CN104504229A - Intelligent bus scheduling method based on hybrid heuristic algorithm - Google Patents

Abstract

The invention discloses an intelligent bus scheduling method based on a hybrid heuristic algorithm. A simulated annealing algorithm and a generic algorithm are combined, and an elitism strategy and a fitness stretching function are added. Individuals with maximum fitness in a population of each generation are directly retained to a next generation, so that the individuals are protected from being damaged by crossover and mutation operation. Through the fitness stretching function, differences among the individuals are reduced at the initial stage of the algorithm, so that the diversity of the population is increased, and the generic algorithm is prevented from falling into a local optimal solution. At the later stage of the algorithm, the differences among the individuals are increased, so that the selection probability of excellent individuals is increased, and a convergence speed is increased. The intelligent bus scheduling method is high in speed; an optimized scheduling plan can be obtained within a short time under the condition of given departure time frequency; and the waiting time of passengers is shortened greatly. The departure frequency can be adjusted dynamically, so that the departure frequency is accordant with the change rule of a total passenger flow volume. The departure time intervals can be adjusted dynamically, so that the waiting time of the passengers is shortened greatly.

Description

A kind of intelligent public transportation dispatching method based on hybrid metaheuristics

Technical field

The invention belongs to city intelligent public transportation system technical field, relate to a kind of intelligent public transportation dispatching method based on hybrid metaheuristics, particularly a kind of method that the departure plan of bus rapid transit is dispatched.

Background technology

Along with the fast development in city, urban population constantly increases, and the quantity of private car, also along with a large amount of growth, causes traffic congestion and problem of environmental pollution is increasingly serious.Give full play to the effect of urban public tranlport system, these problems can be alleviated.But public transport also has the problem that passenger waiting time is longer and passenger satisfaction is lower at present.How effectively to solve existing problem, be the key increasing public transport attractive force.Bus dispatching is the center of the daily operation activity of enterprises of public transport, and it directly has influence on operation cost and passenger satisfaction.The bus dispatching scheme meeting passenger flow rule according to the change adjustment departure interval of the volume of the flow of passengers, can strengthen the specific aim of bus service, decreases the Waiting time of passenger, improve transit quality of service, increase the attractive force of public transport.

The object of bus dispatching is exactly when meeting passenger's trip requirements, saves operation cost as far as possible.These two conflicting requirements cause this to be a multi-objective optimization question.Meanwhile, bus dispatching will be subject to many-sided constraints such as enterprises of public transport's operation cost, Fleet size.Under how meeting volume of the flow of passengers demand and constraint condition at the same time, finding suitable method to determine bus dispatching scheme within the rational time, is the key realizing intelligent bus scheduling.Bus dispatching is divided into static scheduling and dynamic dispatching two parts, and static scheduling mainly refers to the departure time-table of working out every bar circuit, and dynamic dispatching mainly completes and adjusts existing departure time-table when there is the emergency case such as vehicle, passenger flow.In daily operation, static scheduling is main, and dynamic dispatching is auxiliary.The present invention relates generally to the scheduling problem how using the hybrid metaheuristics of improvement to solve bus rapid transit.

At present, have much in the research in this field both at home and abroad, but the concrete condition of each urban mass-transit system is different, there is no a kind of comparatively general method can carrying out bus dispatching in conjunction with history operation data.In these researchs, have a lot of people to use the heuritic approaches such as genetic algorithm, or their innovatory algorithm is used for the optimization of bus dispatching.Genetic algorithm can find optimum solution or the approximate optimal solution of bus dispatching problem within the rational time, and this is also that many researchers use it to solve the reason of bus dispatching.The shortcomings such as but genetic algorithm exists easy Premature Convergence, and efficiency is low.

Summary of the invention

The object of the invention is the deficiency in order to overcome genetic algorithm self, and a kind of method proposing novelty solves the conflict of interest between passenger and bus operation enterprise.Simulated annealing and genetic algorithm combine by the method that the present invention relates to, and add elite's retention strategy and fitness stretch function.Individuality maximum for fitness in every generation population is directly remained into the next generation, avoids it to be destroyed by crossover and mutation operation.Fitness stretch function, in the initial stage of algorithm, cuts down the difference between individuality, thus increases the diversity of population, avoids genetic algorithm to be absorbed in locally optimal solution; At the later stage of algorithm, increase the difference between individuality, thus increase excellent individual by the probability selected, convergence speedup speed.Simulated annealing can increase the local search ability of genetic algorithm, thus accelerates the speed of convergence of genetic algorithm.

The concrete steps of method of the present invention are as follows:

Step (1) reads the record of swiping the card of passenger, the number that statistics is ridden in total number of persons and each time period I every day, obtain every day weather history situation and festivals or holidays situation; Use hierarchy clustering method, cluster analysis is carried out to the historical data obtained; By the number of passengers in total number of persons, the different time sections by bus in the middle of a day, weather condition and festivals or holidays situation be combined into a vector, then operation is normalized to this vector, use the Ward method in system clustering algorithm to carry out cluster operation, extract the feature of each classification according to the result of cluster;

Described record of swiping the card comprises charge time of getting on the bus, website of getting on the bus, get off charge time and get-off stop;

The historical data of described acquisition comprise the record of swiping the card of passenger, weather history situation and festivals or holidays situation;

Step (2) according to the weather forecast information of second day and festivals or holidays situation, from the cluster result of step 1, match a class, and from such, extract a vector as predicted value;

Step (3) is according to predicted value, and in conjunction with the load factor that enterprises of public transport are expected, both are divided by, and obtain the order of classes or grades at school of always dispatching a car of second day;

