By H. T. Lau

ISBN-10: 3540171614

ISBN-13: 9783540171614

ISBN-10: 3642616496

ISBN-13: 9783642616495

In fresh years researchers have spent a lot attempt in constructing effective heuristic algorithms for fixing the category of NP-complete difficulties that are largely believed to be inherently intractable from the computational perspective. even though algorithms were designed and are infamous between researchers, machine courses are both no longer applied on desktops or very tricky to acquire. the aim of this e-book is to supply a resource of FORTRAN coded algorithms for a specific variety of recognized combinatorial optimization difficulties. The e-book is meant for use as a supplementary textual content in combinatorial algorithms, community optimization, operations examine and administration technological know-how. additionally, a quick description on every one set of rules will enable the booklet for use as a handy reference. This paintings do not need been attainable with no the superb amenities of Bell-Northern learn, Canada. H. T. Lau lIe des Soeurs Quebec, Canada August 1986 CONTENTS web page creation half I. INTEGER PROGRAMMING bankruptcy 1. Integer Linear Programming bankruptcy 2. Zero-one Linear Programming 30 bankruptcy three. Zero-one Knapsack challenge 38 half II. community layout bankruptcy four. touring Salesman challenge fifty two bankruptcy five. Steiner Tree challenge eighty one bankruptcy 6. Graph Partitioning ninety eight bankruptcy 7. K-Median situation 106 bankruptcy eight. K-Center situation 114 checklist of Subroutines 123 Bibliographic Notes 124 creation Following the stylish idea of NP-comp1eteness, the belief of constructing effective heuristic algorithms has been gaining its acceptance and significance.

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**Additional info for Combinatorial Heuristic Algorithms with FORTRAN**

**Sample text**

R = R + Ok' 32 C. Subroutine MULKNP Parameters In pu t M number of constraints. N number of variables. A real matrix of dimension M by N containing the coefficients of the M constraints; on output, the matrix A is modified. B real vector of length M containing the right hand sides of the constraints. C real vector of length N containing the coefficients of the objective function. IADIM row dimension of matrix A exactly as specified in the dimension statement of the calling program. Output z NUMSOL ISOL value of the objective function.

170. 442. 525. 511. 593. 546. 564. 617. 0 7 4 1 46 SUBROUTINE KNAPP (N,A,B,C,EPS,M,OBJVAL,NUMSOL,ISOL, WORKl,WORK2,WORK3,WORK4,WORK5, + IWKl,IWK2,IWK3,IWK4,IWK5,IWK6,IWK7) + C C zero-one knapsack heuristic C INTEGER ISOL(N),IWKl(N),IWK2(N),IWK3(N),IWK4(N), IWK6(M),IWK7(N,M) REAL A(N),C(N),WORKl(2,M),WORK2(2,M), + WORK3(N),WORK4(N),WORK5(N) LOGICAL IWK5(M),SWITCH + C C reorder the variables C 10 C BIG = 1. 0 DO 10 I = 1, N WORK3(I) = C(I) / A(I) BIG = BIG + C(I) CALL SORTD(N,WORK3,IWKl) C C calculate the initial parameters C NUMSOL = 0 OBJVAL = O.

Working Storages : WKl real vector of length NN2; the input cost matrix, used in the subroutine PMATCH. WK2 rea 1 vector of length N', used in subroutines MINTRE WK3 real vector of 1 ength N', used in subroutine PMATCH. WK4 real vector of length N·, used in subroutine PMATCH. WK5 real vector of length N', used i n subroutine PMATCH. IWK6 and PMATCH. integer vector of 1 ength NN; IWK6(i) i s one of the end nodes of edge i i n the minimum spanning tree, used in subroutines MINTRE and EULER. 56 IWK7 integer vector of length NN; IWK7( i) is one of the end nodes of edge i in the minimum spanning tree, used in subroutines MINTRE and EULER.

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