CN110689165A - Vehicle path optimization method based on road network reachability - Google Patents
Vehicle path optimization method based on road network reachability Download PDFInfo
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Abstract
A vehicle path optimization method based on road network accessibility comprises the steps of firstly, creating a network data set of a research area, and acquiring real road distance between research object points; then, under the condition of meeting the vehicle load constraint, the distribution center and the customer points adopt a natural number coding mode to carry out coding operation, and the initialization of the population is completed; after the population is crossed and varied, selecting the current population by adopting a roulette mode, screening out chromosomes with higher fitness to form a new population, and repeating the crossing, varying and selecting operations until the termination condition of iteration is met; and finally, outputting the chromosome with the highest fitness in the population, namely the optimal path scheme for vehicle delivery. The invention provides a vehicle path optimization method based on road network accessibility, which is more suitable for practical application.
Description
Technical Field
The invention relates to the fields of GIS technology, logistics distribution, intelligent calculation and computer application, in particular to a vehicle path optimization method based on road network reachability.
Background
With the improvement of economic globalization and informatization degree, the economic development of China obtains fruitful results, and a plurality of emerging industries develop vigorous. In recent years, especially the high-speed development of electronic commerce promotes the great progress of the whole logistics industry, the logistics industry is used as a key link for connecting a product supplier with a demand party, the key role of the logistics industry is reflected more and more, and the logistics industry is used as a third party profit source of modern enterprises. Meanwhile, the logistics industry plays a great role in social development, improvement of working efficiency, optimization of resource structures and the like. In such a background, the government has developed a series of policy measures for supporting the development of third-party logistics so as to promote the healthy and stable development of the whole logistics industry. Logistics distribution is a very important place in third-party logistics systems, and more than half of the cost and even higher cost comes from the distribution links. The rational planning of logistics distribution routes, i.e. vehicle routing problems, has attracted extensive attention from the academic community.
The vehicle path problem, also called vehicle scheduling problem, is one of the core problems in transportation organization optimization, and it optimizes the transportation route of the vehicle to reach the destination with the lowest transportation cost and expense as possible on the premise of meeting the customer demand. In practice, the problem is not limited to the field of logistics distribution, but also has certain application in the fields of aviation, ocean shipping, industrial management and the like, and research results of the problem are used for various combined optimization problems of ship companies in cargo transportation, port and cargo arrangement optimization design, transportation vehicle routing, garbage collection routing, planning and control in a production system and the like. The research on the vehicle path problem influences the development of multiple application fields such as logistics, supply chain management, enterprise resource planning and the like, and still attracts the attention of broad scholars.
At present, most researchers conduct research on the vehicle path problem by abstracting the positions and roads of client points into points and lines in graph theory through a simple modeling mode of the graph theory and conducting research based on the topological relation. In calculating the distance between each client point, a distance formula between two points is used to develop the distance between the two points based on the conversion of the position coordinates of the client point. The data processing mode completely ignores the accessibility of a road network between client points under a real road, the Euclidean distance between two points is not equal to the actual road distance between two client points under the real road, and the real road distance is regressed to the actual application, so that the precision loss is large.
Therefore, the existing vehicle path optimization method has a defect in the accuracy of the application research of the distribution scheme under the real road, and needs to be improved.
Disclosure of Invention
In order to solve the defect that the existing vehicle path optimization method is low in accuracy of a distribution problem solution under a real road, the invention provides a vehicle path optimization method based on road network accessibility.
