scholarly journals A parallel multiple reference point approach for multi-objective optimization

2010 ◽  
Vol 205 (2) ◽  
pp. 390-400 ◽  
Author(s):  
J.R. Figueira ◽  
A. Liefooghe ◽  
E.-G. Talbi ◽  
A.P. Wierzbicki
Keyword(s):  
Reference Point ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multiple Reference ◽  
Reference Point Approach

scholarly journals Non-dominated sorting Harris’s hawk multi-objective optimizer based on reference point approach

2019 ◽  
Vol 15 (3) ◽  
pp. 1603 ◽  
Author(s):  
Shaymah Akram Yasear ◽  
Ku Ruhana Ku-Mahamud
Keyword(s):  
Reference Point ◽  
Pareto Front ◽  
Optimization Problems ◽  
Population Diversity ◽  
Experimental Results ◽  
Multi Objective Optimization ◽  
Next Generation ◽  
Multi Objective ◽  
Objective Space ◽  
Reference Point Approach

A non-dominated sorting Harris’s hawk multi-objective optimizer (NDSHHMO) algorithm is presented in this paper. The algorithm is able to improve the population diversity, convergence of non-dominated solutions toward the Pareto front, and prevent the population from trapping into local optimal. This was achieved by integrating fast non-dominated sorting with the original Harris’s hawk multi-objective optimizer (HHMO).  Non-dominated sorting divides the objective space into levels based on fitness values and then selects non-dominated solutions to produce the next generation of hawks. A set of well-known multi-objective optimization problems has been used to evaluate the performance of the proposed NDSHHMO algorithm. The results of the NDSHHMO algorithm were verified against the results of an HHMO algorithm. Experimental results demonstrate the efficiency of the proposed NDSHHMO algorithm in terms of enhancing the ability of convergence toward the Pareto front and significantly improve the search ability of the HHMO.

ROBUSTNESS OF THE MULTI‐OBJECTIVE MOORA METHOD WITH A TEST FOR THE FACILITIES SECTOR

2009 ◽  
Vol 15 (2) ◽  
pp. 325-375 ◽  
Author(s):  
Willem K. Brauers ◽  
Edmundas K. Zavadskas
Keyword(s):  
Linear Equation ◽  
Reference Point ◽  
Error Term ◽  
Cost Price ◽  
Common Language ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Definition Of ◽  
Moora Method

The definition of robustness in econometrics, the error term in a linear equation, was not only broadened, but in addition moved to the meaning of common language: from a cardinal to a qualitative one. These interpretations were tested by an application on the Facilities Sector in Lithuania. The application is multi‐objective: like costs, experience and effectiveness at the side of the contractors; quality, duration of the work and cost price at the side of the owners. These objectives having all different units the dimensionless ratios of the MOORA method avoids the difficulties of normalization. In a first part of MOORA these ratios were aggregated and in a second one they were used as distances to a reference point. The results of both parts control each other, a test on robustness. Additionally, MOORA shows a robust domination on all other methods of multi‐objective optimization. For the Facilities Sector in Lithuania, both parts of MOORA resulted in a comparable ranking. In this way a double check was made on the robustness of the results. Santrauka Patikimumo apibrėžimas ekonometrikoje, kaip neteisingas terminas tiesinėje lygtyje, buvo ne tik papildytas, bet ir išreikštas įprasta kalba: nuo kiekybinio prie kokybinio. Šios interpretacijos buvo patikrintos taikant jas Lietuvos paslaugų sektoriuje. Taikymas yra daugiatikslis: iš rangovo pusės kaip išlaidos, patirtis, efektyvumas; kokybė, darbo trukmė, kaina iš užsakovo pusės. Minėtieji tikslai turi skirtingus matavimo vienetus. O jų santykiniai dydžiai neturi mato vienetų, todėl taikant MOORA metodą yra išvengiama sunkumų juos normalizuojant. Pirmoje MOORA metodo taikymo dalyje šie santykiai yra sujungiami, o antroje dalyje ieškoma atstumo iki geriausio sprendinio. Abiejų metodo dalių rezultatai pagrindžia sprendinio teisingumą. Tai rodo aiškų MOORA metodo pranašumą, palyginti su kitais daugiatikslio optimizavimo metodais. Taikant abi MOORA metodo dalis Lietuvos paslaugų sektoriui buvo sudarytas lyginamasis rangavimas, buvo atliktas dvigubas rezultatų patikimumo patikrinimas.

