Related papers: Polynomial Time Algorithms and Extended Formulatio…
The main contribution of this paper resides in developing a new algorithmic approach for addressing the continuous-time joint replenishment problem, termed $\Psi$-pairwise alignment. The latter mechanism, through which we synchronize…
Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…
Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…
The main theme of this dissertation is the study of the lattice points in a rational convex polyhedron and their encoding in terms of Barvinok's short rational functions. The first part of this thesis looks into theoretical applications of…
We consider the classic scheduling problem of minimizing the total weighted flow-time on a single machine (min-WPFT), when preemption is allowed. In this problem, we are given a set of $n$ jobs, each job having a release time $r_j$, a…
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a…
We study the problem of finding elements in the intersection of an arbitrary conic variety in $\mathbb{F}^n$ with a given linear subspace (where $\mathbb{F}$ can be the real or complex field). This problem captures a rich family of…
The Unit Commitment (UC) problem is a key optimization task in power systems to forecast the generation schedules of power units over a finite time period by minimizing costs while meeting demand and technical constraints. However, many…
Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…
The daily operation of real-world power systems and their underlying markets relies on the timely solution of the unit commitment problem. However, given its computational complexity, several optimization-based methods have been proposed to…
Aggregations of flexible loads can provide several power system services through demand response programs, for example load shifting and curtailment. The capabilities of demand response should therefore be represented in system operators'…
In this work, we consider a scheduling problem faced by production companies with large electricity consumption. Due to the contract with the electric utility, the production companies are obligated to comply with the total energy…
The Windows Scheduling Problem, also known as the Pinwheel Problem, is to schedule periodic jobs subject to their processing frequency demands. Instances are given as a set of jobs that have to be processed infinitely often such that the…
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…
We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulae for different restricted formula classes. It turns out that for each class from our framework, the above problem…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
Value-oriented forecasts for two-stage power system operational problems have been demonstrated to reduce cost, but prove to be computationally challenging for large-scale systems because the underlying optimization problem must be…
We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex costs and linear state transition function. The action spaces are polyhedral and described by…
One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…
In some important application areas of hard real-time systems, preemptive sporadic tasks with harmonic periods and constraint deadlines running upon a uni-processor platform play an important role. We propose a new algorithm for determining…