3,660 research outputs found
On the van der Waerden numbers w(2;3,t)
We present results and conjectures on the van der Waerden numbers w(2;3,t)
and on the new palindromic van der Waerden numbers pdw(2;3,t). We have computed
the new number w(2;3,19) = 349, and we provide lower bounds for 20 <= t <= 39,
where for t <= 30 we conjecture these lower bounds to be exact. The lower
bounds for 24 <= t <= 30 refute the conjecture that w(2;3,t) <= t^2, and we
present an improved conjecture. We also investigate regularities in the good
partitions (certificates) to better understand the lower bounds.
Motivated by such reglarities, we introduce *palindromic van der Waerden
numbers* pdw(k; t_0,...,t_{k-1}), defined as ordinary van der Waerden numbers
w(k; t_0,...,t_{k-1}), however only allowing palindromic solutions (good
partitions), defined as reading the same from both ends. Different from the
situation for ordinary van der Waerden numbers, these "numbers" need actually
to be pairs of numbers. We compute pdw(2;3,t) for 3 <= t <= 27, and we provide
lower bounds, which we conjecture to be exact, for t <= 35.
All computations are based on SAT solving, and we discuss the various
relations between SAT solving and Ramsey theory. Especially we introduce a
novel (open-source) SAT solver, the tawSolver, which performs best on the SAT
instances studied here, and which is actually the original DLL-solver, but with
an efficient implementation and a modern heuristic typical for look-ahead
solvers (applying the theory developed in the SAT handbook article of the
second author).Comment: Second version 25 pages, updates of numerical data, improved
formulations, and extended discussions on SAT. Third version 42 pages, with
SAT solver data (especially for new SAT solver) and improved representation.
Fourth version 47 pages, with updates and added explanation
Optimisation of Mobile Communication Networks - OMCO NET
The mini conference “Optimisation of Mobile Communication Networks” focuses on advanced methods for search and optimisation applied to wireless communication networks. It is sponsored by Research & Enterprise Fund Southampton Solent University.
The conference strives to widen knowledge on advanced search methods capable of optimisation of wireless communications networks. The aim is to provide a forum for exchange of recent knowledge, new ideas and trends in this progressive and challenging area. The conference will popularise new successful approaches on resolving hard tasks such as minimisation of transmit power, cooperative and optimal routing
Cross-layer design of multi-hop wireless networks
MULTI -hop wireless networks are usually defined as a collection of nodes
equipped with radio transmitters, which not only have the capability to
communicate each other in a multi-hop fashion, but also to route each others’ data
packets. The distributed nature of such networks makes them suitable for a variety of
applications where there are no assumed reliable central entities, or controllers, and
may significantly improve the scalability issues of conventional single-hop wireless
networks.
This Ph.D. dissertation mainly investigates two aspects of the research issues
related to the efficient multi-hop wireless networks design, namely: (a) network
protocols and (b) network management, both in cross-layer design paradigms to
ensure the notion of service quality, such as quality of service (QoS) in wireless mesh
networks (WMNs) for backhaul applications and quality of information (QoI) in
wireless sensor networks (WSNs) for sensing tasks. Throughout the presentation of
this Ph.D. dissertation, different network settings are used as illustrative examples,
however the proposed algorithms, methodologies, protocols, and models are not
restricted in the considered networks, but rather have wide applicability.
First, this dissertation proposes a cross-layer design framework integrating
a distributed proportional-fair scheduler and a QoS routing algorithm, while using
WMNs as an illustrative example. The proposed approach has significant performance
gain compared with other network protocols. Second, this dissertation proposes
a generic admission control methodology for any packet network, wired and
wireless, by modeling the network as a black box, and using a generic mathematical
0. Abstract 3
function and Taylor expansion to capture the admission impact. Third, this dissertation
further enhances the previous designs by proposing a negotiation process,
to bridge the applications’ service quality demands and the resource management,
while using WSNs as an illustrative example. This approach allows the negotiation
among different service classes and WSN resource allocations to reach the optimal
operational status. Finally, the guarantees of the service quality are extended to
the environment of multiple, disconnected, mobile subnetworks, where the question
of how to maintain communications using dynamically controlled, unmanned data
ferries is investigated
Scalable Synthesis and Verification: Towards Reliable Autonomy
We have seen the growing deployment of autonomous systems in our daily life, ranging from safety-critical self-driving cars to dialogue agents. While impactful and impressive, these systems do not often come with guarantees and are not rigorously evaluated for failure cases. This is in part due to the limited scalability of tools available for designing correct-by-construction systems, or verifying them posthoc. Another key limitation is the lack of availability of models for the complex environments with which autonomous systems often have to interact with. In the direction of overcoming these above mentioned bottlenecks to designing reliable autonomous systems, this thesis makes contributions along three fronts.
First, we develop an approach for parallelized synthesis from linear-time temporal logic Specifications corresponding to the generalized reactivity (1) fragment. We begin by identifying a special case corresponding to singleton liveness goals that allows for a decomposition of the synthesis problem, which facilitates parallelized synthesis. Based on the intuition from this special case, we propose a more generalized approach for parallelized synthesis that relies on identifying equicontrollable states.
Second, we consider learning-based approaches to enable verification at scale for complex systems, and for autonomous systems that interact with black-box environments. For the former, we propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. For the latter, we present a data-driven approach based on chance-constrained optimization that allows for a system to be evaluated for specification conformance without an accurate model of the environment. We demonstrate this approach on several tasks, including a lane-change scenario with real-world driving data.
