Coalition Formation For Distributed Constraint Optimization Problems

This dissertation presents our research on coalition formation for Distributed Constraint Optimization Problems (DCOP). In a DCOP, a problem is broken up into many disjoint sub-problems, each controlled by an autonomous agent and together the system of agents have a joint goal of maximizing a global utility function. In particular, we study the use of coalitions for solving distributed k-coloring problems using iterative approximate algorithms, which do not guarantee optimal results, but provide fast and economic solutions in resource constrained environments. The challenge in forming coalitions using iterative approximate algorithms is in identifying constraint dependencies between agents that allow for effective coalitions to form. We first present the Virtual Structure Reduction (VSR) Algorithm and its integration with a modified version of an iterative approximate solver. The VSR algorithm is the first distributed approach for finding structural relationships, called strict frozen pairs, between agents that allows for effective coalition formation. Using coalition structures allows for both more efficient search and higher overall utility in the solutions. Secondly, we relax the assumption of strict frozen pairs and allow coalitions to form under a probabilistic relationship. We identify probabilistic frozen pairs by calculating the propensity between two agents, or the joint probability of two agents in a k-coloring problem having the same value in all satisfiable instances. Using propensity, we form coalitions in sparse graphs where strict frozen pairs may not exist, but there is still benefit to forming coalitions. Lastly, we present a cooperative game theoretic approach where agents search for Nash stable coalitions under the conditions of additively separable and symmetric value functions

Towards efficient planning for real world partially observable domains

In partial fulfillment of the degree of Doctor of Philosophy (Computer Science)</p

A distributed approach for robust, scalable, and flexible dynamic ridesharing

This dissertation provides a solution to dynamic ridesharing problem, a NP-hard optimization problem, where a fleet of vehicles move on a road network and ridesharing requests arrive continuously. The goal is to optimally assign vehicles to requests with the objective of minimizing total travel distance of vehicles and satisfying constraints such as vehicles’ capacity and time window for pick-up and drop-off locations. The dominant approach for solving dynamic ridesharing problem is centralized approach that is intractable when size of the problem grows, thus not scalable. To address scalability, a novel agent-based representation of the problem, along with a set of algorithms to solve the problem, is proposed. Besides being scalable, the proposed approach is flexible and, compared to centralized approach, more robust, i.e., vehicle agents can handle changes in the network dynamically (e.g., in case of a vehicle breakdown) without need to re-start the operation, and individual vehicle failure will not affect the process of decision-making, respectively. In the decentralized approach the underlying combinatorial optimization is formulated as a distributed optimization problem and is decomposed into multiple subproblems using spectral graph theory. Each subproblem is formulated as DCOP (Distributed Constraint Optimization Problem) based on a factor graph representation, including a group of cooperative agents that work together to take an optimal (or near-optimal) joint action. Then a min-sum algorithm is used on the factor graph to solve the DCOP. A simulator is implemented to empirically evaluate the proposed approach and benchmark it against two alternative approaches, solutions obtained by ILP (Integer Linear Programming) and a greedy heuristic algorithm. The results show that the decentralized approach scales well with different number of vehicle agents, capacity of vehicle agents, and number of requests and outperforms: (a) the greedy heuristic algorithm in terms of solution quality and (b) the ILP in terms of execution time

