Multi-objective Optimization: Pareto Optimal Solutions, Properties

2012 ◽  
Keyword(s):  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective

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.

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.

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.

Solving Two Multi-Objective Optimization Problems Using Evolutionary Algorithm

2011 ◽  
pp. 218-233 ◽  
Author(s):  
Ruhul A. Sarker ◽  
Hussein A. Abbass ◽  
Charles S. Newton
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Pareto Optimal ◽  
Multi Criteria Decision Making ◽  
Pareto Optimal Solutions ◽  
Assessment Methodology ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective

Being capable of finding a set of pareto-optimal solutions in a single run is a necessary feature for multi-criteria decision making, Evolutionary algorithms (EAs) have attracted many researchers and practitioners to address the solution of Multi-objective Optimization Problems (MOPs). In a previous work, we developed a Pareto Differential Evolution (PDE) algorithm to handle multi-objective optimization problems. Despite the overwhelming number of Multi-objective Evolutionary Algorithms (MEAs) in the literature, little work has been done to identify the best MEA using an appropriate assessment methodology. In this chapter, we compare our algorithm with twelve other well-known MEAs, using a popular assessment methodology, by solving two benchmark problems. The comparison shows the superiority of our algorithm over others.

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