The technical scheme adopted by the invention to solve the technical problem is as follows:
a vehicle path optimization method based on road network reachability comprises the following steps:
1) the following objective function is established by taking the shortest total route of all the delivery vehicles as an objective:
where K is the number of delivery vehicles, V is the set of delivery centers and all customer points, i, j represents an element in the set V, xijkThe decision variables are 0 and 1, namely the k-th vehicle takes the value of 1 from the client point i to the client point j, otherwise, the k-th vehicle takes the value of 0, dijThe actual road distance from the client point i to the client point j; the constraint conditions are as follows: having only one distribution centre, andsome distribution vehicles take a distribution center as a starting point and an end point, the demand of each customer point is known and is smaller than the maximum bearing capacity Q of the vehicle, each vehicle can distribute a plurality of customer points, but each customer point can be distributed by only one vehicle;
2) setting parameters: the method comprises the following steps of (1) counting the number N of customer points, the maximum load capacity Q of a vehicle, a demand list T of the customer points, a cross probability PC, a variation probability PM, a population size NP and iteration times G;
3) loading a geographic information map of a target area through ArcGIS Pro, creating a corresponding road route layer according to a real road, and completing road network vectorization and geographic registration operation of the target area;
4) constructing a network data set of a target area based on the created road line graph layer, and constructing a point feature graph layer in the network data to represent the geographic positions of a distribution center and a customer point;
5) creating a starting point-destination distance cost analysis matrix D and acquiring the real road distance between a distribution center and a client point based on the reachability of the road network
E.g. d01Representing the real road distance between the distribution center 0 and the customer point 1, d25Represents the actual road distance between customer point 2 to customer point 5;
6) determining the number of delivery vehicles K [ ∑ q ] requiredi/(αQ)]Wherein q isiIndicates the cargo demand of the ith customer site, and alpha is [0,1]]The random restriction factor of (2), (c)]Represents rounding down;
7) and (3) encoding: adopting a natural number coding mode;
8) population initialization, the process is as follows:
8.1) randomly arranging all client points coded according to natural numbers into a line;
8.2)qiindicating the cargo demand of the ith customer site, if satisfied
And is
Inserting 0 behind the a th position of the chromosome, and then repeating the calculation until K-1 0 is inserted to form K vehicle paths;
8.3) inserting 0 into the first and the last chromosome respectively to finally form an initial chromosome;
8.4) iterating the step 8.1 to the step 8.3) to generate an initial population consisting of NP-stripe chromosomes;
9) the cross operation, the process is as follows:
9.1) randomly and repeatedly selecting two chromosomes from the population as parent chromosomes, marking as chrom1 and chrom2, generating a random number r 'in the interval of [0,1], if r' is less than PC, carrying out the following cross operation, otherwise, directly keeping the two chromosomes to the next generation;
9.2) randomly selecting one of the routes of the parent chromosomes chrom1 and chrom2 as L1 and L2;
9.3) putting L1 as a part of child chromosome chrom1 ' at the head, simultaneously adding a client point code which does not comprise a child path L1 in parent chromosome chrom2 to the back of the child path L1 in sequence, and adding a code 0 at the tail, and similarly, obtaining chrom1 ' and chrom2 ' after the same operation is carried out on L2;
9.4) random insertion of K-2 0's into the fragment between the second code 0 and the tail code 0 in the daughter chromosome chrom 1' results in daughter chromosome chrom1 ', which in a similar manner can generate daughter chromosome chrom 2';
9.4) chromosome validity test: calculating the sum of the demands of each vehicle path in the child chromosomes chrom1 'and chrom 2' including the customer points, if the sum of the demands exceeds the vehicle load capacity Q, turning to step 9.3), and re-executing the 0 inserting operation;
9.5) iterating steps 9.1) to 9.4) until all chromosomes are traversed;
10) mutation operation: generating a random number r' in the interval [0,1 ]; if r' is less than PM, randomly selecting two customer point codes in the chromosome, carrying out position interchange, and then checking the legality of the chromosome, namely the required quantity of each line cannot exceed the load of the vehicle, if not, randomly selecting two customers again for code interchange; if r' is less than or equal to PM, directly retaining the current chromosome to the next generation;
11) selecting operation, the process is as follows:
11.1) forming a population with the size of 2NP by the parent population and the offspring population;
11.2) calculating the fitness of each chromosome in the population, fit (i) ═ 1/z, z is an objective function;
11.3) calculating the sum of fitness of all chromosomes in the population sumFit ═ Σ fit (i), i ═ 1,2, …,2 NP;
11.4) calculating the selection probability p (i) ═ fit (i)/sumFit and the cumulative probability ps (i) ═ Σ p (i), i ═ 1,2, …,2NP of each chromosome in the current population;
11.5) generating a random number r in a [0,1] area, if ps (i) > r is satisfied, selecting a first chromosome to enter a new population, otherwise, selecting an ith chromosome which enables ps (i-1) < r < ps (i) to enter the new population;
11.6) repeating the step 11.5) NP times to obtain a new NP population with the size of the population scale;
12) iterating the steps 9) to 11) to the maximum iteration number G, and selecting the chromosome with the highest fitness in the current population as the optimal path.
