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# Muzammil Adulrahman ppt on travelling salesman Problem Based On Mutation Genetic Algorithms

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Muzammil Adulrahman ppt on travelling salesman Problem Based On Mutation Genetic Algorithms An Optimization Theory Approach

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### Muzammil Adulrahman ppt on travelling salesman Problem Based On Mutation Genetic Algorithms

1. 1. BY & 2013
2. 2.  The task of finding the shortest possible path that visits each city exactly once and returns to the initial city has been suggested by many scholars.  Travelling Salesman Problem (TSP) is among the extensively studied optimization problem that has been used to find the shortest possible route.  The TSP has many applications including the following :  Manufacture of microchips  The routing of trucks for packet post pickup  Packet routing in GSM  The delivery of meals to home bound persons etc.
3. 3. GA at a glANCE  GA is an empirical search that mimics the process of natural     evolution GA generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance,, mutation, selection and crossover In GA a space of hypotheses is searched to identify the best hypothesis. The best hypothesis is defined as the one that optimizes a predefined numerical measure for the problem at hand, called the hypothesis fitness GA operates by iteratively updating a pool of hypotheses, called the population
4. 4.  Select: Randomly select members of Population  Crossover: Randomly select pairs of hypotheses from P, to     produce offspring by applying the Crossover operator. Add all offspring to new P1. Mutate: Choose m percent of the members of P, with uniform probability. For each, invert one randomly selected bit in its representation. Update: P ← P1. Evaluate: compute Fitness function Return the hypothesis from P that has the highest fitness.
5. 5. Genetic Algorithm is another technique which can also find solution to TSP due to the following reasons :  Due to their flexibility and robustness  They are also readily amenable to parallel implementation  They are able to solve problems knowing nothing about the problem from the start
6. 6.  Population Size - The population size is the initial number of      random tours that are created when the algorithm starts. Neighborhood / Group Size – In each generation the best 2 tours are the parents. The worst 2 tours get replaced by the children. Mutation % - The percentage that each child after crossover will undergo mutation when a tour is mutated. Nearby Cities - As part of a greedy initial population, the GA will prefer to link cities that are close to each other to make the initial tours. Nearby City Odds % - This is the percent chance that any one link in a random tour in the initial population will prefer to use a nearby city instead of a completely random city. 6. Maximum Generations – Number of crossovers are run before the algorithm is terminated
7. 7.  Fıtness functıon= Least tour dıstance ın a group.  Selectıon method- Determınıstıcs wıth a probabılıty of 1.  Cross over- skıpped.  Mutatıon:  Recıprocal exchange Mutatıon- Two cıtıes are randomly selected and theır posıtıons ın chromosomes are exchanged.  Flıp Mutatıon- The two cıtıes selected are flıpped over, example ıf theır are sıx cıtıes 1, 2, 3, 4, 5, 6 ın the chromosomes and cıtıes at posıtıon 2 and 5 are chosen as a mutatıon poınts, then the new chromosomes after flıpıng posıtıon the gıven posıtıons are 1, 5, 4, 3, 2, 6.  Backward slıde Mutatıon- As the name ımplıes, two mutatıon posıtıons are move to the next posıtıons ın a backward dırectıonwıthın the span of the Mutatıon poınts. Example ıf the above cıtıes posıtıon ın the chromosomes are used and posıtıon 2 and 5 are slıded then the cıtıes posıtıon ın the new chromosomes are1, 3, 4, 5, 2, 6.
8. 8. ALGORITHM  Inıtıalıze the populatıon  Randomly generate the populatıon members.  Calculate the total dıstance for each tour.  Evaluate each tour fıtness ın each group.  Select the tour wıth the least dıstance ıe hıghest fıtness.  Apply Mutatıon to the best offsrıng to get the three new routes.  Set the best route as your new global mınımızer  Iterate whıle number of ıteratıon ıs less than the maxımum ıteratıon untıl the optımal route ıs dıscovered (convergence poınt).  Stop.
9. 9.  An N by N distance matrix was used where N stands for the number of cities.  All the cities were assumed to be points in space and their respective Euclidean distance were computed using the Euclidean equations to get the inputs of the distance matrix (Dmat).  For a real and more practical situation, the exact distances between the cities in consideration can be directly inputed into the distance matrix.  In asymmetric TSP the approach mentioned might not work since the distance travelled to get to city B from A might not necesssarily be the same when coming back to A from B.
10. 10.  The simulation results showed that with a higher number of     iterations a better route is discovered but it takes more time to converge to an optimal solution. With lower population size and a less number of cities little time is required to get the optimal route. The optimal tour distance at a given population and iteration might vary when the same population size and iteration number is used at a different run. It is so because the vertexes of the cities used in Euclidean computation are randomly generated. It can also be proven that to get the best population size that takes little time, a range within Number of Cities * 3 < Population Size < Number of Cities * 5 should be used as suggested by by Nilesh Gambhava and Gopi Sanghani in their papers. Below are the figures of simulation result at different instances.
11. 11. Fig 1 Fig 2
12. 12. Fig 3 Fig 4
13. 13.  Genetic algorithm has been quite an exciting tool for solving optimization problem.  Its flexibility is astonishingly remarkable. This paper has indicated that mutation in genetic is a powerful operator which makes GA to stand tall among its fellow optimization algorithms.  The Mutation operator ensures that trap of local minimum is avoided which is one of the major advantage of GA.  With a better manupilation of this tool in a suitable problem, it is always possible that GA will remained in the mainstrem in the field of optimization.
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