Abstract
Genetic algorithm (GA) is a powerful evolutionary searching technique that is used successfully to solve and optimize problems in different research areas. Genetic Algorithm (GA) considered as one of optimization methods used to solve Travel salesman Problem (TSP). The feasibility of GA in finding TSP solution is dependent on GA operators; encoding method, population size, number of generations in general. In specific, crossover and its probability play a significant role in finding possible solution for Symmetric TSP (STSP). In addition, crossover should be determined and enhanced in term reaching optimal or at least near optimal. In This paper, we spot the light on using modified crossover method called Modified sequential constructive crossover and its impact on reaching optimal solution. To justify the relevance of parameters value in solving TSP, a set comparative analysis conducted on different crossover methods values.
Highlights
The Travelling Salesman Problem (TSP) is a relatively ancient problem: it was precept as forward as 1759 by Euler, who’s interest was in solution the Knights’ tour proposition [1] .The extremity ‘move seller’ was first usage in 1932, in a German Leger ‘The travelling salesman, how and what he should do to get mandate and be fruitful in his businesses, literal by a veteran journey salesman[2].The origins of the TSP in mathematics aren’t understood -all we know for certain is that it occurs around 1931 by the mathematicians Sir William Rowaw Hamilton and Thomas Penyngton Kirkman from Ireland and Britain relatively [2].The TSP is one of hard and old problems in computer science
The TSP is categorized in two groups: symmetric travelling salesman problem (STSP) where the distances between two cities equal forward and backward and there are (n !1)!/2 possible solutions
The HEGAs is developed by using a new encoding, which mixes the binary encoding with the integer encoding using Genetic Algorithm (GA) for investigate TSP problem which each of the vertices has many edges and different cost
Summary
The Travelling Salesman Problem (TSP) is a relatively ancient problem: it was precept as forward as 1759 by Euler, who’s interest was in solution the Knights’ tour proposition [1] .The extremity ‘move seller’ was first usage in 1932, in a German Leger ‘The travelling salesman, how and what he should do to get mandate and be fruitful in his businesses, literal by a veteran journey salesman[2].The origins of the TSP in mathematics aren’t understood -all we know for certain is that it occurs around 1931 by the mathematicians Sir William Rowaw Hamilton and Thomas Penyngton Kirkman from Ireland and Britain relatively [2]. The TSP is one of hard and old problems in computer science. It can be stated as: a graph with vertex (cities), and edge (distance, or travel time etc.). The TSP is categorized in two groups: symmetric travelling salesman problem (STSP) where the distances between two cities equal forward and backward and there are (n !1)!/2 possible solutions. The cost matrix satisfies the triangle inequality whenever cij"Ci k + C k j , for all i,j,k. This is the case of a planar problem for which the vertices are points pi= (xi,yi) in the plane, and cij =. The triangle inequality is satisfied if cii is the length of the shortest path i from j to on G[4]
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