we develop insights into how an (enlarged) inner parallel set, which is the main component for feasible rounding approaches, behaves when we move down a search tree. Our theoretical results show that the number of feasible points obtainable from the inner parallel set is nondecreasing with increasing depth of the search tree. Thus, they hint at the potential benefit of integrating feasible rounding approaches into branch-and-bound methods. Second, based on those insights, we develop a novel primal heuristic for MILPs that fixes variables in a way that promotes large inner parallel sets of child nodes.

Our computational study shows that combining feasible rounding approaches with the presented diving ideas yields a significant improvement over their application in the root node. Moreover, the proposed method is able to deliver best solutions for the MIP solver SCIP for a significant share of problems which hints at its potential to support solving MILPs.

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.

We consider composite minimax optimization problems where the goal is to find a saddle-point of a large sum of non-bilinear objective functions augmented by simple composite regularizers for the primal and dual variables. For such problems, under the average-smoothness assumption, we propose accelerated stochastic variance-reduced algorithms with optimal up to logarithmic factors complexity bounds. In particular, we consider strongly-convex-strongly-concave, convex-strongly-concave, and convex-concave objectives. To the best of our knowledge, these are the first nearly-optimal algorithms for this setting.

In this paper, the unrelated parallel machine scheduling problem with the objective of minimizing the total tardiness is addressed. For such a problem, a mixed-integer linear programming (MILP) formulation, that considers assignment and positional variables, is presented. In addition, an iterated local search (ILS) algorithm that produces high-quality solutions in reasonable times is proposed for large size instances. The ILS robustness was determined by comparing its performance with the results provided by the MILP. The instances used in this paper were constructed under a new approach which results in tighter due dates than the previous generation method for this problem. The proposed MILP formulation was able to solve instances of up to 150 jobs and 20 machines. Regarding the ILS, it yielded high-quality solutions in a reasonable time, solving instances of a size up to 400 jobs and 20 machines. Experimental results confirm that both approaches are efficient and promising.