Solving Multiple Routes Travelling Salesman Problem Using Modified Genetic Algorithm

2012 ◽  
Vol 576 ◽  
pp. 718-722
Author(s):  
Muhammad Ridwan Andi Purnomo ◽  
Mohammad Iqbal ◽  
Mila Faila Sufa
Keyword(s):  
Genetic Algorithm ◽  
Travelling Salesman Problem ◽  
Initial Position ◽  
Mutation Operator ◽  
Shortest Path Algorithm ◽  
Travelling Salesman ◽  
Numerical Examples ◽  
Modified Genetic Algorithm ◽  
Multiple Routes ◽  
Crossover And Mutation

The multiple routes travelling salesman problem (mrTSP) is an extension of the well-known travelling salesman problem (TSP), where there are several points clusters to be visited by salesman. The problem to be solved is how to define the best route in every cluster and initial position of each routes as interconnection points for the salesman. In this paper, modified genetic algorithm (mGA) is proposed in order to solve the mrTSP problem. In the proposed mGA, new heuristic algorithm for crossover and mutation operator based on local shortest path algorithm is proposed in order to assist the mGA to improve 'best solution so far'. Numerical examples are also given to test the performance of proposed mGA when solving mrTSP. The result of the study shows that the mGA is superior compared to conventional GA.

scholarly journals Comparative Study of Prim and Genetic Algorithms in Minimum Spanning Tree and Travelling Salesman Problem

2018 ◽  
Author(s):  
Andysah Putera Utama Siahaan ◽  
Andre Hasudungan Lubis
Keyword(s):  
Genetic Algorithm ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Travelling Salesman Problem ◽  
Operational Cost ◽  
Travelling Salesman ◽  
Maximum Value ◽  
Large Numbers ◽  
Crossover And Mutation ◽  
Better Than

Optimization is the essential thing in an algorithm. It can save the operational cost of an activity. At the Minimum Spanning Tree, the goal to be achieved is how all nodes are connected with the smallest weights. Several algorithms can calculate the use of weights in this graph. Genetic and Primary algorithms are two very popular algorithms for optimization. Prim calculates the weights based on the short-est distance from a graph. This algorithm eliminates the connected loop to minimize circuit. The nature of this algorithm is to trace all nodes to the smallest weights on a given graph. The genetic algorithm works by determining the random value as first initialization. This algorithm will perform selection, crossover, and mutation by the number of rounds specified. It is possible that this algorithm can not achieve the maximum value. The nature of the genetic algorithm is to work with probability. The results obtained are the most optimal results according to this algorithm. The results of this study indicate that the Prim is better than Genetics in determining the weights at the minimum spanning tree while Genetic algorithm is better for travelling salesman problem. Genetics will have maximum results when using large numbers of rotations and populations.

scholarly journals Genetic algorithm based approach to solve travelling salesman problem with one point crossover operator:

2013 ◽  
Vol 10 (3) ◽  
pp. 1393-1400 ◽  
Author(s):  
Sharadindu Roy
Keyword(s):  
Genetic Algorithm ◽  
Travelling Salesman Problem ◽  
Global Optimum ◽  
Traveling Salesman ◽  
Mutation Operator ◽  
Crossover Operator ◽  
Travelling Salesman ◽  
Apply Genetic ◽  
Multiple Copies ◽  
The Traveling Salesman Problem

In this paper, the travelling salesman problem using genetic algorithm has been attempted. In this practical paper solution is easy and we can easily apply genetic operator in this type of problem. Complexity is both in time and space, provided size of the problem an as integer (count is infinite). The solution of the traveling salesman problem is global optimum. There are cities and given distances between them. Traveling salesman has to visit all of them. TSP main objective is to find traveling sequence of cities to minimize the traveling distance.* traverse one time*initially we select parent1 & parent2 by Roulette wheel concept. Apply one point crossover operator on parents and produce the offspring. Again we apply the mutation operator on offspring and created child. But the no. of bits (cities) will be inverted by the mutation operator, that is depended on mutation probability (pm). So one generation contain 6 individual. Then count fitness of the individuals in each generation. For the next generation (for parent1 & parent2) two individuals will be selected whose fitness is best in generation. Here we see crossover between two good solution may not always yield a better or as good a solution. Since parents are good, so the probability of the child being good is high. Every time we have to do, identity the good solution in the population and make multiple copies of the good solution. 

scholarly journals Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Maha Ata Al-Furhud ◽  
Zakir Hussain Ahmed
Keyword(s):  
Genetic Algorithm ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Hybrid Genetic Algorithm ◽  
Travelling Salesman ◽  
Complex Optimization ◽  
Problem Instances ◽  
Search Approach ◽  
Multiple Travelling Salesman Problem

The multiple travelling salesman problem (MTSP), an extension of the well-known travelling salesman problem (TSP), is studied here. In MTSP, starting from a depot, multiple salesmen require to visit all cities so that each city is required to be visited only once by one salesman only. It is NP-hard and is more complex than the usual TSP. So, exact optimal solutions can be obtained for smaller sized problem instances only. For large-sized problem instances, it is essential to apply heuristic algorithms, and amongst them, genetic algorithm is identified to be successfully deal with such complex optimization problems. So, we propose a hybrid genetic algorithm (HGA) that uses sequential constructive crossover, a local search approach along with an immigration technique to find high-quality solution to the MTSP. Then our proposed HGA is compared against some state-of-the-art algorithms by solving some TSPLIB symmetric instances of several sizes with various number of salesmen. Our experimental investigation demonstrates that the HGA is one of the best algorithms.

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