Multiple-objective Optimization Based on a Two-time-scale Neurodynamic System

In this paper, a framework of neurodynamic system consisting of two subsystems with different time-scale is firstly developed for solving multi-objective convex optimization problems. By designing a continuous-time dynamic for weight associated with each single objective function, the multi-objective optimization problem is turned to an optimization problem with a single time-varying objective function. Then the neurodynamic model can be formulated by combining the weight dynamic with existing neurodynamic models for single-objective optimization. By setting different time scale for the two subsystem, it is shown that the trajectory of the state of the neurodynamic system can approximate the whole pareto front well in bi-objective optimization problems. For the many-objective optimization problem, by designing proper dynamics for weight vectors, the whole Pareto-front can be well approximated by a curve generated from the neurodynamic system. Finally, numerical simulation is presented to illustrate the neurodynamic approaches.