5,546 research outputs found
GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs
We present a prototype of a software tool for exploration of multiple
combinatorial optimisation problems in large real-world and synthetic complex
networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial
Explorer), provides a unified framework for scalable computation and
presentation of high-quality suboptimal solutions and bounds for a number of
widely studied combinatorial optimisation problems. Efficient representation
and applicability to large-scale graphs and complex networks are particularly
considered in its design. The problems currently supported include maximum
clique, graph colouring, maximum independent set, minimum vertex clique
covering, minimum dominating set, as well as the longest simple cycle problem.
Suboptimal solutions and intervals for optimal objective values are estimated
using scalable heuristics. The tool is designed with extensibility in mind,
with the view of further problems and both new fast and high-performance
heuristics to be added in the future. GraphCombEx has already been successfully
used as a support tool in a number of recent research studies using
combinatorial optimisation to analyse complex networks, indicating its promise
as a research software tool
QoS Constrained Optimal Sink and Relay Placement in Planned Wireless Sensor Networks
We are given a set of sensors at given locations, a set of potential
locations for placing base stations (BSs, or sinks), and another set of
potential locations for placing wireless relay nodes. There is a cost for
placing a BS and a cost for placing a relay. The problem we consider is to
select a set of BS locations, a set of relay locations, and an association of
sensor nodes with the selected BS locations, so that number of hops in the path
from each sensor to its BS is bounded by hmax, and among all such feasible
networks, the cost of the selected network is the minimum. The hop count bound
suffices to ensure a certain probability of the data being delivered to the BS
within a given maximum delay under a light traffic model. We observe that the
problem is NP-Hard, and is hard to even approximate within a constant factor.
For this problem, we propose a polynomial time approximation algorithm
(SmartSelect) based on a relay placement algorithm proposed in our earlier
work, along with a modification of the greedy algorithm for weighted set cover.
We have analyzed the worst case approximation guarantee for this algorithm. We
have also proposed a polynomial time heuristic to improve upon the solution
provided by SmartSelect. Our numerical results demonstrate that the algorithms
provide good quality solutions using very little computation time in various
randomly generated network scenarios
An Efficient Local Search for Partial Latin Square Extension Problem
A partial Latin square (PLS) is a partial assignment of n symbols to an nxn
grid such that, in each row and in each column, each symbol appears at most
once. The partial Latin square extension problem is an NP-hard problem that
asks for a largest extension of a given PLS. In this paper we propose an
efficient local search for this problem. We focus on the local search such that
the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and
then assigning symbols to at most q empty cells. For p in {1,2,3}, our
neighborhood search algorithm finds an improved solution or concludes that no
such solution exists in O(n^{p+1}) time. We also propose a novel swap
operation, Trellis-swap, which is a generalization of (1,q)-swap and
(2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to
do the same thing. Using these neighborhood search algorithms, we design a
prototype iterated local search algorithm and show its effectiveness in
comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX
and LocalSolver.Comment: 17 pages, 2 figure
Parameter-Independent Strategies for pMDPs via POMDPs
Markov Decision Processes (MDPs) are a popular class of models suitable for
solving control decision problems in probabilistic reactive systems. We
consider parametric MDPs (pMDPs) that include parameters in some of the
transition probabilities to account for stochastic uncertainties of the
environment such as noise or input disturbances.
We study pMDPs with reachability objectives where the parameter values are
unknown and impossible to measure directly during execution, but there is a
probability distribution known over the parameter values. We study for the
first time computing parameter-independent strategies that are expectation
optimal, i.e., optimize the expected reachability probability under the
probability distribution over the parameters. We present an encoding of our
problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem
to computing optimal strategies in POMDPs.
We evaluate our method experimentally on several benchmarks: a motivating
(repeated) learner model; a series of benchmarks of varying configurations of a
robot moving on a grid; and a consensus protocol.Comment: Extended version of a QEST 2018 pape
Anytime Point-Based Approximations for Large POMDPs
The Partially Observable Markov Decision Process has long been recognized as
a rich framework for real-world planning and control problems, especially in
robotics. However exact solutions in this framework are typically
computationally intractable for all but the smallest problems. A well-known
technique for speeding up POMDP solving involves performing value backups at
specific belief points, rather than over the entire belief simplex. The
efficiency of this approach, however, depends greatly on the selection of
points. This paper presents a set of novel techniques for selecting informative
belief points which work well in practice. The point selection procedure is
combined with point-based value backups to form an effective anytime POMDP
algorithm called Point-Based Value Iteration (PBVI). The first aim of this
paper is to introduce this algorithm and present a theoretical analysis
justifying the choice of belief selection technique. The second aim of this
paper is to provide a thorough empirical comparison between PBVI and other
state-of-the-art POMDP methods, in particular the Perseus algorithm, in an
effort to highlight their similarities and differences. Evaluation is performed
using both standard POMDP domains and realistic robotic tasks
Model Predictive Control for Signal Temporal Logic Specification
We present a mathematical programming-based method for model predictive
control of cyber-physical systems subject to signal temporal logic (STL)
specifications. We describe the use of STL to specify a wide range of
properties of these systems, including safety, response and bounded liveness.
For synthesis, we encode STL specifications as mixed integer-linear constraints
on the system variables in the optimization problem at each step of a receding
horizon control framework. We prove correctness of our algorithms, and present
experimental results for controller synthesis for building energy and climate
control
An algebraic multigrid method for mixed discretizations of the Navier-Stokes equations
Algebraic multigrid (AMG) preconditioners are considered for discretized
systems of partial differential equations (PDEs) where unknowns associated with
different physical quantities are not necessarily co-located at mesh points.
Specifically, we investigate a mixed finite element discretization of
the incompressible Navier-Stokes equations where the number of velocity nodes
is much greater than the number of pressure nodes. Consequently, some velocity
degrees-of-freedom (dofs) are defined at spatial locations where there are no
corresponding pressure dofs. Thus, AMG approaches leveraging this co-located
structure are not applicable. This paper instead proposes an automatic AMG
coarsening that mimics certain pressure/velocity dof relationships of the
discretization. The main idea is to first automatically define coarse
pressures in a somewhat standard AMG fashion and then to carefully (but
automatically) choose coarse velocity unknowns so that the spatial location
relationship between pressure and velocity dofs resembles that on the finest
grid. To define coefficients within the inter-grid transfers, an energy
minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific
coarsening schemes and grid transfer sparsity patterns, and so it is applicable
to the proposed coarsening. Numerical results highlighting solver performance
are given on Stokes and incompressible Navier-Stokes problems.Comment: Submitted to a journa
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