CN110276488B - Vehicle path optimization method based on block matrix and fuzzy transportation time - Google Patents

Vehicle path optimization method based on block matrix and fuzzy transportation time Download PDF

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CN110276488B
CN110276488B CN201910526892.1A CN201910526892A CN110276488B CN 110276488 B CN110276488 B CN 110276488B CN 201910526892 A CN201910526892 A CN 201910526892A CN 110276488 B CN110276488 B CN 110276488B
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张文宇
陈子旋
张帅
陈勇
冯睿隽
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Zhejiang University of Finance and Economics
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Abstract

The invention discloses a vehicle path optimization method based on a block matrix and fuzzy transportation time, which comprises the following steps: establishing a path optimization model based on fuzzy transportation time; initializing to obtain a solution of a path optimization model, namely habitats, representing each habitat by adopting a block matrix, calculating a suitability index value of each habitat, and determining an initial optimal solution according to the suitability index value; calculating the migration rate and the migration rate of the population, and performing vector substitution on the block matrix corresponding to the habitat according to the migration rate and the migration rate; calculating the variation rate of the population by using the self-adaptive variation probability and the secondary variation probability, selecting a corresponding habitat for variation operation, and updating the optimal solution; if the iteration times are reached, outputting an optimal solution, namely an optimal transportation scheme; otherwise, the iteration is continued. The method of the invention considers the selection problem of two transportation modes of circular transportation and cross distribution under the condition of fuzzy transportation time, thereby obtaining the optimal transportation scheme under the uncertain condition.

Description

Vehicle path optimization method based on block matrix and fuzzy transportation time
Technical Field
The invention belongs to the technical field of logistics, and particularly relates to a vehicle path optimization method based on a block matrix and fuzzy transportation time.
Background
In recent years, the supply chain that forms the core of an enterprise tightly links suppliers, vendors, distributors, retailers, and consumers by controlling the flow of information, logistics, and funds. As an important component of the supply chain, the problem of vehicle routing in logistics optimization is also gaining increasing attention from many enterprises. However, compared to the conventional vehicle routing problem, the current vehicle routing problem is extremely complex and difficult to solve effectively. On the one hand, due to the difficulty of obtaining accurate and sufficient information, there are many uncertain situations (e.g., transportation time fluctuations caused by climate changes, traffic congestion, weather, etc.) and fuzzy data (e.g., arrival time, demand, etc.) in actual transportation. Therefore, for such complex problems, uncertainty needs to be considered, as using accurate data (such as transit time) to describe the model may produce inaccurate solutions. For example, transit time from one point to another is generally uncertain due to traffic congestion, weather, and other factors. Thus, the arrival time also becomes uncertain, which may result in the cargo not arriving within the specified time window. On the other hand, different transportation modes are suitable for different situations, namely, the selection of the transportation mode has an important influence on the optimization of the vehicle path problem and should be considered. For example, in the cross delivery transportation mode, an inbound vehicle loads goods from a supplier and transports the goods to a cross delivery center, and after the cross delivery center performs sorting and arrangement, the goods are transported to a manufacturer by an outbound vehicle. This process increases shipping time and distance, and costs are correspondingly increased. In contrast, in the circulation transportation mode, the vehicle loads goods from a supplier and directly transports the goods to a manufacturer, and the transportation time is short. Therefore, the cross distribution transportation mode is more suitable for long-distance transportation, and the circulation transportation mode is more suitable for short-distance transportation.
However, existing vehicle path problem studies do not consider both of the above problems simultaneously. Most studies focus on vehicle path optimization problems under uncertainty, without considering transportation mode selection issues. Since efficient representation of mode of transportation selection is a challenging problem. The existing representation method for selecting the transportation mode, such as the representation method based on harmony search and simulated annealing proposed in the prior art, does not consider a plurality of transportation mode selections simultaneously. Meanwhile, the method only considers the problem of transportation mode selection and does not consider the uncertainty of the transportation environment, so that the solution obtained by the method is not accurate enough, and the optimal transportation plan cannot be obtained.
Due to the complexity of the vehicle path problem, many heuristic algorithms are often applied to solve this problem, such as Genetic Algorithm (GA), harmonic search algorithm (HS), variable neighborhood search algorithm (VNS), ant colony Algorithm (ACO), particle swarm algorithm (PSO), and simulated annealing algorithm (SA). In recent years, a biophysical optimization algorithm (BBO), which is an effective algorithm for solving a large-scale optimization problem, has been widely used for manufacturing service supply chain optimization and solution of constraint optimization problems. The BBO algorithm is used for simulating a species migration process, and evolution is carried out through migration operation and variation operation, so that the population tends to be globally optimal. Many experiments prove that when the vehicle path problem is solved, the BBO algorithm is superior to other heuristic algorithms such as PSO and ACO. However, the application environment of the conventional BBO algorithm is relatively limited, and the above problems cannot be comprehensively considered, so an improved BBO algorithm (EBBO) is urgently needed to solve a more reasonable and efficient transportation scheme.
Disclosure of Invention
The invention aims to provide a vehicle path optimization method based on a block matrix and fuzzy transportation time, which considers the selection problem of two transportation modes of circular transportation and cross distribution under the condition of fuzzy transportation time, so that an optimal transportation scheme under the uncertain condition can be obtained.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a vehicle path optimization method based on a block matrix and fuzzy transportation time comprises the following steps:
s1, establishing a transportation mode, a circulating transportation sequence and a path optimization model distributed by a cross distribution center based on fuzzy transportation time;
step S2, initializing to obtain a solution of a path optimization model, namely habitats, representing each habitat by adopting a block matrix, calculating a suitability index value of each habitat, and determining an initial optimal solution according to the suitability index value;
step S3, calculating the migration rate and the migration rate of the population, judging whether to perform the operation of migration in or out of the habitat or not according to the migration rate and the migration rate, and if the operation of migration in or out is required, performing vector substitution on the block matrix corresponding to the habitat to realize the operation of migration in or out of the habitat;
step S4, calculating the variation rate of the population by using the self-adaptive variation probability and the secondary variation probability, selecting a corresponding habitat for variation operation according to the self-adaptive variation probability and the secondary variation probability, and updating the optimal solution;
step S5, judging whether a preset iteration number is reached, and if the preset iteration number is reached, outputting an optimal solution, namely an optimal transportation scheme; otherwise, the iteration continues in step S3.
