An intelligent optimization method for highway route selection based on comprehensive weight and TOPSIS.

In order to accurately analyze and evaluate multi-index and multi-route traffic schemes for comparison and selection, we introduce herein a comprehensive weight and an intelligent selection algorithm for traffic scheme optimization to improve upon the shortcomings of common qualitative and quantitative analysis methods. Firstly, we establish an evaluation index system of transportation by traffic scheme considering the factors of technology, ecological environment, social environment, and economy, based on the whole life cycle. Secondly, the comprehensive weight based on subjective and objective factors is constructed. Finally, we establish an optimization method for transportation schemes by using the comprehensive weight and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model. The results show that the evaluation index system based on the whole life cycle is more comprehensive and accurate. The comprehensive weight vector avoids the defects of single weight methods and makes full use of subjective data and expert opinions. The comprehensive weight vector is introduced into the decision-maker's preference coefficient, so that analysts can determine the scheme according to the subjective and objective information and to the required accuracy. This method uses a large number of evaluation groups to evaluate the scheme, and the evaluation results show greater objectivity and efficiency.

Introduction

The selection of highway route schemes directly influences construction costs; construction and operation safety; the length of the construction period; and the costs relating to operation, management, and maintenance. In practical work, a trial-and-error method based on the work experience of designers and on expert evaluation is not time-consuming, but it can easily miss optimal schemes, and this process cannot be evaluated by experts and stakeholders with a large amount of data. For transportation schemes with complex geographical and societal considerations, it is more difficult to adapt this method to the requirements of scheme optimization. Therefore, a new intelligent optimization method is needed to quickly and comprehensively process data from a large number of evaluators and select the optimal scheme.

Research on highway route schemes has been a topic of considerable interest in the field of highway design. Scholars have carried out extensive research in this field, and many meaningful results have been obtained. Gomes [1] studied the multi-criteria ranking of urban transportation system alternatives. Xiong et al. [2] studied the multi-criteria evaluation approach as applied to urban transportation projects. Kang et al. [3] integrated a genetic algorithm into a GIS platform and combined it with geographic information to optimize highway alignment. Kazemi et al. [4] introduced particle swarm optimization (PSO) and proposed a parallel PSO method to find the optimal solution to a highway alignment problem. Ismutulla et al. [5] applied the theory of the gray correlation degree and built an evaluation method for a highway route scheme based on the gray weighted correlation. Luo et al. [6] proposed a fuzzy comprehensive evaluation and selection method based on fuzzy mathematics. Mu et al. [7] introduced a multilevel fuzzy evaluation method to compare and select a highway route scheme based on multilevel fuzzy evaluation theory. Based on AHP and fuzzy comprehensive evaluation, Zhang et al. [8-10] put forward an optimization method for highway route schemes in the permafrost region of the Qinghai–Tibet Plateau. Sarı and Sen [11] proposed a design for a minimum-cost path algorithm for highway route selection.

Although the evaluation and selection methods [12-16] for highway route schemes can determine a proper route to a certain extent, their evaluation index systems focus on economic and technical indexes during construction and do not completely consider construction costs and environmental influences over the full life cycle. In addition, each subjective or objective weighting method is applied only to assign weights to indexes, which ignores the influences of objective factors, evaluators’ opinions, and analyzers’ preferences on indexes. As a result, the highway route scheme determined is not optimal [17, 18]. In addition, without the help of computers and intelligent technology, these methods cannot adapt to evaluation by a large group, and no feasible algorithm is applied to scheme optimization.

Many MCDM models can be used in optimal selection, such as RAFSI, MABAC, MAIRCA, VIKOR methods [19-22]. This method can make full use of the information of the original data, and its results can accurately reflect the gap between the evaluation schemes. Considering that Similarity to an Ideal Solution (TOPSIS) method is simpler, has no strict restrictions on data distribution and sample size, and is more suitable for internal sorting of sample data, this paper adopts TOPSIS method.On this basis, to make traffic optimization more efficient and scientific by means of big data, the existing research deficiencies and the objective needs of scheme selection should be considered as a whole. This paper proposes a solution that considers the full life cycle as a measurement state and builds an evaluation index system for a route scheme with comprehensive weight as an instrument to comprehensively select the weight for each index, introduces the Technique for Order Preference by TOPSIS model, and selects the optimal scheme from multiple schemes algorithmically. The AHP is effectively combined with the entropy weight method to determine the index weight, which avoids the defects of the single weighting method and takes into consideration the evaluator’s opinions, the actual conditions of the highway, and the analyzer’s preferences for setting the weights of the evaluation index. The selection of the route scheme is consistent with the calculation method for an ideal solution. The TOPSIS method was applied to evaluate a highway route scheme and determine the optimal route scheme based on the final grade.

Materials and methods

Evaluation index system for highway route schemes

Selecting the evaluation index system

When evaluating a highway route scheme, it is necessary to build the evaluation index system first. At present, the commonly used index system generally uses the economic, technical, and environmental indicators during the construction period [11, 23–28]. It does not consider safety factors, and it lacks indicators of maintenance and management costs during the operation period; this cannot accurately and comprehensively reflect the scheme. In order to comprehensively consider the indicators of the scheme, we used the AHP to analyze factors influencing the scheme and built a full-life-cycle index system for highways that considers technology, the ecological environment, the social environment, and engineering economy (see Table 1).

