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This paper presents key enhancements to our previous work~\cite{naghmouchi2024mixed} on a hybrid Benders decomposition (HBD) framework for solving mixed integer linear programs (MILPs). In our approach, the master problem is reformulated as…
Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is…
Recently increasing penetration of renewable energy generation brings challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete…
Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision…
We present a new framework for solving general topology optimization (TO) problems that find an optimal material distribution within a design space to maximize the performance of a structure while satisfying design constraints. These…
Decision trees are a popular machine learning model which are traditionally trained by heuristic methods. Massive improvements in computing power and optimisation techniques has led to renewed interest in learning globally optimal decision…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
Mixed-integer programming (MIP) provides a powerful framework for optimization problems, with Branch-and-Cut (B&C) being the predominant algorithm in state-of-the-art solvers. The efficiency of B&C critically depends on heuristic policies…
We propose the formulation of convex Generalized Disjunctive Programming (GDP) problems using conic inequalities leading to conic GDP problems. We then show the reformulation of conic GDPs into Mixed-Integer Conic Programming (MICP)…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the…
This study presents a discrete physics-informed neural network (dPINN) framework, enhanced with enforced interface constraints (EIC), for modeling physical systems using the domain decomposition method (DDM). Built upon finite element-style…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
Decarbonisation is driving dramatic growth in renewable power generation. This increases uncertainty in the load to be served by power plants and makes their efficient scheduling, known as the unit commitment (UC) problem, more difficult.…
The growth in online shopping and third party logistics has caused a revival of interest in finding optimal solutions to the large scale in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due…
In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer…
Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a…
Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…