The N number of vector of step (4) stochastic generation, the dimension of vector is equal with order of classes or grades at school of always dispatching a car; Each component represents the time of departure of corresponding order of classes or grades at school, the time of departure by minute in units of, set one-component and equal 0, last component equals the number of minutes between the last bus time of departure and first bus time of departure; Component in vector is by order arrangement from small to large, and this N number of vector forms the set P of initial solution ₀, and to set iterations g be 0; Wherein N is even number;

Step (5) sets up the mathematical model of bus dispatching, the shortest in goal-setting fitness function with the stand-by period of passenger, calculates the fitness of each initial solution, is then solved by hybrid metaheuristics;

5-1. uses fitness stretch function to carry out fitness stretched operation, replaces original fitness by the value after stretching;

5-2. according to roulette selection strategy from set P _gany two solutions of middle selection, carry out interlace operation, i.e. Stochastic choice crossover location according to the crossover probability of setting, exchange two parts of separating before and after point of crossing, obtain the solution after two intersections; Then after intersecting to two, solution carries out simulated annealing operation: the fitness calculating the solution after intersecting, if fitness increases, accepts new solution, otherwise accepts new solution with current acceptance probability; Thus the solution that acquisition two is new;

5-3. according to the mutation probability of setting, carry out mutation operation to each component of two new explanations obtained in step 5-2, namely the natural number of a stochastic generation size between former and later two components, replaces original value, obtain the solution after two variations; Then carry out simulated annealing operation: the fitness calculating the solution after variation, if fitness increases, accept new solution, otherwise accept new solution with current acceptance probability; Thus obtain two new solutions, and two that obtain new solutions are put into disaggregation P _g+1;

5-4. repeats step 5-2 and 5-3, until disaggregation P _g+1the number of middle solution is equal with N;

Step (6) upgrades iterations g=g+1, if reached maximum iterations G _max, then disaggregation P is exported _gthe solution that middle fitness is the highest, is the departure time-table after optimization; Otherwise, forward step 5-1 to;

Described iterations G _maxfor positive integer.

Setting up of bus dispatching mathematical model described in step 5 is specific as follows:

(1) the bus dispatching mathematical model described in has following precondition:

After BRT vehicle stops, waiting Passengen is all got on the bus, and there is not trapping phenomena;

, there is not coin or swipe the card on the impact of time of vehicle operation in the mode that BRT adopts car to charge completely outward;

BRT adopts identical vehicle model completely, and amount of seats is identical with maximum passenger carrying capacity;

That does not consider circuit joins car, thinks that vehicle is abundant;

BRT vehicle is dispatched a car by schedule time list;

BRT vehicle is order and sequence consensus of dispatching a car on road, there is not phenomenon of overtaking other vehicles;

Using minute as scheduling least unit;

(2) variable used in the bus dispatching mathematical model described in and implication as follows:

M is the number of times of dispatching a car in whole dispatching cycle;

N is website quantity total on circuit assigned direction;

T _ibe the time of departure of the i-th train in the dispatching cycle, by minute in units of, i=1,2 ..., m;

R _jfor the time dependent arrival rate of a jth website on circuit assigned direction, unit behaviour/minute, j=1,2 ..., n;

T is the total waiting time of passenger in dispatching cycle;

Then

$T=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{r}_j\×\frac{{(t_i-t_{i-1})}^2}{2}$

The cost of bus operation is divided into fixed cost and variable cost, there is not direct relation between bus dispatching and fixed cost; If bus operation income is R in the dispatching cycle, P is that riding fee uses (unit) per capita, L is assigned direction total line length (km), C is the variable cost (unit/km) of public transit vehicle, then the income of public transport company is that gross income deducts total variable cost, specific as follows:

$R=P\×\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{r}_j\×(t_i-t_{i-1})-C\×L\×m$

If μ is passenger waiting time weight coefficient, ν is public transport company's usufruct coefficient; According to secondary penalty method, the objective function of bus dispatching Optimized model is:

minz＝μ×T-ν×R

If N _maxfor maximum appearance of vehicle amount, ρ is for expecting load factor, then Prescribed Properties I:

$\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{r}_j\×(t_i-t_{i-1})\≥\mathrm{\ρ}\×N_{\max },i=\mathrm{2,3},...,m$

In order to ensure rule arrive passenger and random arrive passenger can wait until in the short period of time to wait, if H _minand H _maxbe respectively the minimum and maximum departure interval that public transport company requires, then the departure interval should meet constraint condition II below:

H _min≤t _i-t _i-1≤H _maxi＝2,3,...,m

Cause the non-continuous event of dispatching a car for avoiding simultaneously, if τ is the maximum departure interval difference that public transport company allows, then constraint condition III:

|(t _i+1-t _i)-(t _i-t _i-1)|≤τ i＝2,3,...,m-1

Ensure that the solution produced does not violate the constraint condition of scheduling problem by penalty function method; Based on above description, objective function minf (X) form of scheduling problem is as follows:

$\begin{array}{c}\min f\left(X\right)=\min z+{\mathrm{\ω}}_1\underset{i=2}{\overset{m}{\mathrm{\Σ}}}\left\{\max \right\{0,\mathrm{\ρ}\×N_{\max }-\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{r}_j\×(t_i-t_{i-1})\left\}\right\}+\\ {\mathrm{\ω}}_2\underset{i=2}{\overset{m}{\mathrm{\Σ}}}\left\{\max \right\{0,T_{\min }-(t_i-t_{i-1})\left\}\right\}+\\ {\mathrm{\ω}}_3\underset{i=2}{\overset{m}{\mathrm{\Σ}}}\left\{\max \right\{0,(t_i-t_{i-1})-T_{\max }\left\}\right\}+\\ {\mathrm{\ω}}_4\underset{i=2}{\overset{m-1}{\mathrm{\Σ}}}\left\{\max \right\{0,|(t_{i+1}-t_i)-(t_i-t_{i-1})|-\mathrm{\τ}\left\}\right\}\end{array}$

