Robots in Retirement Homes: Applying Off-the-Shelf Planning and Scheduling to a Team of Assistive Robots

This paper investigates three different technologies for solving a planning and scheduling problem of deploying multiple robots in a retirement home environment to assist elderly residents. The models proposed make use of standard techniques and solvers developed in AI planning and scheduling, with two primary motivations. First, to find a planning and scheduling solution that we can deploy in our real-world application. Second, to evaluate planning and scheduling technology in terms of the ``model-and-solve'' functionality that forms a major research goal in both domain-independent planning and constraint programming. Seven variations of our application are studied using the following three technologies: PDDL-based planning, time-line planning and scheduling, and constraint-based scheduling. The variations address specific aspects of the problem that we believe can impact the performance of the technologies while also representing reasonable abstractions of the real world application. We evaluate the capabilities of each technology and conclude that a constraint-based scheduling approach, specifically a decomposition using constraint programming, provides the most promising results for our application. PDDL-based planning is able to find mostly low quality solutions while the timeline approach was unable to model the full problem without alterations to the solver code, thus moving away from the model-and-solve paradigm. It would be misleading to conclude that constraint programming is ``better'' than PDDL-based planning in a general sense, both because we have examined a single application and because the approaches make different assumptions about the knowledge one is allowed to embed in a model. Nonetheless, we believe our investigation is valuable for AI planning and scheduling researchers as it highlights these different modelling assumptions and provides insight into avenues for the application of AI planning and scheduling for similar robotics problems. In particular, as constraint programming has not been widely applied to robot planning and scheduling in the literature, our results suggest significant untapped potential in doing so.California Institute of Technology. Keck Institute for Space Studie

Optimisation de la planification à court et moyen terme dans les mines souterraines