Preferably, the establishing of the route optimization model based on the transportation mode, the cyclic transportation sequence and the cross distribution center distribution under the fuzzy transportation time includes:
with the maximum manufacturer satisfaction as an optimization target, establishing an objective function as follows:
Figure BDA0002098519290000031
in the formula, s is a fitness function of the satisfaction degree of the manufacturer, G is a manufacturer set, G is a manufacturer G, K is a vehicle set, K is a vehicle K, and r iskgIs satisfied by the manufacturer g and the order of the manufacturer is transported by a circulating transport vehicle k, wkgIs the weight of satisfaction of the manufacturer g and the order of the manufacturer is transported by a circulating transport vehicle k, L is a cross distribution center set, L is a cross distribution center L, rlgIs satisfied by the manufacturer g and the order of the manufacturer is transported through the cross-distribution centre l, wlgIs the weight of satisfaction of the vendor g whose order was shipped through the cross-distribution center l, S is the set of suppliers, i is the supplier i, [ c ]g,dg]Time window required by manufacturer g, DigFor the order of the manufacturer g to the supplier i, DgOrders for vendor g for all suppliers;
y in the objective functionikgAnd xilgIs a decision variable, and
Figure BDA0002098519290000032
Figure BDA0002098519290000033
b in the objective functionkg1、bkg2And bkg3To transport vehicles k by circulationFuzzy time of arrival of order of manufacturer g of the transport, bkgFuzzy number of (b)kgFor the time that the vehicle k reaches the manufacturer g through the circulation transportation, and
bkg＝bki+stki+tig
wherein K belongs to K, G belongs to G, i belongs to S, bkiFor circulating the time of arrival of the transport vehicle k at the supplier i, stkiFor circulating the service time, t, of the transport vehicle k at the supplier iigIs the transit time from supplier i to vendor g, and
stki＝γDigyikg
where γ is the unit product loading or unloading time, DigFor the order of the manufacturer g to the supplier i, yikgIs a decision variable;
f in the objective functionlg1、flg2And flg3Fuzzy time of arrival of order for manufacturer g passing through cross-distribution center l, flgFuzzy number of flgFor the time of arrival of the vehicle at the manufacturer g through the cross distribution center l, and
flg＝alg+tlg
wherein L is belonged to L, G is belonged to G, algTime of departure, t, from the Cross distribution center l for the order of the manufacturer glgFor the transit time from the cross-distribution center l to the manufacturer g, and
Figure BDA0002098519290000041
where γ is the unit product loading or unloading time, TilgFor the initialization time of the transport of vehicles through the cross-distribution centre l to the manufacturer g, q being the manufacturer q, DiqFor orders of manufacturer q to supplier i, xilqAnd xilgAs decision variables, tilFor the transit time of the supplier i to the cross-distribution centre l, DigAn order for vendor g to supplier i.
Preferably, the establishing of the constraint condition according to the objective function includes:
the supplier g can only select one transportation mode for the order of the supplier i:
Figure BDA0002098519290000042
setting that the goods loaded by the circulating transport vehicle k cannot exceed the capacity Q of the vehicle:
Figure BDA0002098519290000043
it is set that the volume Q of an inbound vehicle transported from a supplier i to a cross distribution center l, where the number of vehicles from the supplier i to the cross distribution center l is m, is not exceeded by cargo loaded on the vehicleil：
Figure BDA0002098519290000044
It is set that the capacity Q of an outbound vehicle transported from a cross distribution center l to a manufacturer g, the number of which is n, cannot exceed the capacity Q of the vehiclelg：
Figure BDA0002098519290000045
Setting the order of the manufacturer g transported by the circulating transport vehicle k, the arrival time b thereofkgMust not exceed dgWherein the arrival time bkgIs a fuzzy number of
Figure BDA0002098519290000051
Confidence level of risk exposure is Cr*：
Figure BDA0002098519290000052
Set up throughOrder of manufacturer g transported by fork-dispatching center l, arrival time flgMust not exceed dgWherein the arrival time flgIs a fuzzy number of
Figure BDA0002098519290000053
Confidence level of risk exposure is Cr*：
Figure BDA0002098519290000054
Setting the range of decision variables:
xilg∈{0,1}，i∈S,l∈L,g∈G
yikg∈{0,1}，i∈S,k∈K,g∈G。
preferably, the representing each habitat by using a block matrix includes:
each habitat is composed of a block matrix T ═ Tg]Where g denotes the vendor g, the columns of the block matrix denote vendors, the rows denote vendors, the elements of the block matrix T consist of a number of small matrices TgComposition is carried out;
wherein, the matrix TgThe method comprises the following steps that three lines are included, wherein the first line is an integer from 0 to M, 0 represents that goods are transported in a cross distribution mode, M represents the number of vehicles for circulating transportation, and the integer E belongs to {0, M }, represents that the goods of a corresponding supplier are distributed by the E vehicle through circulating transportation; matrix TgA random real number between 0 and 1, which represents the order of distribution of the circulating transport vehicles, the larger the random real number, which represents that the corresponding supplier is traversed earlier, and the 0 the random real number, which represents that the goods of the corresponding supplier are not distributed by the circulating transport manner; matrix TgThe third row of (a) is a random integer between 0 and n, 0 indicates that the goods of the corresponding supplier are not transported by the cross-distribution manner, n indicates the number of cross-distribution centers, and the random integer F e {0, n } indicates that the goods of the corresponding supplier are transported by the F-th cross-distribution center.
Preferably, if the immigration or emigration operation needs to be performed, the vector substitution is performed on the block matrix corresponding to the habitat to implement the immigration or emigration operation on the habitat, and the immigration or emigration operation on the habitat includes:
the fitness vector in the habitat is represented by a column in the block matrix T, and when the habitat is subjected to the operation of immigration or immigration, the immigration column of the habitat to be immigrated is replaced by the immigration column of the habitat to be immigration, so that vector replacement is completed.