Distributed Target Engagement in Large-scale Mobile Sensor Networks

Sensor networks comprise an emerging field of study that is expected to touch many aspects of our life. Research in this area was originally motivated by military applications. Afterward sensor networks have demonstrated tremendous promise in many other applications such as infrastructure security, environment and habitat monitoring, industrial sensing, traffic control, and surveillance applications. One key challenge in large-scale sensor networks is the efficient use of the network's resources to collect information about objects in a given Volume of Interest (VOI). Multi-sensor Multi-target tracking in surveillance applications is an example where the success of the network to track targets in a given volume of interest, efficiently and effectively, hinges significantly on the network's ability to allocate the right set of sensors to the right set of targets so as to achieve optimal performance. This task can be even more complicated if the surveillance application is such that the sensors and targets are expected to be mobile. To ensure timely tracking of targets in a given volume of interest, the surveillance sensor network needs to maintain engagement with all targets in this volume. Thus the network must be able to perform the following real-time tasks: 1) sensor-to-target allocation; 2) target tracking; 3) sensor mobility control and coordination. In this research I propose a combination of the Semi-Flocking algorithm, as a multi-target motion control and coordination approach, and a hierarchical Distributed Constraint Optimization Problem (DCOP) modelling algorithm, as an allocation approach, to tackle target engagement problem in large-scale mobile multi-target multi-sensor surveillance systems. Sensor-to-target allocation is an NP-hard problem. Thus, for sensor networks to succeed in such application, an efficient approach that can tackle this NP-hard problem in real-time is disparately needed. This research work proposes a novel approach to tackle this issue by modelling the problem as a Hierarchical DCOP. Although DCOPs has been proven to be both general and efficient they tend to be computationally expensive, and often intractable for large-scale problems. To address this challenge, this research proposes to divide the sensor-to-target allocation problem into smaller sub-DCOPs with shared constraints, eliminating significant computational and communication costs. Furthermore, a non-binary variable modelling is presented to reduce the number of inter-agent constraints. Target tracking and sensor mobility control and coordination are the other main challenges in these networks. Biologically inspired approaches have recently gained significant attention as a tool to address this issue. These approaches are exemplified by the two well-known algorithms, namely, the Flocking algorithm and the Anti-Flocking algorithm. Generally speaking, although these two biologically inspired algorithms have demonstrated promising performance, they expose deficiencies when it comes to their ability to maintain simultaneous reliable dynamic area coverage and target coverage. To address this challenge, Semi-Flocking, a biologically inspired algorithm that benefits from key characteristics of both the Flocking and Anti-Flocking algorithms, is proposed. The Semi-Flocking algorithm approaches the problem by assigning a small flock of sensors to each target, while at the same time leaving some sensors free to explore the environment. Also, this thesis presents an extension of the Semi-Flocking in which it is combined with a constrained clustering approach to provide better coverage over maneuverable targets. To have a reliable target tracking, another extension of Semi-Flocking algorithm is presented which is a coupled distributed estimation and motion control algorithm. In this extension the Semi-Flocking algorithm is employed for the purpose of a multi-target motion control, and Kalman-Consensus Filter (KCF) for the purpose of motion estimation. Finally, this research will show that the proposed Hierarchical DCOP algorithm can be elegantly combined with the Semi-Flocking algorithm and its extensions to create a coupled control and allocation approach. Several experimental analysis conducted in this research illustrate how the operation of the proposed algorithms outperforms other approaches in terms of incurred computational and communication costs, area coverage, target coverage for both linear and maneuverable targets, target detection time, number of undetected targets and target coverage in noise conditions sensor network. Also it is illustrated that this algorithmic combination can successfully engage multiple sensors to multiple mobile targets such that the number of uncovered targets is minimized and the sensors' mean utilization factor sensor surveillance systems.is maximized

Computing Convex Coverage Sets for Faster Multi-objective Coordination

In this article, we propose new algorithms for multi-objective coordination graphs (MO- CoGs). Key to the efficiency of these algorithms is that they compute a convex coverage set (CCS) instead of a Pareto coverage set (PCS). Not only is a CCS a sufficient solution set for a large class of problems, it also has important characteristics that facilitate more efficient solutions. We propose two main algorithms for computing a CCS in MO-CoGs. Convex multi-objective variable elimination (CMOVE) computes a CCS by performing a series of agent eliminations, which can be seen as solving a series of local multi-objective subproblems. Variable elimination linear support (VELS) iteratively identifies the single weight vector w that can lead to the maximal possible improvement on a partial CCS and calls variable elimination to solve a scalarized instance of the problem for w. VELS is faster than CMOVE for small and medium numbers of objectives and can compute an ε-approximate CCS in a fraction of the runtime. In addition, we propose variants of these methods that employ AND/OR tree search instead of variable elimination to achieve memory efficiency. We analyze the runtime and space complexities of these methods, prove their correctness, and compare them empirically against a naive baseline and an existing PCS method, both in terms of memory-usage and runtime. Our results show that, by focusing on the CCS, these methods achieve much better scalability in the number of agents than the current state of the art

Constrained Task Assignment and Scheduling on Networks of Arbitrary Topology.

