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1

Wei, Xin. "Multi-Objective Optimization Base on Incremental Pareto Fitness." Advanced Materials Research 1030-1032 (September 2014): 1733–36. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.1733.

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A new multi-objective optimization algorithm based on incrementally Pareto fitness is proposed in this paper. To overcome the directly calculate the Pareto fitness matrix expensively, we adopt to make full use of information of last iteration at each stept to update the Parteto fitness matrix gradually. Experiments proved the highest efficiency of the new method.
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2

Mornati, Fiorenzo. "Pareto Optimality in the work of Pareto." Revue européenne des sciences sociales, no. 51-2 (December 15, 2013): 65–82. http://dx.doi.org/10.4000/ress.2517.

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3

Németh, A. B. "Between Pareto efficiency and Pareto ε-efficiency." Optimization 20, no. 5 (January 1989): 615–37. http://dx.doi.org/10.1080/02331938908843483.

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4

Busino, Giovanni. "Pareto oggi." Revue européenne des sciences sociales, no. XLVIII-146 (July 1, 2010): 113–27. http://dx.doi.org/10.4000/ress.761.

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5

Yeh, Hsiaw-Chan, Barry C. Arnold, and Christopher A. Robertson. "Pareto processes." Journal of Applied Probability 25, no. 2 (June 1988): 291–301. http://dx.doi.org/10.2307/3214437.

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An autoregressive process ARP(1) with Pareto-distributed inputs, analogous to those of Lawrance and Lewis (1977), (1980), is defined and its properties developed. It is shown that the stationary distributions are Pareto. Further, the maximum and minimum processes are asymptotically Weibull, and the ARP(1) process is shown to be closed under maximization or minimization when the number of terms is geometrically distributed. The ARP(1) process leads naturally to an extremal process in the sense of Lamperti (1964). Statistical inference for the ARP(1) process is developed. An absolutely continuous variant of the Pareto process is described.
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6

Makatura, Liane, Minghao Guo, Adriana Schulz, Justin Solomon, and Wojciech Matusik. "Pareto gamuts." ACM Transactions on Graphics 40, no. 4 (August 2021): 1–17. http://dx.doi.org/10.1145/3476576.3476758.

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7

Makatura, Liane, Minghao Guo, Adriana Schulz, Justin Solomon, and Wojciech Matusik. "Pareto gamuts." ACM Transactions on Graphics 40, no. 4 (August 2021): 1–17. http://dx.doi.org/10.1145/3450626.3459750.

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8

Yeh, Hsiaw-Chan, Barry C. Arnold, and Christopher A. Robertson. "Pareto processes." Journal of Applied Probability 25, no. 02 (June 1988): 291–301. http://dx.doi.org/10.1017/s0021900200040936.

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An autoregressive process ARP(1) with Pareto-distributed inputs, analogous to those of Lawrance and Lewis (1977), (1980), is defined and its properties developed. It is shown that the stationary distributions are Pareto. Further, the maximum and minimum processes are asymptotically Weibull, and the ARP(1) process is shown to be closed under maximization or minimization when the number of terms is geometrically distributed. The ARP(1) process leads naturally to an extremal process in the sense of Lamperti (1964). Statistical inference for the ARP(1) process is developed. An absolutely continuous variant of the Pareto process is described.
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9

Ikefuji, Masako, Roger J. A. Laeven, Jan R. Magnus, and Chris Muris. "Pareto utility." Theory and Decision 75, no. 1 (January 26, 2012): 43–57. http://dx.doi.org/10.1007/s11238-012-9293-8.

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10

Green, M. W., and B. C. Arnold. "Pareto Distributions." Applied Statistics 35, no. 2 (1986): 215. http://dx.doi.org/10.2307/2347273.

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11

Malik, Henrick J., and Barry C. Arnold. "Pareto Distributions." Journal of the American Statistical Association 83, no. 401 (March 1988): 269. http://dx.doi.org/10.2307/2288955.

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12

Shanbhag, D. N., and B. C. Arnold. "Pareto Distributions." Journal of the Royal Statistical Society. Series A (Statistics in Society) 152, no. 2 (1989): 253. http://dx.doi.org/10.2307/2982920.

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13

Pillai, R. N. "Semi-Pareto processes." Journal of Applied Probability 28, no. 2 (June 1991): 461–65. http://dx.doi.org/10.2307/3214880.

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Semi-Pareto processes, of which Pareto processes form a proper sub-class, are discussed here. A semi-Pareto process has semi-Pareto inputs. Asymptotic properties of the maximum and minimum of the first n observations are examined as well as the geometric maximum and geometric minimum. A characterization of the semi-Pareto distribution is given. A canonical representation of a special class of Pareto process is also given.
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14

Pillai, R. N. "Semi-Pareto processes." Journal of Applied Probability 28, no. 02 (June 1991): 461–65. http://dx.doi.org/10.1017/s0021900200039826.