Preferably, the calculating the mutation rate of the population by using the adaptive mutation probability and the secondary mutation probability, and selecting a corresponding habitat to perform mutation operation according to the adaptive mutation probability and the secondary mutation probability includes:
adaptive mutation probability mi1Comprises the following steps:
Figure BDA0002098519290000061
in the formula (f)iDenotes the HSI value, f, of the ith habitatmidRepresents the median of the HSI values for all habitats,
Figure BDA0002098519290000062
represents the maximum value of HSI values in all habitats;
probability of quadratic variation mi2Comprises the following steps:
Figure BDA0002098519290000063
in the formula (f)iDenotes the HSI value, f, of the ith habitatmidRepresents the median of the HSI values for all habitats,
Figure BDA0002098519290000064
represents the maximum value of HSI values in the middle 70% of the habitats;
firstly, all habitats are selected as a primary mutation target, and the mutation target is obtained according to the self-adaptive mutation probability mi1Performing first mutation on the corresponding habitat in the first mutation target, and selecting 70% of the habitats with the HSI value in the middle according to the result of the first mutationAs a secondary mutation target, according to the secondary mutation probability mi2And carrying out secondary variation on the corresponding habitat in the secondary variation target.
Preferably, the preset number of iterations includes:
number of manufacturers N in participants if vehicle routing is optimizedgIs 1. ltoreq. NgIf the number of iterations is less than 4, the preset number of iterations is 300; number of manufacturers N in participants if vehicle routing is optimizedgIs NgAnd if the number of iterations is more than or equal to 4, the preset number of iterations is 500.
The invention provides a vehicle path optimization method based on a block matrix and fuzzy transportation time, which comprehensively considers the problems of selection of suppliers, manufacturers and transportation modes, selection of a vehicle circulating transportation sequence and a cross distribution center and the like, and provides a block matrix-based representation method to represent a transportation scheme in a more intuitive, reasonable and efficient manner; expanding the one-dimensional habitat representation in the traditional BBO algorithm into a two-dimensional habitat representation, thereby solving the proposed hybrid vehicle path optimization model; based on the relative difference between the quality of the current habitat and the quality of the intermediate habitat, a self-adaptive mutation probability calculation method is provided, so that the habitats with high quality and low quality have higher probability progression to be better solution, and the evolution probability of the intermediate quality habitat is improved by matching with the provided secondary mutation operation.
Drawings
FIG. 1 is a flow chart of a vehicle path optimization method based on a blocking matrix and fuzzy transit times in accordance with the present invention;
FIG. 2 is a diagram showing a migration operation in embodiment 2 of the present invention;
FIG. 3 is a diagram showing a variation operation in embodiment 3 of the present invention;
FIG. 4 is a graph of manufacturer satisfaction for different population sizes in example 4 of the present invention;
fig. 5 is a manufacturer satisfaction curve for each algorithm for a small vehicle route with a Cr value of 0.4 in example 4 of the present invention;
fig. 6 is a manufacturer satisfaction curve of each algorithm for a large vehicle route with a Cr value of 0.4 in embodiment 4 of the present invention;
FIG. 7 is a graph of manufacturer satisfaction for different Cr values in example 4 of the present invention;
fig. 8 is a graph of manufacturer satisfaction for each algorithm with a Cr value of 0.9 in example 4 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
As shown in fig. 1, in an embodiment, a vehicle path optimization method based on a block matrix and fuzzy transportation time is provided, which considers the selection problem of two transportation modes, namely cyclic transportation and cross delivery, under the condition of fuzzy transportation time, so that an optimal transportation scheme under uncertain conditions can be obtained.
To facilitate understanding of the vehicle path optimization method of the present embodiment, the parameters involved in the present embodiment are first given as follows:
s represents a set of suppliers; g represents a vendor set; n is a radical ofgIndicating the number of manufacturers; l represents a cross distribution center set; k represents a vehicle set; q represents vehicle capacity; gamma represents the unit product loading or unloading time; digRepresenting an order of vendor g for supplier i; t is tijRepresents the transit time from provider i to node j; stkiRepresenting the service time of the circulating transport vehicle k at the node i; bkiRepresents the time when the circulating transport vehicle k arrives at the node i; a islgIndicating that vendor g's order left the cross-distribution centerl is the time; f. oflgRepresents the time of arrival of the vehicle at the manufacturer g through the cross distribution center l; t isilgRepresents the initialization time of the vehicle transport to the manufacturer g through the cross distribution center l; n islgRepresents the number of vehicles from the cross distribution center l to the manufacturer g; m isilRepresents the number of vehicles from supplier i to cross distribution shipping center l; r iskgRepresents the satisfaction of the manufacturer g and the order of the manufacturer is transported by the circulating transport vehicle k; r islgRepresents the satisfaction of the vendor g and the vendor's order is shipped through the cross-distribution center l; w is akgA weight representing the satisfaction of the vendor g and the vendor's order is transported by the loop transport vehicle k; w is algWeight representing the satisfaction of the vendor g and the vendor's order was shipped through the cross-distribution center l; [ c ] isg,dg]Indicating the time window of vendor g.
The present invention focuses on the optimization of vehicle paths so that scanning, sorting and other operations within the warehouse, and cargo delays are not considered in the cross-delivery mode of transportation. Specifically, the vehicle path optimization method based on the block matrix and the fuzzy transportation time comprises the following steps:
and step S1, establishing a transportation mode based on fuzzy transportation time, a circulation transportation sequence and a path optimization model distributed by the cross distribution center.
To better illustrate this model, the present embodiment proposes the following assumptions: all vehicle types are the same; the vendor order for the supplier is less than the capacity of the vehicle; there are enough vehicles to transport the cargo; the service time at a certain point refers to the loading or unloading time at that point; the cross distribution center does not temporarily store the goods, namely the goods are loaded into the outbound vehicle immediately after being unloaded from the inbound vehicle; outbound vehicles that are driving toward the manufacturer must remain at the cross-distribution center until all orders that the manufacturer needs are loaded onto the outbound vehicle.
