Pareto-optimal Solutions for Multi-objective Optimal Control Problems using Hybrid IWO/PSO Algorithm

Document Type : Research Paper


1 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

2 School of Mathematics and Computer Science, Damghan University, Damghan, Iran

3 Department of Mathematics, Payame Noor University, Tehran, Iran


Heuristic optimization provides a robust and efficient approach for
extracting approximate solutions of multi-objective problems because of their
capability to evolve a set of non-dominated solutions distributed along the
Pareto frontier. The convergence rate and suitable diversity of solutions are
of great importance for multi-objective evolutionary algorithms. The focus of
this paper is on a hybrid method combining two heuristic optimization techniques, Invasive Weed Optimization (IWO) and Particle Swarm Optimization
(PSO), to find approximate solutions for multi-objective optimal control problems (MOCPs). In the proposed method, the process of dispersal has been
modified in the MOIWO. This modification will increase the exploration power
of the weeds and reduces the search space gradually during the iteration process. Thus, the convergence rate and diversity of solutions along the Pareto
frontier have been promote. Finally, the ability of the proposed algorithm is
evaluated and compared with conventional NSGA-II and NSIWO algorithms
using three practical MOCPs. The results show that the proposed algorithm
has better performance than others in terms of computing time, convergence
and diversity.