This dissertation develops a framework to address centralized and distributed constrained task assignment and task scheduling problems. This framework is used to prove properties of these problems that can be exploited, develop effective solution algorithms, and to prove important properties such as correctness, completeness and optimality. The centralized task assignment and task scheduling problem treated here is expressed as a vehicle routing problem with the goal of optimizing mission time subject to mission constraints on task precedence and agent capability. The algorithm developed to solve this problem is able to coordinate vehicle (agent) timing for task completion. This class of problems is NP-hard and analytical guarantees on solution quality are often unavailable. This dissertation develops a technique for determining solution quality that can be used on a large class of problems and does not rely on traditional analytical guarantees. For distributed problems several agents must communicate to collectively solve a distributed task assignment and task scheduling problem. The distributed task assignment and task scheduling algorithms developed here allow for the optimization of constrained military missions in situations where the communication network may be incomplete and only locally known. Two problems are developed. The distributed task assignment problem incorporates communication constraints that must be satisfied; this is the Communication-Constrained Distributed Assignment Problem. A novel distributed assignment algorithm, the Stochastic Bidding Algorithm, solves this problem. The algorithm is correct, probabilistically complete, and has linear average-case time complexity. The distributed task scheduling problem addressed here is to minimize mission time subject to arbitrary predicate mission constraints; this is the Minimum-time Arbitrarily-constrained Distributed Scheduling Problem. The Optimal Distributed Non-sequential Backtracking Algorithm solves this problem. The algorithm is correct, complete, outputs time optimal schedules, and has low average-case time complexity. Separation of the task assignment and task scheduling problems is exploited here to ameliorate the effects of an incomplete communication network. The mission-modeling conditions that allow this and the benefits gained are discussed in detail. It is shown that the distributed task assignment and task scheduling algorithms developed here can operate concurrently and maintain their correctness, completeness, and optimality properties.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91527/1/jpjack_1.pd

Hybrid direct and interactive solvers for sparse indefinite and overdetermined systems on future exascale architectures

In scientific computing, the numerical simulation of systems is crucial to get a deep understanding of the physics underlying real world applications. The models used in simulation are often based on partial differential equations (PDE) which, after fine discretisation, give rise to huge sparse systems of equations to solve. Historically, 2 classes of methods were designed for the solution of such systems: direct methods, robust but expensive in both computations and memory; and iterative methods, cheap but with a very problem-dependent convergence properties. In the context of high performance computing, hybrid direct-iterative methods were then introduced inorder to combine the advantages of both methods, while using efficiently the increasingly largeand fast supercomputing facilities. In this thesis, we focus on the latter type of methods with two complementary research axis.In the first chapter, we detail the mechanisms behind the efficient implementation of multigrid methods. The latter makes use of several levels of increasingly refined grids to solve linear systems with a combination of fine grid smoothing and coarse grid corrections. The efficient parallel implementation of such a scheme is a difficult task. We focus on the solution of the problem on the coarse grid whose scalability is often observed as limiting at very large scales. We propose an agglomeration technique to gather the data of the coarse grid problem on a subset ofthe computing resources in order to minimise the execution time of a direct solver. Combined with a relaxation of the solution accuracy, we demonstrate an increased overall scalability of the multigrid scheme when using our approach compared to classical iterative methods, when the problem is numerically difficult. At extreme scale, this study is carried in the HHG framework(Hierarchical Hybrid Grids) for the solution of a Stokes problem with jumping coefficients, inspired from Earth's mantle convection simulation. The direct solver used on the coarse grid is MUMPS,combined with block low-rank approximation and single precision arithmetic.In the following chapters, we study some hybrid methods derived from the classical row-projection method block Cimmino, and interpreted as domain decomposition methods. These methods are based on the partitioning of the matrix into blocks of rows. Due to its known slow convergence, the original iterative scheme is accelerated with a stabilised block version of the conjugate gradient algorithm. While an optimal choice of block size improves the efficiency of this approach, the convergence stays problem dependent. An alternative solution is then introduced which enforces a convergence in one iteration by embedding the linear system into a carefully augmented space.These two approaches are extended in order to compute the minimum norm solution of in definite systems and the solution of least-squares problems. The latter problems require a partitioning in blocks of columns. We show how to improve the numerical properties of the iterative and pseudo-direct methods with scaling, partitioning and better augmentation methods. Both methods are implemented in the parallel solver ABCD-Solver (Augmented Block Cimmino Distributed solver)whose parallelisation we improve through a combination of load balancing and communication minimising techniques.Finally, for the solution of discretised PDE problems, we propose a new approach which augments the linear system using a coarse representation of the space. The size of the augmentation is controlled by the choice of a more or less refined mesh. We obtain an iterative method with fast linear convergence demonstrated on Helmholtz and Convection-Diffusion problems. The central point of the approach is the iterative construction and solution of a Schur complemen