A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. In Actes des Journees Francophones de Programmation et Logique, Lille, France, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....infeasible, i.e. F (y) 1, it follows from the above proposition that inequality (2) is a cutting plane separating y and x (since y) from the convex hull conv(F 1 (0) of F 1 (0) Our first separation heuristic just generates these cuts. Heuristic 2: Next consider the special case [l, u] [0, 1]. We get F 1 (0) # 1, for all y F 1 (1) # . Our second heuristic allows separating possibly fractional points x , 0 1, from conv(F 1 (0) 1. Sort the components of x in non increasing order: x #(1) x #(n) 2. Let r # 1, n be the ....

....that S(z) s 1 , s k , k = S(z) Then F j (z) 0 i# the CP problem t s i [r s i , d s i p s i ,j ] i = 1, k, cumulative( t s1 , p s1 ,j , 1] t sk , p sk ,j , 1] 1, D j (z) has a solution. The constraint cumulative is defined in the usual way [1]. Suppose there are n tasks; task j is characterized by three parameters, which can be either domain variables or values: the starting time start j , the duration dur j , and the amount res j of some resource consumed by the task. We are also given the latest completion time e for all the tasks, ....

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling, 17(7):57 -- 73, 1993.

....(Figure 1) Changing the Representation of Nodes. The Investigator provides a plug in mechanism for changing the representation of variables and propagators. This enables the user to produce a more obvious and intuitive representation. For example, propagators for cumulative constraints [1] in a scheduling application could be represented as Gantt charts, reflecting their role in the concrete application. Interaction with the Oz Explorer. The Investigator is designed to be integrated with the Oz Explorer [16] The Explorer displays the search tree as search proceeds. The default ....

A. Aggound and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling, 17(7):57--73, 1993.

....that this is due to a compiler error since replacing the suspicious code with semantical equivalent code allows us to reproduce in Agents [3] the same results as in Oz. For the first example we have rectangle length L=10 and the sizes are [6 4 4 4 2 2 2 2] and for the second we have L=20 and [9 8 8 7 5 4 4 4 4 4 3 3 3 2 2 1 1] for the sizes. 6 by the constructive approach. If one uses naive labelling, the number of choicepoints is the same for both approaches and examples. For this application, CD is not a good choice. If one uses a special labelling strategy [17] since first fail does not scale up for larger ....

....allow to solve hard scheduling problems [4, 2] for example the proof of optimality for the notorious MT10 problem (see [11] needs about 2000 choices in Oz) These techniques exploit domain specific knowledge. While for hard problems techniques like task intervals [4] or cumulative constraints [1] are used, the bridge problem can be solved by a rather naive labelling strategy 7 and reified constraints needing only 176 backtracking steps. We choose the most demanded resource first and schedule it completely. For this resource we find the tasks which can be first on it, choose the one with ....

A. Aggoun and N. Beldiceanu, 'Extending CHIP in order to solve complex scheduling and placement problems'. Mathl. Comput. Modelling, volume 17, number 7, pp. 57--73, (1993).

....years, constraint programming and especially Finite Domain Programming, has succeeded in solving real world problems in various areas. Moreover, efficient OR techniques were successfully integrated into flexible constraint systems to solve scheduling problems, which are considered extremely hard [7, 3, 1]. Solving a scheduling problem is a difficult undertaking. To solve the problem one has to experiment with several subproblems or variations. Different techniques have to be tested like the kind of constraint propagation, ordering heuristics or search strategies. These experiments should be ....

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling, 17(7):57--73, 1993.

....# # # # # # # # Figure 2.2: Matching variables against values A specialized group of constraints, so called global constraints, which uses various algorithms to achieve higher level of consistency, was developed. Many of global constraints, e.g. serialize, cumulative, diffn [CP89, CP94, AB92, BE94] etc. were developed to solve complex scheduling and geometrical problems [Bel00, KCS A01] 2.2 Dynamic CSP The Constraint Satisfaction model presented in the previous section applies to the problems, i.e. problems which require a one time solution of a system representing all the ....

