Robust Multiobjective Optimization Applied to Optimal Control Problems Using Differential Evolution

2015 ◽  
Vol 38 (4) ◽  
pp. 721-726 ◽  
Author(s):  
Davi L. Souza ◽  
Fran S. Lobato ◽  
Rubens Gedraite
Keyword(s):  
Optimal Control ◽  
Multiobjective Optimization ◽  
Differential Evolution ◽  
Optimal Control Problems ◽  
Control Problems

scholarly journals A Multistrategy-Based Multiobjective Differential Evolution for Optimal Control in Chemical Processes

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Bin Xu ◽  
Xu Chen ◽  
Xiuhui Huang ◽  
Lili Tao
Keyword(s):  
Optimal Control ◽  
Differential Evolution ◽  
Optimal Control Problems ◽  
Chemical Processes ◽  
Selection Strategy ◽  
Control Problems ◽  
Conflicting Objectives ◽  
Efficiency And Effectiveness ◽  
Single Strategy ◽  
Multiobjective Optimal Control

Optimal control problems with multiple conflicting objectives in chemical processes are quite challenging. To solve such problems, we put forward a multistrategy-based multiobjective differential evolution, in which (1) a hybrid selection strategy is incorporated from the motivation of no single strategy outperforming all other ones in every stage; (2) a multipopulation strategy is applied to represent the main population and current optimum, and a cyclic crowding estimation is developed to maintain these optimum; and (3) a multimutation strategy is constructed to improve both exploration and exploitation ability. The effectiveness and efficiency of the proposed algorithm are validated by comparisons with some representative multiobjective evolutionary algorithms over 12 test instances. Moreover, the proposed algorithm is applied to solve 3 multiobjective optimal control problems in chemical processes. The obtained results indicate the efficiency and effectiveness of the proposed algorithm for solving multiobjective optimal control problems.

scholarly journals On a Variational Approach to Optimization of Hybrid Mechanical Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Vadim Azhmyakov ◽  
Ruben Velazquez
Keyword(s):  
Optimal Control ◽  
Multiobjective Optimization ◽  
Optimal Control Problems ◽  
Hybrid Control ◽  
Mechanical Systems ◽  
Optimization Techniques ◽  
Control Problems ◽  
Variational Structure ◽  
Dynamical Optimization ◽  
Hybrid Control Systems

This paper deals with multiobjective optimization techniques for a class of hybrid optimal control problems in mechanical systems. We deal with general nonlinear hybrid control systems described by boundary-value problems associated with hybrid-type Euler-Lagrange or Hamilton equations. The variational structure of the corresponding solutions makes it possible to reduce the original “mechanical” problem to an auxiliary multiobjective programming reformulation. This approach motivates possible applications of theoretical and computational results from multiobjective optimization related to the original dynamical optimization problem. We consider first order optimality conditions for optimal control problems governed by hybrid mechanical systems and also discuss some conceptual algorithms.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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