269 research outputs found
Routing with Reloads
We examine routing problems with reloads, how they can be modeled, their properties and how they can be solved. We propose a simple model, the Pickup and Delivery Problem with Reloads (RPDP), that captures the process of reloading and can be extended for real world applications. We present results that show that the RPDP is solvable in polynomial time if the number of requests is bounded by a constant. Additionally, we examine a special case of the RPDP, the k-Star Hub Problem. This problem is solvable efficiently by network flow approaches if no more than two hubs are available. Otherwise, it is NP-complete. In the second part of this thesis, additional constraints are incorporated into the model and a tabu search heuristic for this problem is presented. The heuristic has been implemented and tested on several benchmarking instances, both artificial and a real-world application. In the appendix, we discuss the application of column generation for a reload problem
Mini-Workshop: Applied Koopmanism
Koopman and PerronâFrobenius operators are linear operators that encapsulate dynamics of nonlinear dynamical systems without loss of information. This is accomplished by embedding the dynamics into a larger infinite-dimensional space where the focus of study is shifted from trajectory curves to measurement functions evaluated along trajectories and densities of trajectories evolving in time. Operator-theoretic approach to dynamics shares many features with an optimization technique: the Lasserre momentâsums-of-squares (SOS) hierarchies, which was developed for numerically solving non-convex optimization problems with semialgebraic data. This technique embeds the optimization problem into a larger primal semidefinite programming (SDP) problem consisting of measure optimization over the set of globally optimal solutions, where measures are manipulated through their truncated moment sequences. The dual SDP problem uses SOS representations to certify bounds on the global optimum. This workshop highlighted the common threads between the operator-theoretic dynamical systems and momentâSOS hierarchies in optimization and explored the future directions where the synergy of the two techniques could yield results in fluid dynamics, control theory, optimization, and spectral theory
Gromov-Wasserstein Distance based Object Matching: Asymptotic Inference
In this paper, we aim to provide a statistical theory for object matching
based on the Gromov-Wasserstein distance. To this end, we model general objects
as metric measure spaces. Based on this, we propose a simple and efficiently
computable asymptotic statistical test for pose invariant object
discrimination. This is based on an empirical version of a -trimmed
lower bound of the Gromov-Wasserstein distance. We derive for
distributional limits of this test statistic. To this end, we introduce a novel
-type process indexed in and show its weak convergence. Finally, the
theory developed is investigated in Monte Carlo simulations and applied to
structural protein comparisons.Comment: For a version with the complete supplement see [v2
Scheduling and discrete event control of flexible manufacturing systems based on Petri nets
A flexible manufacturing system (FMS) is a computerized production system that can simultaneously manufacture multiple types of products using various resources such as robots and multi-purpose machines. The central problems associated with design of flexible manufacturing systems are related to process planning, scheduling, coordination control, and monitoring. Many methods exist for scheduling and control of flexible manufacturing systems, although very few methods have addressed the complexity of whole FMS operations. This thesis presents a Petri net based method for deadlock-free scheduling and discrete event control of flexible manufacturing systems. A significant advantage of Petri net based methods is their powerful modeling capability. Petri nets can explicitly and concisely model the concurrent and asynchronous activities, multi-layer resource sharing, routing flexibility, limited buffers and precedence constraints in FMSs. Petri nets can also provide an explicit way for considering deadlock situations in FMSs, and thus facilitate significantly the design of a deadlock-free scheduling and control system.
The contributions of this work are multifold. First, it develops a methodology for discrete event controller synthesis for flexible manufacturing systems in a timed Petri net framework. The resulting Petri nets have the desired qualitative properties of liveness, boundedness (safeness), and reversibility, which imply freedom from deadlock, no capacity overflow, and cyclic behavior, respectively. This precludes the costly mathematical analysis for these properties and reduces on-line computation overhead to avoid deadlocks. The performance and sensitivity of resulting Petri nets, thus corresponding control systems, are evaluated. Second, it introduces a hybrid heuristic search algorithm based on Petri nets for deadlock-free scheduling of flexible manufacturing systems. The issues such as deadlock, routing flexibility, multiple lot size, limited buffer size and material handling (loading/unloading) are explored. Third, it proposes a way to employ fuzzy dispatching rules in a Petri net framework for multi-criterion scheduling. Finally, it shows the effectiveness of the developed methods through several manufacturing system examples compared with benchmark dispatching rules, integer programming and Lagrangian relaxation approaches
Studies in the completeness and efficiency of theorem-proving by resolution
Inference systems Τ and search strategies E for T are distinguished from proof procedures β = (T,E)
The completeness of procedures is studied by studying
separately the completeness of inference systems and of
search strategies. Completeness proofs for resolution
systems are obtained by the construction of semantic
trees. These systems include minimal Îą-restricted
binary resolution, minimal Îą-restricted M-clash resolution
and maximal pseudo-clash resolution. Certain refinements
of hyper-resolution systems with equality axioms are
shown to be complete and equivalent to refinements of
the pararmodulation method for dealing with equality.
The completeness and efficiency of search strategies
for theorem-proving problems is studied in sufficient
generality to include the case of search strategies for
path-search problems in graphs. The notion of theorem-proving problem is defined abstractly so as to be dual to
that of and" or tree. Special attention is given to
resolution problems and to search strategies which generate
simpler before more complex proofs.
For efficiency, a proof procedure (T,E) requires
an efficient search strategy E as well as an inference
system T which admits both simple proofs and relatively
few redundant and irrelevant derivations. The theory
of efficient proof procedures outlined here is applied
to proving the increased efficiency of the usual method
for deleting tautologies and subsumed clauses. Counter-examples
are exhibited for both the completeness and
efficiency of alternative methods for deleting subsumed
clauses.
The efficiency of resolution procedures is improved
by replacing the single operation of resolving a clash
by the two operations of generating factors of clauses
and of resolving a clash of factors. Several factoring
methods are investigated for completeness. Of these the
m-factoring method is shown to be always more efficient
than the Wos-Robinson method
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