Chrysafis Vogiatzis

Integer programming models for the multidimensional assignment problem with star costs

We consider a variant of the multidimensional assignment problem (MAP) with decomposable costs in which the resulting optimal assignment is described as a set of disjoint stars. This problem arises in the context of multi-sensor multi-target tracking problems, where a set of measurements, obtained from a collection of sensors, must be associated to a set of different targets. To solve this problem we study two different formulations. First, we introduce a continuous nonlinear program and its linearization, along with additional valid inequalities that improve the lower bounds. Second, we state the standard MAP formulation as a set partitioning problem, and solve it via branch and price. These approaches were put to test by solving instances ranging from tripartite to 20-partite graphs of 4 to 30 nodes per partition. Computational results show that our approaches are a viable option to solve this problem. A comparative study is presented.

An integer programming approach for finding the most and the least central cliques

We consider the problem of finding the most and the least “influential” or “influenceable” cliques in graphs based on three classical centrality measures: degree, closeness and betweenness. In addition to standard clique betweenness, which is defined as the proportion of shortest paths between any two graph nodes that pass through the clique, we also consider its optimistic and pessimistic versions, where outside nodes may favor or try to avoid shortest paths passing through the clique, respectively. We discuss the computational complexity issues for these problems and develop linear 0–1 programming formulations for each centrality metric. Finally, we demonstrate the performance of the developed formulations on real-life and synthetic networks, and provide some interesting insights based on the obtained results. In particular, our findings indicate that there are considerable variations between the centrality values of large cliques within the same networks. Moreover, the most central cliques in graphs are not necessarily the largest ones.

Evacuation Modeling and Betweenness Centrality

In this chapter, we consider the problem of efficiently evacuating all people in an urban area from danger zones to safe zones. This problem, which has attracted major scientific interest and has been well-studied in literature, is indeed large-scale, and as such difficult to solve. In this work, we propose a solution method based on an islanding scheme. This decomposition approach takes into consideration the betweenness of a set of nodes in the transportation network, and aims to obtain clusters from those nodes that can be easily solved: the idea is to divide the flow more evenly towards multiple paths to safety, leading to a more robust evacuation process. We portray our results on several synthetic and real-life transportation networks. More importantly, we use a very large-scale network representation of the city of Jacksonville, Florida, in the USA to show that our approaches solve the problem, a feat that proved impossible for commercial solvers. We conclude this study with our observations and plans for future work.

Evacuation Through Clustering Techniques

Evacuation and disaster management is of the essence for any advanced society. Ensuring the welfare and well-being of the citizens even in times of immense distress is of utmost importance. Especially in coastal areas where tropical storms and hurricanes pose a threat on a yearly basis, evacuation planning and management is vital. However, modern metropolitan city evacuations prove to be large-scale optimization problems which cannot be tackled in a timely manner with the computational power available. We propose a clustering technique to divide the problem into smaller and easier subproblems and present numerical results that prove our success.

Graph partitions for the multidimensional assignment problem

In this paper, we consider two decomposition schemes for the graph theoretical description of the axial Multidimensional Assignment Problem (MAP). The problem is defined as finding n disjoint cliques of size m with minimum total cost in Km×n, which is an m-partite graph with n elements per dimension. Even though the 2-dimensional assignment problem is solvable in polynomial time, extending the problem to include n≥3 dimensions renders it

Multilocus phylogenetic analysis with gene tree clustering

\mathcal{NP}

Guest editorial: revised selected papers from the LION 8 conference

-hard. We propose two novel decomposition schemes for partitioning a MAP into disjoint subproblems, that can then be recombined to provide both upper and lower bounds to the original problem. For each of the partitioning schemes, we investigate and compare the efficiency of distinct exact and heuristic methodologies, namely augmentation and partitioning. Computational results for the methods, along with a hybrid one that consists of both partitioning schemes, are presented to depict the success of our approaches on large-scale instances.

Integer programming models for detecting graph bipartitions with structural requirements

Both theoretical and empirical evidence point to the fact that phylogenetic trees of different genes (loci) do not display precisely matched topologies. Nonetheless, most genes do display related phylogenies; this implies they form cohesive subsets (clusters). In this work, we discuss gene tree clustering, focusing on the normalized cut (Ncut) framework as a suitable method for phylogenetics. We proceed to show that this framework is both efficient and statistically accurate when clustering gene trees using the geodesic distance between them over the Billera–Holmes–Vogtmann tree space. We also conduct a computational study on the performance of different clustering methods, with and without preprocessing, under different distance metrics, and using a series of dimensionality reduction techniques. Our results with simulated data reveal that Ncut accurately clusters the set of gene trees, given a species tree under the coalescent process. Other observations from our computational study include the similar performance displayed by Ncut and k-means under most dimensionality reduction schemes, the worse performance of hierarchical clustering, and the significantly better performance of the neighbor-joining method with the p-distance compared to the maximum-likelihood estimation method. Supplementary material, all codes, and the data used in this work are freely available at http://polytopes.net/research/cluster/ online.

A survey of computational methods in protein–protein interaction networks

In February 2014, we had the honor of organizing the eighth installment of the conference series “Learning and Intelligent Optimization” (LION) in Gainesville, Florida, USA. As always, the work presented was at the forefront of research performed between the fields of Artificial Intelligence, Mathematical Programing and Optimization, and Algorithmic Design. The conference was very successful in attracting researchers from around the world who have been pushing the boundaries in the intersection of the above fields, among others. As has become tradition from the earlier, very successful LION conferences, we are happy to dedicate this special issue to extended versions of a selected sample of the work presented in LION 8 in February 2014. For the remainder of the contributions submitted and presented during LION 8, we refer the interested reader to [1]. The spectrum of the topics covered in this special issue ranges from facility location and routing, to job scheduling and robotics, while the techniques and approaches come from fields as diverse as algorithm portfolio techniques, evolutionary algorithms, and hybrid metaheuristics. More specifically this special issue contains the following contributions. The first paper, Bayesian Optimization for Learning Gaits Under Uncertainty by Roberto Calandra, Andre Seyfarth, Jan Peters, and Marc Peter Deisenroth, deals with the problem

Sensors in Transportation and Logistics Networks

The graph bipartitioning problem consists of dividing a graph into two disjoint subgraphs, such that each node is highly similar to others in the same subgraph, but also different from members of the other subgraph, according to some homogeneity criterion. This problem has received significant attention over the last few years because of its applicability in areas as diverse as data classification, image segmentation, and social network analysis. In this article we study a variation of the graph bipartitioning problem in which, in addition to considering homogeneity criteria for generating the partition, we also ensure that one of the subgraphs satisfies a set of predefined structural properties—that is, such a subgraph is required to induce a given motif. We focus our attention on imposing structural constraints that force one of the subgraphs to induce stars, cliques, and clique relaxations (quasi-cliques) and discuss some specific applications for such particular cases. We tackle this problem by modeling it as a general fractional programming optimization problem and study several solution approaches. Moreover, we discuss additional algorithmic enhancements to tackle some of the aforementioned cases, and provide two greedy algorithms for the specific cases of induced cliques and stars, showing the approximation ratio for induced stars. Finally, we test the quality of our approach by solving a collection of several real-life and randomly generated instances with various configurations, analyzing the benefits of the proposed models, as well as possible further extensions.