Edge computing extends traditional cloud services to the edge of the network, closer to users, and is suitable for network services with low latency requirements. With the rise of edge computing, its security issues have also received more and more attention. In this paper, a novel two-phase cycle algorithm is proposed for effective cyber intrusion detection in edge computing based on multi-objective genetic algorithm (MOGA) and modified back propagation neural network (MBPNN), namely TPC-MOGA-MBPNN. In the first phase, the MOGA is employed to build multi-objective optimization model that tries to find Pareto optimal parameter set for MBPNN. The Pareto optimal parameter set is applied for simultaneous minimization of average false positive rate (Avg FPR), mean squared error (MSE), and negative average true positive rate (Avg TPR) in the dataset. In the second phase some MBPNNs are created based on the parameter set obtained by MOGA and are trained to search for more optimal parameter set locally. The parameter set obtained in the second phase is used as the input of the first phase, and the training process is repeated until the termination criteria are reached. Benchmark dataset namely KDD cup 1999 is used to demonstrate and validate the performance of the proposed approach for intrusion detection. The proposed approach can discover a pool of MBPNN based solutions. Combining these MBPNN can significantly improve prediction performance, and a GA is used to find the optimal MBPNN combination. The result shows that the proposed approach could reach an accuracy of 98.81% and a detection rate of 98.23%, which outperform most systems of previous works found in the literature. In addition, the proposed approach is a generalized classification approach that is applicable to the problem of any field having multiple conflicting objectives.