Step S1.1, when establishing a model, firstly, taking the maximum manufacturer satisfaction as an optimization target, and establishing an objective function as follows:
Figure BDA0002098519290000081
in the formula (1), s is a fitness function of the satisfaction degree of manufacturers, G is a manufacturer set, G is a manufacturer G, K is a vehicle set, K is a vehicle K, and rkgIs satisfied by the manufacturer g and the order of the manufacturer is transported by a circulating transport vehicle k, wkgIs the weight of satisfaction of the manufacturer g and the order of the manufacturer is transported by a circulating transport vehicle k, L is a cross distribution center set, L is a cross distribution center L, rlgIs satisfied by the manufacturer g and the order of the manufacturer is transported through the cross-distribution centre l, wlgIs the weight of satisfaction of the vendor g whose order was shipped through the cross-distribution center l, S is the set of suppliers, i is the supplier i, [ c ]g,dg]Time window required by manufacturer g, DigFor the order of the manufacturer g to the supplier i, DgFor the order of the vendor g for all suppliers.
Y in the objective functionikgAnd xilgIs a decision variable, and
Figure BDA0002098519290000091
Figure BDA0002098519290000092
b in the objective functionkg1、bkg2And bkg3Fuzzy time of arrival of order of manufacturer g transported by circulating transport vehicle k, the fuzzy time being bkgFuzzy number of (b)kgFor the time that the vehicle k reaches the manufacturer g through the circulation transportation, and
bkg＝bki+stki+tig (2)
in the formula (2), K belongs to K, G belongs to G, i belongs to S and bkiFor circulating the time of arrival of the transport vehicle k at the supplier i, stkiFor circulating the service time, t, of the transport vehicle k at the supplier iigIs the transit time from supplier i to vendor g, and
stki＝γDigyikg (3)
in the formula (3), γ is the unit loading or unloading time of the product, DigFor the order of the manufacturer g to the supplier i, yikgIs a decision variable;
f in the objective functionlg1、flg2And flg3Fuzzy time of arrival of order for manufacturer g passing through cross-distribution center l, flgFuzzy number of flgFor the time of arrival of the vehicle at the manufacturer g through the cross distribution center l, and
flg＝alg+tlg (4)
in the formula (4), L belongs to L, G belongs to G, algTime of departure, t, from the Cross distribution center l for the order of the manufacturer glgFor the transit time from the cross-distribution center l to the manufacturer g, and
Figure BDA0002098519290000093
in the formula (5), γ is a unit product loading or unloading time, TilgFor the initialization time of the transport of vehicles through the cross-distribution centre l to the manufacturer g, q being the manufacturer q, DiqFor orders of manufacturer q to supplier i, xilgAnd xilqAs decision variables, xilqTaking 1 when the order of the supplier i from the manufacturer q is distributed through the cross distribution center l; otherwise, take 0, tilFor the transit time of the supplier i to the cross-distribution centre l, DigAn order for vendor g to supplier i.
In addition, r in the formula (1)kgThe initial representation method of (1) is:
Figure BDA0002098519290000101
due to the fuzzy time of arrival of the order of the manufacturer g transported by the circulating transport vehicle k
Figure BDA0002098519290000102
Therefore, the formula (6) can be rewritten as the following expression in the objective function:
Figure BDA0002098519290000103
r in formula (1)lgThe initial representation method of (1) is:
Figure BDA0002098519290000104
due to the fuzzy time of arrival of the order by the manufacturer g of the cross-distribution center l
Figure BDA0002098519290000105
Therefore, the formula (8) can be rewritten as the following expression in the objective function:
Figure BDA0002098519290000106
since the order of the manufacturer g can be satisfied by the circular transportation or the cross delivery transportation, the order arrival time of the manufacturer g may be different, and the corresponding satisfaction degree may also be different. To solve this problem, this embodiment assigns a satisfaction weight related to traffic volume to different transportation modes, because vehicles with larger traffic volumes are more likely to arrive on time by manufacturers, and therefore w in formula (1)kgAnd wlgEach can be calculated according to the following formula:
Figure BDA0002098519290000107
Figure BDA0002098519290000108
s1.2, establishing a constraint condition according to the objective function:
the objective function of the proposed model should satisfy various constraints, as shown below.
(1) The order of the supplier i from the manufacturer g can be transported only by one of circular transportation or cross distribution:
Figure BDA0002098519290000109
(2) the goods loaded by the circulating transport vehicle k cannot exceed the capacity Q of the vehicle:
Figure BDA0002098519290000111
(3) inbound vehicles transported from supplier i to cross distribution center l, where the number of vehicles from supplier i to cross distribution center l is m, carry cargo that cannot exceed the capacity Q of the vehicleil：
Figure BDA0002098519290000112
(4) The goods loaded on the outbound vehicle transported from the cross distribution center l to the manufacturer g, the number of which is n, cannot exceed the capacity Q of the vehiclelg：
Figure BDA0002098519290000113
(5) Order of manufacturer g transported by circulating transport vehicle k, its arrival time bkgMust not exceed dg：
bkg≤dg，k∈K,g∈G (16)
(6) Order of manufacturer g transported through cross-distribution center l, arrival time flgMust not exceed dg：
flg≤dg，l∈L,g∈G (17)
(7) If the manufacturer has an order for supplier i and the order is delivered by cyclical transportation, then there is a decision variable z for vehicle k from supplier i to the next node jikjComprises the following steps:
Figure BDA0002098519290000114
(8) if the order of vendor g to supplier i is delivered by circular transport, then there is a decision variable z for vehicle k from supplier i to vendor gikgComprises the following steps:
Figure BDA0002098519290000115
(9) decision variable z for a route from supplier i to manufacturer g for vehicle kikgComprises the following steps:
Figure BDA0002098519290000116
(10) setting the range of decision variables:
xilg∈{0,1}，i∈S,l∈L,g∈G (21)
yikg∈{0,1}，i∈S,k∈K,g∈G (22)
zikj∈{0,1}，i∈S,k∈K,j∈S∪G (23)
in the above constraint, since the transit time is uncertain, and the arrival time and the departure time are also uncertain, the transit time needs to be treated in a fuzzy manner, and the treatment process is as follows:
first, the transit time t of the vehicle k from node i to node j is setijConversion to fuzzy number
Figure BDA0002098519290000121
The arrival time b is obtained by the same methodkgIs a fuzzy number of
Figure BDA0002098519290000122
Time of arrival flgIs a fuzzy number of
Figure BDA0002098519290000123
Therefore, the formulas (16) and (17) can be converted into the following forms:
Figure BDA0002098519290000124
Figure BDA0002098519290000125
to deal with uncertain variables in the optimization model, the present embodiment employs credibility theory to compare fuzzy variables with fixed values to evaluate uncertain values. Therefore, the constraints (24) and (25) can also be converted into the following form:
Figure BDA0002098519290000126
Figure BDA0002098519290000127
wherein,
Figure BDA0002098519290000128
is the arrival time bkgFuzzy random variables of, and
Figure BDA0002098519290000129
Figure BDA00020985192900001210
is the arrival time flgFuzzy random variables of, and
Figure BDA00020985192900001211
Cr*representing the confidence level of the risk undertaking.
