J. N. Hooker, G. Ottosson, E. S. Thorsteinsson, and H.-J. Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Sixteenth National Conference on Artificial Intelligence, AAAI'99, pages 136--141, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....it may possibly infer a cut. However, this happens very seldom. In general, infeasibility is detected as the result of propagation between di#erent constraints. The only known general class of valid inequalities that can be generated by CP in case of infeasibility are so called no good cuts [6] of the following form: i#O i#Z # O 1, for 0 1 variables x i , where O = x i = 1 and Z = x i = 0 . In this paper, we develop a hybrid branch and cut algorithm for MIP problems augmented by monotone constraints that can be handled by CP. The key ingredient of this ....

....during the first LP iteration) b) Since x k now takes its lower bound value, at later stages a new variable will be chosen for branching or the node will be cancelled. 4 An example scheduling problem To illustrate our approach, we consider a generic multiple machine scheduling problem [6, 7, 10]. There are n tasks and m dissimilar machines. Any task can be processed on any machine. The processing cost and the processing time of task i on machine j are c ij and p ij , respectively. Processing of task i can only begin after the release date r i , and must be completed at the latest by the ....

J. N. Hooker, G. Ottosson, E. S. Thorsteinsson, and H.-J. Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Sixteenth National Conference on Artificial Intelligence, AAAI'99, pages 136--141, 1999.

....2.2.5 Close integration of MP and CLP The previous section suggest an extension of mixed integer linear program Hybrid solver ming to mixed logic linear programming, which could also be regarded as a first step in combining the two techniques in a general framework. A next step is made in [OHKT99] where the authors advocate to use neither the CLP nor the IP model but rather to model specifically for a hybrid solver, roughly separating the problem into a discrete part (CLP store) and a continuous part (MP store) This achieves domain reduction on the CLP store (through constraint ....

G. Ottoson, J.N. Hooker, H.-J. Kim, and E.S. Thorsteinsson. On integrating constraint propagation and linear programming for combinatorial optimization. Technical report, Carnegie Mellon University, USA, and Uppsala University, Sweden, January 1999.

....(e.g. consistency checking) but deals only with variables over finite domains. Numerica extends this work by adding a variety of di#erential equation solvers to the mix [ Van Hentenryck, 1997 ] Hooker et al. describe a technique for combining linear programming and constraint propagation [ Hooker et al. 1999 ] Blackbox uses a translate solve decode scheme for planning and satisfiability [ Kautz and Selman, 1998 ] zeno is a causal link temporal planner which handled resources by calling an incremental Simplex algorithm within the plan refinement loop [ Penberthy and Weld, 1994 ] The Graphplan [ ....

J.N. Hooker, G. Ottosson, E.S. Thorsteinsson, and H. Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Artificial Intelligence, Orlando, Florida, July 1999. Menlo Park, Calif.: AAAI Press.

....(e.g. consistency checking) but deals only with variables over finite domains. Numerica extends this work by adding a variety of di#erential equation solvers to the mix [ Van Hentenryck, 1997 ] Hooker et al. describe a technique for combining linear programming and constraint propagation [ Hooker et al. 1999 ] Blackbox uses a translate solve decode scheme for planning and satisfiability [ Kautz Selman, 1998 ] zeno is a causal link temporal planner which handled resources by calling an incremental Simplex algorithm within the planrefinement loop [ Penberthy Weld, 1994 ] The Graphplan [ Blum ....

Hooker, J., Ottosson, G., Thorsteinsson, E., and Kim, H. 1999. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Artificial Intelligence. Orlando, Florida: Menlo Park, Calif.: AAAI Press.

.... used by metric ipp [ Koehler, 1998 ] including a metric version of the ATT Logistics domain [ Kautz and Selman, 1996 ] 2 The LCNF Formalism The LCNF representation combines a propositional logic formula with a set of metric constraints in a style similar to that proposed by Hooker et al. Hooker et al. 1999 ] Truth assignments to the boolean satisfiability portion of the problem define the metric constraint set, and both the satisfiability and metric portions MaxLoad # (load # 30) Statements MaxFuel # (fuel # 15) defining MinFuel # (fuel # 7 load 2) triggered AllLoaded # ....