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Semi-Pareto processes, of which Pareto processes form a proper sub-class, are discussed here. A semi-Pareto process has semi-Pareto inputs. Asymptotic properties of the maximum and minimum of the first n observations are examined as well as the geometric maximum and geometric minimum. A characterization of the semi-Pareto distribution is given. A canonical representation of a special class of Pareto process is also given.
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15

Aron, Raymond. "Lectures de Pareto." Commentaire Numéro168, no. 4 (2019): 725. http://dx.doi.org/10.3917/comm.168.0725.

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16

Gunning, Patricia, Jane M. Horgan, and Gary Keogh. "EFFICIENT PARETO STRATIFICATION." Mathematical Proceedings of the Royal Irish Academy 106A, no. 2 (2006): 131–38. http://dx.doi.org/10.1353/mpr.2006.0018.

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17

Erridge, P. "The Pareto principle." British Dental Journal 201, no. 7 (October 2006): 419. http://dx.doi.org/10.1038/sj.bdj.4814131.

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18

Zeghdoudi, Halim, Lazri Nouara, and Djabrane Yahia. "LINDLEY PARETO DISTRIBUTION." Statistics in Transition New Series 19, no. 4 (2019): 671–92. http://dx.doi.org/10.21307/stattrans-2018-035.

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19

Bose, A., D. Pal, and D. E. M. Sappington. "Pareto-improving inefficiency." Oxford Economic Papers 63, no. 1 (April 12, 2010): 94–110. http://dx.doi.org/10.1093/oep/gpq009.

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20

Bligaard, Thomas, Gisli H. Jóhannesson, Andrei V. Ruban, Hans L. Skriver, Karsten W. Jacobsen, and Jens K. Nørskov. "Pareto-optimal alloys." Applied Physics Letters 83, no. 22 (December 2003): 4527–29. http://dx.doi.org/10.1063/1.1631051.

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21

Nadarajah, Saralees. "Exponentiated Pareto distributions." Statistics 39, no. 3 (June 2005): 255–60. http://dx.doi.org/10.1080/02331880500065488.

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22

Mir, Khurshid Ahmad. "Modified Pareto Distribution." Journal of Modern Mathematics and Statistics 5, no. 1 (January 1, 2011): 17–18. http://dx.doi.org/10.3923/jmmstat.2011.17.18.

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23

Nadarajah, Saralees, and Samuel Kotz. "Financial Pareto ratios." Quantitative Finance 7, no. 3 (June 2007): 257–60. http://dx.doi.org/10.1080/14697680601067604.

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24

Pietrzak, J. "Pareto optimum tests." Computers & Structures 71, no. 1 (March 1999): 35–42. http://dx.doi.org/10.1016/s0045-7949(98)00221-1.

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25

FISH, ERAN. "Against Anonymous Pareto." Utilitas 31, no. 1 (June 18, 2018): 3–19. http://dx.doi.org/10.1017/s0953820818000134.

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The principle known as ‘anonymous Pareto’ has it that an alternative A is better than another, B, in case it is (strictly, non-anonymously) Pareto superior to either B or a permutation of it. It is an attractive idea, offering to apply Pareto-based judgments to a broader range of cases while preserving some of the intuitive appeal of the standard, more familiar principle. This essay considers some ways in which anonymous Pareto is defended and argues against each separately, as well as in more general lines. It suggests that the reasons in light of which people find strict Pareto so compelling are the reasons for doubting the anonymous variation of that principle.
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26

Picard, D. "Evolutionary Pareto distributions." Annales de l'Institut Henri Poincare (B) Probability and Statistics 38, no. 6 (December 2002): 1023–37. http://dx.doi.org/10.1016/s0246-0203(02)01124-x.

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27

Harvey, H. Benjamin, and Susan T. Sotardi. "The Pareto Principle." Journal of the American College of Radiology 15, no. 6 (June 2018): 931. http://dx.doi.org/10.1016/j.jacr.2018.02.026.

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28

Geanakoplos, John, and H. M. Polemarchakis. "Pareto improving taxes." Journal of Mathematical Economics 44, no. 7-8 (July 2008): 682–96. http://dx.doi.org/10.1016/j.jmateco.2007.07.007.

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29

Tullock, Gordon. "Smith v. Pareto." Atlantic Economic Journal 27, no. 3 (September 1999): 254–59. http://dx.doi.org/10.1007/bf02299576.

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30

Miebach, Bernhard. "Parsons/Pareto/Habermas." ProtoSociology 3 (1992): 165–69. http://dx.doi.org/10.5840/protosociology1992331.

