scholarly journals Set-Valued Return Function and Generalized Solutions for Multiobjective Optimal Control Problems (MOC)

2013 ◽  
Vol 51 (3) ◽  
pp. 2379-2405 ◽  
Author(s):  
A. Guigue
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Generalized Solutions ◽  
Control Problems ◽  
Return Function ◽  
Multiobjective Optimal Control

Solving multiobjective optimal control problems using an improved scalarization method

2020 ◽  
Vol 37 (4) ◽  
pp. 1524-1547
Author(s):  
Gholam Hosein Askarirobati ◽  
Akbar Hashemi Borzabadi ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Uniform Distribution ◽  
Optimal Control Problems ◽  
Pareto Frontier ◽  
Optimal Solution ◽  
Control Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multiobjective Optimal Control

Abstract Detecting the Pareto optimal points on the Pareto frontier is one of the most important topics in multiobjective optimal control problems (MOCPs). This paper presents a scalarization technique to construct an approximate Pareto frontier of MOCPs, using an improved normal boundary intersection (NBI) scalarization strategy. For this purpose, MOCP is first discretized and then using a grid of weights, a sequence of single objective optimal control problems is solved to achieve a uniform distribution of Pareto optimal solutions on the Pareto frontier. The aim is to achieve a more even distribution of Pareto optimal solutions on the Pareto frontier and improve the efficiency of the algorithm. It is shown that in contrast to the NBI method, where Pareto optimality of solutions is not guaranteed, the obtained optimal solution of the scalarized problem is a Pareto optimal solution of the MOCP. Finally, the ability of the proposed method is evaluated and compared with other approaches using several practical MOCPs. The numerical results indicate that the proposed method is more efficient and provides more uniform distribution of solutions on the Pareto frontier than the other methods, such a weighted sum, normalized normal constraint and NBI.

A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems

2015 ◽  
Vol 8 (2) ◽  
pp. 253-282
Author(s):  
Mohammad Tanvir Rahman ◽  
Alfio Borzì
Keyword(s):  
Optimal Control ◽  
Nash Equilibrium ◽  
Optimal Control Problems ◽  
Optimal Solution ◽  
Control Problems ◽  
Control Constraints ◽  
Computational Framework ◽  
Local Fourier Analysis ◽  
Multiobjective Optimal Control ◽  
Nonlinear Multigrid

AbstractA finite-element multigrid scheme for elliptic Nash-equilibrium multiobjective optimal control problems with control constraints is investigated. The multigrid computational framework implements a nonlinear multigrid strategy with collective smoothing for solving the multiobjective optimality system discretized with finite elements. Error estimates for the optimal solution and two-grid local Fourier analysis of the multigrid scheme are presented. Results of numerical experiments are presented to demonstrate the effectiveness of the proposed framework.

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