CN110276488B - A vehicle routing optimization method based on block matrix and fuzzy transit time - Google Patents

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

A vehicle routing optimization method based on block matrix and fuzzy transit time

technical field

The invention belongs to the technical field of logistics, and in particular relates to a vehicle path optimization method based on block matrix and fuzzy transit time.

Background technique

In recent years, the supply chain that constitutes the core of an enterprise has closely connected suppliers, manufacturers, distributors, retailers and users by controlling the flow of information, logistics and capital. As an important part of the supply chain, the problem of vehicle routing in logistics distribution optimization has also received more and more attention from enterprises. However, compared with the traditional 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 in actual transportation (such as climate change, traffic jams, fluctuations in transportation time caused by factors such as weather) and fuzzy data (such as arrival time, demand, etc.) . Therefore, for such complex problems, uncertainty needs to be considered, as using precise data (such as transit times) to describe the model may yield inaccurate solutions. For example, the transit time from one point to another is generally indeterminate due to traffic jams, weather, and other factors. As a result, arrival times also become uncertain, which may result in shipments not arriving within the stipulated time window. On the other hand, different transportation modes are suitable for different situations, that is, the choice of transportation mode has an important influence on the optimization of the vehicle routing problem and should also be considered. For example, in cross-docking transportation, inbound vehicles load goods from suppliers and transport them to a cross-distribution center, where they are sorted and sorted, and then transported by outbound vehicles to the manufacturer. This process increases shipping time and distance, and costs accordingly. In contrast, in the round-robin mode of transportation, the vehicle loads the goods from the supplier and transports it directly to the manufacturer, which has a shorter transit time. Therefore, the cross-docking shipping method is more suitable for long-distance shipping, while the circular shipping method is more suitable for short-distance shipping.

However, existing research on vehicle routing problems does not consider the above two problems simultaneously. Most studies focus on vehicle routing optimization problems under uncertainty, and do not consider the problem of transportation mode selection. Because the efficient representation of transport mode selection is a challenging problem. Existing representation methods for transport mode selection, such as a representation method based on harmonic search and simulated annealing proposed in the prior art, do not consider multiple transport mode options at the same time. At the same time, this method only considers the choice of transportation mode, but does not consider the uncertainty of the transportation environment, so the solution obtained by it is not accurate enough, so the optimal transportation plan cannot be obtained.

Due to the complexity of the vehicle routing problem, many heuristic algorithms are often used to solve this problem, such as Genetic Algorithm (GA), Harmony Search (HS), Variable Neighbor Search (VNS), Ant Colony Algorithm (ACO) ), particle swarm optimization (PSO), and simulated annealing (SA). In recent years, the biogeographical optimization algorithm (BBO) has been widely used in the solution of manufacturing service supply chain optimization and constraint optimization problems as an effective algorithm for solving large-scale optimization problems. The BBO algorithm simulates the migration process of species, and evolves through migration operations and mutation operations, and finally makes the population tend to be globally optimal. Many experiments show that the BBO algorithm is superior to other heuristic algorithms such as PSO and ACO when solving the vehicle routing problem. However, the traditional BBO algorithm has a limited application environment and cannot comprehensively consider the above problems. Therefore, an improved BBO algorithm (EBBO) is urgently needed to solve a more reasonable and efficient transportation scheme.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a vehicle path optimization method based on block matrix and fuzzy transportation time, which considers the selection of two transportation modes of circular transportation and cross-delivery under the condition of fuzzy transportation time, so that uncertainties can be obtained. the optimal transportation solution for the situation.