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31

Gunning, Patricia, Jane M. Horgan, and Gary Keogh. "Efficient Pareto Stratification." Mathematical Proceedings of the Royal Irish Academy 106, no. 2 (January 1, 2006): 131–38. http://dx.doi.org/10.3318/pria.2006.106.2.131.

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32

Tremblay, Mark J. "Pareto price discrimination." Economics Letters 183 (October 2019): 108559. http://dx.doi.org/10.1016/j.econlet.2019.108559.

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33

Luenberger, David G. "Dual Pareto Efficiency." Journal of Economic Theory 62, no. 1 (February 1994): 70–85. http://dx.doi.org/10.1006/jeth.1994.1004.

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34

Parks, Robert P. "Pareto irrelevant externalities." Journal of Economic Theory 54, no. 1 (June 1991): 165–79. http://dx.doi.org/10.1016/0022-0531(91)90111-g.

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35

Korhonen, Pekka, and Jyrki Wallenius. "A pareto race." Naval Research Logistics 35, no. 6 (December 1988): 615–23. http://dx.doi.org/10.1002/1520-6750(198812)35:6<615::aid-nav3220350608>3.0.co;2-k.

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36

Li, Miqing, Shengxiang Yang, and Xiaohui Liu. "Pareto or Non-Pareto: Bi-Criterion Evolution in Multiobjective Optimization." IEEE Transactions on Evolutionary Computation 20, no. 5 (October 2016): 645–65. http://dx.doi.org/10.1109/tevc.2015.2504730.

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37

Schoenberg, F. P., and R. D. Patel. "Comparison of Pareto and tapered Pareto distributions for environmental phenomena." European Physical Journal Special Topics 205, no. 1 (May 2012): 159–66. http://dx.doi.org/10.1140/epjst/e2012-01568-4.

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38

Drugan, Mădălina M., and Dirk Thierens. "Stochastic Pareto local search: Pareto neighbourhood exploration and perturbation strategies." Journal of Heuristics 18, no. 5 (July 3, 2012): 727–66. http://dx.doi.org/10.1007/s10732-012-9205-7.

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39

Zhu, Fujin, Jie Lu, Adi Lin, and Guangquan Zhang. "A Pareto-smoothing method for causal inference using generalized Pareto distribution." Neurocomputing 378 (February 2020): 142–52. http://dx.doi.org/10.1016/j.neucom.2019.09.095.

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40

Schnattinger, T., U. Schoning, A. Marchfelder, and H. A. Kestler. "RNA-Pareto: interactive analysis of Pareto-optimal RNA sequence-structure alignments." Bioinformatics 29, no. 23 (September 16, 2013): 3102–4. http://dx.doi.org/10.1093/bioinformatics/btt536.

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41

Kuwajima, Isao, Yusuke Nojima, and Hisao Ishibuchi. "Obtaining accurate classifiers with Pareto-optimal and near Pareto-optimal rules." Artificial Life and Robotics 13, no. 1 (December 2008): 315–19. http://dx.doi.org/10.1007/s10015-008-0544-2.

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42

Cormann, Ulf, and Rolf-Dieter Reiss. "Generalizing the Pareto to the log-Pareto model and statistical inference." Extremes 12, no. 1 (September 16, 2008): 93–105. http://dx.doi.org/10.1007/s10687-008-0070-6.

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43

Askarirobati, Gholam Hosein, Akbar Hashemi Borzabadi, and Aghileh Heydari. "Solving multiobjective optimal control problems using an improved scalarization method." IMA Journal of Mathematical Control and Information 37, no. 4 (October 12, 2020): 1524–47. http://dx.doi.org/10.1093/imamci/dnaa023.

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Abstract Detecting the Pareto optimal points on the Pareto frontier is one of the most important topics in multiobjective optimal control problems (MOCPs). This paper presents a scalarization technique to construct an approximate Pareto frontier of MOCPs, using an improved normal boundary intersection (NBI) scalarization strategy. For this purpose, MOCP is first discretized and then using a grid of weights, a sequence of single objective optimal control problems is solved to achieve a uniform distribution of Pareto optimal solutions on the Pareto frontier. The aim is to achieve a more even distribution of Pareto optimal solutions on the Pareto frontier and improve the efficiency of the algorithm. It is shown that in contrast to the NBI method, where Pareto optimality of solutions is not guaranteed, the obtained optimal solution of the scalarized problem is a Pareto optimal solution of the MOCP. Finally, the ability of the proposed method is evaluated and compared with other approaches using several practical MOCPs. The numerical results indicate that the proposed method is more efficient and provides more uniform distribution of solutions on the Pareto frontier than the other methods, such a weighted sum, normalized normal constraint and NBI.
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44

Abd Raof, Anis Syazwani, Mohd Azmi Haron, Muhammad Aslam Mohd Safari, and Zailan Siri. "Modeling the Incomes of the Upper-Class Group in Malaysia using New Pareto-Type Distribution." Sains Malaysiana 51, no. 10 (October 31, 2022): 3437–48. http://dx.doi.org/10.17576/jsm-2022-5110-26.

