In 2013, Buchheim and Wiegele introduced a quadratic optimisation problem, in which the domain of each variable is a closed subset of the reals. This problem includes several other important problems as special cases. We study some convex sets and polyhedra associated with the problem, and derive several families of strong valid inequalities. We also … Read more
One of the standard approaches for solving time-dependent discrete optimization problems, such as the traveling salesman problem with time-windows or the shortest path problem with time-windows, is to derive a so-called time-indexed formulation. If the problem has an underlying structure that can be described by a graph, the time-indexed formulation is usually based on a … Read more
Influence maximization (IM) is a challenging combinatorial optimization problem on (social) networks given a diffusion model and limited choice for initial seed nodes. In a recent paper an integer programming formalization of IM using the so-called deterministic linear threshold diffusion model was proposed. In fact, it is a special 0-1 linear program in which the … Read more
The field of Statistical Disclosure Control aims at reducing the risk of re-identification of an individual when disseminating data, and it is one of the main concerns of national statistical agencies. Operations Research (OR) techniques were widely used in the past for the protection of tabular data, but not for microdata (i.e., files of individuals … Read more
We consider the task of proving integer infeasibility of a bounded convex set K in R^n using a general branching proof system. In a general branching proof, one constructs a branching tree by adding an integer disjunction at each node, such that the leaves of the tree correspond to empty sets (i.e., K together with … Read more
Linear bilevel optimization problems are often tackled by replacing the linear lower-level problem with its Karush–Kuhn–Tucker (KKT) conditions. The resulting single-level problem can be solved in a branch-and-bound fashion by branching on the complementarity constraints of the lower-level problem’s optimality conditions. While in mixed-integer single-level optimization branch- and-cut has proven to be a powerful extension … Read more
The problem of community detection with two equal-sized communities is closely related to the minimum graph bisection problem over certain random graph models. In the stochastic block model distribution over networks with community structure, a well-known semidefinite programming (SDP) relaxation of the minimum bisection problem recovers the underlying communities whenever possible. Motivated by their superior … Read more
Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. However, the time-varying PV generation is not perfectly known when the system operator decides the HVAC control schedules. To consider the unknown uncertain PV generation, in this paper, we formulate a distributionally robust … Read more
We revisit and strengthen splitting methods for solving doubly nonnegative, DNN, relaxations of the quadratic assignment problem, QAP. We use a modified restricted contractive splitting method, rPRSM, approach. Our strengthened bounds and new dual multiplier estimates improve on the bounds and convergence results in the literature. Citation Department of Combinatorics & Optimization, University of Waterloo, … Read more
A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of n∆ on the proximity of optimal solutions of an Integer Linear Programming problem and its standard linear relaxation. In this bound, n is the number of variables and ∆ denotes the maximum of the absolute values of the subdeterminants of the … Read more