Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

Constraint programming is a paradigm wherein relations between variables are stated in the form of constraints. Many real life problems come from uncertain and dynamic environments, where the initial constraints and domains may change during its execution. Thus, the solution found for the problem may become invalid. The search forrobustsolutions for constraint satisfaction problems (CSPs) has become an important issue in the ¿eld of constraint programming. In some cases, there exists knowledge about the uncertain and dynamic environment. In other cases, this information is unknown or hard to obtain. In this paper, we consider CSPs with discrete and ordered domains where changes only involve restrictions or expansions of domains or constraints. To this end, we model CSPs as weighted CSPs (WCSPs) by assigning weights to each valid tuple of the problem constraints and domains. The weight of each valid tuple is based on its distance from the borders of the space of valid tuples in the corresponding constraint/domain. This distance is estimated by a new concept introduced in this paper: coverings. Thus, the best solution for the modeled WCSP can be considered as a most robust solution for the original CSP according to these assumptionsThis work has been partially supported by the research projects TIN2010-20976-C02-01 (Min. de Ciencia e Innovacion, Spain) and P19/08 (Min. de Fomento, Spain-FEDER), and the fellowship program FPU.Climent Aunés, LI.; Wallace, RJ.; Salido Gregorio, MA.; Barber Sanchís, F. (2013). Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings. Artificial Intelligence Review. 1-26. https://doi.org/10.1007/s10462-013-9420-0S126Climent L, Salido M, Barber F (2011) Reformulating dynamic linear constraint satisfaction problems as weighted csps for searching robust solutions. 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Robustness and stability in dynamic constraint satisfaction problems

Constraint programming is a paradigm wherein relations between variables are stated in the form of constraints. It is well-known that many real life problems can be modeled as Constraint Satisfaction Problems (CSPs). Much effort has been spent to increase the efficiency of algorithms for solving CSPs. However, many of these techniques assume that the set of variables, domains and constraints involved in the CSP are known and fixed when the problem is modeled. This is a strong limitation because many problems come from uncertain and dynamic environments, where both the original problem may evolve because of the environment, the user or other agents. In such situations, a solution that holds for the original problem can become invalid after changes. There are two main approaches for dealing with these situations: reactive and proactive approaches. Using reactive approaches entails re-solving the CSP after each solution loss, which is a time consuming. That is a clear disadvantage, especially when we deal with short-term changes, where solution loss is frequent. In addition, in many applications, such as on-line planning and scheduling, the delivery time of a new solution may be too long for actions to be taken on time, so a solution loss can produce several negative effects in the modeled problem. For a task assignment production system with several machines, it could cause the shutdown of the production system, the breakage of machines, the loss of the material/object in production, etc. In a transport timetabling problem, the solution loss, due to some disruption at a point, may produce a delay that propagates through the entire schedule. In addition, all the negative effects stated above will probably entail an economic loss. In this thesis we develop several proactive approaches. Proactive approaches use knowledge about possible future changes in order to avoid or minimize their effects. These approaches are applied before the changes occur. Thus, our approaches search for robust solutions, which have a high probability to remain valid after changes. Furthermore, some of our approaches also consider that the solutions can be easily adapted when they did not resist the changes in the original problem. Thus, these approaches search for stable solutions, which have an alternative solution that is similar to the previous one and therefore can be used in case of a value breakage. In this context, sometimes there exists knowledge about the uncertain and dynamic environment. However in many cases, this information is unknown or hard to obtain. For this reason, for the majority of our approaches (specifically 3 of the 4 developed approaches), the only assumptions made about changes are those inherent in the structure of problems with ordered domains. Given this framework and therefore the existence of a significant order over domain values, it is reasonable to assume that the original bounds of the solution space may undergo restrictive or relaxed modifications. Note that the possibility of solution loss only exists when changes over the original bounds of the solution space are restrictive. Therefore, the main objective for searching robust solutions in this framework is to find solutions located as far away as possible from the bounds of the solution space. In order to meet this criterion, we propose several approaches that can be divided in enumeration-based techniques and a search algorithm.Climent Aunés, LI. (2013). Robustness and stability in dynamic constraint satisfaction problems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34785TESI

Safe Distributed Coordination of Heterogeneous Robots through Dynamic Simple Temporal Networks

