NUMERICAL SOLUTION OF A CONSTRAINED MULTIOBJECTIVE CONTROL PROBLEM MODELING THE EVOLUTION OF A SOCIAL NETWORK

摘要

In this paper, we explore how to numerically solve a constrained multiobjective optimal control problem (MOCP) modeling the evolution of a social network using an evolutionary algorithm such as Differential Evolution (DE). For the problems under consideration, the constraints are given by a system of ordinary differential equations along with some simple bounds on the state and control vectors. Using weights we form a single objective function as a linear combination of the multiple objective functions. The single objective function thus formed is then minimized. Then, we use the necessary conditions for the constrained optimal control problem adapting DE in a novel and effective way to find an optimal solution. A numerical algorithm is developed to solve the constrained MOCP and is illustrated using a social network model.