CN113656746A - Travel mode chain selection method considering group heterogeneity under dynamic structure - Google Patents
Travel mode chain selection method considering group heterogeneity under dynamic structure Download PDFInfo
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Abstract
The invention discloses a travel mode chain selection method considering group heterogeneity under a dynamic structure, which comprises the following steps: (1) calculating prior probability; (2) calculating an expected utility equation, and determining a value function and a conditional selection probability function specific to the option; (3) calculating a likelihood function; (4) calculating posterior probability, and updating conditional selection probability; (5) calculating a utility parameter and a type parameter; (6) iterative optimization of prior probability, posterior probability and combined likelihood function is carried out by utilizing an expected maximum algorithm, so that utility parameters and type parameters are obtained simultaneously; (7) and (4) carrying out parameter estimation on the utility parameter and the type parameter in the step (6). The invention estimates two kinds of parameters in a dynamic discrete selection model by using a method of combining an EM algorithm and a conditional selection probability operator; through the correlation between the selection before and after the structural modeling of the Markov chain, the selection heterogeneity of the population is classified by adopting the finite mixed distribution assumption, so that the selection mode of the traveler's whole day trip chain is well predicted.
Description
Technical Field
The invention relates to the field of travel mode selection modeling, in particular to a travel mode chain selection method considering group heterogeneity under a dynamic structure.
Background
Along with novel travel mode constantly emerges, outside traffic methods such as traditional public transit, subway, city green travel level has been richened to travel modes such as sharing bicycle, sharing car, car pool, and along with urbanization rapid development, the outside quick expansion in a second line city for people's average distance of going out increases, because the reachability in different areas is different in addition, and single travel mode is often difficult to satisfy passerby's demand. At present, the owned quantity of cars in a large city is still rising, the traveling sharing rate of the cars is very high, but the cars are constrained by congestion, parking charge, few parking spaces and the like, and the traveling mode of changing the cars into other modes presents a rising trend; the multi-mode trip is more obvious in selection of the bus trip because a distance is possibly reserved between the starting point and the getting-on point and between the getting-off point and the destination.
Under the multi-mode travel environment, public travelers want to reduce travel time and improve convenience and comfort degree of travel, transportation service enterprises want to connect services of more travel service providers, and transportation management departments want to assist in regulating and controlling urban travel structures by means of a platform to guide green travel proportion of the public and provide good services for the travelers by providing high-quality service products for profit. Therefore, it is necessary to analyze the travel mode chain of all-day activities of people and mine the selection preference of different groups, thereby providing technical support for achieving the above-mentioned goal.
The traditional travel mode selection mainly relates to single mode selection, namely only options of a single travel mode are provided under certain fixed scenes, parameters are calibrated by using data of one-time travel, and the mode is obviously not suitable for multi-mode travel scenes; additionally, in some activity-based models, taking into account modeling of travel style chains, a challenge is to capture the relationship between the choices before and after. Some simplified processing approaches include: assuming a main travel mode, connecting upper and lower layer selections by using a nested structure, enumerating all possible travel mode combinations and the like, on one hand, the time dynamics of the selection cannot be considered, namely, the current selection can influence the future traffic mode, and the future traffic state can also influence the selection of the current traffic mode; on the other hand, the heterogeneity of different population selections is not considered, and the selection type of the travel mode chain is greatly determined by the preference of people.
Disclosure of Invention
The purpose of the invention is as follows: in view of the above problems, the present invention aims to provide a travel mode chain selection method considering population heterogeneity under a dynamic structure, and predict travel selection modes of different travelers by considering heterogeneity of different populations.
