An efficient recurrent neural network for defensive Stackelberg game

Abstract

This study presents a robust and efficient recurrent neural network (RNN) to solve the continuous defensive location problem (CDLP). CDLP is a bilevel mathematical model, where a planner locates various types of defense facilities for stopping a offender from reaching a critical vertex called core in the network. Due to the NP-hardness of the CDLP, RNN is implemented to find satisfactory solutions on four small-sized, two medium-sized and two larger-sized examples of problem. The numerical experiments show that RNN is able to produce promising results with good execution time and precision when compared with the best previous methods including tabu search (TS), imperialist competitive algorithm (ICA) and hybridization of TS with Levenberg–Marquardt algorithm (HTS) and hybridization of ICA with BFGS algorithm (HICA). The objective values of RNN show that this method stops the attacker at a further distance from the core in comparison with other methods. As well, to validate the efficiency of the proposed RNN, statistical criteria are considered and results are analyzed. For small-sized examples, the computational experiments show that the RNN can obtain solutions as the same as exact approaches but in a shorter runtime.