To achieve the above object, the technical scheme adopted by the present invention is:

A vehicle routing optimization method based on block matrix and fuzzy transit time, including the following steps:

Step S1, establishing a path optimization model based on the mode of transport under the fuzzy transport time, the sequence of circular transport and the allocation of the cross distribution center;

Step S2, initialize to obtain the solution of the path optimization model, namely habitats, and use a block matrix to represent each habitat, calculate the suitability index value of each habitat, and determine the initial optimal solution according to the suitability index value;

Step S3, calculate the in-migration rate and the out-migration rate of the population, and judge whether to carry out the in-migration or out-migration operation to the habitat according to the in-migration rate and the out-migration rate. The block matrix corresponding to the habitat performs vector substitution to realize the in-or-out operation of the habitat;

Step S4, calculating the mutation rate of the population by using the adaptive mutation probability and the secondary mutation probability, selecting the corresponding habitat to perform mutation operation according to the adaptive mutation probability and the secondary mutation probability, and updating the optimal solution;

Step S5, judge whether the preset number of iterations is reached, and if the number of iterations is reached, output the optimal solution, that is, the optimal transportation plan; otherwise, go to Step S3 to continue the iteration.

Preferably, the establishment of a route optimization model based on the transportation mode, circular transportation sequence and cross-distribution center assignment under the fuzzy transportation time includes:

Taking maximizing the manufacturer's satisfaction as the optimization goal, the objective function is established as:

In the formula, s is the fitness function of the manufacturer's satisfaction, G is the set of manufacturers, g is the manufacturer g, K is the set of vehicles, k is the vehicle k, r _kg is the satisfaction of the manufacturer g and the order of the manufacturer is transported by circular transportation. Vehicle k transports, w _kg is the weight of manufacturer g’s satisfaction and the manufacturer’s orders are transported by circular transport vehicle k, L is the set of cross-distribution centers, l is the cross-distribution center l, and r _lg is the satisfaction of manufacturer g And the manufacturer's order is transported through the cross-distribution center l, w _lg is the weight of the satisfaction of the manufacturer g and the manufacturer's order is transported through the cross-distribution center l, S is the supplier set, i is the supplier i, [ c _g ,d _g ] is the time window required by manufacturer g, D _ig is the order of manufacturer g to supplier i, and D _g is the order of manufacturer g to all suppliers;

y _ikg and x _ilg in the objective function are decision variables, and

In the objective function, b _kg1 , b _kg2 , and b _kg3 are the fuzzy time of the arrival of the order of the manufacturer g transported by the circular transport vehicle k, the fuzzy time is the fuzzy number of b _kg , and b _kg is the transport of the vehicle k to the manufacturer through the circular transport time of g, and

b _kg = b _ki + st _ki + t _ig

In the formula, k∈K, g∈G, i∈S, b _ki is the time when the circulating transport vehicle k arrives at supplier i, st _ki is the service time of the circulating transport vehicle k at supplier i, and t _ig is the time from the supplier i the transit time of i to firm g, and

st _ki = γD _ig y _ikg

In the formula, γ is the unit product loading or unloading time, D _ig is the order of manufacturer g to supplier i, and y _ikg is the decision variable;

f _{lg1 , f lg2 ,} and f _lg3 in the objective function are the fuzzy time for the arrival of the order of the manufacturer g through the cross-distribution center l, the fuzzy time is the fuzzy number of f _lg , and f _lg is the vehicle reaching the manufacturer through the cross-distribution center l time of g, and

f _lg = a _lg +t _lg

In the formula, l∈L, _g∈G , alg is the time for the order of manufacturer g to leave the cross-distribution center l, _tlg is the transportation time from the cross-distribution center l to the manufacturer g, and

In the formula, γ is the unit product loading or unloading time, T _ilg is the initialization time of vehicle transportation through the cross-distribution center l to the manufacturer g, q is the manufacturer q, D _iq is the order of the manufacturer q to the supplier i, x _ilq and x _ilg is the decision variable, t _il is the transportation time from supplier i to the cross-distribution center l, and D _ig is the order from manufacturer g to supplier i.