Wherein Cr is*The higher the value, the larger the solution space, the easier it is to obtain a better solution. However, Cr*The larger the value, the greater the risk of failure. In one embodiment, Cr is added*Set in the range [0.4,0.6 ]]Within this range, the manufacturer can obtain the optimal satisfaction, and the fluctuation of the satisfaction of the manufacturer is small, and the failure risk level is within the acceptable range.
In the following embodiment, the optimal transportation scheme is obtained by solving the path optimization model by using a block matrix-based representation method and an EBBO algorithm, and includes:
step S2, initializing to obtain a solution of the path optimization model, namely habitats, representing each habitat by adopting a block matrix, calculating a suitability index value (HSI value) of each habitat, and determining an initial optimal solution according to the suitability index value.
It should be noted that, when determining the initial optimal solution, the solution with the largest HSI value is selected as the optimal solution.
The solution of the path optimization model, i.e. the corresponding transportation scenario, can be seen as a habitat. Since the three sub-problems of transportation mode, circulating transportation sequence and cross distribution center distribution are simultaneously considered, the transportation scheme under the condition of fuzzy transportation time is represented by the block matrix.
The block matrix comprises transportation mode selection, vehicle circulation transportation sequence and selection of a cross distribution center, and one-dimensional habitat representation in the traditional BBO algorithm is expanded into two-dimensional habitat representation, so that the proposed vehicle path optimization model is solved.
Each habitat is composed of a block matrix T ═ Tg]Where g denotes the vendor g, the columns of the block matrix denote vendors, the rows denote vendors, the elements of the block matrix T consist of a number of small matrices TgComposition is carried out;
wherein, the matrix TgThe method comprises the following steps that three lines are included, wherein the first line is an integer from 0 to M, 0 represents that goods are transported in a cross distribution mode, M represents the number of vehicles for circulating transportation, and the integer E belongs to {0, M }, represents that the goods of a corresponding supplier are distributed by the E vehicle through circulating transportation; matrix arrayTgA random real number between 0 and 1, which represents the order of distribution of the circulating transport vehicles, the larger the random real number, which represents that the corresponding supplier is traversed earlier, and the random real number 0, which represents that the goods of the corresponding supplier are not distributed by the circulating transport manner; matrix TgThe third row of (a) is a random integer between 0 and n, 0 indicates that the goods of the corresponding supplier are not transported by the cross-distribution manner, n indicates the number of cross-distribution centers, and the random integer F e {0, n } indicates that the goods of the corresponding supplier are transported by the F-th cross-distribution center.
The method of representing habitat by a block matrix is further illustrated by the following examples.
Example 1:
TABLE 1 habitat based on Block matrix representation
Figure BDA0002098519290000131
Table 1 provides an example of a transportation scheme (habitat) based on a block matrix representation, which contains six suppliers, three vendors and two cross distribution centers. As shown in the first row of the matrix, the two "2" values under suppliers 2 and 5 indicate that the goods of the two suppliers are cyclically transported to the vendor 1 by the vehicle 2. The second row of the matrix indicates that the vehicle 2 first visits the provider 2 and, if the vehicle is not overloaded, continues to visit the provider 5. This process continues until all suppliers are visited or the vehicle is overloaded. If this happens, other vehicles will be selected to visit the remaining suppliers. The third row of the matrix indicates that suppliers not participating in the circuit will be transporting goods by cross-distribution. Here, the goods of the suppliers 3 and 4 are transported to the manufacturer 1 through the cross distribution center 2.
And S3, calculating the migration rate and the migration rate of the population, judging whether to perform the operation of migration in or out of the habitat or not according to the migration rate and the migration rate, and if the operation of migration in or out is required, performing vector substitution on the block matrix corresponding to the habitat to realize the operation of migration in or out of the habitat.
In the migration phase, the higher the HSI value of a habitat, the easier it is for that habitat to share its characteristics with habitats having lower HSI values. In the present application, the HSI value of each habitat is calculated according to formula (1). The change in each solution (i.e., habitat) is determined by mobility. When a solution is selected for change, mobility is used to probabilistically select habitats for migration-out and migration-in operations. The migration rate and the migration rate were calculated as follows:
Figure BDA0002098519290000141
Figure BDA0002098519290000142
wherein k isiThe ranking order of the ith solution is obtained after all solutions are sorted according to the descending order of HSI values of the solutions, n represents the number of the solutions, I represents the maximum migration rate, and E represents the maximum migration rate.
The suitability vector (SIV) in the habitat is represented by a column in the block matrix T, and when the habitat is subjected to an immigration operation or an immigration operation, the immigration column of the habitat to be immigrated is replaced by the immigration column of the habitat to be immigration, so that vector replacement is completed.
The migration operation of the present application for habitat is further described by the following examples.
Example 2:
as shown in fig. 2, four suppliers, two manufacturers and two cross distribution centers are included in one vehicle path optimization. Wherein the second column SIV in habitat i migrates out of the habitat and the third column SIV in habitat j migrates into habitat i. Thus, the second column in habitat i
Figure BDA0002098519290000143
Third column in habitat j
Figure BDA0002098519290000144
Instead. Here, the vector ((2,0.78,0) - (1,0.34,0)) in the habitat i is inhabitedThe vectors in j ((1,0.42,0) - (0,0,2)) are replaced, and the migration is completed.
