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.

scholarly journals Optimization Of Multi-Module CrN/CrCN Coatings

2015 ◽  
Vol 60 (2) ◽  
pp. 1037-1043
Author(s):  
Ł. Szparaga ◽  
P. Bartosik ◽  
A. Gilewicz ◽  
J. Ratajski
Keyword(s):  
Optimization Procedure ◽  
Stress And Strain ◽  
Pareto Optimal ◽  
Mutual Distance ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Decision Criteria ◽  
Decision Variables ◽  
42Crmo4 Steel ◽  
The Stability

Abstract In the paper was proposed optimization procedure supporting the prototyping of the geometry of multi-module CrN/CrCN coatings, deposited on substrates from 42CrMo4 steel, in respect of mechanical properties. Adopted decision criteria were the functions of the state of internal stress and strain in the coating and substrate, caused by external mechanical loads. Using developed optimization procedure the set of optimal solutions (Pareto-optimal solutions) of coatings geometry parameters, due to the adopted decision criteria was obtained. For the purposes of analysis of obtained Pareto-optimal solutions, their mutual distance in the space of criteria and decision variables were calculated, which allowed to group solutions in the classes. Also analyzed the number of direct neighbors of Pareto-optimal solutions for the purposes of assessing the stability of solutions.

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.

scholarly journals Performance evaluation of elitist-mutated multi-objective particle swarm optimization for integrated water resources management

2009 ◽  
Vol 11 (1) ◽  
pp. 79-88 ◽  
Author(s):  
M. Janga Reddy ◽  
D. Nagesh Kumar
Keyword(s):  
Decision Making ◽  
Particle Swarm Optimization ◽  
Resource Management ◽  
Water Resources ◽  
Water Resource Management ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Swarm Optimization ◽  
Multi Objective

Optimal allocation of water resources for various stakeholders often involves considerable complexity with several conflicting goals, which often leads to multi-objective optimization. In aid of effective decision-making to the water managers, apart from developing effective multi-objective mathematical models, there is a greater necessity of providing efficient Pareto optimal solutions to the real world problems. This study proposes a swarm-intelligence-based multi-objective technique, namely the elitist-mutated multi-objective particle swarm optimization technique (EM-MOPSO), for arriving at efficient Pareto optimal solutions to the multi-objective water resource management problems. The EM-MOPSO technique is applied to a case study of the multi-objective reservoir operation problem. The model performance is evaluated by comparing with results of a non-dominated sorting genetic algorithm (NSGA-II) model, and it is found that the EM-MOPSO method results in better performance. The developed method can be used as an effective aid for multi-objective decision-making in integrated water resource management.

scholarly journals Use of multi-objective analysis to reveal the benefits of a water transfer project

2016 ◽  
Vol 17 (1) ◽  
pp. 259-266 ◽  
Author(s):  
Rong Tang ◽  
Chi Zhang ◽  
Wei Ding ◽  
Yu Li ◽  
Huicheng Zhou
Keyword(s):  
Water Supply ◽  
Visual Analytics ◽  
Project Planning ◽  
Water Transfer ◽  
Objective Analysis ◽  
Water Diversion ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective

This paper employs the multi-objective analysis to evaluate the benefits and feasibility of a local water transfer project between two water supply reservoirs in China. Firstly, the multi-objective simulation optimization model of reservoir operation for three scenarios, including no connection, virtual connection, and pipeline connection, are set up considering the compensation role of hydrology and the storage capacity of relevant reservoirs. Secondly, the Pareto-optimal solutions and the selected operation solutions for the three scenarios are analyzed to evaluate the benefits of the transfer project. And visual analytics is used to show and analyze the relation of the three scenarios’ Pareto-optimal solutions intuitively. Lastly, the results show building a pipeline can attain more benefits in reducing the amount of diverted water and water spills for the water supply system, but with some issues such as additional engineering cost and low utilization rate of the diversion pipeline. This study demonstrates that conducting a holistic multi-objective analysis for water transfer options can reveal the full trade-offs between competing objectives, show the relation of different scenarios’ Pareto-optimal solutions and provide support for informed decision-making on water diversion project planning.

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.

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