The technical scheme is as follows: the invention discloses a travel mode chain selection method considering group heterogeneity under a dynamic structure, which comprises the following steps:
(1) utilizing a Logit model to represent the prior probability of each traveler belonging to each unobservable type;
(2) calculating an expected utility equation of a pedestrian belonging to an unobservable type by applying a Bellman optimal criterion, optimizing the expected utility equation, determining a value function specific to an option, and determining a conditional selection probability function by using the value function;
(3) calculating a likelihood function of trip selection of each stage of the travelers by using the conditional selection probability, and then calculating a combined likelihood function of all the travelers for making continuous trip mode selection according to the likelihood function of each stage;
(4) calculating posterior probabilities of the travelers belonging to the unobservable types according to the prior probabilities and the likelihood functions, and updating the conditional selection probabilities by using the posterior probabilities;
(5) calculating utility parameters and type parameters of the dynamic discrete selection model through a maximum likelihood function;
(6) utilizing an expectation-maximization algorithm to iteratively optimize the prior probability, the posterior probability and the combined likelihood function, and maximizing the combined likelihood function to obtain the utility parameter and the type parameter at the same time;
(7) and (4) carrying out parameter estimation on the utility parameters and the type parameters finally obtained in the step (6) by using known data, and using the accuracy of the cross validation model.
Further, the expression of the prior probability in step 1 is:
wherein munζFor travelers n belonging to the unobservable class ζ prior probability, βζFor the type parameter to be estimated, znThe method comprises the steps that a travel attribute vector of a traveler n is defined, the travel attribute vector comprises travel time, travel distance and age of the traveler, zeta is an unobservable type of each traveler, the unobservable type comprises price sensitivity and time sensitivity, variables zeta of the unobservable type are independent and do not change along with time, and l represents all the unobservable types.
Further, at each stage K ∈ {1,2, …, KnThe travelers select from the feasible subsets, and the combined utility comprises three parts by taking the maximum current and reduced future utility values as a selection rule: immediate utility u of current stage kk(xk,yk,akζ), error term ε, and discounting future utility, the state variable of the traveler is x after applying the Bellman optimality criterion and integrating the error term εkWith a non-state variable of ykWhen the expected utility V is of the unobservable type ζk(xk,ykζ) equation is:
wherein a iskShows the actions of the traveler per stage k, CkIs an action akA limited selection set of; epsilonkFor unobserved error variables, ∈k+1Independent of the variables of the preceding stage,. epsilonkIndependent and subject to the same distribution among all stages; state variable xkIncluding the trip purpose P e P, the used trip mode sequence S e S { m }1,m2,…,mk-1The feasible modeThe subset is H epsilon H, the departure time st, st of the current stage is a discrete variable with the interval of half an hour, therefore xk＝{pk,sk,hk,stkIs (0,1) represents a reduction coefficient, XkIs a state variable xkOf a non-state variable ykIncluding population attribute variables and transit times in different ways, mkRepresents the travel pattern used in stage k, f (x)k+1|xk,akζ) denotes a given (x)k,akζ) obtaining the state variable xk+1Transition probability of g (. epsilon.)k) The transition probability of the variables which are not observed is defined, and each variable definition domain is a real number domain; x is the number ofk+1Including xkAll valid information transferred;
to obtain a closed form of the computational structure, let ε be assumedkIndependently and equally distributed in Gumbel of Gumbel, g (epsilon) ═ njg(εj) And thus the utility equation is expected to be simplified to:
wherein v isk(xk,yk,akζ) is an option-specific cost function and γ is an euler constant, then action akThe conditional choice probability expression of (1) is:
wherein a'kSet C for limited selectionkAll of the elements of (a);
expressing the expected utility equation by the conditional choice probability is:
the state vector (x) is known from the above formulak,ykZeta expected utility V)k(xk,ykζ) is the sum of the following values: option specific cost function vk(xk,yk,akζ), the probability of negative condition selection after logarithmic transformation, and the euler constant γ; when selecting akConditional selection probability P (a) ofk|xk,ykζ) is less than a preset threshold value, the expected utility Vk(xk,ykζ) approaches the optimal option-specific cost function vk(xk,yk,akζ) plus a constant γ, indicate different merit functions vk(xk,yk,akζ) is a function of the corresponding conditional probability, then the option-specific cost function expression is:
further, the step (3) of calculating each phase likelihood function includes:
the non-state variable of traveler n is
The state variable is
Make continuous travel selection as
Then at stage k, at the state vector (x)nk,ynkζ) and utility parameter βu＝(βu1,…,βuζ,…,βuZ) Observe the traveler making a choicenkThe likelihood function of (d) is:
wherein f (x)nk+1|xnk,ankζ) is given as (x)nk,ankζ) under xnk+1The transition probability of (2);
the combined likelihood function expression is:
wherein N is the total number of travelers.
