A Quantitative Model of the Multisubject Quality Responsibility of Construction Projects Based on an IPSO

. In order to solve the problem of the quantitative division of multisubject quality responsibility in construction project quality disputes, this article proposes a quantitative model of multisubject quality responsibility division in construction projects based on an improved particle swarm optimization (IPSO). First, this article proposes a set of classifcation guidelines for quality risk behaviors based on the theory of organizational behavior. Trough these, the interconnections between diferent types of risk behaviors and quality defects were explored. Following this, this article explored potential laws among 84 practical judicial cases from China using the IPSO. Te category coefcients of the three types of quality risk behaviors, namely, technical defects, management violations, and irregularities, were obtained in this analysis. Tis article also deduced the mathematical expression of the division of engineering quality responsibility using fuzzy mathematical theory and established a multisubject quality responsibility quantitative model. It was then simulated and applied in four practical judicial cases. Te simulation results revealed that the multisubject quality responsibility quantitative model based on quality risk behavior has good applicability.


Introduction
A construction project quality dispute refers to a dispute put forward by the contracting party when a construction project cannot meet the quality standard agreed upon in the contract due to the failure of other project participants to either fully or partially fulfll their quality responsibilities.Te construction quality dispute, itself, is a dispute between those subject to a level of engineering quality responsibility as stipulated in their contract.As such, the subjects of quality responsibility are also the subjects of quality disputes.Using the explanatory structural model (ISM) as their basis, Kumar Viswanathan et al. [1] developed a dispute causation model that depicts six levels of hierarchy among the identifed factors.Similarly, Naji et al. [2] proposed an improved hybrid fuzzy structural equation model for quantifying the probability of the occurrence of disputes in construction projects, thus enabling project stakeholders to predict, identify, and correctly manage the occurrence of disputes prior to the start of construction.Te prototype proposed by Kassab et al. [3] successfully simulates and predicts the sequence of decisions that occur in case study disputes in the presence of uncertainty.Meanwhile, Wang et al. [4] developed a model for predicting the occurrence of disputes to identify resource allocation strategies for dispute avoidance.Tis model not only is predictive but can also be used to trace back to the factors that caused the dispute.El-Adaway and Kandil [5] created a multi-intelligent body system for construction dispute resolution (MAS-COR) that can derive important legal arguments to help save time and efort for construction claim and dispute professionals.At the same time, Chen et al. [6] designed a construction quality dispute negotiation model based on the research of existing expert systems.Tis model follows a two-way, iterative negotiation process in the dispute negotiation, thus ensuring that the whole negotiation process is fairer and more just.In conclusion, this article summarizes the current status of research on dispute resolution models as shown in Table 1.
After the occurrence of engineering quality disputes, the quantitative analysis of engineering quality responsibility is actually a decision-making process.At present, there are many research results in the application of quantitative methods in the feld of construction engineering.Kannan and Martin [7] presented a comprehensive literature review of English-language scholarly papers on ELECTRE and ELECTRE-based methods; the 544 papers on the application of ELECTRE are examined and further classifed into 13 application areas and a number of subareas, including housing assessments and construction project management.Chen et al. [8] developed a novel ELECTRE III-based MCGDM approach for bid evaluation to solve the indetermination, imprecision, and uncertainty in the bid evaluation process.Chen et al. [9] developed a novel hybrid multicriteria group decision-making model for sustainable building material selection under uncertainty.Khaled and Amr [10] proposed setting quality factors based on the degree of impact of the work on the overall quality of the project and using functions to address the quantifcation of quality.Zhang [11] proposed "quantitative cause-efect analysis" based on AHP method and cause-efect analysis and used it in construction quality management practice.Douer et al. [12] developed the responsibility quantifcation (ResQu) model to compute a measure of operator responsibility.Te application of the above methods provides research exploration for quantitative analysis in the feld of engineering construction, but none of them involves research on the division of quality responsibility.He [13] proposed that fuzzy mathematics and random mathematics are also an indispensable part of the development of mathematics today; therefore, the mathematical expressions of legal acts and legal issues can also be expressed as fuzzy and random expressions.At present, most scholars are focused on how to reduce, entirely avoid, or adopt efective methods for resolving quality disputes after they occur.Tere are a few studies on how to identify quality responsibility subjects, determine the way to assume quality responsibility, and establish a multisubject responsibility model to quantify and calculate the quality responsibility ratio.
