An Integrated CP/OR Method for Optimal Control of Modular Hybrid Systems

This paper concerns the optimal control of modular hybrid systems synchronized by shared variables. Instead of synchronizing the discrete dynamics of the system into one global mode before optimization, Constraint Programming (CP) is used to model the discrete dynamics of each modular system separately. Integrated in the CP solver are also classic Operations Research (OR) models in the form of Nonlinear Programs (NLPs) approximating the continuous dynamics of the system. Using CP considerably decreases the number of NLPs which must be solved, compared to that of using a traditional mixed integer nonlinear programming approach

Scheduling model for systems with complex alternative behaviour

In this paper we propose a flexible model for scheduling problems, which allows the modeling of systems with complex alternative behaviour. This model could for example facilitate the step from process planning model to optimization model. We show how automatic constraint generation can be performed for both Constraint Programming and Mixed Integer Linear Programming (MILP) models. Also, for the MILP case, a new formulation for mutual exclusion of resources is proposed. This new formulation works well for proving optimality in systems with multiple capacity resources. Some benchmarks for such job shop scheduling problems as well as systems with a large number of alternatives are also presented

Energy optimization of trajectories for high level scheduling

Minimization of energy consumption is today an issue of utmost importance in manufacturing industry. A previously presented technique for scheduling of robot cells, which exploits variable execution time for the individual robot operations, has shown promising results in energy minimization. In order to slow down a manipulator's movement the method utilizes a linear time scaling of the time optimal trajectory. This paper attempts to improve the scheduling method by generating energy optimal data using dynamic time scaling. Dynamic programming can be applied to an existing trajectory and generate a new energy optimal trajectory that follows the same path but with another execution time. With the new method, it is possible to solve the optimization problem for a range of execution times in one run. A simple two-joint planar example is presented in which energy optimal dynamic time scaling is compared to linear time scaling. The results show a small decrease in energy usage for minor scaling, but a significant reduction for longer execution times

Optimization of Hybrid Systems with Known Paths

In this paper we study a subset of hybrid systems and present a generalized method for their optimization. We outline Hybrid Cost Automata (HCA), an extension to Hybrid Automata, where discrete and continuous cost expressions are added. The class of hybrid systems with known spatial paths is dened in the context of HCA. This type of system is common in industry where for example AGVs transport goods from one location to another, or manipulators move between joint coordinates. The optimization is performed using Dynamic Programming as a preprocessing step, whereafter Mixed Integer Nonlinear Programming is used for scheduling. A case study of a four robot cell is presented with energy consumption used as a minimization criterion

Optimization of operation sequences using constraint programming

In this paper, we connect the dots: design and optimization of production systems. A possible link between these two areas, is a previously presented modeling language, Sequence Planner Language (SPL). It has been demonstrated how relevant information can be extracted from production systems modeling applications, and converted into SPL. We show how the SPL model can be converted into a constraint programming model for optimization. Also, a useful abstraction concept, work-equivalence, is introduced to enable alternative model formulations. A case study consisting of an aero engine structure assembly plant is presented, in which the efficiency of the resulting constraint programs is investigated. The formulations enabled by abstraction are shown to perform better than the standard formulation

Unified Model for Synthesis and Optimization of Discrete Event and Hybrid Systems

A recently proposed generic discrete event model is further developed and exemplified in this paper. Since every transition is expressed as a predicate on the current and next values of a set of variables, the model is called Predicate Transition Model (PTM). It is briefly illustrated how a number of well known discrete-event models, including automata and Petri nets extended with shared variables, can be formulated and synthesized in the PTM framework. More specifically modular Petri nets with shared variables (PNSVs) are shown to be significantly more readable compared to ordinary Petri nets. PTMs are also naturally extended to hybrid systems, and finally it is shown how easy and efficiently PNSVs can be optimized concerning performance based on Constraint Programming. To summarize, the proposed modeling framework unifies and simplifies both synthesis, optimization and implementation of discrete event systems

Energy Optimization of Multi-robot Systems

This paper presents an optimization algorithm that has been able to save up to 45% of the energy consumption of an industrial multi-robot system. The tool Sequence Planner now includes these algorithms, focusing on minimizing energy consumption. The goal has been to reduce the energy consumption of individual robots and robots interacting in a work station, without changing the original paths or the total cycle time. The presented algorithms are based on an efficient and rapid nonlinear model for optimizing the sequences of operations and the motion trajectories. Smart simplification of the optimization problem together with innovative tools for logging data and executing the optimized trajectories on real robots has resulted in 18% to 45% saving of the energy consumption in the presented test scenarios

A Gossip Algorithm for Home Healthcare Scheduling and Routing Problems

Many people in need of care still live in their homes, requiring the caretakers to travel to them. Assigning tasks to nurses (or caretakers) and scheduling their work plans is an NP-hard problem, which can be expressed as a vehicle routing problem with time windows (VRPTW) that includes additional problem-specific constraints. In this paper, we propose to solve the Home Healthcare Scheduling and Routing Problem (HHCRSP) by a distributed Gossip algorithm. We also apply an extended version called n-Gossip, which provides the required flexibility to balance optimality versus computational speed. We also introduce a relaxation on the optimality of the underlying solver in the Gossip, which speeds up the iterations of the Gossip algorithm, and helps to quickly obtain solutions with good quality

Comparing MILP, CP, and A* for Multiple Stacker Crane Scheduling

This paper describes an optimisation model for the scheduling of a system consisting of three stacker cranes that are restricted to the same track. To improve the efficiency of the solution methods, a novel simplification of the model is presented, which has a low impact on the quality of the solution but greatly decreases its complexity. This model is then used to benchmark several popular solution methods, including both optimal and approximate methods. Some are based on monolithic models, whereas others solve the problem in phases by using sub-problem formulations. The result presented in this paper shows that evaluated solution methods have complementary strengths and weaknesses. Constraint Programming (CP) is very efficient on small scale problems, while Mixed Integer Linear Programming (MILP) scales much better when the number of movement orders increases. However, none of these methods are able to solve large instances of the problem to optimality. To handle the complexity of the problem, approximate solution methods are the only viable option. In this paper we show that promising results can be obtained even with simple methods using well known search algorithms such as A* and Tabu-search. However, preliminary results on more advanced search algorithms show that further improvements may be achieved, allowing the solution of very large problem instances