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. In Actes des Journees Francophones de Programmation end Logique, Lille, 1992.

.... Starto Starto duratino Startt Persnt, Persno,h , 1) where 1 k nperson t and 1 h nperson o . 2. The persons assigned to task t are pairwise different: Persont, k Persont, h for 1 k h nperson t . This timetabling constraint is situated between the cumulative constraint [3] and the non overlapping rectangles constraint [2] in the following sense: First assume that, for each task i, we replace variables Personi,l, Personi,rpersoti by a fixed height nperson i which tells, how many persons task i requires during each instant of its execution. Then the constraint ....

Beldiceanu, N., Aggoun, A.: Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Cornput. Modelling 17 (7):57-73 (1993).

....Constraint Handling Rules. It can also be used to understand the details of constraint propagation methods and the interaction of di erent constraints. Currently, we are trying to provide a plug in mechanism for changing the representation of the constraints. For example, cumulative constraints [15] in a scheduling application could be represented as Gantt charts, re ecting their role in concrete application. VisualCHR is a part of the Java constraint library JACK (Chapter 6) A direction for future work will be the design of an interaction between VisualCHR and a visualization tool for ....

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling, 17(7):57{ 73, 1993.

....below) it is of almost no relevance regarding real world problems. While simple constraints like inequality between variables with small domains can be expressed through naming all incompatible value tuples, one cannot really think of defining complex constrefints like, for example, cumu lative [1], a constrefint for resource allocation problems that ensures that tasks never consume too much of a given resource. Therefore, we think that it is necessary for the above mentioned algorithms to improve them with respect to its constrefint representation: from the extensional to an intensional ....

A. Aggoun and N. Beldiceanu. Extending chip in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling, 1993.

....adequacy for such problem classes for academic examples (cf. M uller et al. 1995] and thus cannot compete with specialized layout algorithms. Therefore, the CHIP sytem [Van Hentenryck, 1989] has been extended by a new primitive constraint in finite domains, the so called cumulative constraint [Aggoun and Beldiceanu, 1993], that allows an improvement in the efficiency of CLP languages for solving hard scheduling and placement problems. A number of CLP languages have been marketed as commercial systems with a C like syntax and are frequently applied to solve combinatorial problems (cf. Cras, 1993, Fron, 1994, ....

....advertisements (similar to the cumulative constraint) in order to allow for an automated logical pagination of yellow pages telephone directories. The following research has also addressed the problem of solving geometric layout as a CSP: Tokuyama et al. 1991] Charman and Trousse, 1993] and [Aggoun and Beldiceanu, 13 1993] deal with rectangles. Hower et al. 1993] 10 employs a global constraint satisfaction solver where all the various layout possibilities get generated by a bottom up approach without the need of an optimization function. Please consult [Hower, 1996] There, in order to reformulate a problem ....

Abderrahmane Aggoun and Nicolas Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computational Modelling, 17(7):57--73, 1993. Pergamon Press Ltd.

....required by the different planning components, including recurrent (for instance hourly, daily or weekly) trips. Our network representation contains for each station a maximum number of trains allowed to be simultaneously waiting at the station. We express this limit as a cumulative constraint [AB93] Trips model individual trains traversing the network. Suitable routes for a given trip are given by the user. A track task represents the traversal of a track by an individual trip. With each task we associate a unique identifier and the departure time and waiting duration at the origin of ....

Aggoun, A., Beldiceanu, N. "Extending CHIP in order to Solve Complex Scheduling and Placement Problems". In Mathematical Computer Modelling 17(7): pp. 57-73, Pergamon Press Ltd. 1993.