Table 1

Evaluation index system for a highway route scheme.

Target layer	Evaluation layer	Operation layer		Classification
Evaluation index sytem for schemes	Technical indexes B1	C11	Route length	Quantitative-
		C12	Minimum curve of horizontal curve	Qualitative-
		C13	Operating speed	Quantitative
		C14	Average longitudinal slope	Quantitative-
		C15	Length of bridge	Quantitative-
		C16	Length of tunnel	Quantitative-
		C17	Coordination of average longitudinal slope	Qualitative+
		C18	Highway capacity	Qualitative+
	Ecological environment indexes B2	C21	Engineering geology	Qualitative+
		C22	Influences on sensitive environmental areas	Qualitative+
		C23	Capacity to resist natural disasters during operation	Qualitative+
		C24	Influences on mineral resources	Qualitative+
		C25	Safety risks during construction	Qualitative+
	Social environment indexes B3	C31	Land acquisition	Quantitative-
		C32	Buildings to be demolished	Qualitative+
		C33	Coordination with transport network in region	Qualitative+
		C34	Coordination with planning for surrounding towns	Quantitative-
	Economic indexes B4	C41	Construction cost	Quantitative-
		C42	Operation, management, and maintenance costs	Quantitative-
		C43	Operation costs of vehicles	Quantitative-
		C44	Construction period	Qualitative+
		C45	Social and economic effect	Qualitative+

In a specific scheme, all or some of the indicators can be selected according to the characteristics of the project, and indicators can be added as required.

Indexes can be divided into qualitative indexes and quantitative indexes based on their classification methods. According to trend, they can be divided into positive and negative categories; for a positive index (marked with “+”), a scheme will be more valuable when it is larger, and for a negative index (marked with “-”), a scheme will be more valuable when it is smaller.

Quantitative indexes

Quantitative indexes are analyzed according to their corresponding values. If there are m evaluation schemes and n quantitative indexes, and each scheme has a quantitative value B for each quantitative index (e.g., scheme length or construction costs), then

For an index with a negative tendency, positive processing (similar to a tendency) [29] is required:

As an example, take three design schemes that were formulated for a certain highway with construction costs (CNY 100 million) of

Qualitative indexes

Qualitative indexes are obtained from fuzzy classifications in the data. The fuzzy classifications have nine levels each: excellent, good, medium, bad, and poor, and large, general, and small. The evaluation scale used is the (1/9, 9) scale method.

Weight vectors of the index system

By getting the score of each index according to the rating method of the evaluators and normalizing the weight of each index [30], subjective randomness and preference can be inferred to a certain extent; this is called the subjective weight. Objective weight is calculated from quantitative indexes. To consider an evaluator’s subjective perception of indexes and objective information among indexes, as well as an analyzer’s preferences, this paper introduces a new method for determining weights, i.e., a comprehensive weight method.

Calculating the subjective weight of an index

The subjective weight is calculated via the analytic hierarchy process (AHP) [31], which is scored by the evaluators according to laws, regulations, experience, and interests. The steps are as follows.

Step 1: Create the weight judgment matrix.

A hierarchy model is established to compare the indexes of the criterion layer, and the relative importance of the indexes is obtained. The judgment matrix is constructed by the (1/9, 9) scale method. See Table 2 for the general form of the judgment matrix.

Table 2

General form of the judgment matrix.

index	F 1 k	…	F j k	…	F n k
F 1 k	f 11 k	…	f 1j k	…	f 1n k
…	…	…	…	…	…
F i k	f i1 k	…	f ij k		f in k
…	…	…	…	…	…
F n k	f n1 k		f nj k		f nn k

In Table 2, h is the total number of evaluators; k denotes the kth evaluator; n is the total number of indicators in the criteria layer; F and F are the ith and jth indicators of the kth evaluator in the criteria layer, respectively; and f is the importance of indicator F compared with indicator F. The value is determined according to the (1/9, 9) scale method by each evaluator.

Step 2: Calculate the relative weight of each factor at each level.

According to the judgment matrix, the eigenvalues and the maximum eigenvalues of each factor are calculated by the square root method.

Here,

M is the row element product of the row in which the i index of the k evaluator in the judgment matrix is located;

is the relative weight of after normalization;

η is the eigenvector;

is the maximum eigenvalue.

Step 3: Calculate the consistency index.

To ensure that a weight is reasonable, it is necessary to check the consistency of each judgment matrix to determine whether it has satisfactory consistency. If it does not, the judgment matrix should be modified until it meets the consistency requirements. The formula for checking consistency is as follows:

where

K is the consistency index;

G is the random consistency ratio;

E is the order of the judgment matrix;

R is the random consistency index corresponding to the order of the judgment matrix.

Step 4: Find the subjective weight vector.

From the weight and the average social impact weight of each evaluation, the subjective weight can be calculated as follows: where , η ≥ 0(j = 1,2,…,n).

Calculating the objective weight of an index

Information entropy is used for finding the objective weight. The data in this method are obtained from a numerical analysis of the highway route scheme evaluation index system.

