Optimality and non-scalar-valued performance criteria
About: This article is published in IEEE Transactions on Automatic Control.The article was published on 1963-01-01. It has received 1106 citations till now. The article focuses on the topics: Scalar (mathematics) & Optimal control.
Citations
More filters
Book•
30 Jun 2002
TL;DR: This paper presents a meta-anatomy of the multi-Criteria Decision Making process, which aims to provide a scaffolding for the future development of multi-criteria decision-making systems.
Abstract: List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.
5,994 citations
Cites background from "Optimality and non-scalar-valued pe..."
...The first engineering application reported in the literature was a paper by Zadeh in the early 1960s (Zadeh, 1963)....
[...]
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
Cites background from "Optimality and non-scalar-valued pe..."
...If all of the weights are positive, the minimum of (12) is Pareto optimal (Zadeh 1963); i.e., minimizing (12) is sufficient for Pareto optimality....
[...]
...If all of the weights are positive, the minimum of (12) is Pareto optimal (Zadeh 1963); i....
[...]
TL;DR: This paper suggests that the emergence of a new and more powerful model calibration paradigm must include recognition of the inherent multiobjective nature of the problem and must explicitly recognize the role of model error.
Abstract: Several contributions to the hydrological literature have brought into question the continued usefulness of the classical paradigm for hydrologic model calibration. With the growing popularity of sophisticated “physically based” watershed models (e.g., land-surface hydrology and hydrochemical models) the complexity of the calibration problem has been multiplied many fold. We disagree with the seemingly widespread conviction that the model calibration problem will simply disappear with the availability of more and better field measurements. This paper suggests that the emergence of a new and more powerful model calibration paradigm must include recognition of the inherent multiobjective nature of the problem and must explicitly recognize the role of model error. The results of our preliminary studies are presented. Through an illustrative case study we show that the multiobjective approach is not only practical and relatively simple to implement but can also provide useful information about the limitations of a model.
1,361 citations
TL;DR: The VIKOR method as mentioned in this paper was developed to solve MCDM problems with conflicting and noncommensurable (different units) criteria, assuming that compromising is acceptable for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria.
1,303 citations
References
More filters
TL;DR: In this paper, the authors considered the special case where the value of the state vector x(t) is restricted by IQ(~) 1 0 for which x( t) = E(t).
127 citations
30 citations