EURO Journal on Computational Optimization最新文献

Optimization of storage using neural networks is now commonly achieved by solving a single optimization problem. We first show that this approach allows solving high-dimensional storage problems, but is limited by memory issues. We propose a modification of this algorithm based on the dynamic programming principle and propose neural networks that outperform classical feedforward networks to approximate the Bellman values of the problem. Finally, we study the stochastic linear case and show that Bellman values in storage problems can be accurately approximated using conditional cuts computed by a very recent neural network proposed by the author. This new approximation method combines linear problem solving by a linear programming solver with a neural network approximation of the Bellman values.

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.

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).

In this paper we deal with a problem associated with frequency assignment. Suppose we have a number of transmitters, each of which has been allocated a frequency. The problem we consider is how, given one (or more) transmitters are requesting a new frequency allocation, for example because of the interference they are currently suffering, to decide the new frequencies. Here we wish to constrain overall interference, but minimise the number of frequency changes needed for transmitters that have not requested a change.

We present an optimisation model for frequency allocation that minimises changes in the existing allocation, whilst limiting interference. We consider the standard mathematical representation of interference in the literature and show that we can represent it in a way that involves far fewer variables and constraints.

We make use of this new representation of interference in our zero-one integer linear program for deciding a new frequency allocation. We also show how our formulation can be adapted to deal with a number of other possibilities, specifically allocating frequencies to new transmitters with known locations and also deciding a location (and frequency) for a single new transmitter.

We present computational results for our approach making use of minimum interference frequency assignment test problems taken from the literature. We compare the results from our new representation of interference with those obtained using the standard representation.

Designing a supply chain to comply with environmental policy requires awareness of how work and/or production methods impact the environment and what needs to be done to reduce those environmental impacts and make the company more sustainable. This is a dynamic process that occurs at both the strategic and operational levels. However, being environmentally friendly does not necessarily mean improving the efficiency of the system at the same time. Therefore, when allocating a production budget in a supply chain that implements the green paradigm, it is necessary to figure out how to properly recover costs in order to improve both sustainability and routine operations, offsetting the negative environmental impact of logistics and production without compromising the efficiency of the processes to be executed. In this paper, we study the latter problem in detail, focusing on the CO₂ emissions generated by the transportation from suppliers to production sites, and by the production activities carried out in each plant. We do this using a novel mathematical model that has a quadratic objective function and all linear constraints except one, which is also quadratic, and models the constraint on the budget that can be used for green investments caused by the increasing internal complexity created by large production flows in the production nodes of the supply network. To solve this model, we propose a multistart algorithm based on successive linear approximations. Computational results show the effectiveness of our proposal.

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.