Wherein minf (X) is for adding the target function value after penalty function, ω ₁, ω ₂, ω ₃, ω ₄be respectively the penalty coefficient of constraint condition I, constraint condition II minimum departure interval, constraint condition II maximum departure interval, constraint condition III correspondence; The vector of the solution X of scheduling problem to be length be m, each component x _irepresent the time of departure of i-th spacing first bus in dispatching cycle, by minute in units of;

In order to ensure that the fitness of each individuality is all greater than 0, also conveniently use roulette selection strategy, converting to objective function the final form obtaining fitness function is simultaneously:

Described simulated annealing can strengthen the local search ability of genetic algorithm, completes after interlace operation and mutation operation in genetic algorithm at every turn, compares the fitness of former and later two individualities, carries out simulated annealing operation; Need in simulated annealing to set initial temperature T ₀, the computing formula of Current Temperatures is:

T*＝T ₀×σ ^g-1

Wherein σ represents the speed that temperature reduces, and its value is 0 < σ < 1, and its value is larger, and it is slower that temperature reduces, and is worth less, and it is faster that temperature reduces; G is the number of times of algorithm current iteration; When the fitness of the new individuality produced reduces, accepting new individual probability is:

$P^{*}=\exp \left(\frac{F\left(X_{\mathrm{new}}\right)-F\left(X_{\mathrm{old}}\right)}{T^{*}}\right)$

Wherein F (X _new), F (X _old) be respectively the fitness of new individuality and former individuality;

Simultaneously there is most outstanding individual physical efficiency to enter the new individuality of generation of future generation smoothly in each population to ensure, in the blending algorithm of simulated annealing and genetic algorithm, adding elite's retention strategy; After often producing new generation population, the fitness value of optimized individual in population more of new generation and previous generation population; If the fitness of the optimized individual of population of new generation is less than the optimized individual of previous generation, then replace the minimum individuality of fitness in a new generation by the optimized individual of previous generation; Otherwise directly enter next iteration.

The form of the stretch function described in step 5-1 is:

$F{\left(X_i\right)}^{\&prime;}=\frac{e^{\mathrm{\&lambda;}\&times;F\left(X_i\right)/T*}}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{\mathrm{\&lambda;}\&times;F\left(X_i\right)/T*}}$

Wherein F (X _i) represent individual X _ifitness, F (X _i) ' be fitness after stretching, T* refers to temperature current in simulated annealing, and N to represent in population individual quantity, and λ represents drawing coefficient;

In order to fitness stretching can be carried out, fitness criteria to be carried out to individualities all in population before the stretching, order

${\mathrm{fitness}}^{\&prime;}=\frac{\mathrm{fitness}}{\max \mathrm{fitness}}$

Wherein fitness refers to individual fitness, and fitness' refers to the fitness after standardization, and max fitness refers to the fitness of optimized individual in current population.

The basic step of the hybrid metaheuristics described in step 5 is as follows:

1). be set as follows the value of parameter: Population Size N, chromosome length L _c, crossover probability P _c, mutation probability P _m, maximum evolutionary generation G _max, initial temperature T ₀, annealing speed σ, drawing coefficient λ;

2). initialization population P ₀, namely the N number of feasible solution of random generation forms initialization population P ₀; Calculate fitness individual in initial population, carry out standardization, stretched operation is carried out to fitness; Setting iterations g is 0;

3). carry out roulette selection, from population P according to the fitness after stretching _gmiddle random selecting two individualities;

4). intersect and simulated annealing operation; Adopt single-point Crossover Strategy, by by two the individual p selected ₁, p ₂by probability P _ccarry out interlace operation and produce two new individual c ₁, c ₂; If F is (c _i) > F (p _i), then accept individual c ₁, otherwise with probability exp ((F (c _i)-F (p _i))/T*) accept new individuality;

5). variation and simulated annealing operation; To the new individual c produced ₁, c ₂carry out mutation operation by turn, if the individual c after variation ₁' fitness increase, then accept variation, otherwise with probability exp ((F (c _i')-F (c _i))/T*) accept new individuality;

6). new two individualities produced are added new population P _g+1in, if P _g+1middle individual amount is less than N, then forward step 3 to), otherwise carry out next step;

7). calculate the fitness of each individuality in new population, column criterionization of going forward side by side operates;

8). fitness stretching is carried out to the individuality in new population;

9). implement elite's retention strategy, replace original seed group with new population;

10). cooling operation;

11). upgrade iterations g=g+1, if reach maximum iteration time G _max, then population P is exported _gin optimum solution, otherwise forward step 3 to).

Beneficial effect of the present invention is as follows:

Fitness drawing process joins in Genetic Simulated Annealing Algorithm by the present invention, improves the shortcoming of the easy Premature Convergence of former algorithm.Compare with former algorithm, the algorithm after improvement is to the objective function optimization better effects if of bus dispatching problem.The method that the present invention relates to is by the operation cost optimization of bus operation enterprise, and passenger waiting time optimization divides and carries out two different stages.Bus operation cost is divided into fixed cost and variable cost, and the main and variable cost of bus dispatching is closely related, and variable cost is primarily of order of classes or grades at school decision of dispatching a car.The optimization of operation cost reasonably predicts the volume of the flow of passengers based on large data, then expects that the vehicle load factor reached calculates total order of classes or grades at school of dispatching a car in conjunction with operation enterprise.The Cost Optimization Approach that the present invention relates to can " my god " level on realize people and the more dispatch a car, the effect that people dispatches a car less.The optimization of passenger waiting time is by using the Genetic Simulated Annealing Algorithm merging fitness drawing process to be optimized for the objective function set up, the bus dispatching plan after being finally optimized.

