This paper introduces a time-varying wastage maximum flow problem (TWMFP) and proposes a time-flow neural network (TFNN) for solving the TWMFPs. The time-varying wastage maximum flow problem is concerned with finding the maximum flow in a network with time-varying arc capacities and additive flow losses on the arcs. This problem has multiple applications in transportation, communication, and financial network. For example, solving the maximum traffic flow of the transportation network and the maximum profit of the financial network. Unlike traditional neural network algorithms, the proposed TFNN does not require any training by means of its time-flow mechanism. The time-flow mechanism is realized by each active neuron sending pulses to its successor neurons. In order to maximize the network flow, the proposed TFNN can be divided into two parts: path-pulse neural networks (PPNNs) and subnet-flow neural networks (SFNN). PPNN is to generate two subnet sets (viz. with wastage arcs and without), and SFNN is to find the maximum flow value of each subnet. The subnet computing strategy of the proposed algorithm greatly improves the solution accuracy of TWMFPs. Theoretical analysis and experiments have proved the effectiveness of TFNN. The experiment results of the transportation network (viz. New York Road) show that the proposed TFNN has better performance (viz. error rate and computational time) compared to classical algorithms.

This paper introduces the constrained multi-objective optimal path problem in time-dependent networks. In the existing literatures, the constraints are all imposed on the objective function while the problem constraints are related to the non-objective function. It is the difference that makes the traditional algorithm unable to get a better solution quality. In this light, we propose a store-and-forward neural network (SFNN) that finds the better result. In the design of SFNN, the topology of neural network is the same as that of time-varying network, and each node is designed as store-and-forward neuron. Each neuron transmits information to other neurons by sending signals. The experimental results show that compared with the traditional methods, the accuracy is significantly improved when the calculation time is acceptable.