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Journal ArticleDOI

The weighted sum method for multi-objective optimization: new insights

01 Jun 2010-Structural and Multidisciplinary Optimization (Springer-Verlag)-Vol. 41, Iss: 6, pp 853-862
TL;DR: This paper investigates the fundamental significance of the weights in terms of preferences, the Pareto optimal set, and objective-function values and determines the factors that dictate which solution point results from a particular set of weights.
Abstract: As a common concept in multi-objective optimization, minimizing a weighted sum constitutes an independent method as well as a component of other methods. Consequently, insight into characteristics of the weighted sum method has far reaching implications. However, despite the many published applications for this method and the literature addressing its pitfalls with respect to depicting the Pareto optimal set, there is little comprehensive discussion concerning the conceptual significance of the weights and techniques for maximizing the effectiveness of the method with respect to a priori articulation of preferences. Thus, in this paper, we investigate the fundamental significance of the weights in terms of preferences, the Pareto optimal set, and objective-function values. We determine the factors that dictate which solution point results from a particular set of weights. Fundamental deficiencies are identified in terms of a priori articulation of preferences, and guidelines are provided to help avoid blind use of the method.
Citations
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Journal ArticleDOI
TL;DR: In this paper, an extensive review in the sphere of sustainable energy has been performed by utilizing multiple criteria decision making (MCDM) technique and future prospects in this area are discussed.
Abstract: In the current era of sustainable development, energy planning has become complex due to the involvement of multiple benchmarks like technical, social, economic and environmental. This in turn puts major constraints for decision makers to optimize energy alternatives independently and discretely especially in case of rural communities. In addition, topographical limitations concerning renewable energy systems which are mostly distributed in nature, the energy planning becomes more complicated. In such cases, decision analysis plays a vital role for designing such systems by considering various criteria and objectives even at disintegrated levels of electrification. Multiple criteria decision making (MCDM) is a branch of operational research dealing with finding optimal results in complex scenarios including various indicators, conflicting objectives and criteria. This tool is becoming popular in the field of energy planning due to the flexibility it provides to the decision makers to take decisions while considering all the criteria and objectives simultaneously. This article develops an insight into various MCDM techniques, progress made by considering renewable energy applications over MCDM methods and future prospects in this area. An extensive review in the sphere of sustainable energy has been performed by utilizing MCDM technique.

983 citations

Journal ArticleDOI
TL;DR: Based on the latent reactive power capability and real power curtailment of single-phase inverters, a new comprehensive PV operational optimization strategy to improve the performance of significantly unbalanced three-phase four-wire low voltage (LV) distribution networks with high residential PV penetrations is proposed in this paper.
Abstract: The rapid uptake of residential photovoltaic (PV) systems is causing serious power quality issues such as significant voltage fluctuation and unbalance that are restricting the ability of networks to accommodate further connections. Based on the latent reactive power capability and real power curtailment of single-phase inverters, this paper proposes a new comprehensive PV operational optimization strategy to improve the performance of significantly unbalanced three-phase four-wire low voltage (LV) distribution networks with high residential PV penetrations. A multiobjective optimal power flow (OPF) problem that can simultaneously improve voltage magnitude and balance profiles, while minimizing network losses and generation costs, is defined and then converted into an aggregated single-objective OPF problem using the weighted-sum method, which can be effectively solved by the global Sequential Quadratic Programming (SQP) approach with multiple starting points in MATLAB. Detailed simulations are performed and analyzed for various operating scenarios over 24 h on a real unbalanced four-wire LV distribution network in Perth Solar City trial, Australia. Finally, smart meter readings are used to justify the validity and accuracy of the proposed optimization model and considerations on the application of the proposed PV control strategy are also presented.

284 citations


Cites methods from "The weighted sum method for multi-o..."

  • ...The most widely used method for solving the MOO problems is the weighted sum method [21]...

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Journal ArticleDOI
01 May 2012
TL;DR: An efficient enough solution based on the K-M algorithm that outperforms significantly the exhaustive search approach is offered.
Abstract: Role assignment is a critical task in role-based collaboration. It has three steps, i.e., agent evaluation, group role assignment, and role transfer, where group role assignment is a time-consuming process. This paper clarifies the group role assignment problem (GRAP), describes a general assignment problem (GAP), converts a GRAP to a GAP, proposes an efficient algorithm based on the Kuhn-Munkres (K-M) algorithm, conducts numerical experiments, and analyzes the solutions' performances. The results show that the proposed algorithm significantly improves the algorithm based on exhaustive search. The major contributions of this paper include formally defining the GRAPs, giving a general efficient solution for them, and expanding the application scope of the K-M algorithm. This paper offers an efficient enough solution based on the K-M algorithm that outperforms significantly the exhaustive search approach.

