Research on the Location Selection Problem of Electric Bicycle Battery Exchange Cabinets Based on an Improved Immune Algorithm

Comments 1: In Section 2, the authors review the existing works from the perspective of location selection theory and method, which implies the major contribution of this work in about the method. However, except a simple experiment about comparing algorithms, no further deep results can be found concerning the method.

Response 1: Thank you for pointing this out. We agree with this comment. In Section 2, we review the existing works and propose the theoretical model of location selection with the goal of maximizing rider satisfaction and maximizing battery switch cabinet service capability based on the point demand theory. Therefore, we have revised Section 5 and added the analysis of performance effect of theoretical model on two object functions to the section 5.3, and further discussed the practical significance of the point demand theory. Then, it is supplemented in the abstract and discussion section, emphasizing the effect of the theoretical model.

Comments 2: Section 3.1 presents much description about the associated problems, while the studied location selection problem in this manuscript receives very little attention. Besides, the relationship between these associated problems and the basic problem is not clear. It may be confused for readers to get the reason of such organization.

Response 2: Thanks for your point. We agree. So, we have revised Section 3.1. Before the description of associated problems, we put forward the basic problems of this paper. Combined with Fig. 1, the whole process of solving the basic problems is described, and associated problems involved in each step are mentioned in the process. This leads to four associated problems in this paper, and illustrates their relationship with the basic problem.

Comments 3: The last assumption of " identical energy storage and performance capabilities" in Section 3.2 is not in line with practical scenarios. This issue should be discussed in future research.

Response 3: Thanks for this point. We agree with this comment. We modify the assumption in this part to be “This paper assumes that R is the maximum tolerable service radius for all e-bike riders.”

Comments 4: There are some problems concerning model construction.

(a) Except  and , the other notations are parameters, not variables.

(b) Use different symbols to distinguish  and  .

(c) what is the difference between  and ? It seems that  represents an index, not the number of nodes.

(d) For each case of formula (10), .e.,  takes a value from set , then is fixed, then we cannot sum  by enumerating j from 1 to .

It is so confused for me to understand this model.

Response 4: Thank you for pointing this out. We agree. Therefore, we reconstructed the model. First, parameters and variables were emphasized and distinguished in Table 1 and subsequent descriptions to avoid confused. Then, we use variable   instead of variable   to distinguish between variable  and variable  . We agree with your suggestion to set parameter as the index of parameter  and parameter  as the total. It is also the index of  for the parameter , so in Eq. (10), we traverse j from 1 to J. We divide the two objective functions by the total number of riders to calculate average rider satisfaction and average battery exchange cabinet service capacity. This will avoid confusion for the reader.

Comments 5: The description of the improved immune algorithm in Table 2 is not concise. It is better to describe each part of the method in detail in the manuscript main text. An additional figure illustration is better to help readers understand the idea of the method.

Response 5: Thanks. We agree with this comment. Therefore, according to the flow of immune algorithm in Table 2, we drew the illustration of the improved immune algorithm as shown in Figure 2. The improvement of immune algorithm is emphasized in the figure.

Comments 6: The proposed model is bi-objective. It is very different for solving bi-objective and single-objective problems, especially in evaluating the quality of solutions. However, I do not see anything concerning solving bi-objective problems in the proposed method.

Response 6: Thank you for pointing this out. We agree. We have sorted out the full paper, emphasizing in each part that this paper is a bi-objective problems, and in the example analysis part, we have modified Table 3, which not only shows the comprehensive objective function value, but also the bi-objective functions of rider satisfaction and battery change cabinet service ability respectively, and also analyzes the performance effect of different objective function in the discussion section, so as to avoid confused among readers.

Comments 7: The experiments about the location selection should be designed in a more comprehensive way. The increase of objective value along with the number of cabinets is self-evident. The comparison of two algorithms is insufficient. What is the traditional immune algorithm like? What kind of instance are tested? The part of the whole experiment section is some kind of rough.

Response 7: Thanks. We agree with this comment. Therefore, we reconstructed the content of the experiment and divided it into four parts, including data preprocessing, kernel density analysis, Theoretical model analysis and algorithm comparison. In the data preprocessing part, the source and processing method of data were explained in detail. In the part of data analysis, the performance of point demand theory in location problem is discussed in detail. Finally, we enrich the verification experiment of the algorithm comparison, and compare the accuracy, search accuracy, stability and convergence of the two algorithms through sensitivity analysis and convergence analysis. Two algorithms were run ten times respectively under six different parameter combinations, totaling 2*3*10*2=120 times. It is concluded that the improved immune algorithm is more excellent.

Comments 8: Some minor comments:

a. P590, the word "future" should be initial capital.

b. Usually, the reference is cited closely after the authors' names, if there are.

c. Fig. 5 and 6 are not clear.

Response 8: Thank you for pointing these minor issues out. We agree with these comments. But for comment a, we did not find the word "future" on P590. For comment b, we reviewed references for full texts and cited them closely after the authors' names in Section 2. For comment c, we have redrawn Fig.5 and 6 as Fig.6 and 7 in Section 5, because we have added Fig.2 in new manuscript.

