Progressively Interactive Evolutionary Multi-Objective Optimization ...

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3 An interactive evolutionary multi-objective optimization method based on polyhedral cones A. Sinha, P. Korhonen, J. Wallenius, and K. Deb In Proceedings of the 2010 Learning and Intelligent <strong>Optimization</strong> Con- ference (LION-2010), pages 318-332. IEEE Press, 2010. 57
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Department of Business Technology P
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Aalto University publication series
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Progressively Interactive Evolution
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Acknowledgements The dissertation h
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II List of Papers 27 1 An interacti
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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
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 67 and 68: the aposteriori approach. This appr
Page 69 and 70: (generations). The value of t is in
Page 71 and 72: zT ) is not greater than ds distanc
Page 73 and 74: 2. Termination parameter: ds = 0.01
Page 75 and 76: f 2 2 + f 2 3 = 3.52 . The decision
Page 77 and 78: Table 6. Distance of obtained solut
Page 79 and 80: metric study has also been performe
Page 81 and 82: 4 An efficient and accurate solutio
Page 83 and 84: e satisfied (Reklaitis et al., 1983
Page 85 and 86: problems, in which the upper level
Page 87 and 88: lems having asingle objective ineac
Page 89 and 90: F2 0.4 0.2 0 −0.2 −0.4 −0.6
Page 91 and 92: the lower level, solution y can be
Page 93 and 94: 4.5.2 ProblemDS1 This problemhas 2K
Page 95 and 96: 4.6 ProblemDS2 Thenextproblemuses
Page 97 and 98: 4.8 ProblemDS4 In this problem, the
Page 99 and 100: on a few rank-one lower level solut
Page 101 and 102: (derived from tmax l , as calculate
Page 103 and 104: conditions (Reklaitis et al., 1983)
Page 105 and 106: 3. Thepreviousapproacheshadafixedpo
Page 107 and 108: LL Function Evals. UL Function Eval
Page 109 and 110: cating the robustness of our proced
Page 111 and 112: the problem with τ = −1 later. F
Page 113 and 114: F2 2.5 2 1.5 1 0.5 0 0 0.2 0.4 0.6
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7 IntroducingFurtherDifficulties in
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Number of Function Evaluations 1e+0
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efficientmannerisnoteasyanddefinite
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Hecheng,L.andWang,Y.(2007). Ageneti
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5 Bilevel multi-objective optimizat
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towards the most preferred solution
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4. Check for termination. The termi
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which is larger than V2, and, the r
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Table 1. Total function evaluations
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Bibliography [1] R. H. Byrd, J. Noc
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