We propose a generic multi-robot planning mechanism that combines an optimal task planner and an optimal path planner to provide a scalable solution for complex multi-robot planning problems. The Integrated planner, through the interaction of the task planner and the path planner, produces optimal collision-free trajectories for the robots. We illustrate our general algorithm on an object pick-and-drop planning problem in a warehouse scenario where a group of robots is entrusted with moving objects from one location to another in the workspace. We solve the task planning problem by reducing it into an SMT-solving problem and employing the highly advanced SMT solver Z3 to solve it. To generate collision-free movement of the robots, we extend the state-of-the-art algorithm Conflict Based Search with Precedence Constraints with several domain-specific constraints. We evaluate our integrated task and path planner extensively on various instances of the object pick-and-drop planning problem and compare its performance with a state-of-the-art multi-robot classical planner. Experimental results demonstrate that our planning mechanism can deal with complex planning problems and outperforms a state-of-the-art classical planner both in terms of computation time and the quality of the generated plan.

Multifidelity simulation methodologies are often used in an attempt to judiciously combine low-fidelity and high-fidelity simulation results in an accuracy-increasing, cost-saving way. Candidates for this approach are simulation methodologies for which there are fidelity differences connected with significant computational cost differences. Physics-informed Neural Networks (PINNs) are candidates for these types of approaches due to the significant difference in training times required when different fidelities (expressed in terms of architecture width and depth as well as optimization criteria) are employed. In this paper, we propose a particular multifidelity approach applied to PINNs that exploits low-rank structure. We demonstrate that width, depth, and optimization criteria can be used as parameters related to model fidelity, and show numerical justification of cost differences in training due to fidelity parameter choices. We test our multifidelity scheme on various canonical forward PDE models that have been presented in the emerging PINNs literature.

We propose our solution to a particular practical problem in the domain of vehicle routing and scheduling. The generic task is finding the best allocation of the minimum number of \emph{mobile resources} that can provide periodical services in remote locations. These \emph{mobile resources} are based at a single central location. Specifications have been defined initially for a real-life application that is the starting point of an ongoing project. Particularly, the goal is to mitigate health problems in rural areas around a city in Romania. Medically equipped vans are programmed to start daily routes from county capital, provide a given number of examinations in townships within the county and return to the capital city in the same day. From the health care perspective, each van is equipped with an ultrasound scanner, and they are scheduled to investigate pregnant woman each trimester aiming to diagnose potential problems. The project is motivated by reports currently ranking Romania as the country with the highest infant mortality rate in the European Union. We developed our solution in two phases: modeling of the most relevant parameters and data available for our goal and then design and implement an algorithm that provides an optimized solution. The most important metric of an output scheduling is the number of vans that are necessary to provide a given amount of examination time per township, followed by total travel time or fuel consumption, number of different routes, and others. Our solution implements two probabilistic algorithms out of which we chose the one that performs the best.

Algorithms learned from data are increasingly used for deciding many aspects in our life: from movies we see, to prices we pay, or medicine we get. Yet there is growing evidence that decision making by inappropriately trained algorithms may unintentionally discriminate people. For example, in automated matching of candidate CVs with job descriptions, algorithms may capture and propagate ethnicity related biases. Several repairs for selected algorithms have already been proposed, but the underlying mechanisms how such discrimination happens from the computational perspective are not yet scientifically understood. We need to develop theoretical understanding how algorithms may become discriminatory, and establish fundamental machine learning principles for prevention. We need to analyze machine learning process as a whole to systematically explain the roots of discrimination occurrence, which will allow to devise global machine learning optimization criteria for guaranteed prevention, as opposed to pushing empirical constraints into existing algorithms case-by-case. As a result, the state-of-the-art will advance from heuristic repairing, to proactive and theoretically supported prevention. This is needed not only because law requires to protect vulnerable people. Penetration of big data initiatives will only increase, and computer science needs to provide solid explanations and accountability to the public, before public concerns lead to unnecessarily restrictive regulations against machine learning.

While there exist several approaches in the constraint programming community to learn a constraint theory, few of them have considered the learning of constraint optimization problems.To alleviate this situation, we introduce an initial approach to learning first-order weighted MAX-SAT theories. It employs inductive logic programming techniques to learn a set of first-order clauses and then uses preference learning techniques to learn the weights of the clauses.In order to learn these weighted clauses, the clausal optimization system uses examples of possible worlds and a set of preferences that state which examples are preferred over other ones.The technique is also empirically evaluated on a number of examples.These experiments show that the system is capable of learning clauses and weights that accurately capture underlying models.

Increasing popularity of mobile route planning applications based on GPS technology provides opportunities for collecting traffic data in urban environments. One of the main challenges for travel time estimation and prediction in such a setting is how to aggregate data from vehicles that have followed different routes, and predict travel time for other routes of interest. One approach is to predict travel times for route segments, and sum those estimates to obtain a prediction for the whole route. We study how to obtain optimal predictions in this scenario. It appears that the optimal estimate, minimizing the expected mean absolute error, is a combination of the mean and the median travel times on each segment, where the combination function depends on the number of segments in the route of interest. We present a methodology for obtaining such predictions, and demonstrate its effectiveness with a case study using travel time data from a district of St. Petersburg collected over one year. The proposed methodology can be applied for real-time prediction of expected travel times in an urban road network.