In the construction industry, about 80-90% of accidents are caused by unsafe behaviors [14].Tus, risky behavior associated with work quality is the main cause of quality problems.It is also the main basis for quantifying the proportion of responsibility placed upon each subject.Te study of quality dispute resolution cannot be separated from the study of the quality risk behavior of a subject.Te one-time customized production method used by construction projects determines the strength of the quality linkage between upstream and downstream subjects [15], and the riskiness of the quality behavior of one subject is likely to be passed on to the subsequent subjects along the chain channel of engineering construction procedure [16].In this system, the riskiness of the quality behavior of upstream subjects will have an important impact on the product quality of downstream subjects [17].Zhang and Li [18] consider engineering quality behavior as an organizational behavior, which can be either positive or negative.Positive quality behavior refers to the actions of those in the construction market subjects that follow the provisions of national laws and regulations and take legal and compliant quality behavior.Contrarily, reverse quality behavior refers to the actions of those construction market subjects that take advantage of the currently prevailing information fragmentation and information asymmetry phenomenon to pursue their own interest maximization and, as a result, engage in behaviors that are detrimental to other subjects or even damage the quality of their projects [19][20][21][22].Terefore, quality risk behavior is a type of reverse organizational behavior.Quality risk behavior, as used in this article, refers to the reverse quality behavior that is detrimental to the engineering quality results made by the construction market subjects in violation of laws and regulations or in breach of their basic duty of care as professional organizations.In a previous study, Ireland [23] studied the reasons behind the failure of engineering projects, and among the 19 reasons he described, 9 are a direct result of the subject's misbehavior.Still, existing scholars mainly focus on the exploration of analysis methods related to behavior selection [24][25][26][27][28][29][30], as well as research on the characteristics, problems, and normative countermeasures of the quality behavior of responsible subjects.Indeed, studies are scarce on the intrinsic mechanisms behind quality risk behavior and quality defects, as well as quality dispute resolution based on the quality risk behavior of subjects.
Due to the lack of theory and a comprehensive model for resolving multisubject quality disputes in arbitration and litigation practice, adjudicators can only make decisions based on the circumstances of the disputed cases and their individual experience.Te invariable result is diferent judgments in similar cases, which fails to protect the legitimate rights and interests of the parties and undermines court justice.Te quantitative model of multisubject responsibility proposed in this article flls this gap and provides an efective quantitative model to encourage more sensible and scientifc adjudication results.Tis article provides the following four main contributions: (1) A classifcation criterion for quality risk behaviors is constructed, and the relationship between diferent types of quality risk behaviors and engineering quality defects is established (2) An IPSO is utilized to achieve an optimal solution method for the category coefcients of the three types of quality risks (3) Te initial assignment of the type coefcient (M IPSO ) T is obtained by using case samples from China and an IPSO experiment (4) Using fuzzy mathematical theory, a mathematical model for quantitative division of the quality responsibility of multiple subjects is established which provides a scientifc and reasonable method for the resolution of multiple subjects' engineering quality disputes Finally, this study is organized into six sections.Following Section 1, Section 2 introduces the classifcation of quality risk behavior and the establishment of multisubject quality responsibility quantitative model.Section 3 elaborates IPSO theory and optimization method of quality risk 2 Mathematical Problems in Engineering behavior type coefcients.Section 4 introduces type coeffcient acquisition and simulation results.Section 5 discusses the management implication of the results and concluding remarks are given in Section 6.Based on the literature research results [31] and expert interviews, the categories of quality risk behavior of construction project participants were modifed and improved, and classifcation guidelines were established according to the results of the quality risk behavior of construction project participants.Te quality risk behavior of the fve possible responsible subjects, the developer, survey company, design institute, construction company, and supervision company, is classifed as the following three types: technical defects, management violations, and irregularities.Background information on the experts who participated in the interviews is presented in Table 2, and a summary of the content of the expert interviews and expert opinions is presented in Table 3. Te classifcation guidelines for the types of behaviors are detailed in Table 4.

