By H. T. Lau

In fresh years researchers have spent a lot attempt in constructing effective heuristic algorithms for fixing the category of NP-complete difficulties that are generally believed to be inherently intractable from the computational standpoint. even if algorithms were designed and are infamous between researchers, computing device courses are both no longer carried out on pcs or very tough to procure. the aim of this ebook is to supply a resource of FORTRAN coded algorithms for a specific variety of recognized combinatorial optimization difficulties. The ebook is meant for use as a supplementary textual content in combinatorial algorithms, community optimization, operations study and administration technology. moreover, a brief description on every one set of rules will let the ebook for use as a handy reference. This paintings do not have been attainable with no the wonderful amenities of Bell-Northern examine, Canada. H. T. Lau lIe des Soeurs Quebec, Canada August 1986 CONTENTS web page advent 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 position 106 bankruptcy eight. K-Center situation 114 checklist of Subroutines 123 Bibliographic Notes 124 advent Following the dependent thought of NP-comp1eteness, the assumption of constructing effective heuristic algorithms has been gaining its reputation and significance.

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**Sample text**

TRUE. GE. LE. LE. LT. LT. GE. GT. GE. 2) THEN ATEMP = A(Jl) JPONT = IPOINT(Jl) A( Jl) = A(1) IPOINT(Jl) = IPOINT(l) Jl = Jl - 1 J2 = J3 GOTO 20 ENDIF RETURN ElIoTI J4 + 1 Chapter 4 TRAVELING SALESMAN PROBLEM A. Problem Description Let G be a complete graph with an associated distance matrix (d ij ) on its edges. The travel salesman probZem is to start from a node in G, visit every other node exactly once and return back to the starting node in such a way that the total traveled distance is minimum.

The value of item j, i and b i represents the upper limit on resource represents the amount of resource i consumed by item j. The problem is to choose a set of valuable items while satisfying the limitations of restricted resources. 1 '" Xi = 0 means that the item i is rejected. The heuristic procedure to be described provides a good approximate solution. It is particularly effective for solving large size problems. Let J S T R set of all n item s , i . e . , J = {1,2, ... ,n} set of accepted items, set of items not in S, i .

GE. LE. GT. N) THEN NUMSOL = N DO 30 I = 1, N OBJVAL = OBJVAL + C(J) ISOL(I) = I RETURN ENDIF EST = O. GE. EQ. OR. GE. LE. LE. 1» GOTO 60 solve the sequence of problems in group one C 70 80 90 WORK1(1,1) O. WORK1(2,1) = O. WORK2 (1 , 1) = O. WORK2 ( 2 , 1) = O. DO 70 I = 2, M WORK1(1,I) = BIG WORK2(1,I) = O. TRUE. LE. NOT. LT. LT. LE. LE. B) THEN GVALUE = O. GT. LT. 0) THEN WORK2(ICOL2,I) = O. GE. LE. GT. EQ. GT. GE. LE. FALSE. IWK6(I) 0 WORK1(1,1) O. WORK1(2,1) O. WORK2 (l , 1 ) 0. DO 140 I = 2, ISUB WORK1(1,I) = BIG I = IWK4(l) + 1 WORK1(1,I) = WORK3(1) IWK6 (1) = 1 IWK7 (l, I) = 1 GOTO 120 49 SWITCH = .