Preferably, constraints are established according to the objective function, including:

Suppose that manufacturer g can only choose one shipping method for the order of supplier i:

It is set that the cargo loaded by the circulating transport vehicle k cannot exceed the capacity Q of the vehicle:

Suppose that an inbound vehicle transported from supplier i to cross-distribution center l cannot load more than the vehicle's capacity Q, where the number of vehicles from supplier i to cross-distribution center l is _mil :

It is assumed that the goods loaded by the outbound vehicle transported from the cross-distribution center l to the manufacturer g cannot exceed the capacity Q of the vehicle, and the number of vehicles from the cross-distribution center l to the manufacturer g is n _lg :

风险承担的置信水平为Cr^*：Suppose that the order of the manufacturer g transported by the circulating transport vehicle k, its arrival time b _kg cannot exceed d _g , where the fuzzy number of the arrival time b _kg is

The confidence level for the exposure is Cr ^* :

风险承担的置信水平为Cr^*：Suppose that the order of manufacturer g transported through the cross distribution center l, its arrival time f _lg cannot exceed d _g , and the fuzzy number of the arrival time f _lg is

The confidence level for the exposure is Cr ^* :

Set the range of the decision variable:

x _ilg ∈ {0,1}, i ∈ S, l ∈ L, g ∈ G

y _ikg ∈ {0,1}, i∈S, k∈K, g∈G.

Preferably, each habitat is represented by a block matrix, including:

Each habitat is represented by a block matrix T = [T _g ], where g represents the manufacturer g, the columns of the block matrix represent the supplier, and the rows represent the manufacturer, and the elements of the block matrix T are composed of many small matrices T _g ;

Among them, the matrix T _g contains three rows, the first row is an integer between 0 and M, 0 indicates that the goods are transported by cross-delivery, M indicates the number of vehicles transported in a circular manner, and the integer E∈{0,M} indicates the corresponding supplier The goods are distributed by the E-th vehicle through cyclic transportation; the second row of the matrix T _g is a random real number between 0 and 1, which represents the order of cyclic transportation vehicles. The larger the random real number, the earlier the corresponding supplier is traversed , and the random real number is 0, which means that the goods of the corresponding supplier are not delivered by cyclic transportation; the third row of the matrix T _g is a random integer between 0 and n, 0 means that the goods of the corresponding supplier are not delivered by cross-delivery, n represents the number of cross-distribution centers, and a random integer F∈{0,n} indicates that the goods of the corresponding supplier are transported through the F-th cross-distribution center.

Preferably, if a move-in or move-out operation is required, vector substitution is performed on the block matrix corresponding to the habitat to implement the move-in or move-out operation on the habitat, including:

The suitability vector in the habitat is represented by a column in the block matrix T. When the habitat is moved in or out, the outgoing column of the habitat to be moved is used to replace the incoming column of the habitat to be moved in. , completes the vector substitution.

Preferably, the adaptive mutation probability and the secondary mutation probability are used to calculate the mutation rate of the population, and the corresponding habitat is selected to perform the mutation operation according to the adaptive mutation probability and the secondary mutation probability, including:

The adaptive mutation probability m _i1 is:

表示所有栖息地中的HSI值的最大值；where f _i represents the HSI value of the ith habitat, f _mid represents the median of the HSI values of all habitats,

represents the maximum value of HSI in all habitats;

The quadratic mutation probability m _i2 is:

表示中间70％的栖息地中的HSI值的最大值；where f _i represents the HSI value of the ith habitat, f _mid represents the median of the HSI values of all habitats,

Represents the maximum value of HSI in the middle 70% of the habitat;

First, all habitats are selected as the primary mutation target, and the corresponding habitats in the primary mutation target are mutated for the first time according to the adaptive mutation probability m _i1 , and the habitats after the first mutation are selected according to the results of the first mutation. The habitats whose HSI value is in the middle 70% are used as the secondary mutation target, and the corresponding habitats in the secondary mutation target are subjected to secondary mutation according to the secondary mutation probability m _i2 .

Preferably, the preset number of iterations includes:

If the number of manufacturers N _g in the participants in vehicle routing optimization is 1≤N _g <4, the preset number of iterations is 300; if the number N _g of manufacturers in the participants in vehicle routing optimization is N _g ≥ 4, then Set the number of iterations to 500.