236 citations


Cites methods from "The weighted sum method for multi-o..."

  • ...Then, we use a typical weighted sum method [16] by normalizing the three factors....

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Journal ArticleDOI
TL;DR: A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner, and is a competitive algorithm for many-objective optimization.
Abstract: Decomposition via scalarization is a basic concept for multiobjective optimization. The weighted sum (WS) method, a frequently used scalarizing method in decomposition-based evolutionary multiobjective (EMO) algorithms, has good features such as computationally easy and high search efficiency, compared to other scalarizing methods. However, it is often criticized by the loss of effect on nonconvex problems. This paper seeks to utilize advantages of the WS method, without suffering from its disadvantage, to solve many-objective problems. A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner. That is, for each search direction, the optimal solution is selected only amongst its neighboring solutions. The neighborhood is defined using a hypercone. The apex angle of a hypervcone is determined automatically in a priori . The effectiveness of MOEA/D-LWS is demonstrated by comparing it against three variants of MOEA/D, i.e., MOEA/D using Chebyshev method, MOEA/D with an adaptive use of WS and Chebyshev method, MOEA/D with a simultaneous use of WS and Chebyshev method, and four state-of-the-art many-objective EMO algorithms, i.e., preference-inspired co-evolutionary algorithm, hypervolume-based evolutionary, $\boldsymbol {\theta }$ -dominance-based algorithm, and SPEA2+SDE for the WFG benchmark problems with up to seven conflicting objectives. Experimental results show that MOEA/D-LWS outperforms the comparison algorithms for most of test problems, and is a competitive algorithm for many-objective optimization.

231 citations


Cites methods from "The weighted sum method for multi-o..."

  • ...As a common concept in multiobjective optimization, the WS method has been discussed prominently in [32], [51], and [52] since its introduction by Zadeh [53]....

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Journal ArticleDOI
TL;DR: The results are compared quantitatively and qualitatively with other algorithms using a variety of performance indicators, which show the merits of this new MOMVO algorithm in solving a wide range of problems with different characteristics.
Abstract: This work proposes the multi-objective version of the recently proposed Multi-Verse Optimizer (MVO) called Multi-Objective Multi-Verse Optimizer (MOMVO). The same concepts of MVO are used for converging towards the best solutions in a multi-objective search space. For maintaining and improving the coverage of Pareto optimal solutions obtained, however, an archive with an updating mechanism is employed. To test the performance of MOMVO, 80 case studies are employed including 49 unconstrained multi-objective test functions, 10 constrained multi-objective test functions, and 21 engineering design multi-objective problems. The results are compared quantitatively and qualitatively with other algorithms using a variety of performance indicators, which show the merits of this new MOMVO algorithm in solving a wide range of problems with different characteristics.

193 citations

References
More filters
Journal ArticleDOI
TL;DR: A method of scaling ratios using the principal eigenvector of a positive pairwise comparison matrix is investigated, showing that λmax = n is a necessary and sufficient condition for consistency.

8,117 citations

Book
26 Sep 2011
TL;DR: This paper is concerned with the development of methods for dealing with the role of symbols in the interpretation of semantics.
Abstract: Preface. Acknowledgements. Notation and Symbols. Part I: Terminology and Theory. 1. Introduction. 2. Concepts. 3. Theoretical Background. Part II: Methods. 1. Introduction. 2. No-Preference Methods. 3. A Posteriori Methods. 4. A Priori Methods. 5. Interactive Methods. Part III: Related Issues. 1. Comparing Methods. 2. Software. 3. Graphical Illustration. 4. Future Directions. 5. Epilogue. References. Index.

4,976 citations


"The weighted sum method for multi-o..." refers background in this paper

  • ...With regards to the design space, minimizing the weighted sum provides a necessary condition if the multiobjective problem is convex, which means the feasible design space is convex (each constraint is convex) and all of the objective functions are convex (Geoffrion 1968; Koski 1985; Miettinen 1999)....

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Journal ArticleDOI
TL;DR: A survey of current continuous nonlinear multi-objective optimization concepts and methods finds that no single approach is superior and depends on the type of information provided in the problem, the user's preferences, the solution requirements, and the availability of software.
Abstract: A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

4,263 citations


"The weighted sum method for multi-o..." refers background or methods in this paper

  • ...In fact, some more complicated methods have been developed so that the shape of the Pareto optimal hypersurface has a minimal affect the accuracy with which it is depicted (Marler and Arora 2004)....