Multientity Engineering Quality Responsibility Analysis Model
Te impact of diferent manifestations of quality risks on project quality can difer greatly.Te construction company and supervision company are mainly responsible for the construction management and supervision of the project.Tey are often tasked with implementing management-type behavior.In this context, the reverse manifestation of risk behavior is more often manifested as irregularities in the management type or irregularities in the quality of risk behavior.Te survey, design, and construction companies exist to provide technical services and perform management responsibilities.Tus, the negative performance of risk behavior in these groups includes both quality risk behavior, such as technical defects and violations in the management and irregularities.
Te quality risk behaviors of the technical defects category are directly related to the determination of the project's quality and can be clarifed by the appraisal report provided by the third-party appraisal agency.In contrast, the role of the noncompliance management category is to be inherently opposed to behaviors explicitly prohibited by laws and regulations.Although this role indirectly afects the quality of a project, this type of behavior cannot be identifed by the appraisal agency.Tere is a type of quality risk behavior that is considered to be outside the framework of laws and regulations.It is neither a type of technical defect identifed by the third-party identifcation agencies as the quality risk behavior nor the quality risk behavior of management violations expressly prohibited by laws and regulations.Tis is a type of quality risk behavior that is either contrary to the provisions of the relevant normative documents, it does not align with the common practice of industry conventions, it violates the principle of honesty and crediting the subject, or it can be avoided based on the premise of the reasonable duty of care expected of professional institutions.Given these qualifcations, such quality risk behaviors are uniformly classifed as irregular quality risk behaviors.Te purpose of a quality risk behavior classifcation study is to categorize and sort out diferent manifestations of quality risk behaviors according to their characteristics and manifestations in order to identify the complex and variable quality risk behaviors of construction project participants and establish the corresponding classifcation guidelines.Based on the above typological identifcation results, the severity of diferent types of quality risk behaviors can be determined quantitatively by using appropriate decision-making methods, thus providing a scientifc and reasonable basis for the allocation of engineering quality responsibilities.Te table of project quality responsibility allocation based on the classifcation criteria of quality risk behaviors is shown in Table 5.
Table 5 shows g denotes the number of units, Z g denotes the share of responsibility of the gth unit, β S , β B , and β P are the coefcients of technical defects, management violations,