....a wider range of examples was possible. A new version of the bridge problem was added. In this version all disjunctions are added to the system before any choices are made. The old version of the bridge problem is called bridge1 , the new version bridge2 . A variant of the perfect square [AB92] was added with small dimensions. Also a Japanese puzzle called suudoku. For comparison the same code was executed in SICStus v2.1 using setarg because the ROPE system on ProLog by BIM and the implementation in Mercury now use totally different data structures. mrope(Mercury) mrope(SICS) ....

Abderrahmane Aggoun and Nicolas Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. JFPL, pages 51--66, 1992.

....it requires the use of cumulative constraints. Even in the case of multiple unit resources, capacity limitations exist. e.g. the capacity of resource group R is given as the sum of the maximum capacity of every resource in R. Cumulative constraints over finite domains were first introduced in [4] to deal with scheduling and placement problems. Cumulative constraints are defined over a set of operations O = fO 1 ; Ong, defining a relation between the set of starting times S = fS 1 ; Sn g, the set of processing times P = fP 1 ; Png, and the set of machines M = fM 1 ; ....

....= fP 1 ; Png, and the set of machines M = fM 1 ; Mng with a given capacity L. The constraint holds if and only if the required capacity is lower than L during the interval given by the minimal starting time given by min 1infS i g and the maximum ending time max 1infS i P i g (see [4] and [15] for a more detailed description) Soft constraints and search. Both, technological (hard) and non technological (soft) constraints (in [8] the terms required and preferential constraints are used) have to be taken into consideration during planning. In principle, soft constraints ....

Aggoun, A.; Beldiceanu, N.: Extending CHIP in Order to Solve Complex Scheduling and Placement Problems, Journ'ees Francophone de la Programmation en Logique, 1992, pp. 52--66

....a logically related segment of a telephone book) The concept of scope is critical, as it provides not just a conceptual tool for the layout designer, but a computational tool for identifying contexts to which constraint classes can be limited. Similar to the idea of cumulative constraints in CHIP [1], the various scopes defined for YPPS expedite the design of layout constraints and their efficient application. YPPS defines and uses the following scopes (fig. 4) ffl Sections consist of a number of n frames, as required to layout a book (n is determined dynamically) n 1 Frame Part 1 Part ....

A. Aggoun and N. Beldiceanu. Extending chip in order to solve complex scheduling and placement problems. In Mathematical and Computational Modelling, volume 17, pages 57--73. 1993.

....(meeting locations) with, for each station, an integer representing the available track resources, that is the maximum number of trains allowed to be simultaneously waiting at the station. We express the constraints on stations representing limits for track resources as cumulative constraints [AB93] A route finally, is represented by a unique identifier and an ordered sequence of locations. The problem of generating suitable routes for a given trip demand on a network, consisting only of locations and tracks, is not currently addressed in our work. We use the following terminology for ....

Aggoun, A., Beldiceanu, N. "Extending CHIP in order to Solve Complex Scheduling and Placement Problems". In Mathematical Computer Modelling 17(7): pp. 57-73, Pergamon Press Ltd. 1993.

....Since the beginning of the 1980s a lot of work has been done in constraint based scheduling. An historical perspective is outlined in [Le Pape 94] The development of tools like CHIP [Van Hentenryck 89] and ILOG Solver [Puget 94] especially when enhanced with cumulative resource constraints [Aggoun 92] formed the basis for the implementation of precise, efficient, flexible and extensible industrial scheduling and resource allocation systems. Electrical Engineering Most of the work done on the use of constraints in the electrical engineering field involves digital circuits. Examples are ....

Aggoun, A., Beldiceanu, N., Extending CHIP in Order to Solve Complex Scheduling and Placement Problems. Actes des premires journes francophones sur la programmation en logique, Lille, France, 1992.

....abstractions (called global constraints) that are intended to facilitate the specification of problems from different fields of applications in a concise and natural way. For example, non preemptive single resource scheduling problems may be expressed by means of the global constraint cumulative [3]. Increasing the expressiveness of single constraints yields interesting perspectives in problem solving: By exploiting the semantics of global constraints, local consistency may be established efficiently at each search node by dedicated propagation algorithms. Frequently, these algorithms are ....