Lastly, we consider the problem of interpreting and verifying learning-based components such as neural networks. We introduce a new method based on Craig's interpolants for computing compact symbolic abstractions of pre-images for neural networks. Our approach relies on iteratively computing approximations that provably overapproximate and underapproximate the pre-images at all layers. Further, building on existing work for training neural networks for verifiability in the classification setting, we propose extensions that allow us to generalize the approach to more general architectures and temporal specifications.</p
Best matching processes in distributed systems
The growing complexity and dynamic behavior of modern manufacturing and service industries along with competitive and globalized markets have gradually transformed traditional centralized systems into distributed networks of e- (electronic) Systems. Emerging examples include e-Factories, virtual enterprises, smart farms, automated warehouses, and intelligent transportation systems. These (and similar) distributed systems, regardless of context and application, have a property in common: They all involve certain types of interactions (collaborative, competitive, or both) among their distributed individuals—from clusters of passive sensors and machines to complex networks of computers, intelligent robots, humans, and enterprises. Having this common property, such systems may encounter common challenges in terms of suboptimal interactions and thus poor performance, caused by potential mismatch between individuals. For example, mismatched subassembly parts, vehicles—routes, suppliers—retailers, employees—departments, and products—automated guided vehicles—storage locations may lead to low-quality products, congested roads, unstable supply networks, conflicts, and low service level, respectively. This research refers to this problem as best matching, and investigates it as a major design principle of CCT, the Collaborative Control Theory.
The original contribution of this research is to elaborate on the fundamentals of best matching in distributed and collaborative systems, by providing general frameworks for (1) Systematic analysis, inclusive taxonomy, analogical and structural comparison between different matching processes; (2) Specification and formulation of problems, and development of algorithms and protocols for best matching; (3) Validation of the models, algorithms, and protocols through extensive numerical experiments and case studies. The first goal is addressed by investigating matching problems in distributed production, manufacturing, supply, and service systems based on a recently developed reference model, the PRISM Taxonomy of Best Matching. Following the second goal, the identified problems are then formulated as mixed-integer programs. Due to the computational complexity of matching problems, various optimization algorithms are developed for solving different problem instances, including modified genetic algorithms, tabu search, and neighbourhood search heuristics. The dynamic and collaborative/competitive behaviors of matching processes in distributed settings are also formulated and examined through various collaboration, best matching, and task administration protocols. In line with the third goal, four case studies are conducted on various manufacturing, supply, and service systems to highlight the impact of best matching on their operational performance, including service level, utilization, stability, and cost-effectiveness, and validate the computational merits of the developed solution methodologies
User hints for optimisation processes
Innovative improvements in the area of Human-Computer Interaction and User Interfaces have en-abled intuitive and effective applications for a variety of problems. On the other hand, there has also been the realization that several real-world optimization problems still cannot be totally auto-mated. Very often, user interaction is necessary for refining the optimization problem, managing the computational resources available, or validating or adjusting a computer-generated solution. This thesis investigates how humans can help optimization methods to solve such difficult prob-lems. It presents an interactive framework where users play a dynamic and important role by pro-viding hints. Hints are actions that help to insert domain knowledge, to escape from local minima, to reduce the space of solutions to be explored, or to avoid ambiguity when there is more than one optimal solution. Examples of user hints are adjustments of constraints and of an objective function, focusing automatic methods on a subproblem of higher importance, and manual changes of an ex-isting solution. User hints are given in an intuitive way through a graphical interface. Visualization tools are also included in order to inform about the state of the optimization process. We apply the User Hints framework to three combinatorial optimization problems: Graph Clus-tering, Graph Drawing and Map Labeling. Prototype systems are presented and evaluated for each problem. The results of the study indicate that optimization processes can benefit from human interaction. The main goal of this thesis is to list cases where human interaction is helpful, and provide an ar-chitecture for supporting interactive optimization. Our contributions include the general User Hints framework and particular implementations of it for each optimization problem. We also present a general process, with guidelines, for applying our framework to other optimization problems
Adaptive Search and Constraint Optimisation in Engineering Design
The dissertation presents the investigation and development of novel adaptive
computational techniques that provide a high level of performance when searching
complex high-dimensional design spaces characterised by heavy non-linear constraint
requirements. The objective is to develop a set of adaptive search engines that will allow
the successful negotiation of such spaces to provide the design engineer with feasible high
performance solutions.
Constraint optimisation currently presents a major problem to the engineering designer and
many attempts to utilise adaptive search techniques whilst overcoming these problems are
in evidence. The most widely used method (which is also the most general) is to
incorporate the constraints in the objective function and then use methods for
unconstrained search. The engineer must develop and adjust an appropriate penalty
function. There is no general solution to this problem neither in classical numerical
optimisation nor in evolutionary computation. Some recent theoretical evidence suggests
that the problem can only be solved by incorporating a priori knowledge into the search
engine.
Therefore, it becomes obvious that there is a need to classify constrained optimisation
problems according to the degree of available or utilised knowledge and to develop search
techniques applicable at each stage. The contribution of this thesis is to provide such a
view of constrained optimisation, starting from problems that handle the constraints on the
representation level, going through problems that have explicitly defined constraints (i.e.,
an easily computed closed form like a solvable equation), and ending with heavily
constrained problems with implicitly defined constraints (incorporated into a single
simulation model). At each stage we develop applicable adaptive search techniques that
optimally exploit the degree of available a priori knowledge thus providing excellent
quality of results and high performance. The proposed techniques are tested using both well
known test beds and real world engineering design problems provided by industry.British Aerospace,
Rolls Royce and Associate
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