G. Ottosson, E.S. Thorsteinsson. Linear Relaxation and Reduced-Cost Based Propagation of Continuous Variable Subscripts. CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:129--138, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... vehicle routing with time windows [49] vehicle routing combined with inventory management [103] crew rostering [27, 101] and the classical transportation problem with piecewise linear costs [128] Other applications include inventory management [131] o#ce cleaning [79] product configuration [115], and generalized assignment problems [40] Most applications seem to have been to scheduling. These include machine scheduling [78, 126] sequencing with setups [48] hoist scheduling [130] employee scheduling [117] dynamic scheduling [47] and lesson timetables [48] Production scheduling ....

Ottosson, G., and E. Thorsteinsson, Linear relaxations and reduced-cost based propagation of continuous variable subscripts, presented at Second International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, University of Paderborn (2000).

....i.e. the same constraint or parts of the model must be present in both CLP and MIP form. It is also vital that the di erent forms 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 ....

.... 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 ....

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Erlendur S. Thorsteinsson and Greger Ottosson. Linear relaxations and reduced-cost based propagation of continuous variable subscripts. Annals of Operations Research, Special Issue on Integration of Constraint Programming, Articial Intelligence and Operations Research Methods, January 2001. Submitted.

.... the integration of specialised graph algorithms, such as matching [20] and network ow algorithms [38] for reducing variable domains in alldifferent and global cardinality constraints; the use of global constraints for optimality reasoning; values are removed from domains if proven sub optimal [20, 42]; the use of relaxations in addition to constraint propagation techniques like linear relaxations [29, 34, 35, 40, 42] or Lagrangian relaxations [15, 19] to provide tight bounds to constraint programming solvers; embedding cutting planes algorithms in global constraints like polyhedral cuts ....

.... variable domains in alldifferent and global cardinality constraints; the use of global constraints for optimality reasoning; values are removed from domains if proven sub optimal [20, 42] the use of relaxations in addition to constraint propagation techniques like linear relaxations [29, 34, 35, 40, 42] or Lagrangian relaxations [15, 19] to provide tight bounds to constraint programming solvers; embedding cutting planes algorithms in global constraints like polyhedral cuts [8, 19, 32] or local cuts derived from constraint propagation [34] 2 To facilitate this discussion we begin with a ....

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Erlendur S. Thorsteinsson and Greger Ottosson. Linear relaxations and reduced-cost based propagation of continuous variable subscripts. Annals of Operations Research, Special Issue on Integration of Constraint Programming, Articial Intelligence and Operations Research Methods, January 2001. Submitted.

....and, e.g. continuous relaxations through Linear 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 ....

.... 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 1999a) and network flow algorithms (Rgin 1999) An important modeling technique from CP used in these approaches are symbolic or global constraints. Decompositional modeling using these high level abstractions is largely ....

[Article contains additional citation context not shown here]

Ottosson, G., and Thorsteinsson, E. S. 2000. Linear relaxations and reduced-cost based propagation of continuous variable subscripts. In CP-AI-OR'00 Workshop on Integration of AI and OR techniques in Constraint Programming for Combinatorial Optimization Problems.

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G. Ottosson, E.S. Thorsteinsson. Linear Relaxation and Reduced-Cost Based Propagation of Continuous Variable Subscripts. CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:129--138, 2000.

No context found.

G. Ottosson and E.S. Thorsteinsson. Linear Relaxation and Reduced-Cost Based Propagation of Continuous Variable Subscripts. Proceedings of the CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:129-138, 2000.

No context found.

G. Ottosson, E.S. Thorsteinsson. Linear Relaxation and Reduced-Cost Based Propagation of Continuous Variable Subscripts. CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:129--138, 2000.

No context found.

G. Ottosson and E.S. Thorsteinsson. Linear Relaxation and Reduced-Cost Based Propagation of Continuous Variable Subscripts. CP-AI-OR'00, Paderborn, 2000, submitted.

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G. Ottosson and E.S. Thorsteinsson. Linear Relaxation and Reduced-Cost Based Propagation of Continuous Variable Subscripts. Proceedings of the CP-AI-OR'00, Paderborn, 2000.

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