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We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…
The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
The detection and classification of intersections between triangles are crucial tasks in a wide range of applications within Computer Graphics and Geometry Processing, including mesh Arrangements, mesh Booleans, and generic mesh processing…
Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the…
The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to…
This paper tackles the problem of finding optimal variable-height transport packaging. The goal is to reduce the empty space left in a box when shipping goods to customers, thereby saving on filler and reducing waste. We cast this problem…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Benders decomposition is widely used to solve large mixed-integer problems. This paper takes advantage of machine learning and proposes enhanced variants of Benders decomposition for solving two-stage stochastic security-constrained unit…
Accurate extrinsic calibration between LiDAR and camera sensors is important for reliable perception in autonomous systems. In this paper, we present a novel multi-objective optimization framework that jointly minimizes the geometric…
In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal…
Edge computing enables data processing closer to the source, significantly reducing latency, an essential requirement for real-time vision-based analytics such as object detection in surveillance and smart city environments. However, these…
A new predictor-corrector type incremental algorithm is proposed for the exact construction of weighted straight skeletons of 2D general planar polygons of arbitrary complexity based on the notion of deforming polygon. In the proposed…
Mixture models are well-established learning approaches that, in computer vision, have mostly been applied to inverse or ill-defined problems. However, they are general-purpose divide-and-conquer techniques, splitting the input space into…
This paper introduces the correlated arc orienteering problem (CAOP), where the task is to find routes for a team of robots to maximize the collection of rewards associated with features in the environment. These features can be…
Once an optimisation problem has been solved, the solution may need adaptation when contextual factors change. This challenge, also known as reoptimisation, has been addressed in various problem domains, such as railway crew rescheduling,…
Quantum optimization as a field has largely been restricted by the constraints of current quantum computing hardware, as limitations on size, performance, and fidelity mean most non-trivial problem instances won't fit on quantum devices.…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
We study the optimal design of heterogeneous Coded Elastic Computing (CEC) where machines have varying computation speeds and storage. CEC introduced by Yang et al. in 2018 is a framework that mitigates the impact of elastic events, where…
In container terminal yards, the Container Rehandling Problem (CRP) involves rearranging containers between stacks under specific operational rules, and it is a pivotal optimization challenge in intelligent container scheduling systems.…
In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is…