And step S4, calculating the variation rate of the population by using the self-adaptive variation probability and the secondary variation probability, and selecting a corresponding habitat to perform variation operation according to the self-adaptive variation probability and the secondary variation probability to update the optimal solution.
The traditional BBO algorithm is evolved through two operations of migration and variation, and shows good searching capability when solving different types of optimization problems. However, habitats with higher HSI values can only be slightly improved by mutation operations and the probability of evolution of habitats with higher HSI values is very small due to the smaller value of the initial maximum mutation rate. To solve this problem, the present embodiment introduces a new adaptive mutation probability and quadratic mutation operation to improve the diversity of the population. Wherein
Adaptive mutation probability mi1Comprises the following steps:
Figure BDA0002098519290000151
in the formula (f)iDenotes the HSI value, f, of the ith habitatmidRepresents the median of the HSI values for all habitats,
Figure BDA0002098519290000152
represents the maximum value of HSI values in all habitats; the intermediate value of the HSI value is understood here to mean that the HSI value of the habitat located in the middle is selected after ranking the habitats from large to small according to the HSI value. For example: if 3 habitats exist, the HSI values after being arranged from large to small are respectively 3, 2 and 1, and the middle value is 2; if there are 4 habitats, their HSI values after the arrangement from large to small are 4, 3, 2, 1 respectively, the intermediate value is 2.5.
Probability of quadratic variation mi2Comprises the following steps:
Figure BDA0002098519290000153
in the formula (f)iDenotes the HSI value, f, of the ith habitatmidRepresents the median of the HSI values for all habitats,
Figure BDA0002098519290000154
represents the maximum value of HSI values in the middle 70% of the habitats; the middle 70% of the habitats is understood here to mean that after arranging the habitats in descending order according to the HSI value, 15% of the number of habitats in each of the front and rear are removed, the habitats in the middle 70% are selected, and the selection is made backwards. For example: if 100 habitats exist, 16 th to 85 th habitats are selected; if 10 habitats exist, selecting backwards and taking 3-9.
Firstly, all habitats are selected as a primary mutation target, and the mutation target is obtained according to the self-adaptive mutation probability mi1Performing first mutation on the corresponding habitat in the first mutation target, selecting 70% of the habitats with the HSI value in the middle of the habitat after the first mutation as the second mutation target according to the result of the first mutation, and performing second mutation according to the second mutation probability mi2And carrying out secondary variation on the corresponding habitat in the secondary variation target.
The self-adaptive mutation probability m provided by the applicationi1The habitat with lower and higher HSI values has higher probability progression to better solution. In addition, in order to overcome the limitation that the habitat with the intermediate HSI value still has smaller probability progression to be more optimal, secondary mutation operation is introduced to improve the mutation probability of the habitat with the intermediate HSI value.
The operation of the present application for habitat mutation is further described by the following examples.
Example 3:
as shown in fig. 3, an example of a variant operation based on the proposed hybrid vehicle path model includes four suppliers, two manufacturers, and two cross distribution centers. In this example, since the mode of transportation of the goods from the supplier 3 to the manufacturer 1 is changed from cross distribution to circular transportation, the goods are transported in a circular manner
Figure BDA0002098519290000161
From 0 to random number0.35，
Figure BDA0002098519290000162
Changing from 2 to 0 accordingly. Similarly, since the transportation mode of the goods from the supplier 3 to the manufacturer 2 is changed from the circulation transportation to the cross distribution, the goods are delivered
Figure BDA0002098519290000163
From random number 0.72 to 0, and
Figure BDA0002098519290000164
correspondingly from 0 to 2. That is, in the mutation operation, the third column ((0,0,2) - (1,0.72,0)) of the habitat i is replaced by the new column ((1,0.35,0) - (0,0, 2)).
Step S5, judging whether a preset iteration number is reached, and if the preset iteration number is reached, outputting an optimal solution, namely an optimal transportation scheme; otherwise, the iteration continues in step S3.
In the embodiment, when the iteration times are preset, the number of manufacturers is set, and if the number of manufacturers N in the participators for optimizing the vehicle path is NgIs 1. ltoreq. NgIf the number of iterations is less than 4, the preset number of iterations is 300; number of manufacturers N in participants if vehicle routing is optimizedgIs NgAnd if the number of iterations is more than or equal to 4, the preset number of iterations is 500.
For example: if the participants of the vehicle path optimization relate to 1 manufacturer, 10 suppliers and 2 cross distribution centers, the preset iteration number is 300; if the participants of the vehicle path optimization involve 4 manufacturers, 30 suppliers and 5 cross-distribution centers, the preset number of iterations is 500.
In order to verify the superiority and feasibility of the vehicle path optimization method based on the block matrix and the fuzzy transportation time, an improved biophysical optimization algorithm (EBBO) is selected and compared with a standard BBO algorithm (BBO), a Genetic Algorithm (GA), a particle swarm algorithm (PSO) and a variable neighborhood search algorithm (VNS) through an embodiment.
Example 4:
to achieve a reasonable population size, this example first tested the performance of the different algorithms at population sizes from 30 to 100 using a small vehicle path containing 10 suppliers, 1 vendor and 2 cross-distribution centers. For each population size, this example was run 50 times under the same conditions, the average optimal vendor satisfaction was calculated, and the maximum number of iterations per run was set to 300. The calculation results are shown in fig. 4.
As shown in fig. 4, the average vendor optimum satisfaction obtained using the EBBO algorithm is higher than the average vendor optimum satisfaction obtained by the other four algorithms over a given population size range. Furthermore, as the population size increased from 30 to 100, the vendor satisfaction curve obtained using the EBBO algorithm remained relatively stable, with a weakly increasing trend for the vendor satisfaction curve obtained using the PSO algorithm. However, the vendor satisfaction curves obtained using the BBO and GA algorithms fluctuate until the population size exceeds 80. The vendor satisfaction curve obtained using the VNS algorithm is also fluctuating and less stable. And when the population size is about 80, the manufacturer satisfaction degree obtained by using the VNS algorithm reaches the optimum. Therefore, the population sizes of the five algorithms are all set to be 80 in subsequent experiments to ensure the fairness of comparison of the five algorithms.
