Pareto optimal solutions for fractional multi-objective optimization problems using MATLAB

2018 ◽  
Vol 73 (3) ◽  
pp. 88-90
Author(s):  
Tarek Abou-El-Enien
Keyword(s):  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective

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.

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.

Presorting as a method of acceleration of algorithms in multi-objective optimization problems

2016 ◽  
Vol 0 (0) ◽  
pp. 5-11
Author(s):  
Andrzej Ameljańczyk
Keyword(s):  
Distance Function ◽  
Pareto Front ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Minkowski Distance ◽  
Finite Set ◽  
Feasible Solutions

The paper presents a method of algorithms acceleration for determining Pareto-optimal solutions (Pareto Front) multi-criteria optimization tasks, consisting of pre-ordering (presorting) set of feasible solutions. It is proposed to use the generalized Minkowski distance function as a presorting tool that allows build a very simple and fast algorithm Pareto Front for the task with a finite set of feasible solutions.

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

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.

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