Achieve following target specifically:

By the record of swiping the card of passenger according to whether being that festivals or holidays and weather condition carry out cluster analysis, the feature of each classification can be extracted.

According to festivals or holidays of second day and weather condition on the basis of historical data, the volume of the flow of passengers can be predicted comparatively accurately.

According to predicting the volume of the flow of passengers that obtain, order of classes or grades at school of reasonably dispatching a car can be calculated, make to dispatch a car order of classes or grades at school according to the volume of the flow of passengers number adjust accordingly.

Can under given order of classes or grades at school condition of dispatching a car, according to the different distribution situation of the volume of the flow of passengers in different time sections in the middle of a day, the departure interval is adjusted, realizes people within the different time periods and the more dispatch a car, the object that people dispatches a car less.But maximum departure interval and minimum departure interval need meet some requirements.

In sum, the invention process effect is as follows:

(1) fast operation, can within a short period of time under given time of departure frequency condition, the operation plan after being optimized, makes the stand-by period of passenger significantly reduce.(2) can according to festivals or holidays and weather condition, dynamic conditioning departure frequency, makes departure frequency meet the Changing Pattern of passenger flow total amount.(3) according to the change of the different time sections volume of the flow of passengers in the middle of a day, the dynamic conditioning departure interval, the stand-by period of passenger can significantly be reduced.

Accompanying drawing explanation

The temperature variant curve of Fig. 1 stretch function.

Fig. 2 history optimized individual fitness change curve.

Fig. 3 history population average fitness change curve.

The contrast of the change of Fig. 4 hybrid metaheuristics history optimized individual fitness and other two kinds of algorithms.

Fig. 5 algorithm flow chart.

Fig. 6 interlace operation process flow diagram.

Fig. 7 mutation operation process flow diagram.

Concrete embodiment

Below in conjunction with drawings and Examples, the invention will be further described.

Based on an intelligent public transportation dispatching method for hybrid metaheuristics, specifically comprise the steps:

Step (1) reads the record of swiping the card of passenger, the number that statistics is ridden in total number of persons and each time period I every day.Capture from 2345 weather forecast websites and perpetual calendar every day weather history situation and festivals or holidays situation.Use hierarchy clustering method, cluster analysis is carried out to the historical data obtained; By the number of passengers in total number of persons, the different time sections by bus in the middle of a day, weather condition and festivals or holidays situation be combined into a vector, then operation is normalized to this vector, use the Ward method in system clustering algorithm to carry out cluster operation, extract the feature of each classification according to the result of cluster.After these operations, we can predict the volume of the flow of passengers comparatively accurately according to the concrete condition of scheduling day.

Record of swiping the card comprises charge time of getting on the bus, website of getting on the bus, get off charge time and get-off stop.

The historical data obtained comprise the record of swiping the card of passenger, weather history situation and festivals or holidays situation.

Step (2) according to the weather forecast information of second day and festivals or holidays situation, from the cluster result of step 1, match a class, and from such, extract a vector as predicted value;

Step (3) is according to predicted value, and in conjunction with the load factor that enterprises of public transport are expected, both are divided by, and obtain the order of classes or grades at school of always dispatching a car of second day;

The N number of vector of step (4) stochastic generation, the dimension of vector is equal with order of classes or grades at school of always dispatching a car.Each component represents the time of departure of corresponding order of classes or grades at school, the time of departure by minute in units of, set one-component and equal 0, last component equals the number of minutes between the last bus time of departure and first bus time of departure; Component in vector is by order arrangement from small to large, and this N number of vector forms the set P of initial solution ₀, and to set iterations g be 0; Wherein N is even number;

Step (5) sets up the mathematical model of bus dispatching, the shortest in goal-setting fitness function with the stand-by period of passenger, calculates the fitness of each initial solution, is then solved by hybrid metaheuristics.

5-1. uses fitness stretch function to carry out fitness stretched operation, replaces original fitness by the value after stretching;

5-2. according to roulette selection strategy from set P _gany two solutions of middle selection, carry out interlace operation, i.e. Stochastic choice crossover location according to the crossover probability of setting, exchange two parts of separating before and after point of crossing, obtain the solution after two intersections; Then the solution after intersecting to two carries out simulated annealing operation: the fitness calculating the solution after intersecting, if fitness increases, accepts new solution, otherwise accepts new solution with current acceptance probability; Thus the solution that acquisition two is new;

5-3. according to the mutation probability of setting, carry out mutation operation to each component of two new explanations obtained in step 5-2, namely the natural number of a stochastic generation size between former and later two components, replaces original value, obtain the solution after two variations.Then carry out simulated annealing operation: the fitness calculating the solution after variation, if fitness increases, accept new solution, otherwise accept new solution with current acceptance probability; Thus obtain two new solutions, and two that obtain new solutions are put into disaggregation P _g+1;

5-4. repeats step 5-2 and 5-3, until disaggregation P _g+1the number of middle solution is equal with N;

Step (6) upgrades iterations g=g+1, if reached maximum iterations G _max, then disaggregation P is exported _gthe solution that middle fitness is the highest, is the departure time-table after optimization.Otherwise, forward step 5-1 to.

Described iterations G _maxfor positive integer.

Setting up of bus dispatching mathematical model described in step 5 is specific as follows:

(1) the bus dispatching mathematical model described in has following precondition:

After BRT vehicle stops, waiting Passengen is all got on the bus, and there is not trapping phenomena.

, there is not coin or swipe the card on the impact of time of vehicle operation in the mode that BRT adopts car to charge completely outward.

BRT adopts identical vehicle model completely, and amount of seats is identical with maximum passenger carrying capacity.

That does not consider circuit joins car, thinks that vehicle is abundant.

BRT vehicle is dispatched a car by schedule time list.