Step 1: Generate the decision matrix. If there are m evaluation schemes and n evaluation indexes, then d (i = 1, 2, …,m; j = 1, 2, …,n), and the index weight matrix D can be expressed as

Step 2: Normalize the decision matrix. To eliminate the influences of each evaluation index on the evaluation of the route scheme due to the different dimensions of each evaluation index, normalization is required. In normalization, a decision matrix D generates a standard matrix V = (v). The normalized value is found as follows:

Step 3: Calculate the weight. If the feature weight of the i evaluation object is P under the j index, then

Step 4: Calculate the entropy e of the j index:

Step 5: Calculate the coefficient of difference d for the j index. For a certain index d, the smaller the difference v is, the larger d will be. When the values of the j indexes for each evaluated object are equal, then e = e and d will be

Step 6: Calculate the entropy weight of each index:

where ≥0 (j = 1, 2, …,n).

Comprehensive weight

To consider an evaluator’s subjective perception of indexes and objective information among indexes, as well as an analyzer’s preferences, we introduce a new method for determining weights, i.e., a comprehensive weight method.

If the comprehensive weight of each index is expressed as where , ω ≥ 0 (j = 1, 2, …, m), z is the evaluation matrix after standardization, then the comprehensive weighted score of a scheme is

To both give consideration to subjective preference (for a subjective or objective weighting method) and make full use of the information provided by the subjective weighting method and the objective weighting method, and thereby achieve unity of the subjective and objective methods, the following optimization decision-making model is established: where 0 ≤ ρ ≤ 1 reflects the decision-maker’s preference for subjective weight, named preference coefficient. The higher the value of ρ is the decision maker prefer subjective weight.

Theorem 1 (S1 Appendix): If (j = 1, 2, …, n), then the optimization formula (15) has a unique solution, which is

TOPSIS evaluation model

Many methods can be used in optimal selection, such as TOPSIS、LBWA [32], FUCOM [33] or BWM models. However, considering that TOPSIS is simpler and more suitable for internal sorting of sample data, this paper adopts TOPSIS. TOPSIS [34, 35] refers to the technique for order preference by similarity to an ideal solution, the basic concept of which is to determine the optimal solution and the worst solution for a normalized original data matrix, then calculate the distance between the evaluated solution and the optimal solution and the worst solution, obtain the nearness degree between the evaluated solution and the optimal solution, and, on this basis, assess the advantages and disadvantages of each evaluated object. This method is widely used in multi-objective scheme selection, such as for highways, electric power, etc. [17, 36–39].

Step 1: If there are n evaluation objects and m evaluation indexes, then we can obtain an m×n initial judgment matrix V:

Step 2: The dimension of each index may be different, so that decision matrix should be normalized:

Where

Step 3: Calculate the weight vector of each index from Eq (16) and generate a weighted judgment matrix.

Step 4: Calculate the positive and negative ideal solutions of the evaluated targets according to the weighted judgment matrix.

The positive ideal solution is :

The negative ideal solution is :

where

j+ refers to the benefit index;

j− refers to the cost index.

Step 5: Calculate the Euclidean distance between each target value and the ideal value, .

Step 6: Calculate the relative degree of closeness of each target, C+.

Step 7: Sort the targets based on the relative degree of closeness and generate the decision criteria. When the C+ value approaches 1, the evaluation object becomes closer to the positive ideal solution.

Results

Highway route scheme optimization algorithm

First, the indicator system of the highway route scheme can be constructed according to the characteristics of the project. All or some of the indicators in Table 1 can be selected, and some indicators can be added according to the characteristics of the project. The qualitative indexes and quantitative indexes in the index system are processed to obtain quantitative and positive index data and to build the initial judgment matrix.

Second, the subjective weight and objective weight are calculated.

Thirdly, the decision maker decided the preference coefficient and calculates the comprehensive weight.

Finally, the TOPSIS model is used to calculate the relative closeness of each scheme, and the optimal scheme is obtained (Fig 1).

Fig 1

The highway route scheme optimization algorithm.

Route scheme selection automation

Highway route optimization algorithm involves a lot of calculation, especially when the number of experts and stakeholders is large. Therefore, it is necessary to use computer to calculate quickly to obtain the optimal scheme (Fig 2).

Fig 2

Scheme optimization process.

Discussion and empirical research

The intelligent optimization method proposed in this paper establishes an index system based on the whole life cycle, which is comprehensive and avoids the adverse impact of incomplete index system on the results. This method takes into account both subjective weight and objective weight, and the two weights are calculated independently. At the same time, in order to consider the focus of decision-makers, preference coefficient is introduced. This method uses computer technology, can adapt to a large number of evaluation population, and can quickly obtain the best scheme after evaluation. It can not only be used in highway scheme selection, but also can be used in other multi-objective scheme selection.

We took the route scheme for a highway in Tibet as an example for evaluation and comparison and obtained the optimal scheme through calculation. The length of the corridor from the Lalangqu to Zhagongqu is approximately 12 km, and it ascends the Xuegula mountain. Due to the complicated topography and geology of the area, a large average longitudinal slope, and a high proportion of bridges and tunnels, three schemes were formulated for comparison. Fig 3 shows the comparison and selection of highway route schemes.

Fig 3

Highway route plan.

Step 1: We obtained the index system data (the qualitative indexes and the quantitative indexes) of a multi-index highway route scheme, and then we built a judgment matrix. See Table 3 for the indexes.

Table 3

Evaluation indexes for the program.

