A Time Wave Neural Network Framework for Solving Time-Dependent Project Scheduling Problems

This paper considers the time-dependent project scheduling problem (TPSP). We propose a time wave neural network (TWNN) framework that is able to achieve the global optimal solution (viz., the optimal project schedule) of the TPSP, which is very difficult to obtain using conventional methods (e.g., Dijkstra's algorithm). The proposed TWNN is a time wave neuron-based neural network without a requirement for any training. In the design of a TWNN, the overall project network of the TPSP is viewed as a neural network, while each node is considered as a wave-based neuron. With this new perspective, the wave-based neuron is constructed based on seven parts: an input, a wave receiver, a neuron state, a time-window selector, a wave generator, a wave sender, and an output. The first three parts are used to receive the waves coming from the predecessor neurons, the fourth part is used to choose the optimal feasible time window, and the remaining three parts are utilized to generate waves for the successive neurons. The main idea of a TWNN is based on the following mechanism: a wave generated from a neuron (node) means that all previous arcs (subprojects) of this neuron have been completed. In particular, the global optimal project scheduling is obtained when a wave is generated by the final destination neuron. To evaluate the performance of a TWNN, the well-known project scheduling problem library data sets are modified and considered in a comparative analysis. Numerical examples are also utilized to demonstrate the robustness of the method.