On the effect of reference point in MOEA/D for multi-objective optimization

2017 ◽  
Vol 58 ◽  
pp. 25-34 ◽  
Author(s):  
Rui Wang ◽  
Jian Xiong ◽  
Hisao Ishibuchi ◽  
Guohua Wu ◽  
Tao Zhang
Keyword(s):  
Reference Point ◽  
Multi Objective Optimization ◽  
Multi Objective

RDS-NSGA-II: a memetic algorithm for reference point based multi-objective optimization

2016 ◽  
Vol 49 (5) ◽  
pp. 828-845 ◽  
Author(s):  
Jesus Alejandro Hernández Mejía ◽  
Oliver Schütze ◽  
Oliver Cuate ◽  
Adriana Lara ◽  
Kalyanmoy Deb
Keyword(s):  
Reference Point ◽  
Memetic Algorithm ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

scholarly journals MULTI-OBJECTIVE OPTIMIZATION FOR FACILITIES MANAGEMENT

2004 ◽  
Vol 5 (4) ◽  
pp. 173-182 ◽  
Author(s):  
Willem K. Brauers
Keyword(s):  
Decision Maker ◽  
Reference Point ◽  
Creative Thinking ◽  
Point Theory ◽  
Facilities Management ◽  
Multi Objective Optimization ◽  
Dimensionless Numbers ◽  
Short Text ◽  
Multi Objective ◽  
Desk Research

The main point of this article is to present in a short text all aspects of Multi ‐ Objective Optimization for Facilities Management, so to say from the cradle until the grave. Additionally, the combination of Multi ‐ Objective Optimization with Nominal Methods and Scenario Writing represents an innovation. It is also stated that all stakeholders interested in the issue, instead of one decision maker, have to be involved. First, desk research will discover all the surrounding conditions of the issue under consideration. Therefore, during a period of creative thinking in a nominal exercise all the main influencing events are recorded and finally ranked. From this information, scenarios for the future of the facilities sector are deduced. On basis of all these data, objectives and alternatives are simulated. A Multi ‐ Objective Optimization for the facilities sector is made possible by two methods: an additive method with ratios and the application of Reference Point Theory. Automatically, using these methods, all objectives are normalized to dimensionless numbers between zero and one. Nevertheless, a problem of importance for each objective may remain. Therefore, two methods are proposed. First, weights are granted in a nonlinear way. Secondly, an objective becomes more important by introducing different attributes for the same objective. The latter method seems to be more refined. In this way, a final ranking of the alternatives for the fulfillment of the objectives is obtained.

scholarly journals Reference Point Based Multi-Objective Optimization of Reservoir Operation: a Comparison of Three Algorithms

2020 ◽  
Vol 34 (3) ◽  
pp. 1005-1020 ◽  
Author(s):  
Rong Tang ◽  
Ke Li ◽  
Wei Ding ◽  
Yuntao Wang ◽  
Huicheng Zhou ◽  
...  
Keyword(s):  
Reference Point ◽  
Reservoir Operation ◽  
Multi Objective Optimization ◽  
Multi Objective

scholarly journals HOW TO INVEST IN BELGIAN SHARES BY MULTIMOORA OPTIMIZATION

2013 ◽  
Vol 14 (5) ◽  
pp. 940-956 ◽  
Author(s):  
Willem K. M. Brauers ◽  
Romualdas Ginevičius
Keyword(s):  
Reference Point ◽  
Point Theory ◽  
Multiple Objectives ◽  
Ratio Analysis ◽  
Multi Objective Optimization ◽  
Dimensionless Numbers ◽  
Multi Objective ◽  
Multiplicative Form ◽  
Objective Reference ◽  
Alternative Solutions

Different multiple objectives expressed in different units make optimization difficult. Therefore, the internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred to weights, which are most of the time used to compare the different units. In addition, the ratio system creates the opportunity to use a second approach: a non-subjective Reference Point Theory. Therefore, the Reference Point Theory uses the ratios found in the ratio system as co-ordinates for the alternative solutions, which are then compared to a Maximal Objective Reference Point. The two approaches form a control on each other. This overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added, three methods assembled under the name of MULTIMOORA. At that moment, the control by three different approaches forms a guaranty for a solution being as non-subjective as possible. As to calculate the sum of three obtained ranks is not allowed, a theory of Ordinal Dominance is developed in order to remain in the ordinal sphere.

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