Nowadays, robotic cells are mostly designed with the main goal to meet the desired production rate without any consideration of the energy efficiency, therefore, it is often possible to achieve significant energy savings without downsizing the production. In our previous study, we established the mathematical formulation of the energy optimization problem, proposed a parallel heuristic, and optimized an existing robotic cell in Skoda Auto, the results of which revealed a 20% reduction in the energy consumption of robot drive systems. This study proposes a novel parallel Branch & Bound algorithm to optimize the energy consumption of robotic cells without deterioration in throughput. The energy saving is achieved by changing robot speeds and positions, applying robot power-saving modes (brakes, bus power off), and selecting an order of operations. The core part of the algorithm is our tight lower bound, based on convex envelopes. Besides the bounding, a Deep Jumping approach is introduced to guide the search to the promising parts of the Branch & Bound tree, and the parallelization accelerates the exploration of the tree. The experimental results revealed that the performance of the parallel algorithm scales almost linearly up to 12 processor cores, and the quality of obtained solutions is better or comparable to other existing works. (C) 2018 Elsevier Ltd. All rights reserved.

A novel mathematical formulation of the energy optimisation problem for robotic lines is presented, which allows minimising the energy consumption in a robotic cell while keeping the required production cycle time. Different energy saving modes of the robots are utilised as well as the fact that the robot energy consumption during its movement depends on the movement duration. This dependency is modelled with a so-called energy function, which can be obtained by measurements, physical modelling of the robots or simulation. Each of these areas is covered by the presented work. The achieved results show there is a good potential to achieve energy savings at existing robotic cells and their series, and an even bigger potential if the presented approach is used during the design phase of new robotic cells.

This study focuses on the energy optimization of industrial robotic cells, which is essential for sustainable production in the long term. A holistic approach that considers a robotic cell as a whole toward minimizing energy consumption is proposed. The mathematical model, which takes into account various robot speeds, positions, power-saving modes, and alternative orders of operations, can be transformed into a mixed-integer linear programming formulation that is, however, suitable only for small instances. To optimize complex robotic cells, a hybrid heuristic accelerated by using multicore processors and the Gurobi simplex method for piecewise linear convex functions is implemented. The experimental results showed that the heuristic solved 93% of instances with a solution quality close to a proven lower bound. Moreover, compared with the existing works, which typically address problems with three to four robots, this study solved real-size problem instances with up to 12 robots and considered more optimization aspects. The proposed algorithms were also applied on an existing robotic cell in Skoda Auto. The outcomes, based on simulations and measurements, indicate that, compared with the previous state (at maximal robot speeds and without deeper power-saving modes), the energy consumption can be reduced by about 20% merely by optimizing the robot speeds and applying power-saving modes. All the software and generated datasets used in this research are publicly available.

The Resource Constrained Project Scheduling Problem, which is considered to be difficult to tackle even for small instances, is a well-known scheduling problem in the operations research domain. To solve the problem we have proposed a parallel Tabu Search algorithm to find high quality solutions in a reasonable time. We show that our parallel Tabu Search algorithm for graphics cards (GPUs) outperforms other existing Tabu Search approaches in terms of quality of solutions and the number of evaluated schedules per second. Moreover, the algorithm for graphics cards is about 10.5/42.7 times faster (J90 benchmark instances) than the optimized parallel/sequential algorithm for the Central Processing Unit (CPU). The same quality of solutions is achieved up to 5.4/22 times faster in comparison to the parallel/sequential CPU algorithm respectively. The advantages of the GPU version arise from the sophisticated data-structures and their suitable placement in the device memory, tailor-made methods, and last but not least the effective communication scheme.

This work proposes a GPU algorithm for a combinatorial problem known in literature as Resource Constrained Project Scheduling Problem. To solve this NP-hard problem, Tabu Search meta-heuristic is selected. All computations are performed on the GPU to minimize required communication bandwidth between the GPU and the CPU. In addition, new evaluation algorithm and effective Tabu List implementation are designed especially for GPUs. Achieved results show that the proposed GPU solution outperforms the equivalent CPU version in both quality of solutions and performance speedup.