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 (MOOCP)'s is introduced‎. ‎In this approach‎, ‎first a discretized form of the time-control space is considered and then‎, ‎a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using a numerical method‎. ‎To do that‎, ‎a modified version of two famous evolutionary genetic algorithm (GA) and particle swarm optimization (PSO) to obtain Pareto optimal solutions of the problem is employed‎. ‎Numerical examples are presented to show the efficiency of the given approach.