Target layer	Evaluation layer	S1	S2	S3
Technical indexes	C11	11.21	10.64	10.80
	C12	600/2	700/2	700/1
	C13	98.4	102.4	103.7
	C14	2.7/3.4	3.6/1.5	3.01/1.15
	C15	2013/7	1767/8	1541/7
	C16	0	4059.5/3	3532/2
	C17	Good	Excellent	Good
	C18	Good	Excellent	Excellent
Ecological environment indexes	C21	Qualified	Average	Average
	C22	Qualified	Good	Good
	C23	Qualified	Good	Good
	C24	Good	Average	Poor
	C25	Good	Poor	Fair
Social environment indexes	C31	833.4	742.8	753.5
	C32	2470	1110	1470
	C33	Good	Average	Average
	C34	Good	Average	Average
Economic indexes	C41	132073	141440	147796
	C42	172	247	235
	C43	2454	2330	2365
	C44	24	38	34
	C45	Good	Excellent	Excellent

Step 2: Twenty-three evaluators, comprising 7 experts and 16 stakeholders, scored the weight of each evaluation index. We calculated the comprehensive weight according to formulas (5), (12), and (16), as shown in Table 4.

Table 4

Weight vectors.

B	C	η	μ	ω
B1- 0.2604	C11	0.0537	0.0407	0.0485
	C12	0.0244	0.0260	0.0251
	C13	0.0197	0.0228	0.0209
	C14	0.0337	0.0326	0.0332
	C15	0.0332	0.0407	0.0362
	C16	0.0429	0.0472	0.0446
	C17	0.0227	0.0212	0.0221
	C18	0.0301	0.0293	0.0298
B2-0.2084	C21	0.0951	0.0875	0.0921
	C22	0.0217	0.0208	0.0214
	C23	0.0326	0.0292	0.0312
	C24	0.0218	0.0329	0.0263
	C25	0.0372	0.0379	0.0375
B3-0.1676	C31	0.0475	0.0629	0.0536
	C32	0.0623	0.0796	0.0692
	C33	0.0241	0.0084	0.0178
	C34	0.0337	0.0168	0.0269
B4-0.3636	C41	0.1717	0.1818	0.1757
	C42	0.0553	0.0346	0.0470
	C43	0.0427	0.0327	0.0387
	C44	0.0313	0.0217	0.0275
	C45	0.0626	0.0928	0.0747

According to the decision-maker’s preference for qualitative and quantitative indexes, the preference coefficient ρ was 0.6.

Step 3: We normalized the judgment matrix and used the calculated comprehensive weight vector to build a weighted decision matrix. See Table 5 for the results.

Table 5

Comprehensive weight vector of the judgement matrix.

C	S1	S2	S3
C11	0.94	1	0.98
C12	0.92	0.94	1
C13	0.94	0.98	1
C14	1	0.75	0.89
C15	0.76	0.87	1
C16	1	0.35	0.41
C17	0.91	1	0.92
C18	0.96	1	0.99
C21	0.46	0.92	1
C22	0.64	1	0.95
C23	1	0.44	0.35
C24	0.46	0.92	1
C25	1	0.12	0.26
C31	0.89	1	0.98
C32	0.44	1	0.75
C33	1	0.76	0.64
C34	1	0.64	0.71
C41	1	0.84	0.81
C42	1	0.69	0.73
C43	0.94	1	0.98
C44	1	0.42	0.69
C45	0.86	1	0.94

Step 4: We calculated the relative degree of closeness between each scheme and the ideal solution. See Table 6 for the results.

Table 6

Evaluation results of the relative degree of closeness.

PROG	S1	S2	S3
Relative degree of closeness	0.853	0.841	0.849

The degrees of closeness are in the order C > C > C, so scheme S1 is the best, followed by scheme S3 and scheme S2. The evaluation results are completely consistent with on-site conditions.

In order to analyze the sensitivity of preference coefficient, we calculated the closeness under different preference coefficients, as shown in Fig 4.

Fig 4

Sensitivity analysis chart of the preference coefficient.

It can be seen from Fig 4 that each scheme has a different closeness with different preference coefficient, and the optimal scheme is finally selected. S1 with high closeness shall be preferred, when ρ ∈ (0,0.651). S2 with high closeness shall be preferred, when ρ∈ (0.0651,1). It shows that the preference coefficient can affect and determine the conclusion of multi-objective scheme selection, that is an important sensitive factor in multi-objective scheme selection.

The CS1 inversly decreased gradually along with the increase of ρ. It suggests that the main reason was that S1 has small scale, low cost and obvious advantages in overall objective indicators, but it covers a lot of land and has a long route, which leads to the low score of the evaluators. Along with ρ increase, C and C are increasing trends, but the increase of S2 is greater, indicating that S2 is right ρ More sensitive. The analysis shows that the main reason is that although S2 tunnel is long, the route mileage is short, avoiding basic farmland, the cost and technical indicators are higher than S3, resulting in higher scores for the evaluators.

