Progressively Interactive Evolutionary Multi-Objective Optimization ...

More documents

Recommendations

Info

Contents I Overview of the Dissertation 1 1 Introduction 3 1.1 Multi-objective Optimization . . . . . . . . . . . . . . . . . . 4 1.2 Domination Concept and Optimality . . . . . . . . . . . . . . 5 1.2.1 Domination Concept . . . . . . . . . . . . . . . . . . . 5 1.3 Decision Making . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Evolutionary Multi-objective Optimization (EMO) Algorithms 10 1.5 Integrating Search and Decision Making . . . . . . . . . . . . 12 1.5.1 A posteriori Approach . . . . . . . . . . . . . . . . . . 12 1.5.2 A priori Approach . . . . . . . . . . . . . . . . . . . . 14 1.5.3 Interactive Approach . . . . . . . . . . . . . . . . . . . 15 1.6 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.7 Summary of Research Papers . . . . . . . . . . . . . . . . . . 18 1.7.1 An Interactive Evolutionary Multi-Objective Optimization Method Based on Progressively Approximated Value Functions . . . . . . . . . . . . . . . . . . 19 1.7.2 Progressively Interactive Evolutionary Multi-Objective Optimization Method Using Generalized Polynomial Value Functions . . . . . . . . . . . . . . . . . . . . . . 19 1.7.3 An Interactive Evolutionary Multi-Objective Optimization Method Based on Polyhedral Cones . . . . 20 1.7.4 An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm . 20 1.7.5 Bilevel Multi-Objective Optimization Problem Solving Using Progressively Interactive EMO . . . . . . . 21 References 23 v
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 11 and 12: Part I Overview of the Dissertation
Page 13 and 14: tives. The utility of the procedure
Page 15 and 16: f2 D C Region Dominated by A B A Re
Page 17 and 18: f2 A B 6 7 1 Strongly Efficient Ine
Page 19 and 20: 1.4 Evolutionary Multi-objective Op
Page 21 and 22: problems. Their strength is particu
Page 23 and 24: 1.5.2 A priori Approach In this app
Page 25 and 26: Minimize/Maximize F(x) = (f1(x), f2
Page 27 and 28: However, it is never guaranteed tha
Page 29 and 30: tion in terms of partial ordering o
Page 32 and 33: References [1] T. Bäck. Evolutiona
Page 34 and 35: [20] A. Jaszkiewicz. Interactive mu
Page 36 and 37: Part II List of Papers 27
Page 38 and 39: An Interactive Evolutionary Multi-O
Page 40 and 41: e needed to make a fast and focused
Page 42 and 43: is at most 10% of the maximum diffe
Page 44 and 45: f 2 V(f)=V 2 A Fig. 6. Dominated re
Page 46 and 47: TABLE I FINAL SOLUTIONS OBTAINED BY
Page 48 and 49: accuracy measure, the number of ove
Page 50 and 51: the positive correlation between ac
Page 52 and 53: ideal ranking (which would have bee
Page 54 and 55: [19] S. Phelps and M. Koksalan, “
Page 56 and 57: Progressively Interactive Evolution
Page 58 and 59:
maximum. Maximize ǫ, subject to Va
Page 60 and 61:
1) Number of points given to the DM
Page 62 and 63:
tions in an earlier study [14]. How
Page 65 and 66:
3 An interactive evolutionary multi
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
Page 115 and 116:
7 IntroducingFurtherDifficulties in
Page 117 and 118:
Number of Function Evaluations 1e+0
Page 119 and 120:
efficientmannerisnoteasyanddefinite
Page 121 and 122:
Hecheng,L.andWang,Y.(2007). Ageneti
Page 123 and 124:
5 Bilevel multi-objective optimizat
Page 125 and 126:
towards the most preferred solution
Page 127 and 128:
4. Check for termination. The termi
Page 129 and 130:
which is larger than V2, and, the r
Page 131 and 132:
Table 1. Total function evaluations
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Bibliography [1] R. H. Byrd, J. Noc
show all

Progressively Interactive Evolutionary Multi-Objective Optimization ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?