BRT vehicle is order and sequence consensus of dispatching a car on road, there is not phenomenon of overtaking other vehicles.

Using minute as scheduling least unit.

(2) variable used in the bus dispatching mathematical model described in and implication as follows:

M is the number of times of dispatching a car in whole dispatching cycle;

N is website quantity total on circuit assigned direction;

T _ibe the time of departure of the i-th train in the dispatching cycle, by minute in units of, i=1,2 ..., m;

R _jfor the time dependent arrival rate of a jth website on circuit assigned direction, unit behaviour/minute, j=1,2 ..., n;

T is the total waiting time of passenger in dispatching cycle.

Then

$T=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_j\&times;\frac{{(t_i-t_{i-1})}^2}{2}$

The cost of bus operation is divided into fixed cost and variable cost, there is not direct relation, therefore only consider variable cost here between bus dispatching and fixed cost.If in the dispatching cycle bus operation income to be R, P be per capita riding fee with (unit), the variable cost (unit/km) of L to be assigned direction total line length (km), C be public transit vehicle.The income of public transport company is that gross income deducts total variable cost, therefore has

$R=P\&times;\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_j\&times;(t_i-t_{i-1})-C\&times;L\&times;m$

If μ is passenger waiting time weight coefficient, ν is public transport company's usufruct coefficient.According to secondary penalty method, the objective function of bus dispatching Optimized model is

minz＝μ×T-ν×R

In order to make full use of public transport resources, public transport company requires that vehicle load factor is higher than expectation load factor.If N _maxfor maximum appearance of vehicle amount, ρ is for expecting load factor, then Prescribed Properties I:

$\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_j\&times;(t_i-t_{i-1})\&GreaterEqual;\mathrm{\&rho;}\&times;N_{\max },i=\mathrm{2,3},...,m$

In order to ensure rule arrive passenger and random arrive passenger can wait until in the short period of time to wait.Suppose H _minand H _maxbe respectively the minimum and maximum departure interval that public transport company requires, then the departure interval should meet constraint condition II below:

H _min≤t _i-t _i-1≤H _maxi＝2,3,...,m

Meanwhile, the difference of the departure interval of adjacent two order of classes or grades at school vehicles should not be too large, avoids causing the non-continuous event of dispatching a car.Suppose that τ is the maximum departure interval difference that public transport company allows, then constraint condition III:

|(t _i+1-t _i)-(t _i-t _i-1)|≤τ i＝2,3,...,m-1

Ensure that the solution produced does not violate the constraint condition of scheduling problem by penalty function method; Based on above description, objective function minf (X) form of scheduling problem is as follows:

$\begin{array}{c}\min f\left(X\right)=\min z+{\mathrm{\&omega;}}_1\underset{i=2}{\overset{m}{\mathrm{\&Sigma;}}}\left\{\max \right\{0,\mathrm{\&rho;}\&times;N_{\max }-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_j\&times;(t_i-t_{i-1})\left\}\right\}+\\ {\mathrm{\&omega;}}_2\underset{i=2}{\overset{m}{\mathrm{\&Sigma;}}}\left\{\max \right\{0,T_{\min }-(t_i-t_{i-1})\left\}\right\}+\\ {\mathrm{\&omega;}}_3\underset{i=2}{\overset{m}{\mathrm{\&Sigma;}}}\left\{\max \right\{0,(t_i-t_{i-1})-T_{\max }\left\}\right\}+\\ {\mathrm{\&omega;}}_4\underset{i=2}{\overset{m-1}{\mathrm{\&Sigma;}}}\left\{\max \right\{0,|(t_{i+1}-t_i)-(t_i-t_{i-1})|-\mathrm{\&tau;}\left\}\right\}\end{array}$

Wherein minf (X) is for adding the target function value after penalty function, ω ₁, ω ₂, ω ₃, ω ₄be respectively the penalty coefficient of constraint condition I, constraint condition II minimum departure interval, constraint condition II maximum departure interval, constraint condition III correspondence.The vector of the solution X of scheduling problem to be length be m, each component x _irepresent the time of departure of i-th spacing first bus in dispatching cycle, by minute in units of.

The objective function of bus dispatching is minimization problem, in order to ensure that the fitness of each individuality (solution in the middle of the corresponding disaggregation of each individuality) is all greater than 0, also conveniently use roulette selection strategy, converting to objective function the final form obtaining fitness function is simultaneously:

Simulated annealing can strengthen the local search ability of genetic algorithm, completes after interlace operation and mutation operation in genetic algorithm at every turn, compares the fitness of former and later two individualities, carries out simulated annealing operation.Need in simulated annealing to set initial temperature T ₀, the computing formula of Current Temperatures is:

T*＝T ₀×σ ^g-1

Wherein σ represents the speed that temperature reduces, and its value is 0 < σ < 1, and its value is larger, and it is slower that temperature reduces, and is worth less, and it is faster that temperature reduces; G is the number of times of algorithm current iteration.When the fitness of the new individuality produced reduces, accepting new individual probability is:

$P^{*}=\exp \left(\frac{F\left(X_{\mathrm{new}}\right)-F\left(X_{\mathrm{old}}\right)}{T^{*}}\right)$

Wherein F (X _new), F (X _old) be respectively the fitness of new individuality and former individuality.

Simultaneously there is most outstanding individual physical efficiency to enter the new individuality of generation of future generation smoothly in each population to ensure, in the blending algorithm of simulated annealing and genetic algorithm, adding elite's retention strategy.After often producing new generation population, the fitness value of optimized individual in population more of new generation and previous generation population.If the fitness of the optimized individual of population of new generation is less than the optimized individual of previous generation, then replace the minimum individuality of fitness in a new generation by the optimized individual of previous generation.Otherwise directly enter next iteration.