The validity of the algorithm (EBBO) of the invention is further verified:
first, a small vehicle routing case containing 10 suppliers, 1 manufacturer and 2 cross-distribution centers was chosen to compare the manufacturer satisfaction.
As shown in fig. 5, the vendor satisfaction obtained using the EBBO algorithm at a Cr value of 0.4 and 300 iterations shows better performance than the other four algorithms. The main reason is that EBBO introduces adaptive mutation probability and secondary mutation operation, increases population diversity and improves the global search capability of the algorithm.
To further demonstrate the effectiveness of the EBBO algorithm of the present invention, this example selects a large vehicle routing case containing 30 suppliers, 4 manufacturers, and 5 cross-distribution centers to compare the manufacturer satisfaction.
As shown in fig. 6, at a Cr value of 0.4 and a number of iterations of 500, the EBBO algorithm of the present invention also exhibited better performance in solving the large-scale hybrid vehicle path problem than the other four algorithms. The reason why the EBBO algorithm exhibits poor convergence in solving a large-scale vehicle path problem is because the time required to find a globally optimal solution also needs to be increased correspondingly when the problem becomes large in scale. Furthermore, the EBBO algorithm introduces quadratic mutation operations, resulting in a slow convergence speed. However, the EBBO algorithm has a better global search capability when solving the large-scale hybrid vehicle path problem, and is superior to the other four algorithms in finding a global optimal solution.
The feasibility of the algorithm (EBBO) of the invention was further verified:
assume that a logistics company is assigned a task to transport parts from six different parts suppliers to a certain car manufacturer, producing clutches, brake discs, steering gears, valves, oil pumps and mufflers. To centralize delivery time, the auto manufacturer receives the package in a time window [11:10,12:50 ].
Since the Cr value affects the optimal solution obtained by the solution, the performance of the EBBO algorithm under different Cr values is tested according to the above assumed task. The experiment was run 50 times for each Cr value, with the maximum number of iterations per run set to 300. The calculation results are shown in fig. 7.
In the figure, when the Cr value ranges from 0.4 to 0.9, the curve is relatively stable. Since the lower Cr, the higher the risk of failure, the most reasonable value of Cr is 0.9. Therefore, Cr was set to 0.9 for further study.
In the above task, when Cr is set to 0.9, a fitness curve as shown in fig. 8 is obtained, from which: as the number of iterations increases, the EBBO algorithm achieves a higher vendor satisfaction than the other four algorithms.
The invention provides a vehicle path optimization method based on a block matrix and fuzzy transportation time, which comprehensively considers the problems of selection of suppliers, manufacturers and transportation modes, selection of a vehicle circulating transportation sequence and a cross distribution center and the like, and provides a block matrix-based representation method to represent a transportation scheme in a more intuitive, reasonable and efficient manner; expanding the one-dimensional habitat representation in the traditional BBO algorithm into a two-dimensional habitat representation, thereby solving the proposed hybrid vehicle path optimization model; based on the relative difference between the quality of the current habitat and the quality of the intermediate habitat, a self-adaptive mutation probability calculation method is provided, so that the habitats with high quality and low quality have higher probability progression to be better solution, and the evolution probability of the intermediate quality habitat is improved by matching with the provided secondary mutation operation.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (4)

1. A vehicle path optimization method based on a block matrix and fuzzy transportation time is characterized by comprising the following steps:
s1, establishing a transportation mode, a circulating transportation sequence and a path optimization model distributed by a cross distribution center based on fuzzy transportation time;
step S2, initializing to obtain a solution of a path optimization model, namely habitats, representing each habitat by adopting a block matrix, calculating a suitability index value of each habitat, and determining an initial optimal solution according to the suitability index value;
step S3, calculating the migration rate and the migration rate of the population, judging whether to perform the operation of migration in or out of the habitat or not according to the migration rate and the migration rate, and if the operation of migration in or out is required, performing vector substitution on the block matrix corresponding to the habitat to realize the operation of migration in or out of the habitat;
step S4, calculating the variation rate of the population by using the self-adaptive variation probability and the secondary variation probability, selecting a corresponding habitat for variation operation according to the self-adaptive variation probability and the secondary variation probability, and updating the optimal solution;
step S5, judging whether a preset iteration number is reached, and if the preset iteration number is reached, outputting an optimal solution, namely an optimal transportation scheme; otherwise, the step S3 is entered for continuing the iteration;
the establishing of the transportation mode, the circulating transportation sequence and the path optimization model distributed by the cross distribution center based on the fuzzy transportation time comprises the following steps:
with the maximum manufacturer satisfaction as an optimization target, establishing an objective function as follows:
Figure FDA0003033855250000011
in the formula, s is a fitness function of the satisfaction degree of the manufacturer, G is a manufacturer set, G is a manufacturer G, K is a vehicle set, K is a vehicle K, and r iskgIs satisfied by the manufacturer g and the order of the manufacturer is transported by a circulating transport vehicle k, wkgIs the weight of satisfaction of the manufacturer g and the order of the manufacturer is transported by a circulating transport vehicle k, L is a cross distribution center set, L is a cross distribution center L, rlgIs satisfied by the manufacturer g and the order of the manufacturer is transported through the cross-distribution centre l, wlgIs the weight of satisfaction of the vendor g whose order was shipped through the cross-distribution center l, S is the set of suppliers, i is the supplier i, [ c ]g,dg]Time window required by manufacturer g, DigFor the order of the manufacturer g to the supplier i, DgOrders for vendor g for all suppliers;
y in the objective functionikgAnd xilgIs a decision variable, and
Figure FDA0003033855250000021
Figure FDA0003033855250000022
b in the objective functionkg1、bkg2And bkg3Fuzzy time of arrival of order of manufacturer g transported by circulating transport vehicle k, the fuzzy time being bkgFuzzy number of (b)kgFor the time that the vehicle k reaches the manufacturer g through the circulation transportation, and