....idea of compiling probabilistic planning problems to majsat [ Majercik and Littman, 1998 ] It seemed that if one could extend the SAT virtual machine to support probabilistic reasoning, then it would be useful to consider the orthogonal extension to handle metric constraints. Hooker at al. Hooker et al. 1999 ] argue convincingly that Operations Research techniques (such as LP) and Artificial Intelligence techniques (such as SAT solving) could be combined to their mutual benefit, and our system bears this notion out. 5 All three sets of runs use minimal conflict sets, learning, and backjumping. ....

J.N. Hooker, G. Ottosson, E.S. Thorsteinsson, and H. Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Artificial Intelligence, Orlando, Florida, July 1999. Menlo Park, Calif.: AAAI Press.

....satisfaction problem. The trivialized objective causes no undue difficulty to the methods we discuss below, and therefore the BLP formulation allows us to accommodate both constraint satisfaction and constrained optimization problems in a common framework (albeit in a more restricted way than [Hooker et al. 1999] ) To illustrate this further, consider a nontrivial optimization problem. CA: An instance of the optimal winner determination problem in combinatorial auctions (CA) is given by a set of items Z= A C B E with available quantities ] C BFE , and a set of bids ab=c d(H C ....

J. Hooker, G. Ottosson, E. Thorsteinsson, and H.-K. Kim. On integrating constraint propagation and linear programming for combinatorial optimization. Proceedings AAAI-99, pages 136--141, 1999.

....satisfaction problem. The trivialized objective causes no undue difficulty to the methods introduced above, and therefore the BLP formulation allows us to accommodate both constraint satisfaction and constrained optimization problems in a common framework (albeit in a more restricted way than [Hooker et al. 1999] ) For this problem we compared the subgradient optimization techniques ESG ASG against state of the art local search methods: DLM, SDF, Novelty , Novelty, WSAT, GSAT and HSAT. However, for reasons of space we report results only Avg. Est. Opt. Fail Opt. Steps Steps sec uf50 (100 problems) ....

J. Hooker, G. Ottosson, E. Thorsteinsson, and H.-K. Kim. On integrating constraint propagation and linear programming for combinatorial optimization. Proceedings AAAI-99, pages 136--141, 1999.

....satisfaction problem. The trivialized objective causes no undue difficulty to the methods we discuss below, and therefore the BLP formulation allows us to accommodate both constraint satisfaction and constrained optimization problems in a common framework (albeit in a more restricted way than [Hooker et al. 1999] ) To illustrate this further, consider a nontrivial optimization problem. CA: An instance of the optimal winner determination problem in combinatorial auctions (CA) is given by a set of items c = fc i g m i=1 with available quantities q = fq i g m i=1 , and a set of bids z = fz j g n j=1 ....

J. Hooker, G. Ottosson, E. Thorsteinsson, and H.-K. Kim. On integrating constraint propagation and linear programming for combinatorial optimization. Proceedings AAAI-99, pages 136--141, 1999.

....time the model is solved. In Darby Dowman and Little [6] a two phase approach is considered. The idea is to first let one solver work on the problem, and then passing on the intermediate result to the other solver. At the time of writing not much work has been done in the field. Hooker et al. [8] presented a new modelling principle called mixed logical linear programming, which unifies the best properties from CSP and ILP. A problem is formulated in two parts, one consisting of logical expressions with discrete variables and the other consisting of linear inequalities. These two separate ....

J.N. Hooker, M.A. Osorio (1999), "On integrating Constraint Propagation and Linear Programming for Combinatorial Optimization", URL: http://ba.gsia.cmu.edu/jnh/papers.html.