The invention has the beneficial effects that: and constructing a road network model by adopting a GIS technology, and creating a corresponding network data set to obtain the real road network distance between a distribution center and a customer point. On the basis, a genetic algorithm with high practicability is applied to solve the basic vehicle path planning problem; in the solving process of the genetic algorithm, the real road distance considering the accessibility of the real road network is adopted, and compared with the Euclidean distance in the traditional method, the real road distance is more convincing and more suitable for practical application.
Drawings
Fig. 1 is a flow chart of a vehicle path optimization method based on road network reachability.
FIG. 2 is a network data set model of a study area.
Fig. 3 is a path diagram of an optimal distribution scheme.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 3, a vehicle path optimization method based on road network reachability includes the following steps:
1) the following objective function is established by taking the shortest total route of all the delivery vehicles as an objective:where K is the number of delivery vehicles, V is the set of delivery centers and all customer points, i, j represents an element in the set V, xijkThe decision variables are 0 and 1, namely the k-th vehicle takes the value of 1 from the client point i to the client point j, otherwise, the k-th vehicle takes the value of 0, dijThe actual road distance from the client point i to the client point j; the constraint conditions are as follows: the method is characterized in that the method is provided with only one distribution center, all distribution vehicles of the distribution center take the distribution center as a starting point and an end point, the demand of each customer point is known and is smaller than the maximum bearing capacity Q of the vehicle, each vehicle can distribute a plurality of customer points, but each customer point can be distributed by only one vehicle;
2) setting parameters: the method comprises the following steps of (1) counting the number N of customer points, the maximum load capacity Q of a vehicle, a demand list T of the customer points, a cross probability PC, a variation probability PM, a population size NP and iteration times G;
3) loading a geographic information map of a target area through ArcGIS Pro, creating a corresponding road route layer according to a real road, and completing road network vectorization and geographic registration operation of the target area;
4) constructing a network data set of a target area based on the created road line graph layer, and constructing a point feature graph layer in the network data to represent the geographic positions of a distribution center and a customer point;
5) creating a starting point-destination distance cost analysis matrix D and acquiring the real road distance between a distribution center and a client point based on the reachability of the road networkE.g. d01Representing the real road distance between the distribution center 0 and the customer point 1, d25Represents the actual road distance between customer point 2 to customer point 5;
6) determining the number of delivery vehicles K [ ∑ q ] requiredi/(αQ)]Wherein q isiIndicates the cargo demand of the ith customer site, and alpha is [0,1]]The random restriction factor of (2), (c)]Represents rounding down;
7) and (3) encoding: the natural number coding method is adopted, if 2 vehicles are used for 8 customer points to perform distribution service, the number 0 can be used for representing the distribution center, 1,2,3, … and 8 represent each customer point, the distribution route can be coded as (0,1,3,7,2,0,5,6,4,8 and 0), and the driving route represented as: (0,1,3,7,2,0) indicates that the delivery route of the first vehicle is from the delivery center 0, and the delivery to the customer sites numbered 1,3,7 and 2 is completed in sequence, and then the delivery is returned to the delivery center, and (0,5,6,4,8,0) indicates that the delivery route of the second vehicle is from the delivery center 0, and the delivery to the customer sites numbered 5,6,4 and 8 is completed in sequence, and then the delivery is returned to the delivery center;
