Combinatorial Optimization

Integrating Power Profile Optimization with Timetabling for Underground Train Networks

Categories (Mixed) Integer Linear Programming, Polyhedra, Transportation Tags , , ,

We study energy-efficient operation of underground train networks by integrating power profile optimization with timetable design in a single mixed-integer optimization framework. The model minimizes traction energy by synchronizing braking and acceleration across trains sharing a power subnetwork to exploit regenerative energy and flexibly allocating running times to promote coasting. Unlike timetable-only approaches with fixed … Read more

Optimal Combinatorial Testing with Constraints: The Balancing Act

Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Graphs and Matroids

Imagine that you are in front of a cockpit with several on–off buttons. If you were to thoroughly test it, you would need to try a prohibitive number of configurations. But since most bugs in practice can be isolated to interactions among few components, having tests that cover every possible pairwise configuration is a good … Read more

Attention Mechanisms in Physics-Inspired Graph Neural Networks for the Max-Cut Problem

Categories Combinatorial Optimization, Graphs and Matroids, Network Optimization Tags , , ,

Physics-Inspired Graph Neural Networks (PI-GNNs) reformulate MAX-CUT as QUBO energy minimization, training a GNN to produce soft binary node assignments without labeled data. The baseline PI-GCN uses static, degree-normalized aggregation, while its attention-augmented counterpart PI-GAT—built on GATv2—introduces additional hyperparameters whose effects remain uncharacterized. This paper addresses that gap through controlled experiments on five Gset benchmark … Read more

Random-Key Optimization for 2D Irregular Packing with Reusable Area Evaluation

Categories Applications - OR and Management Sciences, Meta Heuristics, Parallel Algorithms, Production and Logistics Tags , ,

The diverse constraints of industrial applications lead to variants of 2D irregular packing problems that require tailored solution methods. This paper addresses a real-world industrial challenge by proposing a new problem definition, the Maximum Reusable Contiguous Area Problem (MRCAP), and a novel metric, the Maximum Contiguous Area, developed to measure and maximize the contiguous unused … Read more

A Polynomial-Time Algorithm for Coloring Perfect Graphs Based on Walk Counting

Categories Combinatorial Optimization, Semi-definite Programming Tags , ,

We present a polynomial-time algorithm for optimally coloring perfect graphs that is based entirely on graph-theoretic operations. At its core, the algorithm decides whether a perfect graph contains a clique of a given size by iteratively counting walks in the graph with certain weights assigned to its edges and nonedges. These weights are initialized according … Read more

A Catalog of Formulations for the Multi-Follower Discrete Bilevel Network Design Problem

Categories Bilevel Optimization, Branch and Cut Algorithms, Network Optimization Tags , , ,

Network design problems increasingly arise in settings where strategic infrastructure decisions and operational routing choices are made by different actors. Such interactions are naturally modeled as bilevel problems: a network operator designs or modifies a network, while users respond by selecting routes according to their own utilities. This structure captures many applications in transportation and … Read more

Skip or Insert? A Priori Optimization for the Vehicle Routing Problem with Time Windows and Stochastic Customers

Categories Combinatorial Optimization, Production and Logistics, Stochastic Programming Tags , , , , , , ,

We study an extension of the vehicle routing problem with time windows by incorporating stochastic customers, i.e., ad-hoc service requests. The uncertainty in stochastic customers is captured through scenarios. Two a priori optimization approaches, a classical and a new one lead to two different problems, both of which are modeled as scenario-based two-stage stochastic programs. … Read more

Neural Assortment Optimization

Categories Combinatorial Optimization, Nonsmooth Optimization, Yield Management

Assortment optimization selects a subset of items to maximize expected revenue under a discrete choice model and is widely used in revenue management and online platforms. Its combinatorial nature creates a practical tension among generality, scalability, and provable guarantees: model-specific algorithms can be strong when their structural assumptions hold, but are hard to adapt across … Read more

Optimal Macroitem Sequences in the Precedence Constrained Knapsack Problem

Categories Combinatorial Optimization, Graphs and Matroids, Linear Programming Tags , , ,

The Precedence Constrained Knapsack Problem (PCKP) asks for a maximum-profit subset of items, subject to a knapsack capacity constraint and precedence constraints encoded by a directed acyclic graph. We study the structure of optimal solutions of the Linear Programming (LP) relaxation of the natural Integer Linear Programming formulation of the PCKP. We introduce the notion … Read more

D-optimal partitioning: design of experiments under heterogeneous treatment effects

Categories Combinatorial Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

Modern experimentation in business and public policy often studies targeted interventions whose effects depend on the heterogeneous attributes of individuals. We examine heterogeneous treatment effects through the lens of optimal design of experiments, which allocates treatment decisions to maximize the precision of estimated treatment-covariate interactions. We introduce the D-optimal partitioning problem for balancing the information … Read more