Research on autonomous intelligent systems has focused on how robots can robustly carry out missions in uncertain and harsh environments with very little or no human intervention. Robotic execution languages such as RAPs, ESL, and TDL improve robustness by managing functionally redundant procedures for achieving goals. The model-based programming approach extends this by guaranteeing correctness of execution through pre-planning of non-deterministic timed threads of activities. Executing model-based programs effectively on distributed autonomous platforms requires distributing this pre-planning process. This thesis presents a distributed planner for modelbased programs whose planning and execution is distributed among agents with widely varying levels of processor power and memory resources. We make two key contributions. First, we reformulate a model-based program, which describes cooperative activities, into a hierarchical dynamic simple temporal network. This enables efficient distributed coordination of robots and supports deployment on heterogeneous robots. Second, we introduce a distributed temporal planner, called DTP, which solves hierarchical dynamic simple temporal networks with the assistance of the distributed Bellman-Ford shortest path algorithm. The implementation of DTP has been demonstrated successfully on a wide range of randomly generated examples and on a pursuer-evader challenge problem in simulation

Managing Complex Scheduling Problems with Dynamic and Hybrid Constraints.

The task of scheduling can often be a difficult one because of the inherent complexity of real-world problems. In the field of Artificial Intelligence, many representations and algorithms have been developed to automate the scheduling process. Many state of the art scheduling systems deal with this complexity by making assumptions that simplify the algorithms, but in doing so, miss some opportunities to improve performance. Scheduling problems are temporal in nature, and so they often contain constraints that change over time. Many scheduling systems assume that the problems they are solving are all independent, and so they ignore the similarities between subsequent sets of scheduling constraints. Additionally, scheduling problems often contain a mixture of finite-domain and temporal constraints. Many of the systems that can solve problems of this type do so by creating finite-domain variables to represent the constraints, but then ignore the distinction between the different types of variables when searching for a solution. In this dissertation, I identify opportunities to improve performance by exploiting structure where it has previously been overlooked. Following this approach, I develop a set of techniques that apply to a wide variety of situations that can arise in real-world scheduling problems. First, I consider dynamic scheduling problems with constraints that change over time. To address such problems, I introduce a new representation called the Dynamic Disjunctive Temporal Problem, along with several techniques to improve both efficiency and stability when solving one. Second, I consider scheduling problems in which a mixture of finite-domain and temporal variables can interact through hybrid constraints. I introduce the Hybrid Scheduling Problem to represent such problems, and I present a set of techniques that capitalize on the distinction between variable types to improve efficiency across the problem space. Finally, I conclude by proposing several ways that the dynamic and hybrid representations and techniques can be combined. To compare many of the techniques presented throughout this dissertation in the context of structured, real-world problems, I use them to solve scheduling problems based on actual air traffic control constraints recorded from the Dallas/Fort Worth International Airport.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57625/2/pschwart_1.pd

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Quantum-accelerated constraint programming

Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search. Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the $\texttt{alldifferent}$ global constraint and discuss its applicability to a broader family of global constraints with similar structure. We propose frameworks for the integration of quantum filtering algorithms within both classical and quantum backtracking search schemes, including a novel hybrid classical-quantum backtracking search method. This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.Comment: published in Quantu

Optimal temporal planning at reactive time scales via dynamic backtracking branch and bound

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (p. 110-115).Autonomous robots are being considered for increasingly capable roles in our society, such as urban search and rescue, automation for assisted living, and lunar habitat construction. To fulfill these roles, teams of autonomous robots will need to cooperate together to accomplish complex mission objectives in uncertain and dynamic environments. In these environments, autonomous robots face a host of new challenges, such as responding robustly to timing uncertainties and perturbations, task and coordination failures, and equipment malfunctions. In order to address these challenges, this thesis advocates a novel planning approach, called temporally-flexible contingent planning. A temporally-flexible contingent plan is a compact encoding of methods for achieving the mission objectives which incorporates robustness through flexible task durations, redundant methods, constraints on when methods are applicable, and preferences between methods. This approach enables robots to adapt to unexpected changes on-the-fly by selecting alternative methods at runtime in order to satisfy as best possible the mission objectives. The drawback to this approach, however, is the computational overhead involved in selecting alternative methods at runtime in response to changes.(cont.) If a robot takes too long to select a new plan, it could fail to achieve its near-term mission objectives and potentially incur damage. To alleviate this problem, and extend the range of applicability of temporally-flexible contingent planning to more demanding real-time systems, this thesis proposes a temporally-flexible contingent plan executive that selects new methods quickly and optimally in response to changes in a robot's health and environment. We enable fast and optimal method selection through two complimentary approaches. First, we frame optimal method selection as a constraint satisfaction problem (CSP) variant, called an Optimal Conditional CSP (OCCSP). Second, we extend fast CSP search algorithms, such as Dynamic Backtracking and Branch-and-Bound Search, to solve OCCSPs. Experiments on an autonomous rover test-bed and on randomly generated plans show that these contributions significantly improve the speed at which robots perform optimal method selection in response to changes in their health status and environment.by Robert T. Effinger, IV.S.M