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  • ...To be sure, there are many different approaches for determining the weights (Marler and Arora 2004), but ultimately, however, these are all just different processes for organizing one’s preferences and priorities....

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Book
01 Aug 1989
TL;DR: Mathematical Background Topics from Linear Algebra Single Objective Linear Programming Determining all Alternative Optima Comments about Objective Row Parametric Programming Utility Functions, Nondominated Criterion Vectors and Efficient Points Point Estimate Weighted-sums Approach.
Abstract: Mathematical Background Topics from Linear Algebra Single Objective Linear Programming Determining all Alternative Optima Comments about Objective Row Parametric Programming Utility Functions, Nondominated Criterion Vectors and Efficient Points Point Estimate Weighted-sums Approach Optimal Weighting Vectors, Scaling and Reduced Feasible Region Methods Vector-Maximum Algorithms Goal Programming Filtering and Set Discretization Multiple Objective Linear Fractional Programming Interactive Procedures Interactive Weighted Tchebycheff Procedure Tchebycheff/Weighted-Sums Implementation Applications Future Directions Index.

3,280 citations

Book
01 Jan 1979
TL;DR: On MADM Methods Classification.
Abstract: I. Introduction.- II. Basic Concepts and Foundations.- 1. Definitions.- 1.1 Terms for MCDM Environment.- 1.2 MCDM Solutions.- 2. Models for MADM.- 2.1 Noncompensatory Model.- 2.2 Compensatory Model.- 3. Transformation of Attributes.- 3.1 Quantification of Fuzzy Attributes.- 3.2 Normalization.- 4. Fuzzy Decision Rules.- 4.1 Definition of Fuzzy Set.- 4.2 Some Basic Operations of Fuzzy Sets.- 5. Methods for Assessing Weight.- 5.1 Eigenvector Method.- 5.2 Weighted Least Square Method.- 5.3 Entropy Method.- 5.4 Linmap.- III. Methods for Multiple Attribute Decision Making.- 1. Methods for No Preference Information Given.- 1.1.1 Dominance.- 1.1.2 Maximin.- 1.1.3 Maximax.- 2. Methods for Information on Attribute Given.- 2.1 Methods for Standard Level of Attribute Given.- 2.1.1 Conjunctive Method (Satisficing Method).- 2.1.2 Disjunctive Method.- 2.2 Methods for Ordinal Preference of Attribute Given.- 2.2.1 Lexicographic Method.- 2.2.2 Elimination By Aspects.- 2.2.3 Permutation Method.- 2.3 Methods for Cardinal Preference of Attribute Given.- 2.3.1 Linear Assignment Method.- 2.3.2 Simple Additive Weighting Method.- 2.3.3 Hierarchical Additive Weighting Method.- 2.3.4 ELECTRE Method.- 2.3.5 TOPSIS.- 2.4 Methods for Marginal Rate of Substitution of Attributes Given.- 2.4.1 Hierarchical Tradeoffs.- 3. Methods for Information on Alternative Given.- 3.1 Methods for Pairwise Preference Given.- 3.1.1 LINMAP.- 3.1.2 Interactive Simple Additive Weighting Method.- 3.2 Method for Pairwise Proximity Given.- 3.2.1 Multidimensional Scaling with Ideal Point.- IV. Applications.- 1. Commodity Selection.- 2. Facility Location (Siting) Selection.- 3. Personnel Selection.- 4. Project Selection.- 4.1 Environmental Planning.- 4.2 Land Use Planning.- 4.3 R & D Project.- 4.4 Water Resources Planning.- 4.5 Miscellaneous.- 5. Public Facility Selection.- V. Concluding Remarks.- On MADM Methods Classification.- On Applications of MADM.- On Multiple Objective Decision Making (MODM) Methods.- On Multiattribute Utility Theory (MAUT).- A Choice Rule for MADM Methods.- A Unified Approach to MADM.- On Future Study.- VI. Bibliography.- Books, Monographs, and Conference Proceedings.- Journal Articles, Technical Reports, and Theses.

2,380 citations


"The weighted sum method for multi-o..." refers background in this paper

  • ...Many researchers have, however, developed systematic approaches to selecting weights, surveys of which are provided by Eckenrode (1965), Hobbs (1980), Hwang and Yoon (1981) , and Voogd (1983)....

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