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We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been…
This paper introduces a new optimization model that integrates the multi-port stowage planning problem with the container relocation problem. This problem is formulated as a binary mathematical programming model that must find the…
In order to study real-world systems, many applied works model them through signed graphs, i.e. graphs whose edges are labeled as either positive or negative. Such a graph is considered as structurally balanced when it can be partitioned…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…
A classic network tomography problem is estimation of properties of the distribution of route traffic volumes based on counts taken on the network links. We consider inference for a general class of models for integer-valued traffic. Model…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
This work is a geometrical approach to the optimization problem motivated by transportation system management. First, an attempt has been made to furnish a comprehensive account of geometric programming based on the elementary Finsler…
This work addresses the problem associated with coordinating scheduling decisions among multiple base stations in an LTE-Advanced downlink network in order to manage inter-cell interference with a centralized controller. To solve the…
Motivated by the remarkable interplay between (chordal) graphs and matrix algebra, we associate to each graph a so-called completion number that might encode some aspects of that interplay. We show that this number is not trivial, and we…
We prove that any mixed-integer linear extended formulation for the matching polytope of the complete graph on $n$ vertices, with a polynomial number of constraints, requires $\Omega(\sqrt{\sfrac{n}{\log n}})$ many integer variables. By…
Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are…
introduce {\sc Planar Disjoint Paths Completion}, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph $G,$ $k$…
This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is…
Traffic matrix measurement is fundamental for datacenter operations, but obtaining complete traffic matrices at scale remains challenging due to the prohibitive cost of global fine-grained measurement and partial observations resulting from…
We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In…
This paper introduces the two-level capacitated vehicle routing problem (2S-CVRP). This problem combines the two-level bin packing problem and the vehicle routing problem into an integrated framework. The problem itself is an NP-hard…
Consider a problem where we are given a bipartite graph H with vertices arranged on two horizontal lines in the plane, such that the two sets of vertices placed on the two lines form a bipartition of H. We additionally require that H admits…
Efficient consistency maintenance of incomplete and dynamic real-life databases is a quality label for further data analysis. In prior work, we tackled the generic problem of database updating in the presence of tuple generating constraints…
This paper extends our previous work in [1],[2], on optimal scheduling of autonomous vehicle arrivals at intersections, from one to a grid of intersections. A scalable distributed Mixed Integer Linear Program (MILP) is devised that solves…
This paper analyzes the integration of artificial intelligence (AI) with mixed integer linear programming (MILP) to address complex optimization challenges in air transportation with explainability. The study aims to validate the use of…