1,037 research outputs found
Revisiting the upper bounding process in a safe Branch and Bound algorithm
Finding feasible points for which the proof succeeds is a critical issue in
safe Branch and Bound algorithms which handle continuous problems. In this
paper, we introduce a new strategy to compute very accurate approximations of
feasible points. This strategy takes advantage of the Newton method for
under-constrained systems of equations and inequalities. More precisely, it
exploits the optimal solution of a linear relaxation of the problem to compute
efficiently a promising upper bound. First experiments on the Coconuts
benchmarks demonstrate that this approach is very effective.Comment: Optimization, continuous domains, nonlinear constraint problems, safe
constraint based approaches; 14th International Conference on Principles and
Practice of Constraint Programming, Sydney : Australie (2008
Constraint Programming and Safe Global Optimization
International audienceWe investigate the capabilities of constraints programming techniques in rigor- ous global optimization methods. We introduce different constraint programming techniques to reduce the gap between efficient but unsafe systems like Baron1, and safe but slow global optimization approaches. We show how constraint program- ming filtering techniques can be used to implement optimality-based reduction in a safe and efficient way, and thus to take advantage of the known bounds of the ob- jective function to reduce the domain of the variables, and to speed up the search of a global optimum. We describe an efficient strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equalities and inequalities to compute efficiently a promising upper bound. Experiments on the COCONUT benchmarks demonstrate that these different techniques drastically improve the performances
Revisiting Synthesis for One-Counter Automata
We study the (parameter) synthesis problem for one-counter automata with
parameters. One-counter automata are obtained by extending classical
finite-state automata with a counter whose value can range over non-negative
integers and be tested for zero. The updates and tests applicable to the
counter can further be made parametric by introducing a set of integer-valued
variables called parameters. The synthesis problem for such automata asks
whether there exists a valuation of the parameters such that all infinite runs
of the automaton satisfy some omega-regular property. Lechner showed that (the
complement of) the problem can be encoded in a restricted one-alternation
fragment of Presburger arithmetic with divisibility. In this work (i) we argue
that said fragment, called AERPADPLUS, is unfortunately undecidable.
Nevertheless, by a careful re-encoding of the problem into a decidable
restriction of AERPADPLUS, (ii) we prove that the synthesis problem is
decidable in general and in N2EXP for several fixed omega-regular properties.
Finally, (iii) we give a polynomial-space algorithm for the special case of the
problem where parameters can only be used in tests, and not updates, of the
counter
Learning Score-Optimal Chordal Markov Networks via Branch and Bound
Graphical models are commonly used to encode conditional independence assumptions between random variables. Here we focus on undirected graphical models called chordal Markov networks. Specifically, we will consider the chordal Markov network structure learning problem (CMSL), where the aim is to find (or "learn") a graph structure that best fits the given data with respect to a given decomposable scoring function.
We introduce a branch and bound search algorithm for CMSL which represents chordal Markov network structures as decomposable DAGs. We show how revisiting equivalent solution candidates can be avoided in the search by detecting symmetries among graph structures. For the symmetry breaking we apply specific rules by van Beek and Hoffman (CP 2015), and also propose a new rule that takes advantage of the special nature of decomposable DAGs. In addition, we show how we can achieve on-the-fly score pruning for CMSL.
We also propose methods for obtaining strong upper bounds for CMSL that help us close branches in the search tree. We implement a dynamic programming algorithm to find the optimal Bayesian network structures and then use the scores of those graphs as upper bounds. We also show how we can relax the requirement for decomposability in decomposable DAGs in order to achieve even stronger upper bounds. Furthermore, we propose a method for obtaining an initial lower bound in CMSL by turning a Bayesian network structure into a chordal Markov network structure.
Empirically we show that our approach is competitive with the recently proposed CMSL algorithms by being able to sometimes scale up to 20 variables within 24 hours with unbounded treewidth. We also report that our branch and bound requires considerably less memory than the fastest of the recently proposed algorithms for CMSL
Rehearsal Scheduling Problem
Scheduling is a common task that plays a crucial role in many industries such as manufacturing or servicing. In a competitive environment, effective scheduling is one of the key factors to reduce cost and increase productivity. Therefore, scheduling problems have been studied by many researchers over the past thirty years. Rehearsal scheduling problem (RSP) is similar to the popular resource-constrained project scheduling problem (RCPSP); however, it does not have activity precedence constraints and the resources’ availabilities are not fixed during processing time. RSP can be used to schedule rehearsal in theatre industry or to schedule group scheduling when each member has different sets of available time. In this report, three different approaches are proposed to solve RSP including Constraint Programming, Integer Programming, and Schedule Generation Schemes
Unfolding-based Partial Order Reduction
Partial order reduction (POR) and net unfoldings are two alternative methods
to tackle state-space explosion caused by concurrency. In this paper, we
propose the combination of both approaches in an effort to combine their
strengths. We first define, for an abstract execution model, unfolding
semantics parameterized over an arbitrary independence relation. Based on it,
our main contribution is a novel stateless POR algorithm that explores at most
one execution per Mazurkiewicz trace, and in general, can explore exponentially
fewer, thus achieving a form of super-optimality. Furthermore, our
unfolding-based POR copes with non-terminating executions and incorporates
state-caching. Over benchmarks with busy-waits, among others, our experiments
show a dramatic reduction in the number of executions when compared to a
state-of-the-art DPOR.Comment: Long version of a paper with the same title appeared on the
proceedings of CONCUR 201
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