Progressively Interactive Evolutionary Multi-Objective Optimization ...

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[20] A. Jaszkiewicz. Interactive multiobjective optimization with the pareto memetic algorithm. Foundations of Computing and Decision Sciences, 32(1):15–32, 2007. [21] R. L. Keeney and H. Raiffa. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. New York: Wiley, 1976. [22] J. Knowles and D. Corne. Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In Proceedings of the Fourth International Conference on Evolutionary Multi-Criterion Optimization (EMO-2007), pages 757–771, 2007. (LNCS 4403). [23] P. Korhonen, H. Moskowitz, and J. Wallenius. Multiple criteria decision support - a review. European Journal of Operational Research, 63:361–375, 1992. [24] J. R. Koza. Genetic Programming : On the Programming of Computers by Means of Natural Selection. Cambridge, MA: MIT Press, 1992. [25] M. Mitchell. Introduction to Genetic Algorithms. Ann Arbor, MI: MIT Press, 1996. [26] S. Phelps and M. Koksalan. An interactive evolutionary metaheuristic for multiobjective combinatorial optimization. Management Science, 49(12):1726–1738, December 2003. [27] A. Sinha. Bilevel multi-objective optimization problem solving using progressively interactive evolutionary algorithm. In Evolutionary Multi-Criterion Optimization (EMO-2011). In Press, 2011. [28] A. Sinha, K. Deb, P. Korhonen, and J. Wallenius. Progressively interactive evolutionary multi-objective optimization method using generalized polynomial value functions. In 2010 IEEE Congress on Evolutionary Computation (CEC-2010), pages 1–8. IEEE Press, 2010. [29] A. Sinha, P. Korhonen, J. Wallenius, and K. Deb. An interactive evolutionary multi-objective optimization method based on polyhedral cones. In 2010 Learning and Intelligent Optimization (LION-2010), pages 318–332. IEEE Press, 2010. [30] R. E. Steuer. Multiple Criteria Optimization: Theory, Computation and Application. New York: Wiley, 1986. 25
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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: [9] K. Deb and A. Sinha. An efficie
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 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
Page 86 and 87:
3.2 AlgorithmicDevelopments Onesimp
Page 88 and 89:
more studies are performed, the alg
Page 90 and 91:
4.4 TestProblemTP4 The next problem
Page 92 and 93:
F2 Step 3: Map (U1,U2) to (f1*,f2*)
Page 94 and 95:
F2 1.4 1.2 1 0.8 0.6 0.4 0.2 0 A y1
Page 96 and 97:
• Theupperlevelproblemhas multi-m
Page 98 and 99:
are K + L + 1real-valuedvariablesin
Page 100 and 101:
thereafterinaself-adaptivemannerbyd
Page 102 and 103:
ulation of Nl(x (1) u ) lower level
Page 104 and 105:
NSGA-II is able to bring the member
Page 106 and 107:
F2 0 −0.2 −0.4 −0.6 −0.8
Page 108 and 109:
LL Function Evals. UL Function Eval
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Table 1: Total function evaluations
Page 116 and 117:
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
Page 122 and 123:
Sun, D., Benekohal, R. F., and Wall
Page 124 and 125:
Bilevel Multi-Objective Optimizatio
Page 126 and 127:
The constraint functions g(x) and h
Page 128 and 129:
value function which are required t
Page 130 and 131:
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
Page 136 and 137:
provement in terms of function eval
Page 138:
9HSTFMG*aeafcd+ ISBN: 978-952-60-40
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