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We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. The resulting MIP…
Planning the maintenance of nuclear power plants is a complex optimization problem, involving a joint optimization of maintenance dates, fuel constraints and power production decisions. This paper investigates Mixed Integer Linear…
Recent growing complexity in space missions has led to an active research field of space logistics and mission design. This research field leverages the key ideas and methods used to handle complex terrestrial logistics to tackle space…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…
Uncertainty in surgery durations continues to be difficult to account for in operating room scheduling. In particular, it remains complex to accurately incorporate uncertainty in surgical overtime constraints within mixed-integer linear…
We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions.…
Large-scale spatial data such as air quality, thermal conditions and location signatures play a vital role in a variety of applications. Collecting such data manually can be tedious and labour intensive. With the advancement of robotic…
We study a single-machine scheduling problem with sequence dependent setup times, motivated by applications in manufacturing and service industries - in particular, the calendering stage in rubber flooring production. In this phase, setup…
Multi-Agent Path Finding (MAPF) is a long-standing problem in Robotics and Artificial Intelligence in which one needs to find a set of collision-free paths for a group of mobile agents (robots) operating in the shared workspace. Due to its…
This paper presents a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems. The approach is motivated by first showing that a lattice-based path planner can be…
Space mission planning and spacecraft design are tightly coupled and need to be considered together for optimal performance; however, this integrated optimization problem results in a large-scale Mixed-Integer Nonlinear Programming (MINLP)…
Optimal path planning is prone to convergence to local, rather than global, optima. This is often the case for mobile manipulators due to nonconvexities induced by obstacles, robot kinematics and constraints. This paper focuses on planning…
This paper introduces $\Delta$-MILP, a powerful variant of the mixed-integer linear programming (MILP) optimization framework to solve NASA's Deep Space Network (DSN) scheduling problem. This work is an extension of our original MILP…
Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal…
This paper presents a triple optimization algorithm of two-dimensional space, driving path and driving speed, and iterates in the time dimension to obtain the local optimal solution of path and speed in the optimal driving area. Design…
Applying intelligent robot arms in dynamic uncertain environments (i.e., flexible production lines) remains challenging, which requires efficient algorithms for real time trajectory generation. The motion planning problem for robot…
This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once…
We study the space of optimal schedules for a heat pump with thermal energy storage used in heating a residential building. We model the heating system as a Mixed Integer Linear Program with the objective to minimise the cost of heating. We…
Due to the restricted resources, efficient scheduling in vertiports has received much more attention in the field of Urban Air Mobility (UAM). For the scheduling problem, we utilize a Mixed Integer Linear Programming (MILP), which is often…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…