Eduardo Álvarez-Miranda

The Maximum Weight Connected Subgraph Problem

The Maximum (Node-) Weight Connected Subgraph Problem (MWCS) searches for a connected subgraph with maximum total weight in a node-weighted (di)graph. In this work we introduce a new integer linear programming formulation built on node variables only, which uses new constraints based on node-separators. We theoretically compare its strength to previously used MIP models in the literature and study the connected subgraph polytope associated with our new formulation. In our computational study we compare branch-and-cut implementations of the new model with two models recently proposed in the literature: one of them using the transformation into the Prize-Collecting Steiner Tree problem, and the other one working on the space of node variables only. The obtained results indicate that the new formulation outperforms the previous ones in terms of the running time and in terms of the stability with respect to variations of node weights.

Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90s and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach , where uncertainty is modeled by assumed probability distributions over the space of all possible scenarios and the objective is to find a solution with good probabilistic performance. In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e. , that has the best worst-case performance. In this paper we discuss the computational complexity of some classic combinatorial optimization problems using MMR approach, analyze the design of several algorithms for these problems, suggest the study of some specific research problems in this attractive area, and also discuss some applications using this model.

A note on the Bertsimas & Sim algorithm for robust combinatorial optimization problems

We improve the well-known result presented in Bertsimas and Sim (Math Program B98:49–71, 2003) regarding the computation of optimal solutions of Robust Combinatorial Optimization problems with interval uncertainty in the objective function coefficients. We also extend this improvement to a more general class of Combinatorial Optimization problems with interval uncertainty.

The Rooted Maximum Node-Weight Connected Subgraph Problem

Given a connected node-weighted (di)graph, with a root node r, and a (possibly empty) set of nodes R, the Rooted Maximum Node-Weight Connected Subgraph Problem (RMWCS) is the problem of finding a connected subgraph rooted at r that connects all nodes in R with maximum total weight. In this paper we consider the RMWCS as well as its budget-constrained version, in which also non-negative costs of the nodes are given, and the solution is not allowed to exceed a given budget. The considered problems belong to the class of network design problems and have applications in various different areas such as wildlife preservation planning, forestry, system biology and computer vision.

On exact solutions for the Minmax Regret Spanning Tree problem

The Minmax Regret Spanning Tree problem is studied in this paper. This is a generalization of the well-known Minimum Spanning Tree problem, which considers uncertainty in the cost function. Particularly, it is assumed that the cost parameter associated with each edge is an interval whose lower and upper limits are known, and the Minmax Regret is the optimization criterion. The Minmax Regret Spanning Tree problem is an NP-Hard optimization problem for which exact and heuristic approaches have been proposed. Several exact algorithms are proposed and computationally compared with the most effective approaches of the literature. It is shown that a proposed branch-and-cut approach outperforms the previous approaches when considering several classes of instances from the literature.

Exact approaches for solving robust prize-collecting Steiner tree problems

In the Prize-Collecting Steiner Tree Problem (PCStT) we are given a set of customers with potential revenues and a set of possible links connecting these customers with fixed installation costs. The goal is to decide which customers to connect into a tree structure so that the sum of the link costs plus the revenues of the customers that are left out is minimized. The problem, as well as some of its variants, is used to model a wide range of applications in telecommunications, gas distribution networks, protein–protein interaction networks, or image segmentation.

Alteration of Golgi Structure by Stress: A Link to Neurodegeneration?

The Golgi apparatus is well-known for its role as a sorting station in the secretory pathway as well as for its role in regulating post-translational protein modification. Another role for the Golgi is the regulation of cellular signaling by spatially regulating kinases, phosphatases, and GTPases. All these roles make it clear that the Golgi is a central regulator of cellular homeostasis. The response to stress and the initiation of adaptive responses to cope with it are fundamental abilities of all living cells. It was shown previously that the Golgi undergoes structural rearrangements under various stress conditions such as oxidative or osmotic stress. Neurodegenerative diseases are also frequently associated with alterations of Golgi morphology and many stress factors have been described to play an etiopathological role in neurodegeneration. It is however unclear whether the stress-Golgi connection plays a role in neurodegenerative diseases. Using a combination of bioinformatics modeling and literature mining, we will investigate evidence for such a tripartite link and we ask whether stress-induced Golgi arrangements are cause or consequence in neurodegeneration.

Single-commodity robust network design problem: Complexity, instances and heuristic solutions

We study a single-commodity Robust Network Design problem (RND) in which an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. In each scenario, a subset of the nodes is exchanging flow. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. Previously conducted computational investigations on the problem motivated the study of the complexity of some special cases and we present complexity results on them, including hypercubes. In turn, these results lead to the definition of new instances (random graphs with {−1,0,1} balances) that are computationally hard for the natural flow formulation. These instances are then solved by means of a new heuristic algorithm for RND, which consists of three phases. In the first phase the graph representing the network is reduced by heuristically deleting a subset of the arcs, and a feasible solution is built. The second phase consists of a neighborhood search on the reduced graph based on a Mixed-Integer (Linear) Programming (MIP) flow model. Finally, the third phase applies a proximity search approach to further improve the solution, taking into account the original graph. The heuristic is tested on the new instances, and the comparison with the solutions obtained by Cplex on a natural flow formulation shows the effectiveness of the proposed method.

A multicriteria optimization model for sustainable forest management under climate change uncertainty:an application in Portugal

Abstract We propose a multicriteria decision-making framework to support strategic decisions in forest management, taking into account uncertainty due to climate change and sustainability goals. In our setting, uncertainty is modeled by means of climate change scenarios. The decision task is to define a harvest scheduling that addresses, simultaneously, conflicting objectives: the economic value of the strategy, the carbon sequestration, the water use efficiency for biomass production and the runoff water, during the whole planning horizon. While the first objective is a classical managerial one, the later tree objectives aim at ensuring the environmental sustainability of the forest management plan. The proposed framework is a combination of Goal Programming and Stochastic Programming. Depending on the decision-maker preferences, the model produces harvest scheduling policies that yield different trade-offs among the conflicting criteria. Furthermore, we propose the incorporation of a risk-averse component in order to improve the performance of the obtained policies with respect to their economical value. This novel approach is tested on a real forest, located in central Portugal, which is comprised of a large number of stands (aggregated into 21 strata), climate change is modeled by 32 scenarios, and a planning horizon of 15 years is considered. The obtained results show the capacity of the designed framework to provide a pool of diverse solutions with different trade-offs among the four criteria, giving to the manager the possibility of choosing a harvesting policy that meets her/his requirements.

Vulnerability Assessment of Spatial Networks: Models and Solutions

In this paper we present a collection of combinatorial optimization problems that allows to assess the vulnerability of spatial networks in the presence of disruptions. The proposed measures of vulnerability along with the model of failure are suitable in many applications where the consideration of failures in the transportation system is crucial. By means of computational results, we show how the proposed methodology allows us to find useful information regarding the capacity of a network to resist disruptions and under which circumstances the network collapses.