We address the Undirected Team Orienteering Arc Routing Problem (UTOARP). In this problem, demand is placed at some edges of a given undirected graph and served demand edges produce a profit. Feasible routes must start and end at a given depot and there is a time limit constraint on the maximum duration of each route. … Read more
Derivative-free optimization algorithms are particularly useful for tackling blackbox optimization problems where the objective function arises from complex and expensive procedures that preclude the use of classical gradient-based methods. In contemporary decentralized environments, such functions are defined locally on different computational nodes due to technical or privacy constraints, introducing additional challenges within the optimization process. … Read more
Controlling the dynamics of large-scale networks is essential for a macroscopic reduction of overall consumption and losses in the context of energy supply, finance, logistics, and mobility. We investigate the optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. Graphons represent a limit object of a converging graph sequence … Read more
Multicommodity capacitated network design (MCND) models can be used to optimize the consolidation of shipments within e-commerce fulfillment networks. In practice, fulfillment networks require that shipments with the same origin and destination follow the same transfer path. This unsplittable flow requirement complicates the MCND problem, requiring integer programming (IP) formulations with binary variables replacing continuous … Read more
Service Network Design Problems (SNDPs) are prevalent in the freight industry. While the classic SNDP is defined on a discretized planning horizon with integral time units, the Continuous-Time SNDP (CTSNDP) uses a continuous-time horizon to avoid discretization errors. Existing CTSNDP algorithms primarily rely on the Dynamic Discretization Discovery (DDD) framework, which iteratively refines discretization and … Read more
We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve these programs efficiently, we introduce Lagrangian-integrated L-shaped (\(L^2\)) methods, which guarantee exact solutions when the first-stage decisions are pure binary. For mixed-binary first-stage … Read more
We study multi-follower bilevel optimization problems with binary linking variables where the second level consists of many independent integer-constrained subproblems. This problem class not only generalizes many classical interdiction problems but also arises naturally in many network design problems where the second-level subproblems involve complex routing decisions of the actors involved. We propose a novel … 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
This paper studies the problems of partitioning the vertices of a graph G = (V,E) into (or covering with) a minimum number of low-diameter clusters from the lenses of approximation algorithms and integer programming. Here, the low-diameter criterion is formalized by an s-club, which is a subset of vertices whose induced subgraph has diameter at … Read more
In the quadratic minimum spanning tree problem (QMSTP) one wants to find the minimizer of a quadratic function over all possible spanning trees of a graph. We present a formulation of the QMSTP as a mixed-integer semidefinite program exploiting the algebraic connectivity of a graph. Based on this formulation, we derive a doubly nonnegative relaxation … Read more