The vehicle route optimization method based on block matrix and fuzzy transportation time provided by the present invention comprehensively considers the selection of suppliers, manufacturers, transportation methods, vehicle circulation transportation sequence and selection of cross distribution centers, and proposes a A block matrix-based representation method to represent the transportation scheme in a more intuitive, reasonable and efficient way; the one-dimensional habitat representation in the traditional BBO algorithm is extended to a two-dimensional habitat representation to solve 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, an adaptive mutation probability calculation method is proposed, so that both high-quality and low-quality habitats have a higher probability to evolve into a better solution, and at the same time Cooperate with the proposed quadratic mutation operation to improve the evolutionary probability of intermediate quality habitats.

Description of drawings

Fig. 1 is the flow chart of the vehicle route optimization method based on block matrix and fuzzy transit time of the present invention;

2 is a schematic diagram of a migration operation in Embodiment 2 of the present invention;

3 is a schematic diagram of a mutation operation in Embodiment 3 of the present invention;

Fig. 4 is the manufacturer satisfaction curve graph under different population scales in the embodiment of the present invention 4;

FIG. 5 is a graph of manufacturer satisfaction of each algorithm with a Cr* value of 0.4 and a small vehicle path in Embodiment 4 of the present invention;

FIG. 6 is a graph of manufacturer satisfaction of each algorithm with a Cr* value of 0.4 and a large vehicle path in Embodiment 4 of the present invention;

Fig. 7 is the manufacturer satisfaction curve graph under different Cr* value in the embodiment of the present invention 4;

FIG. 8 is a graph of manufacturer satisfaction of each algorithm when the Cr* value is 0.9 in Example 4 of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Unless otherwise defined, 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 terms used herein in the description of the present invention are for the purpose of describing specific embodiments only, and are not intended to limit the present invention.

As shown in FIG. 1 , in one embodiment, a vehicle route optimization method based on block matrix and fuzzy transit time is provided, and the method considers the two modes of transportation of circular transportation and cross-delivery under the condition of fuzzy transit time. Choose the problem so that you can get the optimal transportation plan under uncertainty.

In order to facilitate the understanding of the vehicle path optimization method of this embodiment, the parameters involved in this embodiment are first given as follows:

S is the set of suppliers; _G is the set of manufacturers; N _g is the number of manufacturers; L is the set of cross-distribution centers; K is the set of vehicles; Q is the vehicle capacity; γ is the unit product loading or unloading time; Supplier i's order; t _ij represents the transportation time from supplier i to node j; st _ki represents the service time of circular transport vehicle k at node i; b _ki represents the time that circular transport vehicle k arrives at node i; a _lg represents The time when the order of manufacturer g leaves the cross-distribution center l; _flg is the time _when the vehicle passing through the cross-distribution center l _arrives at the manufacturer g; The number of vehicles from the cross-distribution center l to the manufacturer g; _mil represents the number of vehicles from the supplier i to the cross-distribution logistics center l; r _kg represents the satisfaction of the manufacturer g and the order of the manufacturer is transported by the circular transport vehicle k; r _lg represents the satisfaction of the manufacturer g and the orders of the manufacturer are transported through the cross distribution center l; w _kg represents the weight of the satisfaction of the manufacturer g and the orders of the manufacturer are transported by the circulating transport vehicle k; w _lg represents the manufacturer g Satisfaction weight and the manufacturer's order is transported through the cross-distribution center l; [c _g ,d _g ] represents the time window of the manufacturer g.

The present invention focuses on the optimization of vehicle paths, so in the cross-delivery mode of transportation, scanning, sorting and other operations in the warehouse, and cargo delays are not considered. Specifically, the vehicle route optimization method based on block matrix and fuzzy transit time includes the following steps:

Step S1, establishing a path optimization model based on the transportation mode, circular transportation sequence and cross-distribution center assignment under the fuzzy transportation time.

