Artificial Bee Colony Algorithm with Proposed Discrete Nearest Neighborhood Algorithm for Discrete Optimization Problems

Abstract

Travelling salesman problem (TSP) is one the problems of NP-complete family, which means finding shortest complete close tour in the graph. This study seeks to solve this problem using Artificial Bee Colony (ABC) Algorithm along with the proposed Discrete Nearest Neighborhood Algorithm (DNNA). DNNA finds shortest path among points by starting from an arbitrary point. In next steps this links will be a guide to make complete tour. In other words the links in partial tours have higher chance to be in the final solution. In order to improve the final solutions of a single created tour, The employee bees’ movement radius has been limited, because of avoidance of long random jump between nodes. To reduce the optimization time of the tours created by the artificial bee colony algorithm, the fixed-radius near neighbor 2-opt algorithm was used as well. In addition, 2 types of scout bee were used for to intensify the probability property of the algorithm. Also, convergence in the probability function of employee bees’ movement was prevented by increasing the number of route-creating tours. The first scout bee applies the proposed DNNA and the secondary scout bee improves the partial tours of employee bees in a probable way. Although Althought the average error of proposed ABC algorithm has been 0.371% higher than best solution of all methods, it could improve the solution of 3 problems with average of 3.305%. The proposed algorithm has been better than basic ABC in all tested problems with average of 0.570%.