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ニュートラルネットワークの利用による多様性維持メカニズムを有する多目的遺伝的アルゴリズム

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(1)2006−MPS−61(11) 1    2006/9/15. 社団法人 情報処理学会 研究報告 IPSJ SIG Technical Report. † †. ††. ,. ††. ,. ††. (Artificial Neural Network:ANN) GA. NSGA-II ANN. NSGA-II. NSGA-II NSGA-II. Mechanism of Multi Objective Genetic Algorithm for maintaining the solution diversity using Neural Network Kenji KOBAYASHI†, Tomoyuki HIROYASU†† ,and Mitsunori MIKI†† †. Graduate School of Knowledge Engineering, Doshisha University ††. Faculty of Engineering, Doshisha University. When multi-objective genetic algorithm is applied to real world problems for deriving Pareto optimum solutions, high calculation cost becomes a problem. One of solutions of this problem is using small number of population size. With this solution, however, it often happens that the diversity of the solutions is lost. Then the solutions which have the sufficient precisions cannot be derived. For overcoming this difficulty, the solutions should be re-placed when the solutions are concentrated on a certain point. To perform this re-placement, inverse analyze to derive the design variables from objects since the solutions are located in the objective space. For this purpose, in this paper, the Artificial Neural Network (ANN) is applied. Using ANN, the solutions which are concentrated on certain points are re-placed and the diversity of the solutions is maintained. In this paper, the new mechanism using ANN to keep the diversity of the solutions is proposed. The proposed mechanism is introduced into NSGA-II and applied for the test functions. It is discussed that in some test functions the proposed mechanism is useful compared to the conventional method. At the same time, it is also discussed that in other functions the proposed mechanism is not useful. In other numerical experiments, the results of the proposed algorithm with plentifully population are discussed and the affection of the proposed mechanism is also described.. 1 (Genetic Algorithm:GA) .. −41−.

(2) 2. solutions. f2. f2. solutions ununiformaly distributed. f1. real solutions distributed. (Artificial Neural Network:ANN). uniformaly distributed. ideal solutions distributed. f1. 1:. 3. ANN. ANN. 3.1. Artificial Neural Network. ANN. GA ANN. ANN ANN ANN 2). 2 2.1. (Multi Layer Perceptron:MLP). GA GA. 3.2. ANN. GA. 1 GA. GA. NSGA-II. 1). ANN 2.2 GA 2 2 2. solutions. f2. 1 1. ununiformaly distributed. f2. 1 solutions uniformaly distributed. linear interpolation. 1. f1 real solutions distributed. 2:. ANN −42−. f1 target solutions distributed.

(3) 3 4.1 ANN. GA. ANN. GA ANN. 3.3 GA. ANN ZDT6. IRN I. (IRN I ) . 2.  100. NAN N : AN N tmax :. 0. GA. t: k:. 4.2. ANN NSGA-II. i=1. Step1: NSGA-II. i. ANN. tmax /NAN N. NSGA-II. Step2-1:. 10. GA. 1. Step2-2: ANN ( Step2-3: n. 1:. ). 6 10 60. n−2. 2 1.0. Step2-4: ANN. 1 20 1/. Step2-5: ANN Step2-6: ANN. ANN. 2. ANN. 20,40. NSGA-II 3. (a). Step2-7: ANN Step1 (i = i + 1) Step2-1 . NSGA-II 3 (b) 3.3 Step2-1 Step2-6 3 (c). . 3. (a). (c). ANN. 4. ANN NSGA-II RNI. −43−. 30.

(4) 4. f2. 2.8. 2.8. 2.7. 2.7. 2.6. 2.6. f2. 2.5. 51.9. 2.4 0. 0.2. 0.4. 0.6. f1. 0.8. 2.3. 1. 0. 0.2. (a)NSGA-IIߦࠃࠅዉ಴ߐࠇߚ୘૕⟲. 0.4. f1. 0.6. 0.8. (b)⵬㑆✢਄ߦ૞ᚑߐࠇߚ୘૕⟲. 2.7. f2. 2.6 2.5 2.4 2.3. 0. 0.2. 0.4. f1. 0.6. 0.8. 48.1. 1. 2.8. f2. Evaluate Num 800. Hybrid NSGA-II. 2.5. 2.4 2.3. Evaluate Num 368. 7 6 5 4 3 2 1 0. f2. 0. 1. 0.2. 0.4. 0.6. 0.8. 1. 7 6 5 4 3 2 1 0 0. 0.2. 3: ANN. 5:. 4 NSGA-II. Hybrid. 0.6. 0.8. (b)NSGA-II(100୘૕. (a)Hybrid(6୘૕. (c)ANNߦࠃࠆᄙ᭽ᕈ⛽ᜬᓟߩ୘૕⟲. 0.4. f1. f1. RNI. 5. NSGA-II. NSGA-II GA ANN. Hybrid NSGA-II. f2. 7 6 5 4 3 2 1 0. f2. 0. 0.2. 0.4. 0.6. 0.8. 1. GA. 38.7. 61.3. 7 6 5 4 3 2 1 0. 5 0. 0.2. 0.4. 0.6. 0.8. f1. f1. (a)Hybridᚻᴺߦࠃࠅᓧࠄࠇߚ⸃. (b)NSGA-IIߦࠃࠅᓧࠄࠇߚ⸃. 4: 30. GA. 1. ANN. RNI. 4 RNI. ANN GA. NSGA-II. GA ANN. 4.3. GA. ANN. NSGA-II. NSGA-II NSGA-II. ANN. 2 2. 3 2:. RNI. 30 5. 2 Hybrid. NSGA-II. 6. 100. 60. 8. 368. 800. 10. 100. 1) Amrit Pratab Kalyanmoy Deb, Samir Agrawal and T. Meyarivan. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: Nsga-ii. In KanGAL report 200001, Indian Institute of Technology, Kanpur, India, 2000. 2) C.Bishop. Neural networks for pattern recognition. Oxford University Press, 1997.. −44−. 1.

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