Calculation Model of Multisubject Engineering Quality
Responsibility Division.Based on the fault imputation principle of engineering quality responsibility, the degree of fault of the quality responsibility subject and the size of the cause force of the act and result can be taken as the main factors in the division of quality responsibility of multiple subjects.As professional subjects of engineering construction, the fve categories of quality responsibility subjects have the obligation of working together to pay attention in order to produce an engineering quality higher than expected of most people in the society.In other words, they are inevitably responsible for any fault presumption results caused by any risky behaviors they themselves engage in.Based on this, the degree of fault can be presumed according to the severity of the quality risk behaviors the responsible subjects are engaging in.Terefore, according to the jurisprudential characteristics of engineering quality responsibility and the principle of the fault imputation of engineering quality responsibility, there are two basic factors that must be considered in the comprehensive evaluation of engineering quality responsibility: (1) the degree to which the responsible subject is at fault, which can be determined by the severity of their quality risk behavior; (2) the size of the cause force that is generated by the quality risk behavior and damage results.Te correlation between the above two factors is also taken into account.According to the principle of fuzzy mathematics, the comprehensive decision-making problem of the division of engineering quality responsibility can be simplifed to a single-factor judging problem as follows: (Degree of fault domain)R(Causal force domain) � (Proportional responsibility domain), ( where R is the operator.Diferent types of risky behaviors have diferent magnitudes of causality for causing the abnormal state of engineering quality, which can be used as the evaluation index of the causality theory domain.Te severity of quality risk behavior can be used as the presumption basis for the degree of fault of the actor subject.Terefore, a set of multiobject quality responsibility allocation methods based on engineering quality risk behavior can be established.Tis method is on the basis of the type of risk behavior corresponding to the engineering quality risk behavior implemented by the responsible subject, the degree of harm of the risk behavior, and the correlation between them.Based on equation (1), the quantitative analysis equation of quality responsibility can be written as (quality risk behavior damage domain)R(quality risk behavior category domain) � (proportional responsibility domain). ( In equation (2), the engineering quality risk behavior harm degree domain refers to the existing degree of harm resulting from the risk behavior engaged in by a subject.It is the degree of fault of the corresponding implementation subject, which is composed of (X 1 , X 2 , ..., X m ).Te quality risk behavior type domain refers to the type of quality risk behavior.Tis is determined by categorizing it according to the characteristics of the diferent types of behavior and the degree of damage caused to the quality of the project.Tis measurement corresponds to the risk behavior and size of the damage caused by the force, which is composed of (Y 1 , Y 2 , ..., Y n ).Te responsibility proportional theory domain says that those subjects who engaged in the quality risk behavior should bear a proportion of quality responsibility, which is expressed by Z: where k is the calculated value of the corresponding responsible subject's quality responsibility and R is the operator.
Given that the subject g has jointly implemented a series of quality risk behaviors leading to the abnormal state of Mathematical Problems in Engineering project quality, when R adopts matrix multiplication operation, the corresponding proportion of quality responsibility to be borne by subject g can be expressed as follows: In equation ( 4), the set of engineering quality risk behaviors and the set of quality risk behavior type correlations need to satisfy the following two conditions: (1) Te quality risk behavior set should satisfy Furthermore, according to the above formula, it can be calculated that Z g responsible subjects should bear the respective quality proportion as follows:

Optimization Method of Quality Risk Behavior Category Coefficients
3.1.IPSO Teory.Each quality risk behavior has a diferent degree of causality for the negative impact on engineering quality resulting from diferent types of behavior.Tis is recorded as the quality risk behavior category coefcient.Te solution of the category coefcients can be determined through the large sample data approach.Te intelligent optimization algorithm can be used to explore the potential connection between the data.Tis can, in turn, make the values of diferent categories of coefcients more scientifc.For this reason, the specifc values of each category of coefcients are selected in this paper using an IPSO.Te particle swarm optimization has good global optimization capability, as it starts from a random solution and ultimately locates the optimal solution through iteration.Te particles in the swarm move once, their positions change accordingly, and then the new individual extremum p best and population extremum g best are obtained after each iteration.For this operation, we assume a D-dimensional target search space has W particles forming a group, where the qth particle can be represented as a D-dimensional degree vector shown in equation ( 6): Ten, the velocity V q of the qth particle can be expressed as in equation ( 7): Te optimal individual extremum p best searched by the qth particle is given by equation ( 8): Te optimal population extremum p best searched by the entire particle population is equation ( 9): After fnding p best and g best , the velocity v id and position Q id of the particles can be updated using equation (10): where t denotes the number of iterations, c 1 and c 2 are the infuence factors, and w denotes the inertia weights.In this article, w is taken as 1, and c 1 and c 2 are updated according to equations ( 11) and (12), which is the reason for calling it an IPSO.T max denotes the maximum number of iterations: 6 Mathematical Problems in Engineering