In step 5-1, the form of stretch function is:

$F{\left(X_i\right)}^{\&prime;}=\frac{e^{\mathrm{\&lambda;}\&times;F\left(X_i\right)/T*}}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{\mathrm{\&lambda;}\&times;F\left(X_i\right)/T*}}$

Wherein F (X _i) represent individual X _ifitness, F (X _i) ' be fitness after stretching, T* refers to temperature current in simulated annealing, and N to represent in population individual quantity, and λ represents drawing coefficient.

Embodiment 1

Illustrate the effect of stretch function in Genetic Simulated Annealing Algorithm below.Work as T*=5000, λ=200, suppose to have 10 individual fitness to be respectively 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0, individual as shown in table 1 by the comparing result of the probability selected before and after stretching.Work as T*=50, λ=200, suppose to have 10 individual fitness to be respectively 0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.80, individual as shown in table 2 by the comparing result of the probability selected before and after stretching.In form, No. represents individual numbering, and fitness represents individual fitness, P ₁individual by the probability selected before representative stretches, P ₂it is individual by the probability selected after representative stretches.From comparing result, obviously can obtain drawing a conclusion: when temperature is higher, after stretched, the difference between individuality reduces; When the temperature is low, stretched, the difference between individuality becomes large.

Individual by the contrast of select probability before and after stretching during table 1 T*=5000

No.	1	2	3	4	5	6	7	8	9	10
											fitness	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
P 1	0.0182	0.0364	0.0545	0.0727	0.0909	0.1091	0.1273	0.1455	0.1636	0.1818
											P 2	0.0982	0.0986	0.0990	0.0994	0.0998	0.1002	0.1006	0.1010	0.1014	0.1018

Individual by the contrast of select probability before and after stretching during table 2 T*=50

No.	1	2	3	4	5	6	7	8	9	10
											fitness	0.71	0.72	0.73	0.74	0.75	0.76	0.77	0.78	0.79	0.80
P 1	0.0940	0.0954	0.0967	0.0980	0.0993	0.1007	0.1020	0.1033	0.1046	0.1060
											P 2	0.0830	0.0864	0.0899	0.0936	0.0974	0.1013	0.1055	0.1098	0.1143	0.1189

Digital scope expressed by the basic data type that programming language can provide is limited, in order to carry out fitness stretching, will carry out fitness criteria before the stretching to individualities all in population, order

${\mathrm{fitness}}^{\&prime;}=\frac{\mathrm{fitness}}{\max \mathrm{fitness}}$

Wherein fitness refers to individual fitness, and fitness' refers to the fitness after standardization, and maxfitness refers to the fitness of optimized individual in current population.

The hybrid metaheuristics after improving finally is used to solve.Fig. 1 gives the process flow diagram of this algorithm, as can be seen from the figure the hybrid metaheuristics improved mainly contains selection, intersection, variation, simulated annealing, elite's reservation, standardization and fitness stretched operation, and in solution procedure, these operations act on colony P one by one _g, then produce population P of new generation _g+1.Fig. 2,3,4 is the comparison diagram of history optimized individual fitness change curve in algorithm implementation, history population average fitness change curve and this algorithm and other two kinds of algorithms respectively.

The basic step of the hybrid metaheuristics described in step 5 is as follows:

12). be set as follows the value of parameter: Population Size N, chromosome length L _c, crossover probability P _c, mutation probability P _m, maximum evolutionary generation G _max, initial temperature T ₀, annealing speed σ, drawing coefficient λ.

13). initialization population P ₀, namely the N number of feasible solution of random generation forms initialization population P ₀.Calculate fitness individual in initial population, carry out standardization, stretched operation is carried out to fitness.The process flow diagram of the stretched operation that Fig. 5 provides.Setting iterations g is 0.

14). carry out roulette selection, from population P according to the fitness after stretching _gmiddle random selecting two individualities.

15). intersect and simulated annealing operation.Adopt single-point Crossover Strategy, by by two the individual p selected ₁, p ₂by probability P _ccarry out interlace operation and produce two new individual c ₁, c ₂.If F is (c _i) > F (p _i), then accept individual c ₁, otherwise with probability exp ((F (c _i)-F (p _i))/T*) accept new individuality.The process flow diagram of this step that what Fig. 6 provided is.

16). variation and simulated annealing operation.To the new individual c produced ₁, c ₂carry out mutation operation by turn, if the individual c after variation ₁' fitness increase, then accept variation, otherwise with probability exp ((F (c _i')-F (c _i))/T*) accept new individuality.The process flow diagram of this step that what Fig. 7 provided is.

17). new two individualities produced are added new population P _g+1in, if P _g+1middle individual amount is less than N, then forward step 3 to), otherwise carry out next step.

18). calculate the fitness of each individuality in new population, column criterionization of going forward side by side operates.

19). fitness stretching is carried out to the individuality in new population.

20). implement elite's retention strategy, replace original seed group with new population.

21). cooling operation.

22). upgrade iterations g=g+1, if reach maximum iteration time G _max, then population P is exported _gin optimum solution, otherwise forward step 3 to).

