From: FAROUK AMINU <f.aminu_at_lancaster.ac.uk>

Date: Mon 27 Nov 2000 05:44:28 PM GMT

Message-ID: <Pine.GSO.4.21.0011271723550.15072-100000@unixc.lancs.ac.uk>

Date: Mon 27 Nov 2000 05:44:28 PM GMT

Message-ID: <Pine.GSO.4.21.0011271723550.15072-100000@unixc.lancs.ac.uk>

Dear Warwick, I realised that other users have not received my recent mail on the subject and hence decided to send this one again. I have made midifications to the problem after sending it to you. I now realised I can use just one predicate for the whole program, I don't know if it is better, but still I have been able to solve the problem in less time that using the earlier formulation. I present the new program here:- :-lib(fd). solve(Arcs, Time):- Arcs = [A1, A2, A3, A4, A5, A6, A7, A8], Arcs::1..8, alldifferent(Arcs), A8 = 1, element(A1, [0, 2, 3, 5, 5, 1, 2, 5], C1), element(A2, [0, 2, 3, 5, 5, 1, 2, 5], C2), element(A3, [0, 2, 3, 5, 5, 1, 2, 5], C3), element(A4, [0, 2, 3, 5, 5, 1, 2, 5], C4), element(A5, [0, 2, 3, 5, 5, 1, 2, 5], C5), element(A6, [0, 2, 3, 5, 5, 1, 2, 5], C6), element(A7, [0, 2, 3, 5, 5, 1, 2, 5], C7), element(A8, [0, 2, 3, 5, 5, 1, 2, 5], C8), Time = [T1, T2, T3, T4, T5, T6, T7, T8, Tot], Matrix = m(r(0,0,2,5,10,5,6,6), r(9,9,0,3,8,3,4,4), r(6,6,3,0,5,0,1,1), r(5,5,7,10,0,13,11,11), r(0,0,2,5,10,5,6,6), r(5,5,2,5,10,5,0,0), r(9,9,0,3,8,3,4,4), r(0,0,2,5,10,5,6,6)), suspend(subscript(Matrix, [1,A1], V1), 3, [A1 -> inst]), suspend(subscript(Matrix, [A1,A2], V2), 3, [A2 -> inst]), suspend(subscript(Matrix, [A2,A3], V3), 3, [A3 -> inst]), suspend(subscript(Matrix, [A3,A4], V4), 3, [A4 -> inst]), suspend(subscript(Matrix, [A4,A5], V5), 3, [A5 -> inst]), suspend(subscript(Matrix, [A5,A6], V6), 3, [A6 -> inst]), suspend(subscript(Matrix, [A6,A7], V7), 3, [A7 -> inst]), suspend(subscript(Matrix, [A7,A8], V8), 3, [A7 -> inst]), (nonvar(A1) -> subscript(Matrix, [1,A1], V1); true), (nonvar(A2) -> subscript(Matrix, [A1,A2], V2); true), (nonvar(A3) -> subscript(Matrix, [A2,A3], V3); true), (nonvar(A4) -> subscript(Matrix, [A3,A4], V4); true), (nonvar(A5) -> subscript(Matrix, [A4,A5], V5); true), (nonvar(A6) -> subscript(Matrix, [A5,A6], V6); true), (nonvar(A7) -> subscript(Matrix, [A6,A7], V7); true), (nonvar(A7) -> subscript(Matrix, [A7,A8], V8); true), TMatrix = r(Tot, T2, T3, T4, T5, T6, T7, T8), D1 #= V1 + C1, D2 #= V2 + C2, D3 #= V3 + C3, D4 #= V4 + C4, D5 #= V5 + C5, D6 #= V6 + C6, D7 #= V7 + C7, D8 #= V8 + C8, T1 #= 0, PR1 #= T1 + D1, PR2 #= PR1 + D2, PR3 #= PR2 + D3, PR4 #= PR3 + D4, PR5 #= PR4 + D5, PR6 #= PR5 + D6, PR7 #= PR6 + D7, PR8 #= PR7 + D8, suspend(subscript(TMatrix, [A1], PR1), 3, [A1 -> inst]), suspend(subscript(TMatrix, [A2], PR2), 3, [A2 -> inst]), suspend(subscript(TMatrix, [A3], PR3), 3, [A3 -> inst]), suspend(subscript(TMatrix, [A4], PR4), 3, [A4 -> inst]), suspend(subscript(TMatrix, [A5], PR5), 3, [A5 -> inst]), suspend(subscript(TMatrix, [A6], PR6), 3, [A6 -> inst]), suspend(subscript(TMatrix, [A7], PR7), 3, [A7 -> inst]), (nonvar(A1) -> subscript(TMatrix, [A1], PR1); true), (nonvar(A2) -> subscript(TMatrix, [A2], PR2); true), (nonvar(A3) -> subscript(TMatrix, [A3], PR3); true), (nonvar(A4) -> subscript(TMatrix, [A4], PR4); true), (nonvar(A5) -> subscript(TMatrix, [A5], PR5); true), (nonvar(A6) -> subscript(TMatrix, [A6], PR6); true), (nonvar(A7) -> subscript(TMatrix, [A7], PR7); true), subscript(TMatrix, [A8], PR8), min_max(labeling(Arcs), Tot). This program gave the following results and it is doing what I wanted. Arcs = [2, 3, 4, 5, 6, 7, 8, 1] Time = [0, 2, 5, 10, 15, 21, 23, 32, 32] Yes (2.65s cpu) Found a solution with cost 32. I hope yopu would not mind runing the program to have a feel of how it works. My only problem at the moment is just what I mentioned in my other mail which is not available in the archive. This formulation seems to work alright but not on much bigger problems. I have tried solving a case with 19 arcs which I attached to you in my last mail but for some reasons the solver gives the following message in the error and messages window:- Found a solution with cost 320. This result came in a fraction of a second. However, it took up to 24 working hrs yet the solver could not prove optimality. It remained working without being able to give any output in the results window. This shows that there might be some uncountable alternatives or just it is the way I formulated the problem. I have tried my possible best to improve the problem by using different definitions to the labeling predicate, yet nothing comes up. I would very much appreciate your comments on how I could improve the formulation given my problem with bigger problem. Thanking you, with regards, Farouk =============================================================================== UMARU FAROUK AMINU DEPARTMENT OF MANAGEMENT SCIENCE LANCASTER UNIVERSITY LANCASTER LA1 4YX U.K. +44 (0)1524 593865 (School) +44 (0)1524 383619 (Home) +44 (0)1524 844885 (Fax)Received on Mon Nov 27 17:44:54 2000

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