8) population initialization, the process is as follows:
8.1) randomly arranging all client points coded according to natural numbers into a line;
8.2)qiindicating the cargo demand of the ith customer site, if satisfied
And is
Inserting 0 behind the a th position of the chromosome, and then repeating the calculation until K-1 0 is inserted to form K vehicle paths;
8.3) inserting 0 into the first and the last chromosome respectively to finally form an initial chromosome;
8.4) iterating the step 8.1 to the step 8.3) to generate an initial population consisting of NP-stripe chromosomes;
9) the cross operation, the process is as follows:
9.1) randomly and repeatedly selecting two chromosomes from the population as parent chromosomes, marking as chrom1 and chrom2, generating a random number r 'in the interval of [0,1], if r' is less than PC, carrying out the following cross operation, otherwise, directly keeping the two chromosomes to the next generation;
9.2) randomly selecting the path of one of the vehicles from parent chromosomes 1 and 2 as L1 and L2, for example, taking 3 vehicles as 9 customer points to complete distribution tasks, the parent chromosome 1 is coded as (0,1,3,4,0,2,5,6,0,9,7,8,0), the path L1 of one of the vehicles is randomly selected as (0,2,5,6,0), the parent chromosome 2 is coded as (0,7,3,4,0,8,5,6,0,9,1,6,0), and the path L2 of one of the vehicles is randomly selected as (0,7,3,4, 0);
9.3) putting L1 as a part of child chromosome chrom1 ' and placing at the head, simultaneously adding the client point code of parent chromosome chrom2 not including child path L1 to the back of child path L1 in sequence, and adding code 0 at the tail, and similarly, after carrying out the same operation on L2, obtaining that the chrom1 ' is (0,2,5,6,0,7,3,4,8,9,1,0) and the chrom2 ' is (0,7,3,4,0,1,2,5,6,9,8,0) at the moment;
9.4) randomly inserting K-2 0's into a segment between the second code 0 and the tail code 0 in the child chromosome chrom 1' to form a child chromosome chrom1 ", and similarly generating a child chromosome chrom 2", wherein in the example, the number K of the vehicles is 3, so that only one 0 needs to be inserted to form a path of 3 vehicles;
9.4) chromosome validity test: calculating the sum of the demands of each vehicle path in the child chromosomes chrom1 'and chrom 2' including the customer points, if the sum of the demands exceeds the vehicle load capacity Q, turning to step 9.3), and re-executing the 0 inserting operation;
9.5) iterating steps 9.1) to 9.4) until all chromosomes are traversed;
10) mutation operation: generating a random number r' in the interval [0,1 ]; if r' is less than PM, randomly selecting two customer point codes in the chromosome, carrying out position interchange, and then checking the legality of the chromosome, namely the required quantity of each line cannot exceed the load of the vehicle, if not, randomly selecting two customers again for code interchange; if r' is less than or equal to PM, directly retaining the current chromosome to the next generation;
11) selecting operation, the process is as follows:
11.1) forming a population with the size of 2NP by the parent population and the offspring population;
11.2) calculating the fitness of each chromosome in the population, fit (i) ═ 1/z, z is an objective function;
11.3) calculating the sum of fitness of all chromosomes in the population sumFit ═ Σ fit (i), i ═ 1,2, …,2 NP;
11.4) calculating the selection probability p (i) ═ fit (i)/sumFit and the cumulative probability ps (i) ═ Σ p (i), i ═ 1,2, …,2NP of each chromosome in the current population;
11.5) generating a random number r in a [0,1] area, if ps (i) > r is satisfied, selecting a first chromosome to enter a new population, otherwise, selecting an ith chromosome which enables ps (i-1) < r < ps (i) to enter the new population;
11.6) repeating the step 11.5) NP times to obtain a new NP population with the size of the population scale;
12) iterating the steps 9) to 11) to the maximum iteration number G, and selecting the chromosome with the highest fitness in the current population as the optimal path.