Further, the posterior probability in step (4) is calculated as follows:
at a given state-a selection pair and a parameter (beta)u,βζ) In the case of (1), the posterior probability expression that the actor n belongs to the unobservable type ζ is:
wherein E is the desired symbol; i represents a flag variable, when ∑ isnWhen ζ is equal to 1, otherwise, it is 0;
the type-specific conditional selection probability obtained from the posterior probability is:
further, the step (5) utility parameter βuAnd a type parameter betaζThe expression is as follows:
respectively to the utility parameter betauAnd a type parameter betaζPerforming first-order derivation:
further, the iterative optimization process in step (6) is as follows:
first, utility parameters and type parameters are initialized
And given state (x)n,ynζ) conditional selection probability p of all options a1(a|xn,ynζ), assuming that at the first iteration, the probability does not vary with type, the (i +1) th iteration proceeds according to the following steps:
(601) according to type parameter
Updating prior probabilities
(602) Computing type-specific likelihood functions
Firstly, calculating a transfer matrix with a specific type according to a box estimation method:
the transition matrix is composed of state transition probabilities, and a likelihood function is obtained through calculation according to the conditional selection probability and the state transition probabilities;
(603) updating the posterior probability according to the prior probability and the likelihood function, wherein the expression is as follows:
(604) maximizing the combined likelihood function:
and (3) providing a new log-likelihood function to replace the previous combined likelihood function, wherein the expression is as follows:
since the posterior probability is outside the log-transition, a new log-likelihood function
Simpler than the previous combined likelihood function Ψ, maximization
To find the optimal utility parameter betauAnd a type parameter betaζ：
(605) Updating the conditional selection probability:
according to the equation relationship between the conditional selection probability and the posterior probability, the updated conditional selection probability expression is as follows:
and ending the iteration updating when the iteration times set previously are reached, and outputting the optimal utility parameters and type parameters.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: estimating two types of parameters in the dynamic discrete selection model by using a method of combining an EM algorithm and a conditional selection probability operator; through the correlation between the selection before and after the structural modeling of the Markov chain, the selection heterogeneity of the group is classified by adopting the finite mixed distribution assumption, so that the selection mode of the traveler's whole day trip chain is better predicted, and different requirements of passengers, traffic service enterprises and traffic transportation management departments are met.
Drawings
FIG. 1 is a graph comparing BIC values for models of different total number of unobserved types;
FIG. 2 is a comparison graph of observed samples and predicted results for each day and each trip;
fig. 3 is a comparison graph of observation samples and predicted results of travel mode proportion.
Detailed Description
The method for selecting a travel mode chain considering group heterogeneity under a dynamic structure includes the following steps:
(1) carrying out selective modeling analysis on the traveler all-day trip mode chain, and representing the prior probability of each traveler belonging to each unobservable type by using a Logit model;
the expression of the prior probability is:
wherein munζFor travelers n belonging to the unobservable class ζ prior probability, βζFor the type parameter to be estimated, znThe travel attribute vector is a travel attribute vector of a traveler n, the travel attribute vector comprises travel time, travel distance and age of the traveler, zeta is an unobservable type to which each traveler belongs, the unobservable type comprises but is not limited to price sensitivity and time sensitivity, namely zeta belongs to Z, variables zeta of the unobservable type are independent and do not change along with time, and l represents all the unobservable types.
(2) Calculating an expected utility equation of which the pedestrian belongs to an unobservable type by applying a Bellman optimal criterion, optimizing the expected utility equation, determining a value function specific to the option, and determining a conditional selection probability function by using the value function.