There are fewer human factors involved in the objective weight, and more evaluators in the objective weight. Considering from the perspective of economy, technology and stakeholders, the two weight schemes have their own advantages and disadvantages. Decision makers have a deeper understanding of the project and give preference factors based on the overall judgment of subjective and objective factors, considering their own interests, the environment during the construction period and the quality of evaluators. Decision makers can not easily judge the impact of preference factors on project conclusions, which not only considers the subjective and objective indicators and the decision-makers’ evaluation of subjective and objective indicators, but also avoids the decision-makers from giving intuitive conclusions, which is conducive to ensuring the scientificity of scheme selection. If construction cost C41, operation, management, and maintenance costs C42 and vehicle operation costs C43 are ignored, then the relative degrees of closeness are in the order C > C > C (Table 7). Therefore, the construction of the indexes directly influences the evaluation results.

Table 7

Evaluation results of the relative degree of closeness.

PROG	S1	S2	S3
Relative degree of closeness	0.841	0.842	0.850

Through the above analysis and calculation, S3 is the optimal scheme. At the same time, the expert scoring method and the general comprehensive weight method are compared. This method is more in line with the expectations of the construction unit and experts.

Conclusions

In this paper, we discussed the limitations of highway route selection. To address these limitations, we built an evaluation index system for highway route schemes based on the full life cycle of the route and proposed a new weight calculation method that uses the preference of decision-makers and comprehensively calculates the subjective weight and objective weight. We used a comprehensive weight vector and the TOPSIS model to build an evaluation system for a highway route scheme, and we verified the validity of this method of scheme evaluation using examples. The following conclusions can be drawn:

The construction of evaluation indexes directly influences the results of scheme evaluation. When subsequent operations, management, and maintenance indexes are included based on the full life cycle, the evaluation results are more accurate.

The comprehensive weight vector can overcome the defects of the single weight method; it not only makes use of objective data, but also fully considers experts’ opinions. The comprehensive weight vector increases the preference coefficient ρ, which is essential different from existing other comprehensive weight methods. The preference coefficient ρ can be determined by the accuracy of subjective and objective information and preference. When the decision-maker obtains the subjective weight and objective weight, through comprehensive analysis of the project, a preference coefficient from the perspective of the interests of the decision-maker is proposed, which can better serve the decision-maker.

The evaluation results for the selected route scheme based on the comprehensive weight model with TOPSIS were basically consistent with on-site conditions; therefore, the method is feasible and valid for comprehensively evaluating a route scheme.

Intelligent computing can be used to form an evaluation of the scheme by a large number of evaluation groups (including experts, stakeholders, etc.), and the evaluation results are more objective. Intelligent Optimization Method can not only be used in highway scheme selection, but also can be used in other multi-objective scheme selection.

In future work, we will further study intelligent optimization methods of highway schemes. For example, we will study the method of selecting project indicators, differentiate the weight calculation methods of experts and stakeholders, and explore whether there is a better evaluation model that could replace TOPSIS.In addition, we will assess the usability of the approach for domain experts. Our ultimate objective is to use our scheme optimization approach for automated incident reporting, which can be made intelligent. The system only needs to input the index of the scheme and the score of the evaluation group, and the preference coefficient of the decision-maker can be used to automatically obtain the optimal scheme. To achieve this aim, we will use examples of potential selected schemes to evaluate the applicability of this method and to identify monitoring activities that may be useful in detecting or investigating the selection of these schemes.

Theorem 1: If (j = 1, 2, …, n), then the optimization formula (15) has a unique solution.

(DOCX)

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Index system data, scored the weight of 23 evaluators.

(XLSX)

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6 May 2021

PONE-D-21-10954

An Intelligent Optimization Method for Highway Route Selection based on Comprehensive weight and TOPSIS

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NASA Earth Observatory (public domain): http://earthobservatory.nasa.gov/

Landsat: http://landsat.visibleearth.nasa.gov/

USGS EROS (Earth Resources Observatory and Science (EROS) Center) (public domain): http://eros.usgs.gov/#

Natural Earth (public domain): http://www.naturalearthdata.com/

4. Please upload a copy of Figure 3, to which you refer in your text on page 10. If the figure is no longer to be included as part of the submission please remove all reference to it within the text.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

Reviewer #3: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Greetings,

The paper needs to be corrected to make it better.

The results of the research should be in the abstract. Materials and Methods should be corrected for example see the following papers:

Pamucar, D., & Ćirović, G. (2018). Vehicle route selection with an adaptive neuro fuzzy inference system in uncertainty conditions. Decision Making: Applications in Management and Engineering, 1 (1), 13-37.

Liu, F., Aiwu, G., Lukovac, V., & Vukic, M. (2018). A multicriteria model for the selection of the transport service provider: A single valued neutrosophic DEMATEL multicriteria model. Decision Making: Applications in Management and Engineering, 1 (2), 121-130.

Noureddine, M., & Ristic, M. (2019). Route planning for hazardous materials transportation: Multicriteria decision making approach. Decision Making: Applications in Management and Engineering, 2 (1), 66-85.

Blagojević, A., Vesković, S., Kasalica, S., Gojić, A., & Allamani, A. (2020). The application of the fuzzy AHP and DEA for measuring the efficiency of freight transport railway undertakings. Operational Research in Engineering Sciences: Theory and Applications, 3 (2), 1-23.

Kasalica, S., Obradović, M., Blagojević, A., Jeremić, D., & Vuković, M. (2020). Models for ranking railway crossings for safety improvement. Operational Research in Engineering Sciences: Theory and Applications, 3 (3), 84-100.