Claims (5)

1., based on an intelligent public transportation dispatching method for hybrid metaheuristics, it is characterized in that comprising the steps:

Step (1) reads the record of swiping the card of passenger, the number that statistics is ridden in total number of persons and each time period I every day, obtain every day weather history situation and festivals or holidays situation; Use hierarchy clustering method, cluster analysis is carried out to the historical data obtained; By the number of passengers in total number of persons, the different time sections by bus in the middle of a day, weather condition and festivals or holidays situation be combined into a vector, then operation is normalized to this vector, use the Ward method in system clustering algorithm to carry out cluster operation, extract the feature of each classification according to the result of cluster;

Described record of swiping the card comprises charge time of getting on the bus, website of getting on the bus, get off charge time and get-off stop;

The historical data of described acquisition comprise the record of swiping the card of passenger, weather history situation and festivals or holidays situation;

Step (2) according to the weather forecast information of second day and festivals or holidays situation, from the cluster result of step 1, match a class, and from such, extract a vector as predicted value;

Step (3) is according to predicted value, and in conjunction with the load factor that enterprises of public transport are expected, both are divided by, and obtain the order of classes or grades at school of always dispatching a car of second day;

The N number of vector of step (4) stochastic generation, the dimension of vector is equal with order of classes or grades at school of always dispatching a car; Each component represents the time of departure of corresponding order of classes or grades at school, the time of departure by minute in units of, set one-component and equal 0, last component equals the number of minutes between the last bus time of departure and first bus time of departure; Component in vector is by order arrangement from small to large, and this N number of vector forms the set P of initial solution ₀, and to set iterations g be 0; Wherein N is even number;

Step (5) sets up the mathematical model of bus dispatching, the shortest in goal-setting fitness function with the stand-by period of passenger, calculates the fitness of each initial solution, is then solved by hybrid metaheuristics;

5-1. uses fitness stretch function to carry out fitness stretched operation, replaces original fitness by the value after stretching;

5-2. according to roulette selection strategy from set P _gany two solutions of middle selection, carry out interlace operation, i.e. Stochastic choice crossover location according to the crossover probability of setting, exchange two parts of separating before and after point of crossing, obtain the solution after two intersections; Then after intersecting to two, solution carries out simulated annealing operation: the fitness calculating the solution after intersecting, if fitness increases, accepts new solution, otherwise accepts new solution with current acceptance probability; Thus the solution that acquisition two is new;

5-3. according to the mutation probability of setting, carry out mutation operation to each component of two new explanations obtained in step 5-2, namely the natural number of a stochastic generation size between former and later two components, replaces original value, obtain the solution after two variations; Then carry out simulated annealing operation: the fitness calculating the solution after variation, if fitness increases, accept new solution, otherwise accept new solution with current acceptance probability; Thus obtain two new solutions, and two that obtain new solutions are put into disaggregation P _g+1;

5-4. repeats step 5-2 and 5-3, until disaggregation P _g+1the number of middle solution is equal with N;

Step (6) upgrades iterations g=g+1, if reached maximum iterations G _max, then disaggregation P is exported _gthe solution that middle fitness is the highest, is the departure time-table after optimization; Otherwise, forward step 5-1 to;

Described iterations G _maxfor positive integer.

2. a kind of intelligent public transportation dispatching method based on hybrid metaheuristics as claimed in claim 1, is characterized in that setting up of the bus dispatching mathematical model described in step 5 is specific as follows:

(1) the bus dispatching mathematical model described in has following precondition:

After BRT vehicle stops, waiting Passengen is all got on the bus, and there is not trapping phenomena;

, there is not coin or swipe the card on the impact of time of vehicle operation in the mode that BRT adopts car to charge completely outward;

BRT adopts identical vehicle model completely, and amount of seats is identical with maximum passenger carrying capacity;

That does not consider circuit joins car, thinks that vehicle is abundant;

BRT vehicle is dispatched a car by schedule time list;

BRT vehicle is order and sequence consensus of dispatching a car on road, there is not phenomenon of overtaking other vehicles;

Using minute as scheduling least unit;

(2) variable used in the bus dispatching mathematical model described in and implication as follows:

M is the number of times of dispatching a car in whole dispatching cycle;

N is website quantity total on circuit assigned direction;

T _ibe the time of departure of the i-th train in the dispatching cycle, by minute in units of, i=1,2 ..., m;

R _jfor the time dependent arrival rate of a jth website on circuit assigned direction, unit behaviour/minute, j=1,2 ..., n;

T is the total waiting time of passenger in dispatching cycle;

Then

$T=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_j\&times;\frac{{(t_i-t_{i-1})}^2}{2}$

The cost of bus operation is divided into fixed cost and variable cost, there is not direct relation between bus dispatching and fixed cost; If bus operation income is R in the dispatching cycle, P is that riding fee uses (unit) per capita, L is assigned direction total line length (km), C is the variable cost (unit/km) of public transit vehicle, then the income of public transport company is that gross income deducts total variable cost, specific as follows:

$R=P\&times;\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_j\&times;(t_i-t_{i-1})-C\&times;L\&times;m$

If μ is passenger waiting time weight coefficient, ν is public transport company's usufruct coefficient; According to secondary penalty method, the objective function of bus dispatching Optimized model is:

minz＝μ×T-ν×R

If N _maxfor maximum appearance of vehicle amount, ρ is for expecting load factor, then Prescribed Properties I:

$\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_j\&times;(t_i-t_{i-1})\&GreaterEqual;\mathrm{\&rho;}\&times;N_{\max },i=\mathrm{2,3},...,m$

In order to ensure rule arrive passenger and random arrive passenger can wait until in the short period of time to wait, if H _minand H _maxbe respectively the minimum and maximum departure interval that public transport company requires, then the departure interval should meet constraint condition II below:

H _min≤t _i-t _i-1≤H _maxi＝2,3,...,m

Cause the non-continuous event of dispatching a car for avoiding simultaneously, if τ is the maximum departure interval difference that public transport company allows, then constraint condition III:

|(t _i+1-t _i)-(t _i-t _i-1)|≤τ i＝2,3,...,m-1

Ensure that the solution produced does not violate the constraint condition of scheduling problem by penalty function method; Based on above description, objective function minf (X) form of scheduling problem is as follows:

