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1 1 ( ) 1 GA GA GA MOGA (Multple-Objectve Genetc Algorthm) GA GA GA MOGA GA GA MOGA GA GA

2 3.1MOGA ( ) x x j f = f, f, 1 2 L, f q x x j x j f ( x ) f ( x ) f ( x ) f ( x ) L f ( x ) f ( x ) ( ) ( ) 1 1 j 2 2 j q q j x f x j f (24) (24) x j x x j x j MOGA [9] t (15) t p x x t (, t) = 1+ rank x (25) p f MOGA f 1 15 [3] F( x ) F ( x ) F( x ) F ( x ) = (26) s ( d( x, x )) j s [3] j 2

3 d s( d) = 1 σ 0 share α σ < σ σ σ share share (27) d = d( x, x j) x, x j d MOGA GA σ share α σ share M m [9] Nσ q 1 share q ( M m + σ ) ( M m ) share = 1 = 1 σ share q = 0 (28) N α ) 2) 3) GA 3.2 x, y 0 < x < 1 0 < y < x + y < 1 x, y Chld1 = ran1 Parent1 + (1-ran1) Parent2 + 2m (ran2-0.5) Chld2 = (1-ran1) Parent1 + ran1 Parent2 + 2m (ran2-0.5) (29) Parent1,2 Chld1,2 ran1,2 [0,1] ran1 [-0.5,1.5]

4 ( 0.2) SUS [10] Smple GASGA Eltst Recombnaton (ER) CHC[11] (FS) CSN [12] CSN [12] GA solutons Exact Pareto front a) Pareto solutons obtaned from SGA + FS c) Pareto solutons obtaned from CHC + FS b) Pareto solutons obtaned from ER + FS 16

5 a) Pareto solutons obtaned from SG A+ CSN b) Pareto solutons obtaned from CHC + CSN 17CSN SGA ER CHC FS SGAER CHC FS CSN 17 SGA CSN FS SGA FS CSN CHC CSN SGA CSN CHC FS FS CSN FS (28) CSN SST SST SST SST

6 GA SST GA NEC SX-4 32CPU

7 1 C root 2 C knk b 2 b (deg) (deg) C root 1020 C knk 315 b 1 27 b tp knk t/c 0.02 P 0 P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 root P 2 P 3 P 4 P 5 P 6 P 1 P 0 P 7 P x/c Z P4 34% X P % Z P3 =Z P4 = Z P5 X P 0=X P 1 19 tp camber/c 0 C C 3 C 0 C 1 C 2 C 3 root knk C C x/c 20 T 2 T 1 T 0 T 3 T 4 T 5 twst angle (deg) 10 T T T 2 T3 T 4 T y/b 21

8 3 TVD LU-SGS FLO-27[13] Pareto soluton C D (transonc) Mnmum Bendng Moment Bendng Moment Mnmum C D (transonc) Pareto soluton Optmal Drecton C D (supersonc) C D (supersonc) Mnmum 22

9 C D (supersonc) Mnmum transonc drag Mnmum bendng moment C D (transonc) Mnmum supersonc drag 23 NAL 2 [14]NAL NAL NAL 2 C D (supersonc) Pareto soluton A Pareto soluton B Pareto soluton C NAL 2nd NAL 2nd C D (transonc) 24NAL2

10 NAL 2nd A B C 25NAL2 1 Aspect C D (M0.9) C D (M2.0) Bendng Rato ( 10-4 ) ( 10-4 ) Moment A B C NAL2nd NAL 2nd Aspect Rato C D(M2.0) Bendng Moment Pareto Soluton NAL 2nd C D(M0.9) NAL2 24 NAL NAL 2 26 NAL F16

11 MOGA [1] Vanderplaats, G. N., Numercal Optmzaton Technques for Engneerng Desgn: wth Applcatons, McGraw-Hll, Inc., New York (1984). [2] Press, W. H., et al., Numercal Recpes n FORTRAN : the art of scentfc computng, 2 nd ed., Cambrdge Unversty Press, Cambrdge (1992). [3] Goldberg, D. E., Genetc Algorthms n Search, Optmzaton & Machne Learnng, Addson-Wesley Publshng Company, Inc., Readng (1989). [4] Vanderplaats, G. N., Approxmaton Concepts for Numercal Arfol Optmzaton, NASA TP-1370 (1979). [5] Hcks, R. M. and Henne, P. A., Wng Desgn by Numercal Optmzaton, Journal of Arcraft, Vol. 15, pp (1978). [6],,, (1994). [7] Katz, J. and Plotkn, A., LOW-SPEED AERODYNAMICS from Wng Theory to Panel Methods, McGraw-Hll, Inc., NewYork (1991). [8] Vanderplats, G. N., ADS-A FORTRAN Program for Automated Desgn Synthess, Verson 3.00, Engneerng Desgn Optmzaton, Inc., Calforna (1988). [9] Fonseca, C. M. and Flemng, P. J., Genetc Algorthms for Multobjectve Optmzaton: Formulaton, Dscusson and Generalzaton, Proceedngs of the 5th Internatonal Conference on Genetc Algorthms, Morgan Kaufmann Publshers, San Mateo, Calforna, pp (1993). [10] Baker, J. E., Reducng Bas and Ineffcency n the Selecton Algorthm, Proceedngs of the Second Internatonal Conference on Genetc Algorthms, Morgan Kaufmann

12 Publshers, San Mateo, Calforna, pp (1987). [11] Eshelman, L. J., The CHC Adaptve Search Algorthm: How to Have Safe Search When Engagng n Nontradtonal Genetc Recombnaton, Foundatons of Genetc Algorthms, Morgan Kaufmann Publshers, San Mateo, Calforna, pp (1991). [12] Goldberg, D. E. and Wang, L., Adaptve Nchng va Coevolutonary Sharng, Quaglarella, D., Peraux, J., Polon, C. and Wnter, G. (Eds.), Genetc Algorthms and Evoluton Strateges n Engneerng and Computer Scence, John Wley and Sons, Chchester pp (1998). [13] Jameson, A. and Caughey, D. A., A Fnte Volume Method For Transonc Potental Flow Calculatons, AIAA paper Amercan Insttute of Aeronautcs and Astronautcs, Reston, VA (1977) [14] Iwamya, T., NAL SST Project and Aerodynamc Desgn of Expermental Arcraft, Proceedngs of the Fourth ECCOMAS Computatonal Flud Dynamcs Conference, Vol. 2, John Wley & Sons, Chchester, UK, pp (1998).

> σ, σ j, j σ j, σ j j σ σ j σ j (t) = σ (t ) σ j (t) = σ () j(t ) n j σ, σ j R lm σ = σ j, j V (8) t σ R σ d R lm σ = σ d V (9) t Fg.. Communcaton ln

> σ, σ j, j σ j, σ j j σ σ j σ j (t) = σ (t ) σ j (t) = σ () j(t ) n j σ, σ j R lm σ = σ j, j V (8) t σ R σ d R lm σ = σ d V (9) t Fg.. Communcaton ln IIC-- Dstrbuted Cooperatve Atttude Control for Multple Rgd Bodes wth Communcaton Delay Yoshhro achbana, oru Namerkawa (Keo Unversty) Abstract hs paper descrbes dstrbuted cooperatve atttude consensus and

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橡ｊｔｔｃ２.PDF