Algorithms cannot be results. Algorithms are a paper methodology. Correct this and better explain the methodology. The selection Discussion and empirical research is debatable. First is the Case study, then the results. There is no discussion. The results are incomplete. One result must be obtained with the TOPSIS method, and then a sensitivity analysis must be performed, in order to exclude some criteria, etc. It is necessary to make scenarios and then discuss all these results.

The conclusion should include the most important results, research limits and guidelines for future research.

Adjust the paper according to the guidelines.

Reviewer #2: First of all, the paper “An Intelligent Optimization Method for Highway Route Selection based on Comprehensive weight and TOPSIS” aims and scope match those of PLOS ONE, so the paper is adequate for this journal. This paper presents an application of TOPSIS for route selection selection. However based on my opinion it needs substantial improvements to be considered for publication in PLOS ONE. I would suggest a series of changes that in my opinion would improve the paper, in special for the reader.

- I suggest the authors to improve the introduction section. Authors should better highlight the objective of their work and to what extent it contributes to close a gap in the existing literature and/or practice. What is the innovative value of the contribution proposed by the authors?

- In introduction section authors should provide more information about existing MCDM models used in the field and their benefits/weaknesses.

- Why you have used TOPSIS method? Why not RAFSI, MABAC, MAIRCA, VIKOR methdos? This should be discussed. The authors need to discuss their contributions compared to those in related papers. The authors must clearly discuss the significance of the research problem in the first section.

- Add separate literature review section. You should provide more recent references published in last two-three years. Remove references published before 2017.

- The authors should explain why they insist in practically using the Comprehensive weight model. Why not LBWA, FUCOM or BWM models?

- You should provide step by step calculations for provided methodology, especially Comprehensive weight model. You should explain in detail this methodology.

- Explain in more details in the data used in the case study, the data for the testing, the criterion for the accuracy, and others to claim these points.

- Validation section is missing. How we can judge about these results? Comparisons with existing algorithms from the literature is missing.

- Discussion section is missing. How should we know about the quality of these solutions? Could you compare these results with some existing approaches in literature? The improvement must be discussed.

- The conclusion section seems to rush to the end. The authors will have to demonstrate the impact and insights of the research. The authors need to clearly provide several solid future research directions. Clearly state your unique research contributions in the conclusion section. Add limitations of the model. No bullets should be used in your conclusion section.

Reviewer #3: This paper constructed a comprehensive weight and an intelligent selection algorithm for traffic scheme optimization. Firstly, the authors established an evaluation index system considering the factors of the whole of life cycle. Secondly, the AHP method is used to determine the index weight, and the authors proposed the comprehensive weight algorithm based on subjective and objective factors. Finally, the TOPSIS method is used to rank the schemes. An application illustrates the effectiveness of the proposed method. However, there are some points the author needs to consider as follows:

1. It is suggested that the authors introduce the organization of this paper in the end of introduction.

2. Page 9, line 5, “and each scheme m has a quantitative value B_{ij}” should be “and each scheme has a quantitative value b_{ij} for each quantitative index”.

3. Page 10, line 16, “and f_i^k is the importance of indicator F_i^k compared with indicator F_j^k” should be “and f_{ij}^k is the importance of indicator F_i^k compared with indicator F_j^k”.

4. Page 11, formula (7), what does the symbols “x_{ij}, max(x_j), min(x_j)” stand for? Maybe they are “d_{ij}”, “max_j(d_{ij})” and “min_j(d_{ij})”.

5. Page 12, formula (14), what does the symbols “f_i” and “z_{ij}” stand for?

6. Page 12, formula (15), “where \\rho reflects the decision-maker’s preference for objective or subjective weight.” Does it reflect the preference of decision makers for objective or subjective weights here? The higher the value of \\rho is, does the decision maker prefer subjective weight or objective weight?

7. Page 12, in theorem 1, “formula (10)” should be “formula (15)”.

8. Page 13, in step 3, “formula (18)” should be “formula (16)”.

9. It is suggested that the authors compare the proposed comprehensive weight method with existing comprehensive weight methods.

10. It is suggested that the authors add a sensitivity analysis with variable \\rho.

Based on these comments, I suggest MAJOR REVISIONS before its acceptance.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

5 Nov 2021

Response to Journal Requirements

Point: 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and（1）

Response: We revised according to requirements.

Point: 2. Please amend your list of authors on the manuscript to ensure that each author is linked to an affiliation. Authors’ affiliations should reflect the institution where the work was done (if authors moved subsequently, you can also list the new affiliation stating “current affiliation:….” as necessary).

Response: We have revised the Authors’ affiliations. We listed Professor Cao Zhen of Xi'an University of architecture and technology as the author and considered his contribution in Major Revision.

Point: 3. We note that [Figure 2] in your submission contain [map] images which may be copyrighted. All PLOS content is published under the Creative Commons Attribution License (CC BY 4.0), which means that the manuscript, images, and Supporting Information files will be freely available online, and any third party is permitted to access, download, copy, distribute, and use these materials in any way, even commercially, with proper attribution. For these reasons, we cannot publish previously copyrighted maps or satellite images created using proprietary data, such as Google software (Google Maps, Street View, and Earth). For more information, see our copyright guidelines: http://journals.plos.org/plosone/s/licenses-and-copyright.

Response: We measured the topographic data and processed the topographic map in three dimensions and contour color separation. The graphic is made by us and there is no copyright problem.

