Progressively Interactive Evolutionary Multi-Objective Optimization ...

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References [1] T. Bäck. Evolutionary Algorithms in Theory and Practice. New York: Oxford University Press, 1996. [2] J. Branke and K. Deb. Integrating user preferences into evolutionary multi-objective optimization. In Y. Jin, editor, Knowledge Incorporation in Evolutionary Computation, pages 461–477. Hiedelberg, Germany: Springer, 2004. [3] J. Branke, S. Greco, R. Slowinski, and P. Zielniewicz. Interactive evolutionary multiobjective optimization using robust ordinal regression. In Proceedings of the Fifth International Conference on Evolutionary Multi-Criterion Optimization (EMO-09), pages 554– 568. Berlin: Springer-Verlag, 2009. [4] C. A. C. Coello, D. A. VanVeldhuizen, and G. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Boston, MA: Kluwer, 2002. [5] J. L. Cohon. Multicriteria programming: Brief review and application. In J. S. Gero, editor, Design Optimization, pages 163–191. New York: Academic Press, 1985. [6] K. Deb. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley, 2001. [7] K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2):182–197, 2002. [8] K. Deb and D. Saxena. Searching for Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In Proceedings of the World Congress on Computational Intelligence (WCCI-2006), pages 3352– 3360, 2006. 23
[9] K. Deb and A. Sinha. An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm. Evolutionary Computation Journal, 18(3):403–449, 2010. [10] K. Deb, A. Sinha, P. Korhonen, and J. Wallenius. An interactive evolutionary multi-objective optimization method based on progressively approximated value functions. IEEE Transactions on Evolutionary Computation, 14(5):723–739, 2010. [11] K. Deb, J. Sundar, N. Uday, and S. Chaudhuri. Reference point based multi-objective optimization using evolutionary algorithms. International Journal of Computational Intelligence Research (IJCIR), 2(6):273–286, 2006. [12] D. B. Fogel. Evolutionary Computation. Piscataway, NY: IEEE Press, 1995. [13] J. W. Fowler, E. S. Gel, M. Koksalan, P. Korhonen, J. L. Marquis, and J. Wallenius. Interactive evolutionary multi-objective optimization for quasi-concave preference functions. [14] A. M. Geoffrion. Proper efficiency and theory of vector maximization. Journal of Mathematical Analysis and Applications, 22(3):618– 630, 1968. [15] A. M. Geoffrion, J. S. Dyer, and A. Feinberg. An interactive approach for multi-criterion optimization with an application to the operation of an academic department. Management Science, 19(4):357–368, 1972. [16] D. E. Goldberg. Genetic Algorithms for Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley, 1989. [17] G. W. Greenwood, X. Hu, and J. G. D’Ambrosio. Fitness functions for multiple objective optimization problems: Combining preferences with pareto rankings. [18] J. Horn. Multicriterion decision making. In Handbook of Evolutionary Computation, pages F1.9:1–15. Bristol: Institute of Physics Publishing and New York: Oxford University Press, 1997. [19] C.-L. Hwang and A. S. M. Masud. Multiple Objective Decision Making – Methods and Applications: A State-of-the-art Survey. Berlin: Springer-Verlag, 1979. 24
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 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 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
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An EfficientandAccurateSolution Met
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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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Page 112 and 113:
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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
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