In this work we propose a simultaneous scheduling and control optimization formulation to address both optimal steady-state production and dynamic product transitions in multiproduct tubular reactors working in several parallel production lines. Because the problem involves integer and continuous variables and the dynamic behavior of the underlying system the resulting optimization problem is c...

Software product line (SPL) engineering involves the modeling, analysis, and configuration of variability-rich systems. We improve the performance of the multi-objective optimization of SPLs in Alloy by several orders of magnitude with two techniques. First, we rewrite the model to remove binary relations that map to integers, which enables removing most of the integer atoms from the universe. ...

We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations of the form yI = ∏ i∈I xi over the 0−1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained zeroone polynomial optimization problem. We de...

Integration of scheduling and control can improve the overall performance of a manufacturing process. However, the integration leads to a mixed-integer dynamic optimization problem (MIDO), which could be challenging to solve. We propose a novel algorithm based on the generalized Bender decomposition method that takes advantage of the special structure of the integrated problem. It decomposes th...

We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations of the form yI = ∏ i∈I xi over the 0−1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained binary polynomial optimization problem. We def...

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variable dimension. We discuss some of the many applications of this theory including to quadratic prog...

We present a Mixed Integer Linear Programming (MILP) approach in order to model the non-linear problem of minimizing tire noise function. In recent work, we proposed an exact solution for Tire Noise Optimization Problem, dealing with APproximation (TNOP-AP). Here study original modeling EXact- or real-noise (TNOP-EX) and propose new scheme obtain TNOP-EX. Relying on TNOP-AP, use Branch&Cut ...

In many transportation systems, a mismatch between the associated design and planning decisions demand is typically encountered. A tailored system not only appealing to operators, which could have better knowledge of their operational costs, but also users, since they would benefit from an increase in level service satisfaction. Hence, it important explicitly allow for interactions two model go...