Optimal Acquisition Method of Category Coefcients.
In order to apply the IPSO to the category coefcient acquisition, the objective function of the IPSO needs to be set as in equation ( 13), while the optimization search direction of this objective function corresponds with the direction of the minimum value of equation ( 13): In equation ( 13), b denotes the number of the subject involved in the case, B denotes the maximum value of the subject involved in the case, W l j u is the true responsibility proportion of the uth unit of the jth sample, and W l j u is the estimated responsibility proportion of the uth unit of the jth sample.
Using equations ( 6)-( 13), the specifc steps of the category coefcient optimization acquisition method can be obtained as detailed below, and the whole fowchart of this IPSO can be shown in Figure 1: Step 1: we set the percentage of three types as the variables to be optimized, where population size is W, the maximum number of iterations t is T max , the range of individual is '(Q min , Q max ), the range of particle update velocity is (V min , V max ), and the objective function is equation (13).
Step 2: we randomly initialize the position and velocity of the particles and set the number of iterations t to 1.We calculate the objective function value F 1 of each particle based on the position and velocity of the particle.Ten, we obtain the initial minimum values of the objective function F ε , the initial individual extreme value p ε best , and the initial population extreme value g ε best .
Step 3: we update the position and velocity of each particle according to equation (10)

Simulation Verification
4.1.Type Coefcient Acquisition.In order to determine the category coefcients of quality risk behavior, this article selects 84 typical multiobject engineering quality dispute cases from China Judgment Document Network as the case traceability source for particle swarm optimization solution.
Te subjects involved can be divided into the following types: two-party subject, three-party subject, four-party subject, and fve-party subject type.Te subjects meanwhile can be taken as the following: the developer as A, survey company as B, construction company as C, supervision company as D, and design institute as E. Te combination pattern and number distribution of responsible subjects are detailed in Figure 2.
Although the selection of cases inevitably bears some traces of selectivity, the selection of the exemplary cases used here has some compilation factors and the public attitudes of courts in diferent places towards these cases vary greatly.Tus, these selections represent precisely the mainstream judges' understanding of the cases and therefore have research value.At the same time, cases from multiple locations were carefully selected to reduce the imbalance of the infuence of geography on the resultant verdicts and to ensure the universality of the obtained research results.Te distribution of regions and the number of subjects involved in the cases are detailed in Table 6.
Te parameters of the IPSO itself have a certain infuence on its optimization results.Terefore, based on the above samples, the IPSO method and the category coefcient constraints, the maximum and minimum values of the particles can only be 1 and 0, respectively, in order to obtain more scientifc category coefcients.Tis article mainly focuses on the population size, iteration number, and particle update speed involved in the IPSO as Experiment 1, Experiment 2, and Experiment 3 are conducted.

Experiment 1.
We set the maximum number of iterations as 200 and the maximum and minimum values of particle update speed as 1 and −1, respectively, and then change the particle population size to 10, 100, 500, 1000, 1500, and 2000 in turn.Following this, the iteration diagram of the IPSO can be obtained as shown in Figure 1.
Figure 3 shows the minimum value of the objective function decreases as the population size increases.However, it is also clear that when the population size is 1000, 1500, and 2000, the minimum values of their three objective functions are basically the same.Tis indicates that when the population size reaches a certain level, the minimum value of the objective function also tends to be stable.Based on experiment 1, therefore, the population size used in this article is set as 1500.
After the population size was determined, Experiment 2 was conducted in this paper.

