Modern Heuristic Techniques for Combinatorial ProblemsC. R. Reeves Experienced researchers describe the latest types of heuristic procedures. Artificial networks, simulated annealing, Tabu search, Lagrangean relaxation, genetic algorithms and evaluation of heuristics are among the subjects discussed. |
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Page 206
... graph bisection problem ( b ) A K = 4 graph partition problem ( c ) A N = 4 TSP problem halves such that the connectivity ( cutsize ) between the two halves is minimized . The problem is mapped onto the Hopfield energy function ( cf ...
... graph bisection problem ( b ) A K = 4 graph partition problem ( c ) A N = 4 TSP problem halves such that the connectivity ( cutsize ) between the two halves is minimized . The problem is mapped onto the Hopfield energy function ( cf ...
Page 211
... Graph Partition Problem A generalization of the graph bisection problem is graph partitioning ( GPP ) , where the N nodes are to be partitioned into K subsets of N / K nodes , again with minimal cutsize ( see Figure 5.4b ) . This re ...
... Graph Partition Problem A generalization of the graph bisection problem is graph partitioning ( GPP ) , where the N nodes are to be partitioned into K subsets of N / K nodes , again with minimal cutsize ( see Figure 5.4b ) . This re ...
Page 222
... GRAPH PARTITION K = 10 N = 100 Neural Network < Nsweep > = 57 400 450 cutsize 500 Figure 5.10 : Comparison of Potts neural network solutions versus simu- lated annealing and random distributions for a 10 x 100 graph partition problem ...
... GRAPH PARTITION K = 10 N = 100 Neural Network < Nsweep > = 57 400 450 cutsize 500 Figure 5.10 : Comparison of Potts neural network solutions versus simu- lated annealing and random distributions for a 10 x 100 graph partition problem ...
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annealing algorithm applications approach aspiration assignment problem attributes binary chromosome combinatorial optimization components computational constraints convergence cooling cost function crossover current solution defined diversification dual ascent evaluations example feasible solution frequency from-attribute genetic algorithms given graph partition implementation integer knapsack problem Lagrange multipliers Lagrangean heuristic Lagrangean relaxation linear programming local optimum lower bound LP relaxation method modules multiplier adjustment mutation neighbourhood search neighbourhood structure neural network neurons number of iterations objective function operator optimal solution optimum original problem parallel parameters particular penalty performance possible Potts prob problem reduction procedure random randomly scheduling problem schema schemata selected set covering problem simulated annealing solution space strategies subgradient optimization subset swap tabu restrictions tabu search tabu tenure tabu-active techniques temperature tion to-attribute travelling salesman problem tree node tree search updating variables vector Walsh functions