By Edward K. Baker, Anito Joseph, Anuj Mehrotra, Michael A. Trick

This publication represents the result of cross-fertilization among OR/MS and CS/AI. it really is this interface of OR/CS that makes attainable advances that may now not were accomplished in isolation. Taken jointly, those articles are indicative of the state of the art within the interface among OR/MS and CS/AI and of the excessive quality of study being carried out by means of individuals of the INFORMS Computing Society.

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Figure 9. 653. Triangles are Steiner nodes, black circles are terminal nodes. The lighter the cell, the more costly it is. A Genetic Algorithm for Solving the Euclidean Non-Uniform Steiner Tree Problem 45 Figure 10. 744. Triangles are Steiner nodes, black circles are terminal nodes. The lighter the cell, the more costly it is. Figure 11. 028. Triangles are Steiner nodes, black circles are terminal nodes. The lighter the cell, the more costly it is. Our GA was usually able to find the optimal solution for this problem.

To obtain the actual effect of- (? m I - l]'Ak = e ' B"^Ak + (-1)*(1) = ? - 1. Since X B b - (B~*N)XN, where the cardinality effect is given by - (B"^N)XN , the cardinality effect for the augmented problem is simply - ( T ~ ' N ) X N , then the cardinality effect for the m+T^ row becomes - (? 2ik- 1) . 2 An Illustrative Example Consider the problem PO with matrix A and objective function vector c. 75, 0, 0). 5. Note that this value is not the objective function value for this weighted set partitioning problem, but rather the simple sum of the basic variable values.

1992). Large chques elude the metropolis process. Random tures and Algorithms 3:4, 347-360. S. A. A. Trick. (2002). Computational Challenge on Graph Coloring and its Generalizations International Symposium on Mathematical Programming, Copenhagen, Denmark. L. (1989). Modeling and strong linear programs for mixed integer programming. W. ), Springier-Verlag Berlin, Heidelberg, 1-43. N. and P. M. Pardalos. (1996). An algorithm for finding the maximum clique on an arbitrary graph, Second DIM ACS Challenge: Cliques, Coloring, and Satisfiability, DIM ACS Series on Discrete Mathematics and Theoritical Computer Science, D.