At each stage K e {1,2, …, KnThe travelers choose from the feasible subsetTaking the maximum current and reduced future utility values as selection rules, the combined utility comprises three parts: immediate utility u of current stage kk(xk,yk,akζ), error term ε, and discounting future utility, the state variable of the traveler is x after applying the Bellman optimality criterion and integrating the error term εkWith a non-state variable of ykWhen the expected utility V is of the unobservable type ζk(xk,ykζ) equation is:
wherein a iskShows the actions of the traveler per stage k, CkIs an action akA limited selection set of; epsilonkFor unobserved error variables, ∈k+1Independent of the variables of the preceding stage,. epsilonkIndependent and subject to the same distribution among all stages; state variable xkIncluding the trip purpose P e P, the used trip mode sequence S e S { m }1,m2,…,mk-1The feasible mode subset is H ∈ H, the departure time st, st of the current stage is a discrete variable with the interval of half an hour, therefore xk＝{pk,sk,hk,stkIs (0,1) represents a reduction coefficient, XkIs a state variable xkOf a non-state variable ykIncluding population attribute variables and transit times in different ways, mkRepresents the travel pattern used in stage k, f (x)k+1|xk,akζ) denotes a given (x)k,akζ) obtaining the state variable xk+1Transition probability of g (. epsilon.)k) The transition probability of the variables which are not observed is defined, and each variable definition domain is a real number domain; x is the number ofk+1Including xkAll valid information transferred;
to obtain a closed form of the computational structure, let ε be assumedkIndependently and equally distributed in Gumbel of Gumbel, g (epsilon) ═ njg(εj) And thus the utility equation is expected to be simplified to:
wherein v isk(xk,yk,akζ) is an option-specific cost function and γ is an euler constant, then action akThe conditional choice probability expression of (1) is:
wherein a'kSet C for limited selectionkAll of the elements of (a);
expressing the expected utility equation by the conditional choice probability is:
the state vector (x) is known from the above formulak,ykZeta expected utility V)k(xk,ykζ) is the sum of the following values: option specific cost function vk(xk,yk,akζ), the probability of negative condition selection after logarithmic transformation, and the euler constant γ; when selecting akConditional selection probability P (a) ofk|xk,ykζ) approaches 1, the desired utility Vk(xk,ykζ) approaches the optimal option-specific cost function vk(xk,yk,akζ) plus a constant γ, indicate different merit functions vk(xk,yk,akζ) is a function of the corresponding conditional probability, then the option-specific cost function expression is:
(3) calculating a likelihood function of trip selection of each stage of the travelers by using the conditional selection probability, and then calculating a combined likelihood function of all the travelers for making continuous trip mode selection according to the likelihood function of each stage;
the non-state variable of traveler n is
The state variable is
Make continuous travel selection as
Then at stage k, at the state vector (x)nk,ynkζ) and utility parameter βu＝(βu1,…,βuζ,…,βuZ) Observe the traveler making a choicenkThe likelihood function of (d) is:
wherein f (x)nk+1|xnk,ankζ) is given as (x)nk,ankζ) under xnk+1The transition probability of (2);
the combined likelihood function expression is:
wherein N is the total number of travelers.
(4) Calculating posterior probabilities of the travelers belonging to the unobservable types according to the prior probabilities and the likelihood functions, and updating the conditional selection probabilities by using the posterior probabilities;
at a given state-a selection pair and a parameter (beta)u,βζ) In the case of (1), the traveler n is of the unobservable type ζThe posterior probability expression is:
wherein E is the desired symbol; i represents a flag variable, when ∑ isnWhen ζ is equal to 1, otherwise, it is 0;
the type-specific conditional selection probability obtained from the posterior probability is:
(5) calculating utility parameters and type parameters of the dynamic discrete selection model by maximizing a likelihood function, the utility parameter betauAnd a type parameter betaζThe expression is as follows:
respectively to the utility parameter betauAnd a type parameter betaζPerforming first-order derivation:
(6) utilizing an expectation-maximization algorithm to iteratively optimize the prior probability, the posterior probability and the combined likelihood function, and maximizing the combined likelihood function to obtain the utility parameter and the type parameter at the same time;
first, utility parameters and type parameters are initialized
And given state (x)n,ynζ) conditional selection probability p of all options a1(a|xn,ynζ), assuming that at the first iteration, the probability does not vary with type, the (i +1) th iteration proceeds according to the following steps:
(601) according to type parameter
Updating prior probabilities
(602) Computing type-specific likelihood functions
Firstly, calculating a transfer matrix with a specific type according to a box estimation method:
the transition matrix is composed of state transition probabilities, and a likelihood function is obtained through calculation according to the conditional selection probability and the state transition probabilities;
(603) updating the posterior probability according to the prior probability and the likelihood function, wherein the expression is as follows:
(604) maximizing the combined likelihood function:
and (3) providing a new log-likelihood function to replace the previous combined likelihood function, wherein the expression is as follows:
due to the backThe probability of experience is outside the log-transition, so a new log-likelihood function
Simpler than the previous combined likelihood function Ψ, maximization
To find the optimal utility parameter betauAnd a type parameter betaζ：
(605) Updating the conditional selection probability:
according to the equation relationship between the conditional selection probability and the posterior probability, the updated conditional selection probability expression is as follows:
and ending the iteration updating when the iteration times set previously are reached, and outputting the optimal utility parameters and type parameters.