Experiment 2.
We set the population size as 1500; the maximum and minimum values of particle update rate as 1 and −1, respectively.We change the number of iterations to 10, 100, 200, 400, 600, and 800 in turn, after which the iteration diagram of the IPSO can be obtained as shown in Figure 4.
Based on Figure 4, as the maximum number of iterations increases, the minimum value of the objective function decreases before it increases.Tis means that the maximum number of iterations is not as large as it has the potential to be.For this reason, based on Experiment 2, the maximum number of iterations was set to 200 in this article.Figure 5 shows that, as the particle update speed increases, the minimum value of the objective function will frst increase and then decrease.However, it does not reach the initial minimum value.Terefore, based on Figure 4, the minimum and maximum values of the particle update speed were selected as −0.01 and 0.01 in this article.

Mathematical Problems in Engineering
Based on the above case samples and experiments using the IPSO, it is found that the IPSO is able to follow the specifed search direction.When it reaches the minimum ftness value, its output optimal variables are shown in equation (14), which represents the coefcient of quality risk behavior type of technical defects, the coefcient of quality risk behavior type of management violations, and the coefcient of quality risk behavior type of irregularities: Moreover, as shown in the theory of traditional PSO, the update rule of PSO depends on c 1 and c 2 .In the traditional PSO, c 1 and c 2 are set manually, which may not have the best result.However, in this article, through IPSO, c 1 and c 2 can automatically change with iteration number and then the best result can be obtained.Tis point can be supported by Figure 6.
As shown in Figure 6, with diferent c 1 and c 2 , diferent iteration curves can be obtained.However, IPSO has the minimum ftness value.Hence, IPSO is better than traditional PSO because IPSO can automatically set c 1 and c 2 .Tis is the advantage of IPSO and the reason why this article utilizes IPSO.

Modeling and Calculation.
In this article, a total of four practical engineering quality dispute cases involving two, three, four, and fve responsible subjects were selected as the validation cases of the model.Tese are indicated by the codes Subject II, Subject III, Subject IV, and Subject V, respectively.Te (M IPSO ) T value obtained from equation (13) represents the type coefcient for three types of quality risk behaviors, namely, technical defect class, irregular management class, and nonstandard class.When the subjects involved in the practice cases do not display a certain type of risk behavior or only two types of the specifed quality risk behaviors occur, it is necessary to perform normalization for the two types of risk behaviors that are occurring.Te processing results are detailed in Table 7.
Taking the case code Subject IV as an example, all parties, including the developer, supervision company, design institute, and construction company, engaged in one or more quality risk behaviors and were at fault for the resulting building collapse that was caused in the case.Te quality risk behaviors and risk behavior categories of the above four responsible parties are summarized in Table 8.
Chen et al.'s [32] method was used to determine the severity for diferent quality risk behaviors, and the determination values for the SUBJECT IV case are detailed in Table 9.
Based on the simulation determination results seen in Table 9, the judgment matrices of quality risk behavior sets of technical defects and management violations were constructed and the judgment coefcients were calculated, respectively.Te results are detailed in Tables 10  and 11.
According to equation ( 4), the corresponding parameters were assigned to the calculation, and the simulation calculation results were obtained as detailed in Table 12.

Comparison of Model Calculation Results and Litigation
Practice Results.Te simulation results of Subject II, Subject III, and Subject V were obtained by referring to the modeling and calculation process of Subject IV.Te simulation results  Mathematical Problems in Engineering of Subject II, Subject III, Subject IV and Subject V are comparable to the practice judgment values as shown in Figure 7.

Objective
From Figure 7, we can see that the simulation results of the construction company and supervision company are in good agreement with the judgment values in practice.Mathematical Problems in Engineering Te reason is that the risk behavior of the construction company and supervision company are relatively simple, and the identifcation of practices is straightforward.Te simulation results of the construction company, design company, and survey company are diferent from judgment values in practice.Te main reason is that the construction company, design company, and survey company have more forms of risk behavior in practice and are harder to categories, so the identifcation of risk behavior in practice is prone to bias due to the discretion of the judges.In addition, the deviation of the simulation results of Subject IV and Subject V from the actual judgment values is signifcantly smaller than that of Subject II and Subject III.Te main reason is that when the number of subjects and the types and numbers of risk behaviors implemented increase, the initial assignment of the type coefcient (M IPSO ) T can be better corrected to reduce dispersion.Overall, the simulation results obtained by the multisubject liability model established in this article are in high agreement with the actual determination values.
responsibility disputes.Based on the quantitative model proposed in this article, the court or arbitration commission can develop a quality responsibility quantitative software program with territorial application value to assist judges in case hearing, so as to improve the efciency of case hearing and make more scientifc and reasonable judgment conclusions.

