A neural approach to topological optimization of communication networks, with reliability constraints

Consider network topological optimization under a reliability constraint. The objective is to find the topological layout of links, at minimal cost, under the constraint: all-terminal network reliability is not less than a given level of system reliability. The all-terminal reliability is Pr{every pair of nodes in the network can communicate with each other}. This paper presents a new approach based on artificial neural networks (ANN) for solving the problem. The problem is mapped onto an optimization ANN (OPTI-net) by constructing an energy function whose minimization process drives the neural network into one of its stable states. This stable state corresponds to a solution for the network design problem. The OPTI-net favors states that correspond to a selection of links with an overall reliability greater than or equal to a threshold value. Among these states it also favors the one which has the lowest total cost. Hysteresis McCulloch-Pitts neuron model is used in the solution, due to its performance and fast convergence. Considering the NP-hard complexity of the exact reliability calculation, together with the iterative behavior of the neural networks, bounds for the all-terminal reliability are used. This paper introduces new upper and lower bounds that are functions of the link selection and uses them to represent the network reliability. The neural network is tested via computer simulation using three problem sets. The first two sets are used to compare the results obtained by this method to those obtained by previous heuristics. The third test set contains five networks of larger sizes for which no results have been reported by previous methods. This paper rinds the optimal or near-optimal solutions for most of the problems in a relatively short time. The OPTI-net found many good solutions for a 50-vertex 1225-arc network in 1/2 CPU hour. For each problem instance, many solutions are found at each run of the simulator. The strengths of this neural network approach are very slowly increasing computation time with respect to network size, effective optimization, and flexibility. The OPTI-net is very effective in identifying optimal, or suboptimal, solutions even in search spaces up to ≈1016 for a fully connected network with 50 vertexes. The OPTI-net is the first approach to be applied on such large networks. The simulation results show that the neural approach is more efficient in designing networks of large sizes compared to other heuristic techniques