Obtaining an optimal utility parameter beta by optimizing a dynamic discrete selection model without considering heterogeneityuAs an initial value of the EM algorithm, an initial type parameter beta is setζIs 0; meanwhile, considering that the convergence speed of the EM algorithm is low near the optimal value, after iteration is carried out for a plurality of times, the result is input into the step (5) and a direct optimization method is adopted to obtain the final two types of parameter estimation results.
(7) And (4) carrying out parameter estimation on the utility parameters and the type parameters finally obtained in the step (6) by using known data, and using the accuracy of the cross validation model.
The embodiment will be further described by taking the selection of a travel mode chain of residents in a city (e.g., Nanjing city). The data comprises 10285 families, 28931 travelers and 49210 travel records, the travel purposes comprise work, study, shopping, home returning, entertainment, business travel, pick-up, unit returning and the like, and the travel modes comprise walking, bicycles, shared bicycles, buses, subways, taxis, cars and transfer. Annual income in family attributes, gender in personal attributes, whether a driving license, occupation and a school calendar exist or not, and purpose and departure time in travel attributes are disassembled into dummy variables by using one-hot codes, other variables are used as continuous variables, different travel records of the same person in one day are connected in series, and a travel mode chain is obtained and used as a label of a model.
Finite selection set CkIt needs to be defined in connection with the current state with the following constraints:
if the private vehicle has been used and parked, the collection will not include the pattern unless a re-retrieval is required on the way back; the number of stages of one trip is not more than 5, and the selection set of the fifth trip or the last trip does not include a bus trip mode; other transportation modes are needed to be connected before and after the bus trip; a continuous sequence of shared cars (bicycles), private cars (bicycles) is not possible; the transfer inside the bus needs to be considered. And (3) utilizing an EM algorithm to complete parameter estimation, adjusting the number of unobservable types zeta, the utility parameters and different variable combinations in the type parameters, and selecting an optimal model according to the Bayesian information content BIC value. Figure 1 is a graph of BIC values for models across the total number of different unobserved types, indicating that the sample population shares two significant heterogeneities. Table 1 shows the estimation results of type parameters, and this embodiment is described by taking two unobservable types, type 1 and type 2 as examples, where all the type parameters βζSignificant at the 95% significance level, the comparison of coefficients between the two unobservable types provides qualitative information, with a high annual income, large family size, and a high probability of male travelers in one or more parking spaces belonging to the second type; similarly, travelers traveling on weekdays and closer to bus stops have a high probability of belonging to the first type, and the prior probability formula is used to divide all travelers in the sample into two parts, with the first type accounting for 61.2% and greater than 38.8% of the second type. Calculating the average value of travel time and cost of each type of sample, further describing each type qualitatively and belonging to the second typeA part of passengers have higher sensitivity to travel cost than a second part; the second type of passenger has a higher intrinsic preference for automobiles and is highly time sensitive, consistent with high-income, large family-scale male travelers. Tables 2 to 5 show the estimation results of the utility parameters, all the utility parameters are significant at a significance level of 90%, and the position variables, the family attribute variables (family income per year, vehicle holding capacity, and the number of workers), the personal attribute variables (sex, work, school calendar, and presence or absence of driving license), and the travel attribute variables (travel purpose, cost, time, travel mode usage, etc.) of the travel mode all have different degrees of influence trends on the two types, and are in accordance with the time sensitivity and price sensitivity of the above analysis.
TABLE 1 type parameter estimation results
Note: and represent significance levels of 1% and 5%, respectively.
