## Modern heuristic techniques for combinatorial problems |

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annealing algorithm applications approach aspiration assignment problem attributes binary chromosome colouring combinatorial optimization combinatorial optimization problems components computational constraints convergence cooling cost function crossover current solution defined diversification dual ascent evaluations example feasible solution Figure formulation frequency from-attribute genetic algorithms given graph partition implementation integer knapsack problem Lagrange multipliers Lagrangean heuristic Lagrangean relaxation linear programming lower bound LP relaxation method minimize modules multiplier adjustment mutation neighbour neighbourhood search neighbourhood structure neural network neurons number of iterations objective function obtained Ops.Res optimal solution optimum original problem parameter 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 term tion to-attribute travelling salesman problem tree node tree search updating variables vector Walsh functions