RÉSUMÉ: La présente thèse s’inscrit dans le mouvement de numérisation des mines souterraines en s’attaquant au problème de planification. L’objectif global de la thèse est de fournir un outil d’optimisation des planifications à court et moyen terme permettant l’accès rapide à une solution optimale. La planification dans les mines souterraines pour ces horizons de temps est un problème difficile pour plusieurs raisons, notamment de par le grand nombre de ressources nécessaires, le grand nombre d’endroits de travail, les implications à long terme difficiles à prévoir et le niveau de précision requis. De manière plus spécifique, les objectifs de recherche sont de développer un modèle de programmation mathématique à court terme, un autre à court et moyen terme et un dernier en programmation par contraintes pour le court et moyen terme et de comparer ensuite les différentes approches. La revue de la littérature disponible sur le sujet montre que la majorité des travaux sur la planification minière portent sur les mines en fosses. Bien qu’elles aient certaines ressemblances, les mines en fosse et les mines souterraines sont malgré tout trop différentes pour simplement appliquer les solutions de l’une à l’autre. On constate d’ailleurs cette disparité dans la différence entre l’offre commerciale de produits d’optimisation pour les deux types de mines. Au sein de la littérature portant sur le souterrain, la majorité des publications portent sur la planification à long terme. Quelques modèles sont disponibles pour les horizons de temps à court et moyen terme, mais sont spécifiques à certaines mines. De cette littérature, l’ensemble des modèles est basé sur la programmation mathématique, à l’exception d’un modèle de planification en temps réel, mais qui constitue un problème différent de celui présenté ici. Un premier modèle de planification à court terme est présenté avec pour fonction objectif de maximiser les tonnes extraites tout en gardant un minimum de production de minerai pour chaque période de temps. Les variables utilisées pour la planification représentent des périodes d’une semaine et le modèle peut être résolu pour des exmeplaires allant jusqu’à six mois. Plusieurs tests sont effectués sur des données inspirées d’une mine canadienne et une analyse détaillée des solutions montre la grande différence entre la solution de la relaxation linéaire et le problème entier. Un exemple d’application réel est ensuite démontré afin de fournir les explications sur comment le modèle serait appliqué dans un tel contexte. Un deuxième modèle en programmation mathématique est présenté pour la planification intégrée à court et moyen terme. Les variables de planification y représentent des périodes d’une semaine pour les trois premiers mois de planification et des périodes de trois mois pour les suivantes. Un premier objectif consiste à maximiser la valeur actuelle nette des activités planifiées, mais un second est aussi présenté où la valeur absolue de la valeur actuelle nette est maximisée. Il est démontré que le deuxième objectif permet une meilleure utilisation des ressources tout en conservant le même niveau de production, et correspond mieux à ce qui serait implémenté en un contexte réel. De plus, on démontre que la relaxation linéaire de ce dernier est beaucoup plus près de la solution entière, facilitant ainsi la résolution du problème. Un exemple d’application à des scénarios réaliste est ensuite présenté pour fournir un cadre d’application au modèle et les avantages de la planification à court et moyen terme intégré sont présentés. Un troisième modèle est ensuite introduit, celui-ci utilisant la programmation par contraintes. L’objectif utilisé est de maximiser la valeur actuelle nette des activités. Le choix de ce dernier est fait afin de fournir une base de comparaison connue pour les modèles de programmation mathématique et de programmation par contraintes. Les résultats démontrent que ce nouveau modèle permet de résoudre avec une précision au quart de travail des exemplaires de plus d’un an. Une adaptation du modèle précédent permet de démontrer qu’aucune des exemplaires ne peut être résolue par celui-ci à ce niveau de précision et pour tel horizon de planification. La thèse se conclut en présentant quelques travaux en cours comme le développement d’un modèle de planification en temps réel et une adaptation du modèle de programmation par contraintes à un problème de mine en fosse. L’inclusion de l’aspect stochastique dans le modèle est finalement discutée ainsi que le potentiel d’une application réelle à une mine en production.----------ABSTRACT: This thesis is part of the current trend of digitization in underground mines by addressing the problem of mine planning. The overall objective of the thesis is to provide a tool for short and medium-term optimization of plannings, allowing optimal solutions to be found in a short time. Underground mine planning for these time horizons is a difficult problem for a number of reasons, including the number of resources required, the large number of work places, the long-term implications of short-term decisions and the level of accuracy required. More specifically, the research objectives are to develop a mathematical programming model for short-term, another for short- and medium-term and a last one using constraint programming for the short- and medium-term and then compare the different approaches. A review of the available literature shows that the majority of work in mine planning is about open-pit mines. Even though they have some similarities, open-pit mines and underground mines are still too different to simply apply the solutions from one to the other. This discrepancy in the difference between the commercial offer of optimization products for both types of mines is another proof of this. Within the underground literature, the majority of publications focus on long-term planning. Some models are available for short- and mediumterm time horizons, but are mine specific. From this literature, all the models are based on mathematical programming, with the exception of one real-time planning model, but it adresses a very different problem from the one presented here. First a short-term planning model is presented with an objective function of maximizing tonnes mined while keeping a minimum of ore production for each time period. The planning variables represent one-week periods and the model can be solved for instances of up to six months. Several tests are carried out on data inspired by a Canadian mine and a detailed analysis of the solutions shows the large gap between the solution of the linear relaxation and the integer solution. An example of a real application is then shown to provide explanations of how the model would be applied in this context. A second model using mathematical programming is presented for integrated short- and medium-term planning. The planning variables represent one-week periods for the first three months and three-month periods for the following ones. The first objective is to maximize the net present value of the planned activities, but a second one is to maximize the absolute value of the net present value. It is then shown that the second objective allows for a better use of the resources while keeping the same level of production, and better corresponds to what would be implemented in a real-life context. It is shown that the linear relaxation of the latter is much closer to the integer solution, facilitating the resolution of the problem. An example of a realistic application to scenarios is then presented to provide a framework of application for the model and the benefits of an integrated short- and medium-term planning are presented. A third model is introduced using constraint programming. The objective is to maximize the net present value of the activities planned. The choice of objective is made in order to provide a known basis of comparison for mathematical programming and constraint programming models. The results show that this new model allows to solve instances of more than one year at a precision of a work shift. A modification of the previous model shows that none of the instances can be solved using the mathematical programming model at this level of precision and this planning horizon. The thesis concludes by presenting some work in progress including the development of a real-time planning model and the modification of the constraint programming model so that it can be applied to an open-pit mine problem. The inclusion of the stochastic aspect in the model is finally discussed as well as the potential for an application to a mine in production