Point: 3.2. If you are unable to obtain permission from the original copyright holder to publish these figures under the CC BY 4.0 license or if the copyright holder’s requirements are incompatible with the CC BY 4.0 license, please either i) remove the figure or ii) supply a replacement figure that complies with the CC BY 4.0 license. Please check copyright information on all replacement figures and update the figure caption with source information. If applicable, please specify in the figure caption text when a figure is similar but not identical to the original image and is therefore for illustrative purposes only.

The following resources for replacing copyrighted map figures may be helpful:

USGS National Map Viewer (public domain): http://viewer.nationalmap.gov/viewer/

The Gateway to Astronaut Photography of Earth (public domain): http://eol.jsc.nasa.gov/sseop/clickmap/

Maps at the CIA (public domain): https://www.cia.gov/library/publications/the-world-factbook/index.html and https://www.cia.gov/library/publications/cia-maps-publications/index.html

NASA Earth Observatory (public domain): http://earthobservatory.nasa.gov/

Landsat: http://landsat.visibleearth.nasa.gov/

USGS EROS (Earth Resources Observatory and Science (EROS) Center) (public domain): http://eros.usgs.gov/#

Natural Earth (public domain): http://www.naturalearthdata.com/

Response: we have measured the topographic data along the line and processed the topographic map in three dimensions and contour color separation. The graphic is made by ourselves and there is no copyright problem.

Point: 4. Please upload a copy of Figure 3, to which you refer in your text on page 10. If the figure is no longer to be included as part of the submission please remove all reference to it within the text.

Response: We had upload a copy of Figure 3.

Response to Reviewer’s Comments

Reviewer #1:

Point 1: The results of the research should be in the abstract. Materials and Methods should be corrected for example see the following papers:

We revised the reference documents and improved the materials and methods.

Pamucar, D., & Ćirović, G. (2018). Vehicle route selection with an adaptive neuro fuzzy inference system in uncertainty conditions. Decision Making: Applications in Management and Engineering, 1 (1), 13-37.

Liu, F., Aiwu, G., Lukovac, V., & Vukic, M. (2018). A multicriteria model for the selection of the transport service provider: A single valued neutrosophic DEMATEL multicriteria model. Decision Making: Applications in Management and Engineering, 1 (2), 121-130.

Noureddine, M., & Ristic, M. (2019). Route planning for hazardous materials transportation: Multicriteria decision making approach. Decision Making: Applications in Management and Engineering, 2 (1), 66-85.

Blagojević, A., Vesković, S., Kasalica, S., Gojić, A., & Allamani, A. (2020). The application of the fuzzy AHP and DEA for measuring the efficiency of freight transport railway undertakings. Operational Research in Engineering Sciences: Theory and Applications, 3 (2), 1-23.

Kasalica, S., Obradović, M., Blagojević, A., Jeremić, D., & Vuković, M. (2020). Models for ranking railway crossings for safety improvement. Operational Research in Engineering Sciences: Theory and Applications, 3 (3), 84-100.

Response：We revised the References and improved the Materials and Methods.

Point 2: Algorithms cannot be results. Algorithms are a paper methodology. Correct this and better explain the methodology. The selection Discussion and empirical research is debatable. First is the Case study, then the results. There is no discussion. The results are incomplete. One result must be obtained with the TOPSIS method, and then a sensitivity analysis must be performed, in order to exclude some criteria, etc. It is necessary to make scenarios and then discuss all these results.

Response：We have updated the Discussion and empirical research. The sensitivity analysis with variable Rho is added base on the comments. After analysis, the variable Rho directly affects the closeness and project.

Point 3: The conclusion should include the most important results, research limits and guidelines for future research.

Response：We rewrote the conclusions and added research results, research limitations and guidelines for future research.

Point 4: Adjust the paper according to the guidelines.

Response：Revised according to comments.

Reviewer #2:

Point 1: I suggest the authors to improve the introduction section. Authors should better highlight the objective of their work and to what extent it contributes to close a gap in the existing literature and/or practice. What is the innovative value of the contribution proposed by the authors?

Response：We rewrote the Introductions, highlight the objectives of previous work and the extent to which it contributes to bridging gaps in existing literature and practice.

Point 2: In introduction section authors should provide more information about existing MCDM models used in the field and their benefits/weaknesses.

Response：Revised according to comments.

Point 3: Why you have used TOPSIS method? Why not RAFSI, MABAC, MAIRCA, VIKOR methdos? This should be discussed. The authors need to discuss their contributions compared to those in related papers. The authors must clearly discuss the significance of the research problem in the first section.

Response：Revised according to comments. It is supplemented in Introduction.

Point 4: Add separate literature review section. You should provide more recent references published in last two-three years. Remove references published before 2017.

Response：Revised according to comments. Several references have been added and removed some references published before 2017.

Point 5: The authors should explain why they insist in practically using the Comprehensive weight model. Why not LBWA, FUCOM or BWM models?

Response：Revised according to comments. It is supplemented in TOPSIS Evaluation Model. LBWA, FUCOM or BWM models can also be used. However, considering that TOPSIS is simpler and can make full use of the existing data, it is more suitable for internal sorting of sample data, this paper adopts TOPSIS.

Point 6: You should provide step by step calculations for provided methodology, especially Comprehensive weight model. You should explain in detail this methodology.

