Approximate Pareto Optimal Solutions of Multi-objective Optimal Control Problems by Evolutionary Algorithms

In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems is offered. The first, adiscretized form of the time-control space is considered. Then, corresponding to a piecewise linear control form discretized time-control space and a numerical approach ofsolving differential equations, a piecewise linear trajectory is obtained .A numerical integration method allow us to discretize the objective functions and so a special multiobjective optimization problem is created. A modified evolutionary algorithm for obtaining Pareto optimal solutions of new problem with considering the final state conditions is proposed, to extract approximate solutions of original problem. Numerical example is presented to show the proficiency of the given approach

Keywords:

Multi-objective optimal control problem , Pareto solution , Evolutionary algorithm , Discretization , Approximate