ECONOMIC ENVIRONMENTAL DISPATCH BY A MODE TECHNIQUE

2008 ◽  
Vol 17 (03) ◽  
pp. 499-512 ◽  
Author(s):  
C. K. PANIGRAHI ◽  
R. CHAKRABARTI ◽  
P. K. CHATTOPADHYAY
Keyword(s):  
Optimization Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Sample Test ◽  
Optimal Set ◽  
Mode Technique

Multi-objective differential evolution (MODE) is proposed to handle economic environmental dispatch problem, which is a multi-objective optimization problem (MOOPs) with competing and noncommensurable objectives. The proposed approach has a good performance in finding a diverse set of solutions and in converging near the true Pareto-optimal set. Numerical results for two sample test systems have been presented to demonstrate the capabilities of the proposed approach to generate well-distributed Pareto-optimal solutions of economic environmental dispatch problem in one single run. Simulation results with the proposed approach have been validated with Non-dominated Sorting Genetic Algorithm-II.

scholarly journals Multi-Objective Optimization of Impedance Parameters in a Prosthesis Test Robot

2015 ◽  
Author(s):  
Poya Khalaf ◽  
Hanz Richter ◽  
Antonie J. van den Bogert ◽  
Dan Simon
Keyword(s):  
Control System ◽  
Motion Tracking ◽  
Optimization Problem ◽  
Peak Load ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Rms Error ◽  
Optimal Set

We design a control system for a prosthesis test robot that was previously developed for transfemoral prosthesis design and test. The robot’s control system aims to mimic human walking in the sagittal plane. It has been seen in previous work that trajectory control alone fails to produce human-like forces. Therefore, we utilize an impedance controller to achieve reasonable tracking of motion and force simultaneously. However, these objectives conflict. Impedance control design can therefore be viewed as a multi-objective optimization problem. We use an evolutionary multi-objective strategy called Multi-Objective Invasive Weed Optimization (MOIWO) to design the impedance controller. The multi-objective optimization problem admits a set of equally valid alternative solutions known as the Pareto optimal set. We use a pseudo weight vector approach to select a single solution from the Pareto optimal set. Simulation results show that a solution that is selected for pure motion tracking performs very accurate motion tracking (RMS error of 0.06 cm) but fails to produce the desired forces (RMS error of 70% peak load). On the other hand, a solution that is selected for pure force tracking successfully tracks the desired force (RMS error of 12.7% peak load) at the expense of motion trajectory errors (RMS error of 4.5 cm).

Solving Expensive Multi-Objective Optimization Problems by Kriging Model with Multi-Point Updating Strategy

2014 ◽  
Vol 685 ◽  
pp. 667-670 ◽  
Author(s):  
Ding Han ◽  
Jian Rong Zheng
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Average Distance ◽  
Kriging Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Good Convergence ◽  
Multi Objective

A method which utilizes Kriging model and a multi-point updating strategy is put forward for solving expensive multi-objective optimization problems. Assisted by a defined cheaper multi-objective optimization problem and a maximum average distance criterion, multiple updating points can be found. The proposed method is tested on two numerical functions and a ten-bar truss problem, the results show that the proposed method is efficient in obtaining Pareto optimal solutions with good convergence and diversity when the same computation resource is used comparing with two other methods.

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.

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.

Sirocco Fan Design for Residential Ventilation Through Multi-Objective Optimization to Enhance Aerodynamic Performance

2012 ◽  
Author(s):  
Jin-Hyuk Kim ◽  
Kyung-Hun Cha ◽  
Kwang-Yong Kim
Keyword(s):  
Total Pressure ◽  
Stokes Equations ◽  
Pressure Rise ◽  
Total Efficiency ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Sirocco Fan

A multi-objective optimization of a sirocco fan for residential ventilation has been carried out in the present work. A hybrid multi-objective evolutionary algorithm combined with response surface approximation is applied to optimize the total-to-total efficiency and total pressure rise of the sirocco fan for residential ventilation. Three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model are discretized by finite volume method and solved on hexahedral grids for the flow analysis. Numerical results are validated with the experimental data for the total-to-total efficiency and total pressure. The total-to-total efficiency and total pressure rise of the sirocco fan are used as objective functions for the optimization. In order to improve the total-to-total efficiency and total pressure rise of the sirocco fan, four variables defining the scroll cut-off angle, scroll diffuser expansion angle, hub ratio and the blade exit angle, respectively, are selected as the design variables in this study. Latin-hypercube sampling as design-of-experiments is used to generate the design points within the design space. A fast non-dominated sorting genetic algorithm with an ε–constraint strategy for the local search is applied to determine the global Pareto-optimal solutions. The trade-off between two objectives is determined and discussed with respect to the representative clustered optimal solutions in the Pareto-optimal solutions compared to the reference shape.

Pareto Front Estimation for Decision Making

2014 ◽  
Vol 22 (4) ◽  
pp. 651-678 ◽  
Author(s):  
Ioannis Giagkiozis ◽  
Peter J. Fleming
Keyword(s):  
Pareto Front ◽  
Computational Cost ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Number Of Solutions ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Problem Instances ◽  
Optimal Set ◽  
Optimisation Algorithms

The set of available multi-objective optimisation algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However, this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult—mainly due to the computational cost—to use a population large enough to ensure the likelihood of obtaining a solution close to the DM's preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimisation algorithm for two-objective and three-objective problem instances.

scholarly journals A Multi-Objective Solution of Green Vehicle Routing Problem

2019 ◽  
Vol 10 (1) ◽  
pp. 31-44 ◽  
Author(s):  
Özgür Kabadurmuş ◽  
Mehmet Serdar Erdoğan ◽  
Yiğitcan Özkan ◽  
Mertcan Köseoğlu
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Alternative Fuel ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Routing Problem ◽  
Multi Objective

Abstract Distribution is one of the major sources of carbon emissions and this issue has been addressed by Green Vehicle Routing Problem (GVRP). This problem aims to fulfill the demand of a set of customers using a homogeneous fleet of Alternative Fuel Vehicles (AFV) originating from a single depot. The problem also includes a set of Alternative Fuel Stations (AFS) that can serve the AFVs. Since AFVs started to operate very recently, Alternative Fuel Stations servicing them are very few. Therefore, the driving span of the AFVs is very limited. This makes the routing decisions of AFVs more difficult. In this study, we formulated a multi-objective optimization model of Green Vehicle Routing Problem with two conflicting objective functions. While the first objective of our GVRP formulation aims to minimize total CO2 emission, which is proportional to the distance, the second aims to minimize the maximum traveling time of all routes. To solve this multi-objective problem, we used ɛ-constraint method, a multi-objective optimization technique, and found the Pareto optimal solutions. The problem is formulated as a Mixed-Integer Linear Programming (MILP) model in IBM OPL CPLEX. To test our proposed method, we generated two hypothetical but realistic distribution cases in Izmir, Turkey. The first case study focuses on an inner-city distribution in Izmir, and the second case study involves a regional distribution in the Aegean Region of Turkey. We presented the Pareto optimal solutions and showed that there is a tradeoff between the maximum distribution time and carbon emissions. The results showed that routes become shorter, the number of generated routes (and therefore, vehicles) increases and vehicles visit a lower number of fuel stations as the maximum traveling time decreases. We also showed that as maximum traveling time decreases, the solution time significantly decreases.

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