Weiszfeld, tree-seed, and whale optimization algorithms comparison via locating transportation facilities with weightings considering the vulnerability and uncertainty.

Searching for an optimum transportation facility location with emergency equipment and staff is essential for a specific region or a country. In this direction, this study addresses the following problems. First, the performances of the Weiszfeld, tree-seed, and whale optimization algorithms are compared, which is the first of its kind in the literature. Second, a new approach that tests the importance parameters' effectiveness in searching for an optimum transportation facility location with emergency equipment and staff is proposed. The Weiszfeld algorithm finds viable solutions with compact data, but it may not handle big data. In contrast, the flexibility of the tree-seed and whale optimization algorithm is literally an advantage when the number of parameters and variables increases. Therefore, there is a notable need to directly compare those algorithms' performances. If we do, the significance of extending the number of parameters with multiple weightings is appraised. According to the results, the Weiszfeld algorithm can be an almost flexible technique in continuous networks; however, it has reasonable drawbacks with discrete networks, while the tree-seed and whale optimization algorithms fit such conditions. On the other hand, these three methods do not show a fluctuating performance compared to one another based on the locating transportation facilities, and thus they deliver similar performance. Besides, although the value of accuracy is high with the application of the conventional technique Weiszfeld algorithm, it does not provide a significant performance accuracy advantage over the meta-heuristic methods.