Table 2 parameter estimation result of travel mode position variable
Note: indicates a level of significance of 10%.
TABLE 3 estimation results of parameters of family attribute variables
TABLE 4 estimation results of parameters of personal attribute variables
Table 5 parameter estimation results of travel attribute variables
In the embodiment, the performance of the dynamic discrete selection model and the overfitting of the estimation parameters are cross-verified by comparing the characteristics of the observation sample and the prediction result. The samples are broken into two data sets in a disorderly order: one set contains 80% of the data used to train the dynamic model, and the second set contains 20% of the observations used to predict the travel mode chain. Checking the prediction capability of the model by using known attribute parameters (such as travel time, cost, travel starting time and the like) to generate 10 pairs of training sets and matching verification sets, wherein the prediction accuracy of the model on a trip (trip) mode chain and a multi-trip (journey) mode chain respectively reaches 93.13% and 89.06%; meanwhile, in order to better visualize the predicted performance, some aggregation attributes (the number of patterns used in one day, the number of modes used in each trip and the proportion of modes) are also used for evaluating the predicted performance, and the observed and predicted results are averaged on 10 verification sets. Comparison between observations and predictions as shown in fig. 2, fig. 3 shows the results of the validation and comparison of the mode occupancy, with some values of the model predictions differing by no more than 2.5% from the observation samples. The above verification results confirm that the model can accurately characterize the selection mode of the actor mode chain.
Claims (7)
1. A travel mode chain selection method considering population heterogeneity under a dynamic structure is characterized by comprising the following steps:
(1) utilizing a Logit model to represent the prior probability of each traveler belonging to each unobservable type;
(2) calculating an expected utility equation of a pedestrian belonging to an unobservable type by applying a Bellman optimal criterion, optimizing the expected utility equation, determining a value function specific to an option, and determining a conditional selection probability function by using the value function;
(3) calculating a likelihood function of trip selection of each stage of the travelers by using the conditional selection probability, and then calculating a combined likelihood function of all the travelers for making continuous trip mode selection according to the likelihood function of each stage;
(4) calculating posterior probabilities of the travelers belonging to the unobservable types according to the prior probabilities and the likelihood functions, and updating the conditional selection probabilities by using the posterior probabilities;
(5) calculating utility parameters and type parameters of the dynamic discrete selection model through a maximum likelihood function;
(6) utilizing an expectation-maximization algorithm to iteratively optimize the prior probability, the posterior probability and the combined likelihood function, and maximizing the combined likelihood function to obtain the utility parameter and the type parameter at the same time;
(7) and (4) carrying out parameter estimation on the utility parameters and the type parameters finally obtained in the step (6) by using known data, and using the accuracy of the cross validation model.
2. A method of selecting a travel mode chain according to claim 1, wherein the expression of the prior probability of step 1 is:
wherein munζFor travelers n belonging to the unobservable class ζ prior probability, βζFor the type parameter to be estimated, znAnd the travel attribute vector is a travel attribute vector of the traveler n, the travel attribute vector comprises travel time, travel distance and traveler age, zeta is an unobservable type to which each traveler belongs, and l represents all unobservable types.
