Cluster Analysis and Switching Algorithm of Multi-Objective Optimal Control Design

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Zhi-Chang Qin ◽  
Jian-Qiao Sun
Keyword(s):  
Optimal Control ◽  
Cluster Analysis ◽  
Control Algorithm ◽  
Control Design ◽  
Optimal Designs ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Multi Objective ◽  
Switching Algorithm ◽  
Optimal Controllers

The multi-objective optimal control design usually generates hundreds or thousands of Pareto optimal solutions. How to assist a user to select an appropriate controller to implement is a postprocessing issue. In this paper, we develop a method of cluster analysis of the Pareto optimal designs to discover the similarity of the optimal controllers. After we identify the clusters of optimal controllers, we develop a switching strategy to select controls from different clusters to improve the performance. Numerical and experimental results show that the switching control algorithm is quite promising.

Cluster Analysis and Switching Control: A Post-Processing of Multi-Objective Optimal Designs

2016 ◽  
Author(s):  
Zhi-Chang Qin ◽  
Jian-Qiao Sun
Keyword(s):  
Cluster Analysis ◽  
Control Algorithm ◽  
Switching Control ◽  
Optimal Designs ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Post Processing ◽  
Multi Objective ◽  
Optimal Controllers

The multi-objective optimal control design usually generates hundreds or thousands of Pareto optimal solutions. How to assist an user to select an appropriate controller to implement is a post-processing issue. In this paper, we develop a method of cluster analysis of the Pareto optimal designs to discover the similarity of the optimal controllers. After we identify the clusters of optimal controllers, we then develop a switching strategy to select controls from different clusters to improve the performance. Numerical results show that the switching control algorithm is quite promising.

Multiobjective Weighting Selection for Optimization-Based Control Design

1997 ◽  
Vol 122 (3) ◽  
pp. 567-569 ◽  
Author(s):  
Ricardo H. C. Takahashi ◽  
Juan F. Camino and ◽  
Douglas E. Zampieri ◽  
Pedro L. D. Peres
Keyword(s):  
Control Design ◽  
Active Suspension ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Cost Functional ◽  
Design Variables ◽  
Optimal Controllers ◽  
Selection For ◽  
Multiobjective Design

A methodology for the multiobjective design of controllers is presented, motivated by the problem of designing an active suspension controller. This problem has, as a particular feature, the possibility of being defined with two design variables only. The multiobjective controller is searched inside the space of “optimal controllers” defined by a weighted cost functional. The weightings are taken as the optimization variables for the multiobjective design. The method leads to (local) Pareto-optimal solutions and allows the direct specification of controller constraints in terms of some primary objectives which are taken into account in the multiobjective search. [S0022-0434(00)01403-9]

scholarly journals Single- and Multi-Objective Optimization of a Dual-Chamber Microbial Fuel Cell Operating in Continuous-Flow Mode at Steady State

Processes ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 839
Author(s):  
Ibrahim M. Abu-Reesh
Keyword(s):  
Flow Rate ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Dual Chamber ◽  
Worst Case ◽  
Multi Objective ◽  
Model Based ◽  
Conflicting Objectives

Microbial fuel cells (MFCs) are a promising technology for bioenergy generation and wastewater treatment. Various parameters affect the performance of dual-chamber MFCs, such as substrate flow rate and concentration. Performance can be assessed by power density ( PD ), current density ( CD ) production, or substrate removal efficiency ( SRE ). In this study, a mathematical model-based optimization was used to optimize the performance of an MFC using single- and multi-objective optimization (MOO) methods. Matlab’s fmincon and fminimax functions were used to solve the nonlinear constrained equations for the single- and multi-objective optimization, respectively. The fminimax method minimizes the worst-case of the two conflicting objective functions. The single-objective optimization revealed that the maximum PD ,   CD , and SRE were 2.04 W/m2, 11.08 A/m2, and 73.6%, respectively. The substrate concentration and flow rate significantly impacted the performance of the MFC. Pareto-optimal solutions were generated using the weighted sum method for maximizing the two conflicting objectives of PD and CD in addition to PD and SRE   simultaneously. The fminimax method for maximizing PD and CD showed that the compromise solution was to operate the MFC at maximum PD conditions. The model-based optimization proved to be a fast and low-cost optimization method for MFCs and it provided a better understanding of the factors affecting an MFC’s performance. The MOO provided Pareto-optimal solutions with multiple choices for practical applications depending on the purpose of using the MFCs.

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.

New Dynamic Multi-Objective Constrained Optimization Evolutionary Algorithm

2015 ◽  
Vol 32 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Chun-An Liu ◽  
Yuping Wang ◽  
Aihong Ren
Keyword(s):  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Constrained Optimization Problem ◽  
Multi Objective ◽  
Time Period ◽  
Pareto Fronts

For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed into a dynamic bi-objective constrained optimization problem based on the dynamic mean rank variance and dynamic mean density variance of the evolution population. The evolution operators and a self-check operator which can automatically checkout the change of time parameter are introduced to solve the optimization problem efficiently. And finally, a dynamic multi-objective constrained optimization evolutionary algorithm is proposed. Also, the convergence analysis for the proposed algorithm is given. The computer simulations are made on four dynamic multi-objective optimization test functions and the results demonstrate that the proposed algorithm can effectively track and find the varying Pareto optimal solutions or the varying Pareto fronts with the change of time.

scholarly journals GENERATING PARETO OPTIMAL SOLUTIONS OF MULTI-OBJECTIVE LFPP WITH INTERVAL COEFFICIENTS USING E-CONSTRAINT METHOD

2015 ◽  
Vol 20 (3) ◽  
pp. 329-345 ◽  
Author(s):  
Suvasis Nayak ◽  
Akshay Ojha
Keyword(s):  
Closed Interval ◽  
Fuzzy Programming ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective ◽  
Decision Variables ◽  
Interval Coefficients ◽  
Constraint Method ◽  
Linear Fractional Programming Problem

This paper illustrates a procedure to generate pareto optimal solutions of multi-objective linear fractional programming problem (MOLFPP) with closed interval coefficients of decision variables both in objective and constraint functions. E-constraint method is applied to produce pareto optimal solutions comprising most preferred solution to satisfy all objectives. A numerical example is solved using our proposed method and the result so obtained is compared with that of fuzzy programming which justifies the efficiency and authenticity of the proposed method.

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