....(e.g. consistency checking) but deals only with variables over finite domains. Numerica extends this work by adding a variety of differential equation solvers to the mix [ Van Hentenryck, 1997 ] Hooker et al. describe a technique for combining linear programming and constraint propagation [ Hooker et al. 1999 ] Blackbox uses a translate solve decode scheme for planning and satisfiability [ Kautz and Selman, 1998 ] zeno is a causal link temporal planner which handled resources by calling an incremental Simplex algorithm within the plan refinement loop [ Penberthy and Weld, 4 All three sets of ....

J.N. Hooker, G. Ottosson, E.S. Thorsteinsson, and H. Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Artificial Intelligence, Orlando, Florida, July 1999. Menlo Park, Calif.: AAAI Press.

.... of the same constraint communicate (intra constraint communication) This is what we have previously termed mixed propagation of mixed CLP MIP global constraints [20, 21, 24] This holds regardless of the scheme used, be it (Tight) Cooperation [2, 22] Mixed Logical Linear Programming (MLLP) [15, 16, 20, 21, 24], Branch and Check (see Sec. 3) or some other integration approach [3, 6, 7, 18, 23] This double modelling could be explicit, but most preferably it should be implicit, i.e. mixed global constraints should post and dynamically update a linear relaxation of themselves, in addition to the ....

....only a special type of linear constraints, so linear relaxations take this idea a step further and open up many more possibilities in CLP MIP integration. We will exemplify this based on our experiences when developing the Branch andCheck framework and also based on our previous line of research [15, 16, 20, 21, 24]. The paper is organised as follows. This section outlined the focus of this research. Section 2 reviews the history of e orts in integrating CLP and MIP along with two classical MIP techniques, Benders Decomposition and Branch and Bound. In Sec. 3 we introduce the Branch and Check framework, ....

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John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, and Hak-Jin Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Articial Intelligence (AAAI-99), pages 136141. AAAI, The AAAI Press/The MIT Press, July 1999.

....Inference. AMS Subject classi cation: 68N99,68Q99,68T99,90C05,90C11,90C27. 1. Introduction In this paper we continue exploring the integration of constraint programming and mathematical programming, speci cally Constraint Propagation (CP) and Linear Programming (LP) extending our previous work [11,12,13,14,15]. In particular, we examine in more detail how to model for a hybrid solver and how to solve hybrid models, inter alia by giving speci c examples. We also provide benchmarks for a production planning problem. The main contributions of this paper are: Mixed global constraints connecting CP and ....

....its relation to disjunctive programming. A mixed global constraint for semi continuous piecewise linear functions. A scheme for bidirectional inference between CP and LP, i.e. between the Finite Domain constraint store (FD store) and the Linear Programming constraint store (LP store) [14]. We take advantage of the fact that some discrete variables will have discrete values satisfying the continuous constraints by chance , i.e. given a solution to the linear part, consistant values can be found for the discrete part, giving a full solution to the problem. New search ....

[Article contains additional citation context not shown here]

John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, and Hak-Jin Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Articial Intelligence (AAAI-99), pages 136141. AAAI, The AAAI Press/The MIT Press, July 1999.

No context found.

John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, and HakJin Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Articial Intelligence (AAAI-99), pages 136141. AAAI, The AAAI Press/The MIT Press, July 1999.

....a single global constraint that invokes the relaxations and constraint propagation methods described here. Various schemes have been proposed for combining optimization and constraint programming. To solve xed charge network ow problems we use a hybrid approach that we and others developed in [2, 3, 5, 6, 7, 8]. The present paper is part of a research program that investigates the robustness of this approach over a wide variety of problems. We chose the FCNF problem despite the fact that it is already rather well suited for a traditional mixed integer programming (MILP) approach. It has a succinct ....

J. N. Hooker, G. Ottosson, E. Thorsteinsson, and Hak-Jin Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceeedings, 16th National Conference on Articial Intelligence, pages 136-141, Cambridge, 1999. MIT Press.

