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Aalto University publication series DOCTORAL DISSERTATIONS 17/2011 Progressively Interactive Evolutionary Multiobjective Optimization Ankur Sinha Aalto University School of Economics Department of Business Technology
Aalto University publication series DOCTORAL DISSERTATIONS 17/2011 © Ankur Sinha ISBN 978-952-60-4053-0 (pdf) ISBN 978-952-60-4052-3 (printed) ISSN-L 1799-4934 ISSN 1799-4942 (pdf) ISSN 1799-4934 (printed) Aalto Print Helsinki 2011
Page 1: Department of Business Technology P
Page 5 and 6: Progressively Interactive Evolution
Page 7: Acknowledgements The dissertation h
Page 10 and 11: II List of Papers 27 1 An interacti
Page 12 and 13: 1 Introduction Many real-world appl
Page 14 and 15: • f(x (1) ) ≥ f(x (2) ) fi(x (1
Page 16 and 17: for a maximization problem. Mathema
Page 18 and 19: • x (1) ∼ x (2) ⇔ x (1) and x
Page 20 and 21: Start Initialise Population Assign
Page 22 and 23: ithm can approximate the Pareto-opt
Page 24 and 25: Minimize/Maximize F(x) = (f1(x), f2
Page 26 and 27: the search is chosen. A scalarizing
Page 28 and 29: of the papers is provided in this s
Page 30: problems. The study discusses some
Page 33 and 34: [9] K. Deb and A. Sinha. An efficie
Page 35 and 36: [31] L. Thiele, K. Miettinen, P. Ko
Page 37 and 38: 1 An interactive evolutionary multi
Page 39 and 40: DM and an MCDM-based EMO algorithm
Page 41 and 42: In Step 2, points in the best non-d
Page 43 and 44: esulting constraints then become ki
Page 45 and 46: mechanisms) and their emphasis of n
Page 47 and 48: f2 10 8 6 4 2 P1 P2 Most preferred
Page 49 and 50: DM calls. As mentioned earlier, the
Page 51 and 52: A linear value function similar to
Page 53 and 54:
on developed value function. For ex
Page 55 and 56:
2 Progressively interactive evoluti
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DM one or more pairs of alternative
Page 59 and 60:
f 2 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 P
Page 61 and 62:
TABLE III DISTANCE OF OBTAINED SOLU
Page 63:
The PI-EMO-VF algorithm has been te
Page 66 and 67:
An Interactive Evolutionary Multi-O
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direction has been done by Phelps a
Page 70 and 71:
0 ∀ i ∈ {1, . . . , M}, then th
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f2 0000000000000 1111111111111 0000
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Table 1. Final solutions obtained b
Page 76 and 77:
Table 4. Distance of obtained solut
Page 78 and 79:
DM Calls and Func. Evals. (in thous
Page 80 and 81:
13. P. Korhonen and J. Laakso, “A
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An EfficientandAccurateSolution Met
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eight differentproblems areshown. A
Page 86 and 87:
3.2 AlgorithmicDevelopments Onesimp
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more studies are performed, the alg
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4.4 TestProblemTP4 The next problem
Page 92 and 93:
F2 Step 3: Map (U1,U2) to (f1*,f2*)
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F2 1.4 1.2 1 0.8 0.6 0.4 0.2 0 A y1
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• Theupperlevelproblemhas multi-m
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are K + L + 1real-valuedvariablesin
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thereafterinaself-adaptivemannerbyd
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ulation of Nl(x (1) u ) lower level
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NSGA-II is able to bring the member
Page 106 and 107:
F2 0 −0.2 −0.4 −0.6 −0.8
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LL Function Evals. UL Function Eval
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Table 1: Total function evaluations
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Difference in HV, DH(T) 350000 3000
Page 118 and 119:
Table 4: Comparison of function eva
Page 120 and 121:
Deb, K. and Sinha, A. (2009a). Cons
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Sun, D., Benekohal, R. F., and Wall
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Bilevel Multi-Objective Optimizatio
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The constraint functions g(x) and h
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value function which are required t
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to get close to the most preferred
Page 132 and 133:
F2 0.4 0.2 0 −0.2 Lower level P
Page 134 and 135:
F2 2 1.5 1 0.5 Most Preferred Point
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provement in terms of function eval
Page 138:
9HSTFMG*aeafcd+ ISBN: 978-952-60-40
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