Conclusion
In this article, a detailed study was conducted on classifcation criteria, category coefcients acquisition, and responsibility quantifcation calculation for the multisubject quality responsibility model of construction projects.Based on this, the following conclusions were reached: (1) Te concept of quality risk behavior classifcation criterion and type coefcient was proposed based on the theory of organizational behavior.Te initial assignment of (M IPSO ) T was carried out for three types of quality risk behavior category coefcients using the IPSO.Tis process verifed by simulation that (M IPSO ) T has good applicability.
(2) When determining the division of quality responsibility between two or three responsible parties, the determination of responsibility depends entirely on the initial assignment of the type coefcient (M IPSO ) T , especially when the types of quality risk behaviors implemented by each responsible party are diferent.Tis cannot be combined with the actual situation of quality disputes, and it is more discrete.On the contrary, when the number of responsible subjects and the type and number of risk behaviors performed by each subject is larger, the severity determination coefcient of the same type of quality risk behaviors needs to be introduced in conjunction with the actual situation of the disputed case.Tis corrects the dispersion problem caused by the initial assignment of the type coefcient (M IPSO ) T .In this way, the simulation efect is better.(3) Te method provided in this article can quantitatively calculate the division ratio of multisubject quality responsibility.However, the number of cases is not very large.To further improve the accuracy of the method, the more cases should be collected.
(4) Te quality responsibility division model for multiple quality subjects established in this article is efective when applied in the context of a multisubject quality dispute resolution.
However, the model developed in this article did not take into account the infuence of external factors such as natural environmental changes or natural disasters on the allocation of quality responsibility, and the reasons for the high correlation between the type of quality risk behavior and quality results need to be further explored.Furthermore, the samples in this article were drawn from only one country, which has some limitations in terms of representativeness.In future studies, external factors such as natural environmental changes or natural disasters should be considered in the model, while increasing the number and diversity of samples, so as to build a multisubject quality responsibility quantitative division model with wider applicability and practicality.

Figure 2 :Figure 1 :
Figure 2: Combination pattern and number distribution of responsible subjects.

Figure 3 :
Figure 3: Iteration diagram of IPSO with diferent number of populations.

Table 1 :
Literature review of dispute resolution models.

Table 2 :
Background information on the experts participating in the interviews.

Table 3 :
Expert interview content and conclusions.
Laws and regulations, regulatory documents, technical appraisal reports, conventions and practices in the industry, etc.5What suggestions would you give for the classifcation of engineering quality risk behavior?Give full consideration to the main precepts and classifcation standards of quality risk behavior 6What do you think is the signifcance of the classifcation of engineering quality risk behavior to the resolution of multisubject quality disputes?Classifcation can provide a quantitative basis for the severity of diferent types of quality risk behavior 7 Do judges or arbitrators take the impact of poor-quality behavior on quality liability into account in practical dispute resolution?Yes, as there is no classifcation standard and the decision is left to the discretion of the adjudicator on a case-by-case basis

Table 4 :
Guidelines for categorizing the quality risk behavior of construction project participants.

Table 5 :
Project quality responsibility allocation table.
, set the number of iterations t to t + 1, then calculate the objective function value F t , obtain the minimum value of the function value F t , the individual extreme value p t best , and the population extreme value g t best , and determine whether the updated value F t is less than F ε .If yes, then let F ε �

Table 6 :
Regional distributions of cases and the number of subjects involved.