3. A method of travel mode chain selection according to claim 2, characterised in that at each stage K e {1,2, …, K ∈ {1,2, … }nThe travelers fromAnd selecting from the feasible subsets to maximize the current and reduced future utility values as a selection rule, wherein the combined utility comprises three parts: immediate utility u of current stage kk(xk,yk,akζ), error term ε, and discounting future utility, the state variable of the traveler is x after applying the Bellman optimality criterion and integrating the error term εkWith a non-state variable of ykWhen the expected utility V is of the unobservable type ζk(xk,ykζ) equation is:
wherein a iskShows the actions of the traveler per stage k, CkIs an action akA limited selection set of; epsilonkFor unobserved error variables, ∈k+1Independent of the variables of the preceding stage,. epsilonkIndependent at all stages and subject to the same distribution; state variable xkIncluding the trip purpose P e P, the used trip mode sequence S e S { m }1,m2,…,mk-1The feasible mode subset is H ∈ H, the departure time st, st of the current stage is a discrete variable with the interval of half an hour, therefore xk＝{pk,sk,hk,stkIs (0,1) represents a reduction coefficient, XkIs a state variable xkOf a non-state variable ykIncluding population attribute variables and transit times in different ways, mkRepresents the travel pattern used in stage k, f (x)k+1|xk,akζ) denotes a given (x)k,akζ) obtaining the state variable xk+1Transition probability of g (. epsilon.)k) The transition probability of the variables which are not observed is defined, and each variable definition domain is a real number domain; x is the number ofk+1Including xkAll valid information transferred;
to obtain a closed form of the computational structure, let ε be assumedkIndependently and equally distributed in Gumbel of Gumbel, g (epsilon) ═ njg(εj)，It is thus desirable that the utility equation be simplified to:
wherein v isk(xk,yk,akζ) is an option-specific cost function and γ is an euler constant, then action akThe conditional choice probability expression of (1) is:
wherein a'kSet C for limited selectionkAll of the elements of (a);
expressing the expected utility equation by the conditional choice probability is:
the state vector (x) is known from the above formulak,ykZeta expected utility V)k(xk,ykζ) is the sum of the following values: option specific cost function vk(xk,yk,akζ), the probability of negative condition selection after logarithmic transformation, and the euler constant γ; when selecting akConditional selection probability P (a) ofk|xk,ykζ) is less than a preset threshold value, the expected utility Vk(xk,ykζ) approaches the optimal option-specific cost function vk(xk,yk,akζ) plus a constant γ, indicate different merit functions vk(xk,yk,akζ) is a function of the corresponding conditional probability, then the option-specific cost function expression is:
4. a method of selecting a travel mode chain according to claim 3, wherein said step (3) of calculating each phase likelihood function includes:
the non-state variable of traveler n is yn＝{yn1,…,yn,(Kn+1)Is x, the state variablen＝{xn1,…,xn,(Kn+1)Making continuous travel selection as an＝{an1,…,anKnAt stage k, at state vector (x)nk,ynkζ) and utility parameter βu＝(βu1,…,βuζ,…,βuZ) Observe the traveler making a choicenkThe likelihood function of (d) is:
wherein f (x)nk+1|xnk,ankζ) is given as (x)nk,ankζ) under xnk+1The transition probability of (2);
the combined likelihood function expression is:
wherein N is the total number of travelers.
5. A method of selecting a travel mode chain according to claim 4, wherein the posterior probability of step (4) is calculated by:
at a given state-a selection pair and a parameter (beta)u,βζ) In the case of (1), the posterior probability expression that the actor n belongs to the unobservable type ζ is:
wherein E is the desired symbol; i represents a flag variable, when ∑ isnWhen ζ is equal to 1, otherwise, it is 0;
the type-specific conditional selection probability obtained from the posterior probability is:
6. a method for selecting a travel mode chain according to claim 5, wherein the utility parameter β of step (5)uAnd a type parameter betaζThe expression is as follows:
respectively to the utility parameter betauAnd a type parameter betaζPerforming first-order derivation:
7. a method of travel mode chain selection according to claim 6, wherein the iterative optimization of step (6) is performed by:
first, utility parameters and type parameters are initialized
And given state (x)n,ynζ) conditional selection probability p of all options a1(a|xn,ynζ) assuming the first iterationInstead, the probability does not vary with type, and the (i +1) th iteration proceeds according to the following steps:
(601) according to type parameter
Updating prior probabilities
602) Computing type-specific likelihood functions
Firstly, calculating a transfer matrix with a specific type according to a box estimation method:
the transition matrix is composed of state transition probabilities, and a likelihood function is obtained through calculation according to the conditional selection probability and the state transition probabilities;
(603) updating the posterior probability according to the prior probability and the likelihood function, wherein the expression is as follows:
(604) maximizing the combined likelihood function:
and (3) providing a new log-likelihood function to replace the previous combined likelihood function, wherein the expression is as follows:
maximization
To find optimal utility parametersβuAnd a type parameter betaζ：
(605) Updating the conditional selection probability:
according to the equation relationship between the conditional selection probability and the posterior probability, the updated conditional selection probability expression is as follows:
and ending the iteration updating when the iteration times set previously are reached, and outputting the optimal utility parameters and type parameters.
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