....inference can be applied to constraints whose linearization is a part of a larger linear programming relaxation. Finally, we show how this ts nicely into the modeling framework Mixed Logical Linear Programming (MLLP) and a hybrid CLP MIP solver, which is a part of our previous line of research [11, 12, 17, 18]. This paper is structured as follows. Section 2 introduces our application, a class of con guration problems, with CLP, MIP and hybrid MLLP models. Sections 3 and 4 describe how the variable subscripts are linearized in MLLP. Section 5 describes reduced costs and how they can be used for ....

John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, and Hak-Jin Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Articial Intelligence (AAAI-99), pages 136141. AAAI, The AAAI Press/The MIT Press, July 1999.

....Programming (LP) are now widely acknowledged. Increasingly, techniques from OR are being applied within CP frameworks, and vice versa. Examples of the former include several Integer Programming (IP) techniques, such as linear relaxations (Ottosson Thorsteinsson 2000; Ottosson, Thorsteinsson, Hooker 1999; Refalo 1999; 2000; Rodosek, Wallace, Hajian 1997) Lagrangian relaxations (Caseau Laburthe 1997b; Focacci, Lodi, Milano 2000) variable fixing through reduced costs (Focacci, Lodi, Milano 1999a; Ottosson Thorsteinsson 2000) and specialized graph algorithms, such as matching (Focacci, Lodi, Milano ....

Hooker, J. N.; Ottosson, G.; Thorsteinsson, E. S.; and Kim, H.-J. 1999a. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Artificial Intelligence (AAAI-99), 136--141. AAAI.

....inference can be applied to constraints whose linearization is a part of a larger linear programming relaxation. Finally, we show how this ts nicely into the modeling framework Mixed Logical Linear Programming (MLLP) and a hybrid CLP MIP solver, which is a part of our previous line of research [9, 10, 14, 15]. This paper is structured as follows. Section 2 introduces our application, a class of con guration problems, with CLP, MIP and hybrid MLLP models. Sections 3 and 4 describe how the variable subscripts are linearized in MLLP. Section 5 describes reduced costs and how they can be used for ....

John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, and Hak-Jin Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Articial Intelligence (AAAI-99), pages 136141. AAAI, The AAAI Press/The MIT Press, July 1999.

....(ILOG Solver) solvers [48] Despite these developments, no generally accepted principle or scheme has evolved for the merger of optimization and constraint satisfaction. The purpose here is to propose such a scheme for unifying the solution methods of the two elds. We address elsewhere [27, 28, 30] the issue of a uni ed modeling framework. Our scheme is based on exploiting two dualities: the duality of search vs. inference and the duality of strengthening vs. relaxation. Some of these ideas are anticipated in [22] Branching algorithms provide one example of these dualities at work. The ....

John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, and Hak-Jin Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Articial Intelligence (AAAI-99), pages 136141. AAAI, The AAAI Press/The MIT Press, July 1999.

....disjunctive programming. 29th September Delta A mixed global constraint for semi continuous piecewise linear functions. ffl A scheme for bidirectional inference between CP and LP, i.e. between the Finite Domain constraint store (FD store) and the Linear Programming constraint store (LP store) [12]. ffl New search strategies for hybrid models. The last few years have seen increasing interest and eoeort in the integration of constraint programming and mathematical programming. The main objective of such an integration is to take advantage of both the inference through CP and the ....

....in two synchronized search trees; and, 17] automatically produces and updates a shadow copy of a CLP model on the continuous side, with constraint propagation and linear relaxations in a single search tree. A common feature of these methods is to communicate bounds, as introduced in [2] In [12], we advocate to use neither the CLP nor the IP model but rather to model speci cally for the hybrid solver, roughly separating the problem into a discrete part (FD store) and a continuous part (LP store) This achieves domain reduction on the FD store (constraint propagation) inference from the ....

John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, and Hak-Jin Kim. On integrating constraint propagation and linear programming for combinatorial optimization. In Proceedings of the Sixteenth National Conference on Artiøcial Intelligence (AAAI-99), pages 136141. AAAI, The AAAI Press/The MIT Press, July 1999.

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