Response：In this paper, Materials and Methods are the whole process of calculation, which is proved in Appendix A. We also added the explanation of preference coefficient according to the Comments.

Point 7: Explain in more details in the data used in the case study, the data for the testing, the criterion for the accuracy, and others to claim these points.

Response：Revised according to comments. It is supplemented in Discussion and empirical research.

Point 8: Validation section is missing. How we can judge about these results? Comparisons with existing algorithms from the literature is missing.

Response：Revised according to comments. The comprehensive weight vector increases the preference coefficient ρ, which is essential different from existing other comprehensive weight methods. T

Point 9: Discussion section is missing. How should we know about the quality of these solutions? Could you compare these results with some existing approaches in literature? The improvement must be discussed.

Response：Revised according to comments. The comprehensive weight vector increases the preference coefficient ρ, which is essential different from existing other comprehensive weight methods. The preference coefficient ρ which can be determined by the accuracy of subjective and objective information and preference. When the decision-maker obtains the subjective weight and objective weight, through comprehensive analysis of the project, a preference coefficient from the perspective of the interests of the decision-maker is proposed, which can better serve the decision-maker. Intelligent computing can be used to form an evaluation of the scheme by a large number of evaluation groups (including experts, stakeholders, etc.), and the evaluation results are more objective.

Point 10: The conclusion section seems to rush to the end. The authors will have to demonstrate the impact and insights of the research. The authors need to clearly provide several solid future research directions. Clearly state your unique research contributions in the conclusion section. Add limitations of the model. No bullets should be used in your conclusion section.

Response：Revised according to comments.

Reviewer #3:

Point: 1.It is suggested that the authors introduce the organization of this paper in the end of introduction.

Response：Revised according to comments.

Point: 2. Page 9, line 5, “and each scheme m has a quantitative value B_{ij}” should be “and each scheme has a quantitative value b_{ij} for each quantitative index”.

Response: We have modified for “and each scheme has a quantitative value Bij for each quantitative index” ( Line 24 ).

Point: 3. Page 10, line 16, “and f_i^k is the importance of indicator F_i^k compared with indicator F_j^k” should be “and f_{ij}^k is the importance of indicator F_i^k compared with indicator F_j^k”.

Response: We have modified for “and f_{ij}^k is the importance of indicator F_i^k compared with indicator F_j^k”.” ( Line 24 ).

Point: 4. Page 11, formula (7), what does the symbols “x_{ij}, max(x_j), min(x_j)” stand for? Maybe they are “d_{ij}”, “max_j(d_{ij})” and “min_j(d_{ij})”.

Response : We have modified, “xij, max(xj), min(xj)” are “dij”, “max(dj)” and “min(dj)”

Point: 5. Page 12, formula (14), what does the symbols “f_i” and “z_{ij}” stand for?

Response : fi is comprehensive weighted score, is the evaluation matrix after standardization.

Point: 6. Page 12, formula (15), “where \\rho reflects the decision-maker’s preference for objective or subjective weight.” Does it reflect the preference of decision makers for objective or subjective weights here? The higher the value of \\rho is, does the decision maker prefer subjective weight or objective weight?“where\\rho

Response : where reflects the decision-maker’s preference for subjective weight. The higher the value of ρ is the decision maker prefer subjective weight.

Point: 7. Page 12, in theorem 1, “formula (10)” should be “formula (15)”.

Response : We have modified “formula (10)” for “formula (15)”. Also we have modified “From formula (12)” for “From formula (27)”.

Point: 8. Page 13, in step 3, “formula (18)” should be “formula (16)”.

Response : We have modified “formula (18)” for “formula (16)”.

Point: 9. It is suggested that the authors compare the proposed comprehensive weight method with existing comprehensive weight methods.

Response：Revised according to comments.

Point: 10. It is suggested that the authors add a sensitivity analysis with variable \\rho.

Response：The sensitivity analysis with variable Rho is added according to the comments. After analysis, the variable Rho directly affects the closeness and project selection.

Submitted filename: Response to Reviewers.doc

Click here for additional data file.

30 Dec 2021

An intelligent optimization method for highway route selection based on comprehensive weight and TOPSIS

PONE-D-21-10954R1

Dear Dr. Liu,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Dragan Pamucar

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: (No Response)

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Greetings,

The authors followed all the suggestions. The paper should now be accepted for publication.

All best

Reviewer #2: The authors have addressed the point of my concern. I am happy with their corrections. Hence, I would like to recommend this manuscript to be published.

Reviewer #3: The authors address the issues of the previous version well. But there are still some minor problems.

1. In formula (7), “max(d_j)” ”min(d_j)”should be “man_i(d_{ij})”and “min_i(d_{ij})”. “d_j” is defined in formula (10).

2. In formula (13), “sum_{j=1}^{m}w_l=1” should be “sum_{j=1}^{m}w_j=1”.

3. In formulas (23) and (24), “f_{ij}” should be “z_{ij}”, “f_j^+” should be “z_j^+”, f_j^-” should be “z_j^-”.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

16 Feb 2022

PONE-D-21-10954R1

An intelligent optimization method for highway route selection based on comprehensive weight and TOPSIS

Dear Dr. Liu:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Dragan Pamucar

Academic Editor

PLOS ONE