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In this paper, we study the fundamental problem of finding a stable matching in two-sided matching markets. In the classic variant, it is assumed that both sides of the market submit a ranked list of all agents on the other side. However,…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…
Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have…
The Joint Routing-Assignment (JRA) optimization problem simultaneously determines the assignment of items to placeholders and a Hamiltonian cycle that visits each node pair exactly once, with the objective of minimizing total travel cost.…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
We have focused on Answer Set Programming (ASP), more specifically, answer set counting, exploring both exact and approximate methodologies. We developed an exact ASP counter, sharpASP, which utilizes a compact encoding for propositional…
We give a 3/2-approximation algorithm for stable matchings that runs in $O(m)$ time. The previously best known algorithm by McDermid has the same approximation ratio but runs in $O(n^{3/2}m)$ time, where $n$ denotes the number of people and…
The feasibility-seeking approach provides a systematic scheme to manage and solve complex constraints for continuous problems, and we explore it for the floorplanning problems with increasingly heterogeneous constraints. The classic…
Exactly solving multi-objective integer programming (MOIP) problems is often a very time consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such…
We investigate the complexity of approximately counting stable roommate assignments in two models: (i) the $k$-attribute model, in which the preference lists are determined by dot products of "preference vectors" with "attribute vectors"…
Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control…
In the university timetabling problem, sometimes additions or cancellations of course sections occur shortly before the beginning of the academic term, necessitating last-minute teaching staffing changes. We present a decision-making…
The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…
This paper addresses the deadline-constrained task offloading and resource allocation problem in multi-access edge computing. We aim to determine where each task is offloaded and processed, as well as corresponding communication and…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
This paper considers the maximization of the expected maximum value of a portfolio of random variables subject to a budget constraint. We refer to this as the optimal college application problem. When each variable's cost, or each college's…
Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been…
The balance between convergence and diversity is a key issue of evolutionary multi-objective optimization. The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of…
The seminar assignment problem is a variant of the generalized assignment problem in which items have unit size and the amount of space allowed in each bin is restricted to an arbitrary set of values. The problem has been shown to be…