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Company LOGO Searching Solutions of C-TSP Harbin Institute of Technology Lecturer: HUA Dingguo Tutor: YAN Jihong Utilizing GA

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Contents GA Introduction 2 Searching Result 4 Definition of C-TSP 31 Searching Process 33 References 5

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1. Definition of C-TSP What is C-TSP? C-TSP: China Travelling Salesman Problem Cities: 31 cities including [1] Beijing, Shanghai, Tientsin, Shijiazhuang, Taiyuan, Hohhot, Shenyang, Changchun, Harbin, Sian, Lanzhou, Yinchuan, Xining, Urumqi, Jinan, Nanking, Hangzhou, Hefei, Nanchang, Foochow, Taipei, Chengchow, Wuhan, Changsha, Canton, Nanning, Haikou, Chengdu, Guiyang, Kunming, Lhasa

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1. Definition of C-TSP Starting point: Beijing Destination: Back to Beijing Constraint: Every city has to be visited Every city except Beijing can be visited for ONLY ONCE Searching Target: The shortest travelling path

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Straight-Line Path Only straight- line path is considered for the simplicity of the problem Direct Arrival Direct arrival can be realized between any 2 of the 31 cities Assumptions 1. Definition of C-TSP

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2. GA Introduction Inverse Mutation Mutation Distance related FitnessEvaluation Roulette Selection Oder Crossover Crossover Population Near-Optimal Solution

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2.1 Population & Encode Population: The scale of initial population is very crucial to the performance of GA; If the scale is too small, the diversity is not guaranteed; If the scale is too large, the computing is hence time consuming; The scale is finally determined as 500 Problem Scale Relatively Small

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2.1 Population & Encode Encode Since the cities can be denoted as integers 1-Beijing; 2-Shanghai; 3- Tientsin … Every chromosome can be encoded in the form of integer string of 1 to 31 which is arranged in a random order Example 1-23-7-4-17-12-31-8-29-18-45-9-6-30-22-26-28-27-20-16-2-24- 3-5-19-25-14-10-21-11-13

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2.2 Fitness Evaluation Distance is the major concern of C-TSP the fitness value of one chromosome can be calculated as follows: First, a pseudo fitness value f is obtained by Eq. 1 Second, Fitness value F can be obtained through linear fitness scaling f F average Eq. 1

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2.3 GA Operators Selection Operator one Roulette

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2.3 GA Operator Crossover Order Crossover Operator two 11- 3- 4- 5- 7-10- 6-15- 9- 1- 2 3- 5- 4- 7- 6-11- 1- 2- 9-15-10 4- 5- 7-10- 6 4- 7- 6-11- 1

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2.3 GA Operator Crossover Order Crossover Operator two x- 3- x- 5- x-10- x-15- 9- x- 2 3- x- x- x- x-11- 1- 2- 9-15-x 9-15- 4- 5- 7-10- 6- 3-11- 1- 2 9 - 2- 4- 7- 6-11- 1- 3- 5-10-15

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2.3 GA Operator Mutation Inverse Mutation Operator three 11- 3- 4- 5- 7-10- 6-15- 9- 1- 2 11- 3- 6-10- 7- 5- 4-15- 9- 1- 2

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3 Searching Process The 100 th Generation

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3 Searching Process The 500 th Generation

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3 Searching Process The 1000 th Generation

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3 Searching Process Evolution G 1000 G 500 G 200 G 100

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4 Searching Result 试验次数最优旅行路线距离 /kilometer 获得代数 115655.0093675 215965.1518819 315860.9205851 415896.8518375 515908.5454394 615468.3336863 715665.0205690 816612.9431847 915849.3315719 1017015.8367937

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4 Searching Result The Near Optimal Solution obtained by Hopfield Artificial Neural Networks is 15904 Kilometers [1] GA found 6 better solutions ! In 10 experiments The best is 15468 Kilometers !

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4 Searching Result Near-Optimal solution obtained by Hopfield ANN

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4 Searching Result Near-Optimal solution obtained by GA

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References [1]JIN Pan, FAN Junbo, TAN Yongdong. Neural Networks and Neural Computer: Theory · Application [M]. Chengdu: Southwest Jiaotong University Press, 1991: 375-376

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Company LOGO Harbin Institute of Technology

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