$\begin{array}{c}\min f\left(X\right)=\min z+{\mathrm{\&omega;}}_1\underset{i=2}{\overset{m}{\mathrm{\&Sigma;}}}\left\{\max \right\{0,\mathrm{\&rho;}\&times;N_{\max }-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_j\&times;(t_i-t_{i-1})\left\}\right\}+\\ {\mathrm{\&omega;}}_2\underset{i=2}{\overset{m}{\mathrm{\&Sigma;}}}\left\{\max \right\{0,T_{\min }-(t_i-t_{i-1})\left\}\right\}+\\ {\mathrm{\&omega;}}_3\underset{i=2}{\overset{m}{\mathrm{\&Sigma;}}}\left\{\max \right\{0,(t_i-t_{i-1})-T_{\max }\left\}\right\}+\\ {\mathrm{\&omega;}}_4\underset{i=2}{\overset{m-1}{\mathrm{\&Sigma;}}}\left\{\max \right\{0,|(t_{i+1}-t_i)-(t_i-t_{i-1})|-\mathrm{\&tau;}\left\}\right\}\end{array}$

Wherein minf (X) is for adding the target function value after penalty function, ω ₁, ω ₂, ω ₃, ω ₄be respectively the penalty coefficient of constraint condition I, constraint condition II minimum departure interval, constraint condition II maximum departure interval, constraint condition III correspondence; The vector of the solution X of scheduling problem to be length be m, each component x _irepresent the time of departure of i-th spacing first bus in dispatching cycle, by minute in units of;

In order to ensure that the fitness of each individuality is all greater than 0, also conveniently use roulette selection strategy, converting to objective function the final form obtaining fitness function is simultaneously:

3. a kind of intelligent public transportation dispatching method based on hybrid metaheuristics as claimed in claim 1, it is characterized in that described simulated annealing can strengthen the local search ability of genetic algorithm, complete in genetic algorithm after interlace operation and mutation operation at every turn, relatively the fitness of former and later two individualities, carries out simulated annealing operation; Need in simulated annealing to set initial temperature T ₀, the computing formula of Current Temperatures is:

T*＝T ₀×σ ^g-1

Wherein σ represents the speed that temperature reduces, and its value is 0 < σ < 1, and its value is larger, and it is slower that temperature reduces, and is worth less, and it is faster that temperature reduces; G is the number of times of algorithm current iteration; When the fitness of the new individuality produced reduces, accepting new individual probability is:

$P^{*}=\exp \left(\frac{F\left(X_{\mathrm{new}}\right)-F\left(X_{\mathrm{old}}\right)}{T^{*}}\right)$

Wherein F (X _new), F (X _old) be respectively the fitness of new individuality and former individuality;

Simultaneously there is most outstanding individual physical efficiency to enter the new individuality of generation of future generation smoothly in each population to ensure, in the blending algorithm of simulated annealing and genetic algorithm, adding elite's retention strategy; After often producing new generation population, the fitness value of optimized individual in population more of new generation and previous generation population; If the fitness of the optimized individual of population of new generation is less than the optimized individual of previous generation, then replace the minimum individuality of fitness in a new generation by the optimized individual of previous generation; Otherwise directly enter next iteration.

4. a kind of intelligent public transportation dispatching method based on hybrid metaheuristics as claimed in claim 1, is characterized in that the form of the stretch function described in step 5-1 is:

$F{\left(X_i\right)}^{\&prime;}=\frac{e^{\mathrm{\&lambda;}\&times;F\left(X_i\right)/T*}}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{\mathrm{\&lambda;}\&times;F\left(X_i\right)/T*}}$

Wherein F (X _i) represent individual X _ifitness, F (X _i) ' be fitness after stretching, T* refers to temperature current in simulated annealing, and N to represent in population individual quantity, and λ represents drawing coefficient;

In order to fitness stretching can be carried out, fitness criteria to be carried out to individualities all in population before the stretching, order

${\mathrm{fitness}}^{\&prime;}=\frac{\mathrm{fitness}}{\max \mathrm{fitness}}$

Wherein fitness refers to individual fitness, and fitness' refers to the fitness after standardization, and max fitness refers to the fitness of optimized individual in current population.

5. a kind of intelligent public transportation dispatching method based on hybrid metaheuristics as claimed in claim 1, is characterized in that the basic step of the hybrid metaheuristics described in step 5 is as follows:

1). be set as follows the value of parameter: Population Size N, chromosome length L _c, crossover probability P _c, mutation probability P _m, maximum evolutionary generation G _max, initial temperature T ₀, annealing speed σ, drawing coefficient λ;

2). initialization population P ₀, namely the N number of feasible solution of random generation forms initialization population P ₀; Calculate fitness individual in initial population, carry out standardization, stretched operation is carried out to fitness; Setting iterations g is 0;

3). carry out roulette selection, from population P according to the fitness after stretching _gmiddle random selecting two individualities;

4). intersect and simulated annealing operation; Adopt single-point Crossover Strategy, by by two the individual p selected ₁, p ₂by probability P _ccarry out interlace operation and produce two new individual c ₁, c ₂; If F is (c _i) > F (p _i), then accept individual c ₁, otherwise with probability exp ((F (c _i)-F (p _i))/T*) accept new individuality;

5). variation and simulated annealing operation; To the new individual c produced ₁, c ₂carry out mutation operation by turn, if the individual c after variation ₁' fitness increase, then accept variation, otherwise with probability exp ((F (c _i')-F (c _i))/T*) accept new individuality;

6). new two individualities produced are added new population P _g+1in, if P _g+1middle individual amount is less than N, then forward step 3 to), otherwise carry out next step;

7). calculate the fitness of each individuality in new population, column criterionization of going forward side by side operates;

8). fitness stretching is carried out to the individuality in new population;

9). implement elite's retention strategy, replace original seed group with new population;

10). cooling operation;

11). upgrade iterations g=g+1, if reach maximum iteration time G _max, then population P is exported _gin optimum solution, otherwise forward step 3 to).