Co-evolutionary Hybrid Bi-level Optimization

Multi-level optimization stems from the need to tackle complex problems involving multiple decision makers. Two-level optimization, referred as ``Bi-level optimization'', occurs when two decision makers only control part of the decision variables but impact each other (e.g., objective value, feasibility). Bi-level problems are sequential by nature and can be represented as nested optimization problems in which one problem (the ``upper-level'') is constrained by another one (the ``lower-level''). The nested structure is a real obstacle that can be highly time consuming when the lower-level is $\mathcal{NP}-hard$. Consequently, classical nested optimization should be avoided. Some surrogate-based approaches have been proposed to approximate the lower-level objective value function (or variables) to reduce the number of times the lower-level is globally optimized. Unfortunately, such a methodology is not applicable for large-scale and combinatorial bi-level problems. After a deep study of theoretical properties and a survey of the existing applications being bi-level by nature, problems which can benefit from a bi-level reformulation are investigated. A first contribution of this work has been to propose a novel bi-level clustering approach. Extending the well-know ``uncapacitated k-median problem'', it has been shown that clustering can be easily modeled as a two-level optimization problem using decomposition techniques. The resulting two-level problem is then turned into a bi-level problem offering the possibility to combine distance metrics in a hierarchical manner. The novel bi-level clustering problem has a very interesting property that enable us to tackle it with classical nested approaches. Indeed, its lower-level problem can be solved in polynomial time. In cooperation with the Luxembourg Centre for Systems Biomedicine (LCSB), this new clustering model has been applied on real datasets such as disease maps (e.g. Parkinson, Alzheimer). Using a novel hybrid and parallel genetic algorithm as optimization approach, the results obtained after a campaign of experiments have the ability to produce new knowledge compared to classical clustering techniques combining distance metrics in a classical manner. The previous bi-level clustering model has the advantage that the lower-level can be solved in polynomial time although the global problem is by definition $\mathcal{NP}$-hard. Therefore, next investigations have been undertaken to tackle more general bi-level problems in which the lower-level problem does not present any specific advantageous properties. Since the lower-level problem can be very expensive to solve, the focus has been turned to surrogate-based approaches and hyper-parameter optimization techniques with the aim of approximating the lower-level problem and reduce the number of global lower-level optimizations. Adapting the well-know bayesian optimization algorithm to solve general bi-level problems, the expensive lower-level optimizations have been dramatically reduced while obtaining very accurate solutions. The resulting solutions and the number of spared lower-level optimizations have been compared to the bi-level evolutionary algorithm based on quadratic approximations (BLEAQ) results after a campaign of experiments on official bi-level benchmarks. Although both approaches are very accurate, the bi-level bayesian version required less lower-level objective function calls. Surrogate-based approaches are restricted to small-scale and continuous bi-level problems although many real applications are combinatorial by nature. As for continuous problems, a study has been performed to apply some machine learning strategies. Instead of approximating the lower-level solution value, new approximation algorithms for the discrete/combinatorial case have been designed. Using the principle employed in GP hyper-heuristics, heuristics are trained in order to tackle efficiently the $\mathcal{NP}-hard$ lower-level of bi-level problems. This automatic generation of heuristics permits to break the nested structure into two separated phases: \emph{training lower-level heuristics} and \emph{solving the upper-level problem with the new heuristics}. At this occasion, a second modeling contribution has been introduced through a novel large-scale and mixed-integer bi-level problem dealing with pricing in the cloud, i.e., the Bi-level Cloud Pricing Optimization Problem (BCPOP). After a series of experiments that consisted in training heuristics on various lower-level instances of the BCPOP and using them to tackle the bi-level problem itself, the obtained results are compared to the ``cooperative coevolutionary algorithm for bi-level optimization'' (COBRA). Although training heuristics enables to \emph{break the nested structure}, a two phase optimization is still required. Therefore, the emphasis has been put on training heuristics while optimizing the upper-level problem using competitive co-evolution. Instead of adopting the classical decomposition scheme as done by COBRA which suffers from the strong epistatic links between lower-level and upper-level variables, co-evolving the solution and the mean to get to it can cope with these epistatic link issues. The ``CARBON'' algorithm developed in this thesis is a competitive and hybrid co-evolutionary algorithm designed for this purpose. In order to validate the potential of CARBON, numerical experiments have been designed and results have been compared to state-of-the-art algorithms. These results demonstrate that ``CARBON'' makes possible to address nested optimization efficiently