-- This paper addresses the problem of motion planning for differential drive micro-mobility platforms. This class of vehicle is designed to perform small-distance transportation of passengers and goods in structured environments. Our approach leverages mixed-integer linear programming (MILP) to compute global optimal collision-free trajectories taking into account the kinematics and dynamics of the vehicle. We propose novel constraints for intersample collision avoidance and demonstrate its effectiveness using pick-up and delivery missions and statistical analysis of Monte Carlo simulations. The results show that the novel formulation provides the best trajectories in terms of time expenditure and control effort when compared to two state-of-the-art approaches.

Home Energy Management Systems (HEMS) have emerged as a pivotal tool in the smart home ecosystem, aiming to enhance energy efficiency, reduce costs, and improve user comfort. By enabling intelligent control and optimization of household energy consumption, HEMS plays a significant role in bridging the gap between consumer needs and energy utility objectives. However, much of the existing literature construes consumer comfort as a mere deviation from the standard appliance settings. Such deviations are typically incorporated into optimization objectives via static weighting factors. These factors often overlook the dynamic nature of consumer behaviors and preferences. Addressing this oversight, our paper introduces a multi-mode Deep Reinforcement Learning-based HEMS (DRL-HEMS) framework, meticulously designed to optimize based on dynamic, consumer-defined preferences. Our primary goal is to augment consumer involvement in Demand Response (DR) programs by embedding dynamic multi-mode preferences tailored to individual appliances. In this study, we leverage a model-free, single-agent DRL algorithm to deliver a HEMS framework that is not only dynamic but also user-friendly. To validate its efficacy, we employed real-world data at 15-minute intervals, including metrics such as electricity price, ambient temperature, and appliances' power consumption. Our results show that the model performs exceptionally well in optimizing energy consumption within different preference modes. Furthermore, when compared to traditional algorithms based on Mixed-Integer Linear Programming (MILP), our model achieves nearly optimal performance while outperforming in computational efficiency.

Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.

In this paper, we investigate the constraint typology of mixed-integer linear programming MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning, resource allocation, timetabling optimization problems, providing optimized business solutions for industry sectors such as: manufacturing, agriculture, defence, healthcare, medicine, energy, finance, and transportation. Despite the numerous real-life Combinatorial Optimization Problems found and solved, and millions yet to be discovered and formulated, the number of types of constraints, the building blocks of a MILP, is relatively much smaller. In the search of a suitable machine readable knowledge representation for MILPs, we propose an optimization modelling tree built based upon an MILP ontology that can be used as a guidance for automated systems to elicit an MILP model from end-users on their combinatorial business optimization problems.

A live interactive narrative (LIN) is an experience where multiple players take on fictional roles and interact with real-world objects and actors to participate in a pre-authored narrative. Temporal properties of LINs are important to its viability and aesthetic quality and hence deserve special design consideration. In this paper, we tackle the largely overlooked problem of scheduling a multiplayer interactive narrative and propose the Live Interactive Narrative Scheduling Problem (LINSP), which handles reasoning under temporal uncertainty, resource scheduling, and non-linear plot choices. We present a mixed-integer linear programming formulation of the problem and empirically evaluates its scalability over large narrative instances.

We are concerned with controlling dynamical systems, such as self-driving cars and smart buildings, in a manner that guarantees that they satisfy complex task specifications. Mixed integer linear programming has recently proven to be a powerful tool for such problems, enabling the computation of optimal plans that satisfy complex temporal constraints for high-dimensional, dynamical systems. These optimization-based approaches find solutions quickly for challenging (and previously unsolvable) planning problems. Framing temporal logic planning as constrained optimization also presents exciting new areas of research.