Abstract
The classical traveling salesman problem(TSP) is simple to state but difficult a problem to solve. TSP seeks to determine the total distance or cost of visiting (n-1) cities or points and returning to the starting city or point. In this research, the Genetic Algorithm (GA) technique is utilized for solving the problem of finding the optimal tour around the nine Niger Delta state capitals in Nigeria which is an example of a traveling salesman problem. The partially mapped(PMX) crossover operator and the inversion mutation operator techniques were employed due to their simplicity. Genetic algorithms are evolutionary techniques used in solving optimization problems according to the survival of the fittest. The method does not provide an optimal exact solution, rather, it gives an approximated result in time. Data required for the tour were obtained from an online google map website where the distances between the state capitals and their coordinates (longitude and latitudes) were obtained. The MATLAB software which is suitable for scientific computations was used in coding the results show that the BB algorithm yielded an optimal tour of 1351km with a cyclic tour of (X3,1), (X1,9), (X9,6), (X6,8), (X8,4), (X4,7), (X7,5), (X5,2), (X2,3) and then (X3,1) after nine (9) iterations. Solving using the genetic algorithm with the four genetic parameters population size(N), maximum generation(G), crossover probability (Pc), and mutation probability(Pn) were used and set to 30; 10; 0.8; and 0.1 respectively yielded an optimal path of (8476125398) which is with an optimal tour of 1124.0KMs. genetic algorithm yielded an improved result.
Highlights
Routing models, according to Pekár et al (2020), are one of the most common discrete and combinatorial optimization problems in practice
The MATLAB software was used in coding the results show that the branch and bound (BB) algorithm yielded an optimal tour of 1351km with a cyclic tour of (X3,1), (X1,9), (X9,6), (X6,8), (X8,4), (X4,7), (X7,5), (X5,2), (X2,3) and (X3,1) in 9 iteration circles
The Traveling Salesman Problem (TSP) is adjudged as the simplest and most popular of routing problems that seeks the smallest total distance of cyclic travel through an N set of points or cities such that each point or city is visited precisely once and the traveler returning to the starting city Nigeria (2021)
Summary
Routing models, according to Pekár et al (2020), are one of the most common discrete and combinatorial optimization problems in practice They are models used in organizing a collection of things like positions, job schedules, towns, places, and so on, into orders or paths that could sometimes form all points into a single sequence or requiring several routes Danusaputro et al (1990). The Traveling Salesman Problem (TSP) is adjudged as the simplest and most popular of routing problems that seeks the smallest total distance of cyclic travel through an N set of points or cities such that each point or city is visited precisely once and the traveler returning to the starting city Nigeria (2021). The tour whose total distance or cost is the least is the optimal solution
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