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122
Highlevel Counterexamples for Probabilistic Automata
"... Abstract. Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system’s states, both of which are of ..."
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Abstract. Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system’s states, both of which are of limited use in manual debugging. Many probabilistic systems are described in a guarded command language like the one used by the popular model checker PRISM. In this paper we describe how a minimal subset of the commands can be identified which together already make the system erroneous. We additionally show how the selected commands can be further simplified to obtain a wellunderstandable counterexample. 1
A RelaxandCut Framework for Gomory MixedInteger Cuts
"... Gomory MixedInteger Cuts (GMICs) are widely used in modern branchandcut codes for the solution of MixedInteger Programs. Typically, GMICs are iteratively generated from the optimal basis of the current Linear Programming (LP) relaxation, and immediately added to the LP before the next round of ..."
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Gomory MixedInteger Cuts (GMICs) are widely used in modern branchandcut codes for the solution of MixedInteger Programs. Typically, GMICs are iteratively generated from the optimal basis of the current Linear Programming (LP) relaxation, and immediately added to the LP before the next round of cuts is generated. Unfortunately, this approach is prone to instability. In this paper we analyze a different scheme for the generation of rank1 GMICs read from a basis of the original LP—the one before the addition of any cut. We adopt a relaxandcut approach where the generated GMICs are not added to the current LP, but immediately relaxed in a Lagrangian fashion. Various elaborations of the basic idea are presented, that lead to very fast— yet accurate—variants of the basic scheme. Very encouraging computational results are presented, with a comparison with alternative techniques from the literature also aimed at improving the GMIC quality. We also show how our method can be integrated with other cut generators, and successfully used in a cutandbranch enumerative framework.
Branching on nonchimerical fractionalities
 OR Letters
"... Abstract In this paper we address methods for selecting the branching variable in an enumerative exact algorithm for MixedInteger Programsa crucial step for the effectiveness of the resulting method. Many branching rules have been proposed in the literature, most of which are based on the impact ..."
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Abstract In this paper we address methods for selecting the branching variable in an enumerative exact algorithm for MixedInteger Programsa crucial step for the effectiveness of the resulting method. Many branching rules have been proposed in the literature, most of which are based on the impact of branching constraints on the LP solution values at the child nodes. Among them, strong branching turns out to be the most effective strategy in reducing the number of branching nodes, though its associated overhead may be substantial in most cases. In this paper we present heuristics to speedup the strong branching computation, and also to reduce the set of candidate branching variables by removing the variables whose fractionality is just chimerical, in the sense that it can be fixed by allowing for a little worsening of the objective function. Extensive computational results on instances from the literature are presented, showing that an average speedup of two can be achieved with respect to a standard full strong branching implementation. This is particularly encouraging if one considers the proofofconcept nature of our implementation.
Could we use a million cores to solve an integer program?
 Mathematical Methods of Operations Research
, 2012
"... Abstract Given the steady increase in cores per CPU, it is only a matter of time before supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linea ..."
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Abstract Given the steady increase in cores per CPU, it is only a matter of time before supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best practices in sequential solution of ILPs will be effective in massively parallel environments.
BranchandCut techniques for solving realistic . . .
"... We study a planning problem arising in SDH/WDM multilayer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixedinteger ..."
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We study a planning problem arising in SDH/WDM multilayer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixedinteger programming formulation for a predefined set of admissible logical links that takes many practical side constraints into account, including node hardware, several bit rates, and survivability against single physical node or link failures. This model is solved using a branchandcut approach with problemspecific preprocessing, MIPbased heuristics, and cutting planes based on either of the two layers. On several realistic twolayer planning scenarios, we show that these ingredients can be very useful to reduce the optimality gaps in the multilayer context.
Automatically Improving the Anytime Behaviour of Optimisation Algorithms: Supplementary material. http:
, 2012
"... Abstract Optimisation algorithms with good anytime behaviour try to return as highquality solutions as possible independently of the computation time allowed. Designing algorithms with good anytime behaviour is a difficult task, because performance is often evaluated subjectively, by plotting the ..."
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Abstract Optimisation algorithms with good anytime behaviour try to return as highquality solutions as possible independently of the computation time allowed. Designing algorithms with good anytime behaviour is a difficult task, because performance is often evaluated subjectively, by plotting the tradeoff curve between computation time and solution quality. Yet, the tradeoff curve may be modelled also as a set of mutually nondominated, biobjective points. Using this model, we propose to combine an automatic configuration tool and the hypervolume measure, which assigns a single quality measure to a nondominated set. This allows us to improve the anytime behaviour of optimisation algorithms by means of automatically finding algorithmic configurations that produce the best nondominated sets. Moreover, the recently proposed weighted hypervolume measure is used here to incorporate the decisionmaker's preferences into the automatic tuning procedure. We report on the improvements reached when applying the proposed method to two relevant scenarios: (i) the design of parameter variation strategies for MAXMIN Ant System, and (ii) the tuning of the anytime behaviour of SCIP, an opensource mixed integer programming solver with more than 200 parameters.
MILP Software
"... This article concerns software for solving a general Mixed Integer Linear Program (MILP) in the form min{c T x: Ax ≥ b, x ≥ 0, xj ∈ Z ∀j ∈ I}. (1) The algorithmic approach relies on the iterative solution, through generalpurpose ..."
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This article concerns software for solving a general Mixed Integer Linear Program (MILP) in the form min{c T x: Ax ≥ b, x ≥ 0, xj ∈ Z ∀j ∈ I}. (1) The algorithmic approach relies on the iterative solution, through generalpurpose
Towards Solverindependent Propagators
, 2012
"... We present an extension to indexicals to describe propagators for global constraints. The resulting language is compiled into actual propagators for different solvers, and is solverindependent. In addition, we show how this highlevel description eases the proof of propagator properties, such as co ..."
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We present an extension to indexicals to describe propagators for global constraints. The resulting language is compiled into actual propagators for different solvers, and is solverindependent. In addition, we show how this highlevel description eases the proof of propagator properties, such as correctness and monotonicity. Experimental results show that propagators compiled from their indexical descriptions are sometimes not significantly slower than builtin propagators of Gecode. Therefore, our language can be used for the rapid prototyping of new global constraints.
Nonlinear pseudoboolean optimization: Relaxation or propagation?
 IN SAT 2009
, 2009
"... PseudoBoolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudoBoolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a lin ..."
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PseudoBoolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudoBoolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branchandcutandpropagate framework, resulting in an efficient nonlinear pseudoBoolean solver.
Review of mixedinteger nonlinear and generalized disjunctive programming applications in Process Systems Engineering
, 2014
"... In this chapter we present some of the applications of MINLP and generalized disjunctive programming (GDP) in process systems engineering (PSE). For a comprehensive review of mixedinteger nonlinear optimization we refer the reader to the work by Belotti et al.[1]. Bonami et al.[2] review convex MI ..."
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In this chapter we present some of the applications of MINLP and generalized disjunctive programming (GDP) in process systems engineering (PSE). For a comprehensive review of mixedinteger nonlinear optimization we refer the reader to the work by Belotti et al.[1]. Bonami et al.[2] review convex MINLP algorithms and software in more detail. Tawarmalani and Sahinidis[3] describe global optimization theory,