bkg＝bki+stki+tig
wherein K belongs to K, G belongs to G, i belongs to S, bkiFor circulating the time of arrival of the transport vehicle k at the supplier i, stkiFor circulating the service time, t, of the transport vehicle k at the supplier iigIs the transit time from supplier i to vendor g, and
stki＝γDigyikg
where γ is the unit product loading or unloading time, DigFor the order of the manufacturer g to the supplier i, yikgIs a decision variable;
f in the objective functionlg1、flg2And flg3Fuzzy time of arrival of order for manufacturer g passing through cross-distribution center l, flgFuzzy number of flgFor the time of arrival of the vehicle at the manufacturer g through the cross distribution center l, and
flg＝alg+tlg
wherein L is belonged to L, G is belonged to G, algTime of departure, t, from the Cross distribution center l for the order of the manufacturer glgFor the transit time from the cross-distribution center l to the manufacturer g, and
Figure FDA0003033855250000023
where γ is the unit product loading or unloading time, TilgFor the initialization time of the transport of vehicles through the cross-distribution centre l to the manufacturer g, q being the manufacturer q, DiqFor orders of manufacturer q to supplier i, xilqAnd xilgAs decision variables, tilFor the transit time of the supplier i to the cross-distribution centre l, DigAn order for vendor g to supplier i;
wherein, establishing constraint conditions according to the objective function comprises:
the supplier g can only select one transportation mode for the order of the supplier i:
Figure FDA0003033855250000031
setting that the goods loaded by the circulating transport vehicle k cannot exceed the capacity Q of the vehicle:
Figure FDA0003033855250000032
it is set that the volume Q of an inbound vehicle transported from a supplier i to a cross distribution center l, where the number of vehicles from the supplier i to the cross distribution center l is m, is not exceeded by cargo loaded on the vehicleil：
Figure FDA0003033855250000033
It is set that the capacity Q of an outbound vehicle transported from a cross distribution center l to a manufacturer g, the number of which is n, cannot exceed the capacity Q of the vehiclelg：
Figure FDA0003033855250000034
Setting the order of the manufacturer g transported by the circulating transport vehicle k, the arrival time b thereofkgMust not exceed dgWherein the arrival timebkgIs a fuzzy number of
Figure FDA0003033855250000035
Confidence level of risk exposure is Cr*：
Figure FDA0003033855250000036
Setting the order of manufacturer g transported through the cross-distribution center l and the arrival time flgMust not exceed dgWherein the arrival time flgIs a fuzzy number of
Figure FDA0003033855250000037
Confidence level of risk exposure is Cr*：
Figure FDA0003033855250000038
Setting the range of decision variables:
xilg∈{0,1}，i∈S,l∈L,g∈G
yikg∈{0,1}，i∈S,k∈K,g∈G；
the method comprises the following steps of calculating the mutation rate of a population by utilizing the self-adaptive mutation probability and the secondary mutation probability, and selecting a corresponding habitat to perform mutation operation according to the self-adaptive mutation probability and the secondary mutation probability, wherein the method comprises the following steps:
adaptive mutation probability mi1Comprises the following steps:
Figure FDA0003033855250000039
in the formula (f)iDenotes the HSI value, f, of the ith habitatmidRepresents the median of the HSI values for all habitats,
Figure FDA0003033855250000041
represents the maximum value of HSI values in all habitats;
probability of quadratic variation mi2Comprises the following steps:
Figure FDA0003033855250000042
in the formula (f)iDenotes the HSI value, f, of the ith habitatmidRepresents the median of the HSI values for all habitats,
Figure FDA0003033855250000043
represents the maximum value of HSI values in the middle 70% of the habitats;
firstly, all habitats are selected as a primary mutation target, and the mutation target is obtained according to the self-adaptive mutation probability mi1Performing first mutation on the corresponding habitat in the first mutation target, selecting 70% of the habitats with the HSI value in the middle of the habitat after the first mutation as the second mutation target according to the result of the first mutation, and performing second mutation according to the second mutation probability mi2And carrying out secondary variation on the corresponding habitat in the secondary variation target.
2. The block matrix and fuzzy transit time based vehicle path optimization method of claim 1, wherein said representing habitats with block matrices comprises:
each habitat is composed of a block matrix T ═ Tg]Where g denotes the vendor g, the columns of the block matrix denote vendors, the rows denote vendors, the elements of the block matrix T consist of a number of small matrices TgComposition is carried out;
wherein, the matrix TgThe method comprises the following steps that three lines are included, wherein the first line is an integer from 0 to M, 0 represents that goods are transported in a cross distribution mode, M represents the number of vehicles for circulating transportation, and the integer E belongs to {0, M }, represents that the goods of a corresponding supplier are distributed by the E vehicle through circulating transportation; matrix TgRepresents the order of delivery of the circulating transport vehicles, the larger the random real number, the earlier the corresponding supplier isIs traversed, and the random real number is 0, which indicates that the goods of the corresponding supplier are not distributed in a circulating transportation mode; matrix TgThe third row of (a) is a random integer between 0 and n, 0 indicates that the goods of the corresponding supplier are not transported by the cross-distribution manner, n indicates the number of cross-distribution centers, and the random integer F e {0, n } indicates that the goods of the corresponding supplier are transported by the F-th cross-distribution center.
3. The block matrix and fuzzy transportation time based vehicle path optimization method of claim 2, wherein if an immigration or an emigration operation is required, performing vector substitution on the block matrix corresponding to the habitat to realize the immigration or the emigration operation on the habitat comprises:
the fitness vector in the habitat is represented by a column in the block matrix T, and when the habitat is subjected to the operation of immigration or immigration, the immigration column of the habitat to be immigrated is replaced by the immigration column of the habitat to be immigration, so that vector replacement is completed.
4. The block matrix and fuzzy transit time based vehicle path optimization method of claim 1, wherein said predetermined number of iterations comprises:
number of manufacturers N in participants if vehicle routing is optimizedgIs 1. ltoreq. NgIf the number of iterations is less than 4, the preset number of iterations is 300; number of manufacturers N in participants if vehicle routing is optimizedgIs NgAnd if the number of iterations is more than or equal to 4, the preset number of iterations is 500.
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