In this embodiment, taking the distribution of 20 client points in the coastal river area in hangzhou city as an example, a vehicle path optimization method based on road network reachability includes the following steps:
1) the following objective function is established by taking the shortest total route of all the delivery vehicles as an objective:
where K is the number of delivery vehicles, V is the set of delivery centers and all customer points, i, j represents an element in the set V, xijkThe decision variables are 0 and 1, namely the k-th vehicle takes the value of 1 from the client point i to the client point j, otherwise, the k-th vehicle takes the value of 0, dijThe actual road distance from the client point i to the client point j; the constraint conditions are as follows: the method is characterized in that the method is provided with only one distribution center, all distribution vehicles of the distribution center take the distribution center as a starting point and an end point, the demand of each customer point is known and is smaller than the maximum bearing capacity Q of the vehicle, each vehicle can distribute a plurality of customer points, but each customer point can be distributed by only one vehicle;
2) setting parameters: the number N of customer points is 20, the maximum vehicle load Q is 3, the demand amount list T of customer points is [0.2,0.3,0.3,0.3,0.3,0.5,0.8,0.4,0.5,0.7,0.7,0.6,0.2,0.2,0.4,0.3,0.4,0.2,0.5,0.2], the crossover probability PC is 0.9, the variation probability PM is 0.05, the population size NP is 50, and the number of iterations G is 500;
3) loading a geographic information map of a target area through ArcGIS Pro, creating a corresponding road route layer according to a real road, and completing road network vectorization and geographic registration operation of the target area;
4) constructing a network data set of a target area based on the created road line graph layer, and constructing a point feature graph layer in the network data to represent the geographic positions of a distribution center and a customer point;
5) creating a starting point-destination distance cost analysis matrix D and acquiring the real road distance between a distribution center and a client point based on the reachability of the road network
E.g. d01Representing the real road distance between the distribution center 0 and the customer point 1, d25Represents the actual road distance between customer point 2 to customer point 5;
6) determining the number of delivery vehicles K [ ∑ q ] requiredi/(αQ)]Wherein q isiIndicates the cargo demand of the ith customer site, and alpha is [0,1]]The random restriction factor of (2), (c)]Represents rounding down;
7) and (3) encoding: the natural number coding method is adopted, if 2 vehicles are used for 8 customer points to perform distribution service, the number 0 can be used for representing the distribution center, 1,2,3, … and 8 represent each customer point, the distribution route can be coded as (0,1,3,7,2,0,5,6,4,8 and 0), and the driving route represented as: (0,1,3,7,2,0) indicates that the delivery route of the first vehicle is from the delivery center 0, and the delivery to the customer sites numbered 1,3,7 and 2 is completed in sequence, and then the delivery is returned to the delivery center, and (0,5,6,4,8,0) indicates that the delivery route of the second vehicle is from the delivery center 0, and the delivery to the customer sites numbered 5,6,4 and 8 is completed in sequence, and then the delivery is returned to the delivery center;
8) population initialization, the process is as follows:
8.1) randomly arranging all client points coded according to natural numbers into a line;
8.2)qiindicating the cargo demand of the ith customer site, if satisfiedAnd isInserting 0 behind the a th position of the chromosome, and then repeating the calculation until K-1 0 is inserted to form K vehicle paths;
8.3) inserting 0 into the first and the last chromosome respectively to finally form an initial chromosome;
8.4) iterating the step 8.1 to the step 8.3) to generate an initial population consisting of NP-stripe chromosomes;
9) the cross operation, the process is as follows:
