Weakness: 1. As I just mentioned, the paper only analyzed, under which cases will the Algorithm 1 converges to permutations as local minima. However, it will be better if the quality of this kind of local minima could be analyzed (e.g. the approximation ratio of these local minima, under certain assumptions). 2. This paper is not very easy to follow. First, many definitions are used before they are defined. For example, on line 59 in Theorem 1, the authors used the definition of "conditionally positive definite function of order 1", which is defined on line 126 in Definition 2. Also, the author used the definition "\epsilon-negative definite" on line 162, which is defined on line 177 in Definition 3. It will be better if the authors could define those important concepts before using them. Second, the introduction is a little bit too long (more than 2.5 pages) and many parts of that are repeated in Section 2 and 3. It might be better to restructure the first 3 sections for a little bit. Third, it will be good if more captions could be added to the figures in the experiment section so that the readers could understand the results more easily. 3. For the description of Theorem 3, from the proof it seems that we need to use Equation 12 as a condition. It will be better if this information is included in the theorem description to avoid confusions (though I know this is mentioned right before the theorem, it is still better to have it in the theorem description). Also, for the constant c_1, it is better to give it an explicit formula in the theorem. Reference: [1] Burkard, R. E., Cela, E., Pardalos, P. M., and Pitsoulis, L. S. (1998). The quadratic assignment problem. In Handbook of combinatorial optimization, pages 1713â1809. Springer.
1. As I just mentioned, the paper only analyzed, under which cases will the Algorithm 1 converges to permutations as local minima. However, it will be better if the quality of this kind of local minima could be analyzed (e.g. the approximation ratio of these local minima, under certain assumptions).