Comments 1: Line 446, the improvement of the traditional immune algorithm is as follows: the introduction of multi-point mutation operator in the mutation process and the addition of guided mutation to the mutation operator.   Why should these two factors be improved?   Please specify the impact of these two factors on the algorithm.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have added the flow chart for immune algorithms in Section 4.2, as shown in Fig. 2. In this figure, the improvement of our immune algorithm is emphasized, and the variation brought by introducing multi-point variation, guided variation and local search is discussed by comparing with the single point variation and small amount variation of the traditional immune algorithm, and the prediction effect of the improved immune algorithm is described.

Comments 2: Line 493, the termination conditions of local search, such as the number of iterations or the improvement degree of the objective function, are not specified in detail and need to be further clarified.

Response 2: Thanks for your point. We agree. So, we added the description of the termination condition, one is to reach the optimal value, and two is to exceed the number of iterations. As soon as one of these conditions is met, the local search terminates.

Comments 3:  Line.498, the specific sources of electric vehicle riding data, such as data collection methods and data contents, are not explained in the paper, the validity and reliability of the data need to be further explained.

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, we reconstructed the experimental part and divided it into four parts, including data preprocessing, kernel density analysis, data analysis, and algorithm comparison. In the data preprocessing, the data source and processing method are expounded.

Comments 4: Line 561, The paper merely contrasts the improved immune algorithm with the traditional one regarding solving speed, stability, and search accuracy, without delving into the particular strengths of the improved algorithm, such as the effectiveness of specific mutation operations or local search strategies.

Response 4: Thank you for pointing this out. We agree with this comment. Therefore, we enrich the verification experiment of the algorithm comparison, and compare the accuracy, search accuracy, stability and convergence of the two algorithms through sensitivity analysis and convergence analysis. Two algorithms were run ten times respectively under six different parameter combinations, totaling 2*3*10*2=120 times. It is concluded that the improved immune algorithm is more excellent, the effectiveness of mutational mutation, guide and local search on the improvement of traditional immune algorithm is also verified.

Comments 1: There is one significant issue, which raises concerns of the Referee. The manuscript presents an improved model, but does not provide an assessment of its quality and reliability. The differences between the previous model and the solution proposed by the authors are minor. Therefore, there is a doubt about the uncertainty of the obtained results. Moreover, the authors presented only calculations for a selected case. When presenting a new computational model, it should be verified on various cases. Otherwise, the claim about the superiority of the proposed model in relation to the previously used one should be questioned. Finding a selected case in which a given algorithm is better than another does not mean that it is more suitable for general use.

Response 1: Thank you for pointing this out. We agree with this comment. We reconstructed the content of the experiment and divided it into four parts, including data preprocessing, kernel density analysis, Theoretical model analysis and algorithm comparison. In the data preprocessing part, the source and processing method of data were explained in detail. In the part of data analysis, the performance of point demand theory in location problem is discussed in detail. Finally, we enrich the verification experiment of the algorithm comparison, and compare the accuracy, search accuracy, stability and convergence of the two algorithms through sensitivity analysis and convergence analysis. Two algorithms were run ten times respectively under six different parameter combinations, totaling 2*3*10*2=120 times. It is concluded that the improved immune algorithm is more excellent.

Comments 2: There are some other issues that need to be addressed before the manuscript can be published in Sustainability:

1. A sentence should not start with a symbol, e.g. instead of r is the demand coefficient (L.299), use The parameter r is the demand coefficient. There are some other similar cases in the manuscript e.g. L.302, L.303, L. 324, etc.

2. Table 1 should be reorganized i.e. split it into two columns: Column 1 – symbol, Column 2 – variable. The sign “=” is unnecessary.

3. Table 2 also require significant changes. Maybe a flowchart would be a better option?

4. The variable parameters for calculations should be gathered in table (L. 520- 525)

5. There are a lot of small editorial issues such as a lack of space near [36] in line 240; h should be replaced with h (L.320); in line 394 and 411 are used unnecessary sign “。”

Response 2: Thank you for pointing these other issues out. We agree with these comments. We have revised these points.

For issue 1, we have checked the full text and avoided the problems of having a symbol at the beginning of the sentence, such as replacing r with The parameter r in the new manuscript in L.315. Also modified other similar cases in the new manuscript e.g. L.316, L.317, L. 319, etc.

For issue 2, we have split Table 1 into two columns in L.433: Column 1 – symbol, Column 2 – variable. And the sign “=” has been removed.

For issue 3, we have supplemented Fig. 2. Improved immune algorithm process to illustrate the flow in Table 2.

For issue 4, we have gathered the variable parameters for calculations in Table 3 (L. 565).

For issue 5, we have solved these small editorial issues, such as the lack of space has been replenished near [36] in line 241; h has been replaced by h (L.336); in line 404 and 421 the unnecessary sign “。” has been removed.