9.1) randomly and repeatedly selecting two chromosomes from the population as parent chromosomes, marking as chrom1 and chrom2, generating a random number r 'in the interval of [0,1], if r' is less than PC, carrying out the following cross operation, otherwise, directly keeping the two chromosomes to the next generation;
9.2) randomly selecting the path of one of the vehicles from parent chromosomes 1 and 2 as L1 and L2, for example, taking 3 vehicles as 9 customer points to complete distribution tasks, the parent chromosome 1 is coded as (0,1,3,4,0,2,5,6,0,9,7,8,0), the path L1 of one of the vehicles is randomly selected as (0,2,5,6,0), the parent chromosome 2 is coded as (0,7,3,4,0,8,5,6,0,9,1,6,0), and the path L2 of one of the vehicles is randomly selected as (0,7,3,4, 0);
9.3) putting L1 as a part of child chromosome chrom1 ' and placing at the head, simultaneously adding the client point code of parent chromosome chrom2 not including child path L1 to the back of child path L1 in sequence, and adding code 0 at the tail, and similarly, after carrying out the same operation on L2, obtaining that the chrom1 ' is (0,2,5,6,0,7,3,4,8,9,1,0) and the chrom2 ' is (0,7,3,4,0,1,2,5,6,9,8,0) at the moment;
9.4) randomly inserting K-2 0's into a segment between the second code 0 and the tail code 0 in the child chromosome chrom 1' to form a child chromosome chrom1 ", and similarly generating a child chromosome chrom 2", wherein in the example, the number K of the vehicles is 3, so that only one 0 needs to be inserted to form a path of 3 vehicles;
9.4) chromosome validity test: calculating the sum of the demands of each vehicle path in the child chromosomes chrom1 'and chrom 2' including the customer points, if the sum of the demands exceeds the vehicle load capacity Q, turning to step 9.3), and re-executing the 0 inserting operation;
9.5) iterating steps 9.1) to 9.4) until all chromosomes are traversed;
10) mutation operation: generating a random number r' in the interval [0,1 ]; if r' is less than PM, randomly selecting two customer point codes in the chromosome, carrying out position interchange, and then checking the legality of the chromosome, namely the required quantity of each line cannot exceed the load of the vehicle, if not, randomly selecting two customers again for code interchange; if r' is less than or equal to PM, directly retaining the current chromosome to the next generation;
11) selecting operation, the process is as follows:
11.1) forming a population with the size of 2NP by the parent population and the offspring population;
11.2) calculating the fitness of each chromosome in the population, fit (i) ═ 1/z, z is an objective function;
11.3) calculating the sum of fitness of all chromosomes in the population sumFit ═ Σ fit (i), i ═ 1,2, …,2 NP;
11.4) calculating the selection probability p (i) ═ fit (i)/sumFit and the cumulative probability ps (i) ═ Σ p (i) for each chromosome in the current population, i ═ 1,2, …,2 NP;
11.5) generating a random number r in a [0,1] area, if ps (i) > r is satisfied, selecting a first chromosome to enter a new population, otherwise, selecting an ith chromosome which enables ps (i-1) < r < ps (i) to enter the new population;
11.6) repeating the step 11.5) NP times to obtain a new NP population with the size of the population scale;
12) and (5) iterating the steps 9) to 11) to the maximum iteration number of 500 to obtain the chromosome with the highest fitness in the current population as [0,3,8,13,17,4,5,1,0,2,6,7,9,15,20,12,0,16,10,19,18,14,11,0], namely the optimal result of the distribution scheme.
Taking an example that one distribution center in the coastal river area of Hangzhou city distributes to 20 customer points, a flow chart of a research method is shown in FIG. 1, a network data set of a research area is shown in FIG. 2, and a road network model including the distribution centers and the customer points is shown in FIG. 3. The optimal distribution route scheme is obtained by applying the method, namely the distribution scheme of three vehicles is as follows in sequence: [0,3,8,13,17,4,5,1,0], [0,2,6,7,9,15,20,12,0] and [0,16,10,19,18,14,11,0 ].
The foregoing is a predictive effect of one embodiment of the invention, which may be adapted not only to the specific embodiments described above, but also to various modifications thereof without departing from the basic inventive concept and without exceeding the scope of the invention.