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling, 17(7):57--73, 1993.

....algorithms for the full RFP. 1 Many well studied scheduling problems, which were in demonstrated [10] to be RFP instances, happen also to be KRFP instances, including: the traditional scheduling benchmark, job shop scheduling [14] multiple capacity job shop scheduling [27] ship loading [1, 22] bridge building [2] We shall describe the three components of the KRFP (activities, resources and time constraints) before giving a full problem de nition. In the following, variable symbols are italicized (e.g. quantity i ) while constant symbols are not (e.g. r i ) 3.3. Activities of the ....

Abderrahmane Aggoun and Nicolas Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Premieres Journees Francophones sur la Programation en Logique, 1992.

....flow problems may be solved directly by specialized algorithms [2, 8] our goal here is to handle e#ciently problems in constraint programming that involve network flows as a subproblem. Global constraints are a key concept of constraint programming. They were first introduced in the Chip system [1, 5]. Since that time, they have been continuously studied in the literature. Recent work on global constraints includes, e.g. 12, 16, 17] A classification scheme for global constraints is presented in [4] The role of global constraints for the integration of constraint programming and ....

....by propagation) 0 1 2 3 4 5 6 7 (2,8) 0,3) 1,5) 1,6) 1,5) 2,4) 0,5) 0,3) 2,5) 1,4) 2,5) 1,3) 1,3) 0,8) 0,9) 1,5) 7 3 5 4 1 2 1 3 5 5 3 1 1 3 8 4 Fig. 3. Maximum flow: network n = 8; m = 16; s = 0; t = 7; NodeType = supply,supply,supply,supply,supply,supply,demand] Edge = [0,1], 0,2] 0,3] 1,2] 1,3] 1,4] 2,3] 2,5] 2,6] 3,4] 3,5] 4,5] 4,7] 5,7] 6,5] 6,7] LoCap = 2,1,0,1,2,1,0,0,2,1,1,2,1,0,1,0] UpCap = 8,5,3,6,4,5,5,3,5,5,4,5,3,8,3,9] Demand[v] 0, v #= s, t; Demand[s] # [0,16] Demand[t] # [0,16] Flow[e] # [LoCap[e] UpCap[e] e = 0, ....

[Article contains additional citation context not shown here]

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling, 17(7):57 -- 73, 1993.

.... f log f Check if there exists an array element with value 0 2 f 2 f log f Compute the index of a random array element with value 0 1 log f 9 overlap. This constraint is a special case of the di n constraint [2] and has been used to model a wide range of placement and scheduling problems [1]. It could be implemented by decomposition into a conjunction of m(m 1) 2 pairwise non overlapping constraints: C ij (hX i ; w i ; Y i ; h i i; hX j ; w j ; Y j ; h j i) X i w i X j X j w j X i Y i h i Y j Y j h j Y i (1) where we denote by the tuple hX i ; w i ; Y i ; h ....

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling, 17(7):57-73, 1993.

No context found.

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. In Actes des Journees Francophones de Programmation et Logique, Lille, France, 1992.

No context found.

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling, 1993.

No context found.

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Premieres Journees Francophones sur la Programmation en Logique, 1992.

No context found.

A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling, 17(7):57-73, 1993.

No context found.

A. Aggoun and N. Beldiceanu, Extending CHIP in order to Solve Complex Scheduling and Placement Problems, Mathl. Comput. Modelling, vol. 17, no. 7, pp. 57--73, Pergamon Press Ltd., 1993.

No context found.

Abderrahmane Aggoun and Nicolas Beldiceanu [1993]. Extending CHIP in Order to Solve Complex Scheduling and Placement Problems. Mathematical and Computer Modelling, 17(7):57-73, 1993.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC