Home healthcare (HHC) is a service that dispatches caregivers to people in need of healthcare who live in the home. The task assignment and route generation for caregivers can be formulated as an extension of the well-known vehicle routing problem with time windows (VRPTW). Currently, the most successful exact algorithms for VRPTW are based on a framework combining column generation (CG) and branching. Although such methods could be successful for HHC routing and scheduling problem (HHCRSP) as well, fast approximate algorithms are appealing, especially for large problems. In an early version of this paper, we employed a heuristic distributed gossip algorithm to solve HHCRSP. In this paper, we integrate the gossip algorithm with a local solver based on CG, which makes it an effective algorithm for larger problem instances. As it will be shown with extensive numerical experiments, for large problem instances, gossip-CG performs better than the pure CG.

Many people in need of care still live in their homes, requiring the caretakers to travel to them. Assigning the people to caretakers and generating their schedules can be formulated as a mixed integer linear programming problem (MILP) that inherits many features of the well-known vehicle routing problem with time windows (VRPTW). Currently, the most successful exact algorithms for VRPTW are based on branch and price framework, which combine column generation (CG) and branching. While these methods could be successful for Home Healthcare Routing and Scheduling Problem (HHCRSP) as well, fast approximate algorithms are appealing, especially for large problems. We recently employed a heuristic distributed gossip algorithm to solve HHCRSP. The method had the potential to provide approximate solutions for relatively large problem instances, but its effectiveness was limited to the performance of its local MILP solver. In this paper, we integrate the gossip algorithm with a local solver based on CG, which makes it an effective algorithm for larger problem instances. We also provide numerical experiments and complexity evaluations of the improved gossip algorithm (gossip-CG) with the standard gossip (gossip-MILP) and CG, and show that gossip-CG outperforms the pure CG in case of large problems.

This paper, as an outcome of the EU project AREUS, heralds an optimization procedure that reduces up to 30% of energy consumption and up to 60% in peak power for the trajectories that have been tested on real industrial robots. We have evaluated a number of cost functions and tested our algorithm for a variety of scenarios such as varying cycle times, payloads, and single/multirobot cases in both ac- and dc-operated robot cells. The significance of our work is not only in the impressive savings, simplicity of implementation, and preserving path and cycle time, but also in the variety of test scenarios that include different kinds of KUKA robots. We have carried out the optimization and experiments in as realistic conditions as possible.

A systematic method to evaluate the conflict between robustness, stability, and energy consumption is proposed in this paper. Energy optimization is combined with robust scheduling techniques to analyze the tradeoff. In rescheduling, slack is often used to protect a schedule from disruptions. However, results from the literature on energy minimization show that a reduction in energy consumption is achieved by extending the execution time of operations. Thus, slack in schedules is diminished on behalf of longer execution times. The proposed method, which quantitatively shows this conflict, is based on a multiobjective optimization formulation where efficient computation of the involved criteria is developed. This includes a convex surrogate stability measure that makes it possible to evaluate different operation sequences by a mixed-integer nonlinear programming formulation. Previous works connecting the two research fields use simulation for analyzing the impact of disruptions in order to generate robust production schedules. Our results show that an increase in energy efficiency comes at a cost of reducing stability and robustness and hence becoming more sensitive to disruptions.

In this paper, a predicate transition model for discrete-event systems is generalized to include continuous dynamics, and the result is a modular hybrid predicate transition model. Based on this model, a hybrid Petri net including explicit differential equations and shared variables is also proposed. It is then shown how this hybrid Petri net model can be optimized based on a simple and robust nonlinear programming formulation. The procedure only assumes that desired sampled paths for a number of interacting moving devices are given, while originally equidistant time instances are adjusted to minimize a given criterion. This optimization of hybrid systems is also applied to a real robot station with interacting devices, which results in about 30% reduction in energy consumption. Moreover, a flexible online and event-based information architecture called the Tweeting Factory is proposed. Simple messages (tweets) from all kinds of equipment are combined into high-level knowledge, and it is demonstrated how this information architecture can be used to support optimization of robot stations.

This paper concerns the energy optimization of systems with interacting robots. Pseudo spectral optimal control is used to collocate the continuous time dynamics of each robot. The resulting model is a multi stage, multi robot, trajectory planning problem with timing constraints. In the case of a given task sequence, the mathematical formulation is that of a Nonlinear Programming problem. We present two example problems where three 3-DoF robots work together. For the case the problem consists of undetermined sequences, we outline an algorithm which integrates Operations Research methods with those of Constraint Programming.

In this paper, we propose a logic-based Benders decomposition (LBBD), as well as an LBBD/gossip method to solve the heterogeneous multi-vehicle routing problem (HMVRP). HMVRP is a newly formalized extension of the NP-hard multi-traveling salesman problem (mTSP). First, a hybrid algorithm based on LBBD is formulated that decomposes the HMVRP into an assignment problem and a cluster of sequencing problems. The former is solved by a mixed integer linear programming (MILP) solver, and the latter by a dedicated TSP solver. Then, a gossip algorithm is constructed which utilizes the mentioned LBBD for local optimization to achieve better computational efficiency. The use of LBBD remarkably reduces the CPU time. Furthurmore, integrating the three layers of gossip algorithm, LBBD and the TSP solver, results in a very efficient solution method.

This paper concerns the reduction of energy use in manufacturing industry. If individual robot movements in a system are preprocessed using Dynamic Programming, one can attain a Mixed Integer Nonlinear Program (MINLP) which models the energy consumption of the complete system. This model can then be solved to optimality using mathematical programming. We have previously shown proof of concept for this energy reduction method. In this paper, we apply state of the art MINLP methods to a number of problems in order benchmark their effectiveness. Algorithms used are Nonlinear Programming based Branch and Bound (NLP-BB), Outer Approximation (OA), LP/NLP based Branch and Bound (LP/NLP-BB) and Extended Cutting Plane (ECP). Benchmarks show that the NLP-BB does not perform well for nonlinear scheduling problems. This is due to the weak lower bounds of the integer relaxations. For scheduling problems with nonlinear costs, ECP and in particular LP/NLP-BB are shown to outperform both NLP-BB and OA. The resulting energy optimal schedules for the examples show a significant decrease in energy consumption.

The reduction of energy consumption is today addressed with great effort in manufacturing industry. In this paper, we improve upon a previously presented method for robotic system scheduling. By applying dynamic programming to existing trajectories, we generate new energy optimal trajectories that follow the same path but in a different execution time frame. With this new method, it is possible to solve the optimization problem for a range of execution times for the individual operations, based on one simulation only. The minimum energy trajectories can then be used to derive a globally energy optimal schedule. A case study of a cell comprised of four six-link manipulators is presented, in which energy optimal dynamic time scaling is compared to linear time scaling. The results show that a significant decrease in energy consumption can be achieved for any given cycle time.