Claims (1)
1. A vehicle path optimization method based on road network reachability is characterized by comprising the following steps:
1) the following objective function is established by taking the shortest total route of all the delivery vehicles as an objective:where K is the number of delivery vehicles, V is the set of delivery centers and all customer points, i, j represents an element in the set V, xijkThe decision variables are 0 and 1, namely the k-th vehicle takes the value of 1 from the client point i to the client point j, otherwise, the k-th vehicle takes the value of 0, dijThe actual road distance from the client point i to the client point j; the constraint conditions are as follows: the method is characterized in that the method is provided with only one distribution center, all distribution vehicles of the distribution center take the distribution center as a starting point and an end point, the demand of each customer point is known and is smaller than the maximum bearing capacity Q of the vehicle, each vehicle can distribute a plurality of customer points, but each customer point can be distributed by only one vehicle;
2) setting parameters: the method comprises the following steps of (1) counting the number N of customer points, the maximum load capacity Q of a vehicle, a demand list T of the customer points, a cross probability PC, a variation probability PM, a population size NP and iteration times G;
3) loading a geographic information map of a target area through ArcGIS Pro, creating a corresponding road route layer according to a real road, and completing road network vectorization and geographic registration operation of the target area;
4) constructing a network data set of a target area based on the created road line graph layer, and constructing a point feature graph layer in the network data to represent the geographic positions of a distribution center and a customer point;
5) creating a starting point-destination distance cost analysis matrix D and acquiring the real road distance between a distribution center and a client point based on the reachability of the road network
E.g. d01Representing the real road distance between the distribution center 0 and the customer point 1, d25Represents the actual road distance between customer point 2 to customer point 5;
6) determining the number of delivery vehicles K [ ∑ q ] requiredi/(αQ)]Wherein q isiIndicates the cargo demand of the ith customer site, and alpha is [0,1]]The random restriction factor of (2), (c)]Represents rounding down;
7) and (3) encoding: adopting a natural number coding mode;
8) population initialization, the process is as follows:
8.1) randomly arranging all client points coded according to natural numbers into a line;
8.2)qiindicating the cargo demand of the ith customer site, if satisfied
And is
Inserting 0 behind the a th position of the chromosome, and then repeating the calculation until K-1 0 is inserted to form K vehicle paths;
8.3) inserting 0 into the first and the last chromosome respectively to finally form an initial chromosome;
8.4) iterating the step 8.1 to the step 8.3) to generate an initial population consisting of NP-stripe chromosomes;
9) the cross operation, the process is as follows:
9.1) randomly and repeatedly selecting two chromosomes from the population as parent chromosomes, marking as chrom1 and chrom2, generating a random number r 'in the interval of [0,1], if r' is less than PC, carrying out the following cross operation, otherwise, directly keeping the two chromosomes to the next generation;
9.2) randomly selecting one of the routes of the parent chromosomes chrom1 and chrom2 as L1 and L2;
9.3) putting L1 as a part of child chromosome chrom1 ' at the head, simultaneously adding a client point code which does not comprise a child path L1 in parent chromosome chrom2 to the back of the child path L1 in sequence, and adding a code 0 at the tail, and similarly, obtaining chrom1 ' and chrom2 ' after the same operation is carried out on L2;
9.4) random insertion of K-2 0's into the fragment between the second code 0 and the tail code 0 in the daughter chromosome chrom 1' results in daughter chromosome chrom1 ', which in a similar manner can generate daughter chromosome chrom 2';
9.4) chromosome validity test: calculating the sum of the demands of each vehicle path in the child chromosomes chrom1 'and chrom 2' including the customer points, if the sum of the demands exceeds the vehicle load capacity Q, turning to step 9.3), and re-executing the 0 inserting operation;
9.5) iterating steps 9.1) to 9.4) until all chromosomes are traversed;
10) mutation operation: generating a random number r' in the interval [0,1 ]; if r' is less than PM, randomly selecting two customer point codes in the chromosome, carrying out position interchange, and then checking the legality of the chromosome, namely the required quantity of each line cannot exceed the load of the vehicle, if not, randomly selecting two customers again for code interchange; if r' is less than or equal to PM, directly retaining the current chromosome to the next generation;
11) selecting operation, the process is as follows:
11.1) forming a population with the size of 2NP by the parent population and the offspring population;
11.2) calculating the fitness of each chromosome in the population, fit (i) ═ 1/z, z is an objective function;
11.3) calculating the sum of fitness of all chromosomes in the population sumFit ═ Σ fit (i), i ═ 1,2, …,2 NP;
11.4) calculating the selection probability p (i) ═ fit (i)/sumFit and the cumulative probability ps (i) ═ Σ p (i), i ═ 1,2, …,2NP of each chromosome in the current population;
11.5) generating a random number r in a [0,1] area, if ps (i) > r is satisfied, selecting a first chromosome to enter a new population, otherwise, selecting an ith chromosome which enables ps (i-1) < r < ps (i) to enter the new population;
11.6) repeating the step 11.5) NP times to obtain a new NP population with the size of the population scale;
12) iterating the steps 9) to 11) to the maximum iteration number G, and selecting the chromosome with the highest fitness in the current population as the optimal path.
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