The restoration of a power system after an extended blackout starts around units with enhanced technical capabilities, referred to as black start units (BSUs). We examine the planning problem of optimally allocating these units on the grid subject to a budget constraint. We present a mixed integer programming model based on current literature in power … Read more
We study deep neural networks with binary activation functions (BDNN), i.e. the activation function only has two states. We show that the BDNN can be reformulated as a mixed-integer linear program which can be solved to global optimality by classical integer programming solvers. Additionally, a heuristic solution algorithm is presented and we study the model … Read more
A generating function technique for solving integer programs via the evaluation of complex path integrals is discussed from a theoretical and computational perspective. Applying the method to solve knapsack feasibility problems, it is demonstrated how the presented numerical integration algorithm benefits from pre-optimizing the path of integration. After discussing the algorithmic set-up in detail, a … Read more
Using the weighted geometric series expansion, it is shown how integer programming can be solved by evaluating complex path integrals based on a multi-path version of Cauchy’s integral formula. In contrast to existing generating function approaches, the algorithm relies only on complex quadrature and no algebraic techniques are needed. In view of fast implementations of … Read more
In most project portfolio selection (PPS) situations, the presence of multiple attributes and decision-maker preference is inevitable. As Multi-criteria Decision Analysis (MCDA) methods provide a framework well-suited to deal with these challenges in PPS problems, the use of MCDA methods in real-life PPS problems has increased in recent years. This paper provides a comprehensive literature … 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
This paper addresses a real-life personnel scheduling problem in the context of Covid-19 pandemic, arising in a large Italian pharmaceutical distribution warehouse. In this case study, the challenge is to determine a schedule that attempts to meet the contractual working time of the employees, considering the fact that they must be divided into mutually exclusive … Read more
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, … Read more
We describe an algorithmic framework generalizing the well-known framework originally introduced by Benders. We apply this framework to several classes of optimization problems that fall under the broad umbrella of multilevel/multistage mixed integer linear optimization problems. The development of the abstract framework and its application to this broad class of problems provides new insights and … Read more
Cutting planes accelerate branch-and-bound search primarily by cutting off fractional solutions of the linear programming (LP) relaxation, resulting in tighter bounds for pruning the search tree. Yet cutting planes can also reduce backtracking by excluding inconsistent partial assignments that occur in the course of branching. A partial assignment is inconsistent with a constraint set when … Read more