Artificial Bee Colony Algorithm to Solve the Shortest Route Problem with Fuzzy Arc Weight

Abstract

The shortest path problem usually assumes a clear value (crisp) for the weights of each route. However, the crisp weight sometimes ends up ambiguous in practice in the daily life. The number of arc weights is calculated using fuzzy logic, α-cut fuzzy numbers. The Artificial Bee Colony (ABC) algorithm that adopts bee behavior in food searching is used to solve the shortest path problem. This study discusses how to solve numerical problems to find the shortest path using the Artificial Bee Colony algorithm if the arc weights are fuzzy numbers. The algorithm starts with finding the initial solution using Algorithm 1 and then calculated each distance using the sum of α-cut methods. After that, do a local search for each initial solution using the genetic algorithm mutation operator, then searched the distance amount using the same way then compared using the result of distance . The next step was to calculate the fitness value of each solution that would be used to calculate the probability value. The final step was to improve the solution, and an improved solution is said to be a solution if it does not improve again anymore. The calculation process was done repeatedly from the second step to the maximum iteration, i.e. when iteration had reached the limit or the iteration limit fails. Based on the calculation process using ABC algorithm in the case of numerical example, delivery of clean water supply in Gunung Kidul Regency, obtained the shortest route, that is route 1,2,3,5,6 with interval distance equal to 459, 9142.