T concept of dominance among nodes of a branch-and-bound tree, although known for a long time, is typically not exploited by general-purpose mixed-integer linear programming (MILP) codes. The starting point of our work was the general-purpose dominance procedure proposed in the 1980s by Fischetti and Toth, where the dominance test at a given node of the branch-and-bound tree consists of the (po...

In recent years, Mixed Integer Linear Programming (MILP) has been successfully applied in searching for differential characteristics and linear approximations in block ciphers and has produced the significant results for some ciphers such as SIMON (a family of lightweight and hardware-optimized block ciphers designed by NSA) etc. However, in the literature, the MILP-based automatic search algor...

Minimum-distance controlled tabular adjustment methods (CTA), an its variants, are considered an emerging perturbative approach for tabular data protection. Given a table to be protected, the purpose of CTA is to find the closest table that guarantees protection levels for the sensitive cells. We consider the most general CTA formulation which includes binary variables, thus providing protected...

We present optimal solutions to the test scheduling problem for core-based systems. Given a set of tasks (test sets for the cores), a set of test resources (e.g. test buses, BIST hardware) and a test access architecture, we determine start times for the tasks such that the total test application time is minimized. We show that the test scheduling decision problem is equivalent to the m-processo...

The primary goal of this thesis is to study transmission line reactance tweaking, as a mechanism for both post-disturbance control and pre-disturbance resilience enhancement in a transmission network, and develop an optimization framework for evaluating the efficacy of this mechanism in both scenarios. We start by developing a mixed-integer linear programming (MILP) formulation for tracking the...

Jeroslow and Lowe gave an exact geometric characterization of subsets of R that are projections of mixed-integer linear sets, a.k.a MILP-representable sets. We give an alternate algebraic characterization by showing that a set is MILP-representable if and only if the set can be described as the intersection of finitely many affine Chvátal inequalities. These inequalities are a modification of a...

Exact and heuristic methods for solving difficult optimization problems have been usually considered as two completely different approaches, with each of them being extensively studied by a different research community and used in different fields of application. In this work we propose a scheme for the integration and cooperation of an exact method, based on mixed-integer linear programming (M...

Two new Mixed Integer Linear Programming (MILP) formulations for modeling a univariate piecewise linear function f were introduced in Li et al. (2008). The first formulation (given by (1)–(3) in Li et al.) uses “Big-M” type constraints, so we denote it by LiBigM. The second formulation (given by (23)–(33) in Li et al.) uses a number of binary variables that is logarithmic in the number of segme...

Deep Neural Networks (DNNs) are very popular these days, and are the subject of a very intense investigation. A DNN is made by layers of internal units (or neurons), each of which computes an affine combination of the output of the units in the previous layer, applies a nonlinear operator, and outputs the corresponding value (also known as activation). A commonly-used nonlinear operator is the ...

State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a network of tracks. In this paper we consider the problem of controlling the route of each DCV in the system. In general this results in a nonlinear, nonconvex, mixed integer optimization problem which is usually very expen...