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The new Pareto-type distribution has been previously introduced as an alternative to the conventional Pareto distribution in modeling income distribution. It is claimed to provide better flexibility for mathematical simplicity of probability functions and has a more straightforward mathematical form. In this study, the new Pareto-type distribution is used to model the income of the Malaysian upper-class group. The threshold is determined using the fixed proportion technique and the maximum likelihood estimator method is used to estimate the shape parameter. Then, the goodness-of-fit of the fitted new Pareto model is measured using the coefficient of determination, R2 and Kolmogorov–Smirnov statistics. We also measure the income inequality among the Malaysian top income earners using the Lorenz curve, Gini and Theil indices based on the fitted new Pareto model. Finally, the new Pareto distribution is compared to alternative distributions to analyze which model can give the best fit for the data. Our analysis shows that the Pareto type-1 and the new Pareto models are well fitted to the top income data for all years considered. However, the new Pareto model provides better flexibility which covering more incomes in the upper tail of the distribution than the Pareto type-1 model.
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45

Zanni, Alberto. "Marshall and Pareto on Cournot's Elasticity and on W. Thornton." STUDI ECONOMICI, no. 102 (June 2011): 77–88. http://dx.doi.org/10.3280/ste2010-102003.

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Pareto is ungenerous towards Cournot, even if not as much as Marshall. The author thus goes on and analyses a writing by Pareto (1875) on Thornton, brought to light in 2005. Since in 1875 Pareto does not know Marshall, while he has already in mind the concept of elasticity, the a. deduces that Pareto has no intellectual debt towards Marshall for what concerns the theory of comparative costs developed by Pareto in the(1906). The a. concludes saying that Pareto recognises all his main intellectual debts, except for Cournot. Baumol and Goldfield's contrary opinion is due to a linguistic barrier.
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46

Tahir, Muhammad Hussain, Gauss M. Cordeiro, Muhammad Mansoor, Muhammad Zubair, and Ayman Alzaatreh. "The Kumaraswamy Pareto IV Distribution." Austrian Journal of Statistics 50, no. 5 (August 25, 2021): 1–22. http://dx.doi.org/10.17713/ajs.v50i5.96.

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We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. It hasincreasing, decreasing, upside-down bathtub, bathtub, J and reversed-J shaped hazard rate shapes. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments,Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments and generating function. We provide the density function of the order statistics and their moments. The Renyi and q entropies are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of three real-life data sets. In fact, our proposed model provides a better fit to these data than the gamma-Pareto IV, gamma-Pareto, beta-Pareto,exponentiated Pareto and Pareto IV models.
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47

Kaliszewski, Ignacy, and Janusz Miroforidis. "Primal–Dual Type Evolutionary Multiobjective Optimization." Foundations of Computing and Decision Sciences 38, no. 4 (December 1, 2013): 267–75. http://dx.doi.org/10.2478/fcds-2013-0013.

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Abstract A new, primal-dual type approach for derivation of Pareto front approximations with evolutionary computations is proposed. At present, evolutionary multiobjective optimization algorithms derive a discrete approximation of the Pareto front (the set of objective maps of efficient solutions) by selecting feasible solutions such that their objective maps are close to the Pareto front. As, except of test problems, Pareto fronts are not known, the accuracy of such approximations is known neither. Here we propose to exploit also elements outside feasible sets with the aim to derive pairs of Pareto front approximations such that for each approximation pair the corresponding Pareto front lies, in a certain sense, in-between. Accuracies of Pareto front approximations by such pairs can be measured and controlled with respect to distance between such approximations. A rudimentary algorithm to derive pairs of Pareto front approximations is presented and the viability of the idea is verified on a limited number of test problems.
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48

He, Qinghai, and Weili Kong. "Structure of Pareto Solutions of Generalized Polyhedral-Valued Vector Optimization Problems in Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/619206.

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In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.
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49

Wu, Jin, and Shapour Azarm. "Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set." Journal of Mechanical Design 123, no. 1 (January 1, 2000): 18–25. http://dx.doi.org/10.1115/1.1329875.

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In this paper, several new set quality metrics are introduced that can be used to evaluate the “goodness” of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include hyperarea difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer to either monitor the quality of an observed Pareto solution set as obtained by a multiobjective optimization method, or compare the quality of observed Pareto solution sets as reported by different multiobjective optimization methods. A vibrating platform example is used to demonstrate the calculation of these metrics for an observed Pareto solution set.
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50

Tappy, Denis. "Pareto et Ernest Roguin." Revue européenne des sciences sociales, no. XLVIII-146 (July 1, 2010): 33–44. http://dx.doi.org/10.4000/ress.751.

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