Problem definition: More than one-third of US domestic flights are operated by regional airlines. This paper focuses on optimizing medium-term schedule planning decisions for a network of regional airlines through the joint optimization of frequency planning, timetable development, fleet assignment, and some limited aspects of route planning, while capturing passengers’ travel decisions through a general … Read more
In this paper, a class of bilevel programming problems is studied, in which the lower level is a quadratic programming problem, and the upper level problem consists of a nonlinear objective function with coupling constraints. An iterative process is developed to generate a sequence of points, which converges to the solution of this problem. In … Read more
Binary bilevel programs are notoriously difficult to solve due to the absence of strong and efficiently computable relaxations. In this work, we introduce a novel single-level reformulation of these programs by leveraging a network flow-based representation of the follower’s value function, utilizing decision diagrams and linear programming duality. This approach enables the development of scalable … Read more
We study the lift-and-project rank of the stable set polytope of graphs with respect to the Lovász–Schrijver SDP operator \( \text{LS}_+ \) applied to the fractional stable set polytope. In particular, we show that for every positive integer \( \ell \), the smallest possible graph with \( \text{LS}_+ \)-rank \( \ell \) contains \( 3\ell … Read more
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite relaxation and propose a randomized rounding algorithm to generate feasible solutions from the relaxation. Second, we derive constant-factor approximation guarantees for our algorithm. When optimizing … Read more
Single-source capacitated facility location problems are well studied in the operations research literature, yet classic problems often lack practicability by disregarding the customers’ perspective: An authority that assigns customers to open facilities deprives customers from choosing facilities according to their individual preferences. In reality, this can render solutions infeasible, as customers may deviate to their … Read more
The increasing penetration of renewable energy and rising electricity demand are driving the need to integrate new buses and transmission lines into transmission grids. These trends are reshaping transmission expansion planning (TEP), motivating the development of effective methodologies to manage the resulting complexity. This paper introduces the longest shortest-path connection (LSPC) algorithm, a graph-based method … Read more
This paper develops a unified game-theoretical framework for data classification and network discovery based on pairwise influences in multivariate categorical choices. Data points, interpreted as individuals, are connected through a signed weighted graph and take values according to a voting rule that aggregates the influence of attractive (friend-like) and repulsive (enemy-like) neighbors. The framework consists … Read more
The traveling salesman problem is a widely studied classical combinatorial problem for which there are several integer linear formulations. In this work, we consider the Miller-Tucker-Zemlin (MTZ), Desrochers-Laporte (DL) and Single Commodity Flow (SCF) formulations. We argue that the choice of some parameters of these formulations is arbitrary and, therefore, there are families of formulations … Read more
Given graph G = (V,E) with vertex set V and edge set E, the max k-cut problem seeks to partition the vertex set V into at most k subsets that maximize the weight (number) of edges with endpoints in different parts. This paper proposes a graph folding procedure (i.e., a procedure that reduces the number … Read more