2010

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Optimization of n+1 queens problem using neural networks and ‘the proximity rule of initialization’
(UMT.Lahore, 2010) Muhammad Waqas
The neural networks proved very handy in order to solve combinatorial optimization problems for the last two decades. Especially the Hopfield-Tank neural network model is extensively applied to obtaining an optimal/feasible solution to many different NP combinatory optimization problems like travelling salesman problem (TSP) and NP-hard combinatory optimization problem like N Queens Problem. This thesis describes a neural network optimizer/scheduler that optimizes a solution for a highly complicated version of N Queens Problem, i.e. N+1 non-threatening Queens on a N*N chessboard with an intermediate pawn on it. The behavior of the network is evaluated using asynchronous as well as synchronous mode of updating the neurons. Theoretical soundness of the network is established with simulation. Simulations show that the proposed neural network is capable of finding the optimized solution and is convergent to the global minima in 90% of the trials with polynomial average computational complexity.