In this article, we have introduced an advanced new method of solving a traveling salesman problem (TSP) with the whale optimization algorithm (WOA), and K-means which is a partitioning-based algorithm used in clustering. The whale optimization algorithm first was introduced in 2016 and later used to solve a TSP problem. In the TSP problem, finding the best path, which is the path with the lowest value in the fitness function, has always been difficult and time-consuming. In our algorithm, we want to find the best tour by combining it with K-means which is a clustering method. In other words, we want to divide our problem into smaller parts called clusters, and then we join the clusters based on their distances. To do this, the WOA algorithm, TSP, and K-means must be combined. Separately, the WOA-TSP algorithm which is an unclustered algorithm is also implemented to be compared with the proposed algorithm. The results are shown through some figures and tables, which prove the effectiveness of this new method.

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p>In this study, we compare a cluster-based whale optimization algorithm (WOA) with an uncombined method to find a more optimized solution for a traveling salesman problem (TSP). The main goal is to reduce the time of solving a TSP. First, we solve the TSP with the Whale optimization algorithm, later we solve it with the combined method of solving TSP which uses the clustering method, called BIRCH (balanced iterative reducing and clustering using hierarchies). Birch builds a clustering feature (CF) tree and then applies one of the clustering methods (for ex. K-means) to cluster data. Experiments performed on three datasets show that the convergence time improves by using the combined algorithm.</p></div></div></div>