- Page 1 and 2: Department of Business Technology P
- Page 3 and 4: Aalto University publication series
- 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: [31] L. Thiele, K. Miettinen, P. Ko
- 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
- Page 57 and 58: 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
- Page 68 and 69: direction has been done by Phelps a
- Page 70 and 71: 0 ∀ i ∈ {1, . . . , M}, then th
- Page 72 and 73: f2 0000000000000 1111111111111 0000
- Page 74 and 75: 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
- Page 82 and 83: An EfficientandAccurateSolution Met
- Page 84 and 85: eight differentproblems areshown. A
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3.2 AlgorithmicDevelopments Onesimp
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more studies are performed, the alg
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4.4 TestProblemTP4 The next problem
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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
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F2 0 −0.2 −0.4 −0.6 −0.8
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LL Function Evals. UL Function Eval
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LL Function Evals. UL Function Eval
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LL Function Evals. UL Function Eval
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Table 1: Total function evaluations
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Difference in HV, DH(T) 350000 3000
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Table 4: Comparison of function eva
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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
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F2 0.4 0.2 0 −0.2 Lower level P
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F2 2 1.5 1 0.5 Most Preferred Point
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provement in terms of function eval
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9HSTFMG*aeafcd+ ISBN: 978-952-60-40