To better illustrate this model, this example makes the following assumptions: all vehicles are of the same type; the manufacturer's order to the supplier is less than the capacity of the vehicle; there are enough vehicles to transport the goods; the service time at a certain point refers to the Loading or unloading time at point; cross-distribution centers do not temporarily store goods, i.e. goods are loaded into outbound vehicles immediately after unloading from inbound vehicles; outbound vehicles heading for the manufacturer must remain at the cross-distribution center until required by the manufacturer All orders are loaded onto this outbound vehicle.

Step S1.1. When establishing the model, first take maximizing the manufacturer's satisfaction as the optimization goal, and establish the objective function as:

In formula (1), s is the fitness function of the manufacturer's satisfaction, G is the manufacturer set, g is the manufacturer g, K is the vehicle set, k is the vehicle k, r _kg is the satisfaction of the manufacturer g and the manufacturer's order is Transported by the circular transport vehicle k, w _kg is the weight of the satisfaction of the manufacturer g and the order of the manufacturer is transported by the circular transport vehicle k, L is the set of cross-distribution centers, l is the cross-distribution center l, and r _lg is the manufacturer g and the manufacturer's order is transported through the cross-distribution center l, w _lg is the weight of the satisfaction of the manufacturer g and the manufacturer's order is transported through the cross-distribution center l, S is the supplier set, and i is the supplier i, [c _g ,d _g ] is the time window required by manufacturer g, D _ig is the order of manufacturer g to supplier i, and D _g is the order of manufacturer g to all suppliers.

y _ikg and x _ilg in the objective function are decision variables, and

In the objective function, b _kg1 , b _kg2 , and b _kg3 are the fuzzy time of the arrival of the order of the manufacturer g transported by the circular transport vehicle k, the fuzzy time is the fuzzy number of b _kg , and b _kg is the transport of the vehicle k to the manufacturer through the circular transport time of g, and

b _kg = b _ki +st _ki +t _ig (2)

In formula (2), k ∈ K, g ∈ G, i ∈ S, b _ki is the time when the circular transport vehicle k arrives at supplier i, st _ki is the service time of the circular transport vehicle k at supplier i, and t _ig is the transit time from supplier i to firm g, and

st _ki = γD _ig y _ikg (3)

In formula (3), γ is the unit product loading or unloading time, D _ig is the order from manufacturer g to supplier i, and y _ikg is the decision variable;

f _{lg1 , f lg2 ,} and f _lg3 in the objective function are the fuzzy time for the arrival of the order of the manufacturer g through the cross-distribution center l, the fuzzy time is the fuzzy number of f _lg , and f _lg is the vehicle reaching the manufacturer through the cross-distribution center l time of g, and

f _lg = a _lg +t _lg (4)

In formula (4), l∈L, _g∈G , alg is the time when the order of manufacturer g leaves the cross-distribution center l, _tlg is the transportation time from the cross-distribution center l to the manufacturer g, and

In formula (5), γ is the unit product loading or unloading time, T _ilg is the initialization time of vehicle transportation to manufacturer g through the cross-distribution center l, q is manufacturer q, D _iq is the order of manufacturer q to supplier i, x _ilg and x _ilq are decision variables, x _ilq is taken as 1 when the order from manufacturer q to supplier i is delivered by cross-distribution center l; otherwise, it is taken as 0, and t _il is the transportation time from supplier i to cross-distribution center l , D _ig is the order from manufacturer g to supplier i.

In addition, the initial representation of r _kg in formula (1) is:

故可将公式(6)改写为如下形式，即目标函数中的表示方式：The fuzzy time due to the arrival of the order from firm g transported by the circular transport vehicle k is

Therefore, formula (6) can be rewritten as the following form, that is, the representation in the objective function:

The initial representation of r _lg in formula (1) is:

故可将公式(8)改写为如下形式，即目标函数中的表示方式：Since the fuzzy time for the arrival of the order from firm g through the cross-distribution center l is

Therefore, formula (8) can be rewritten as the following form, that is, the representation in the objective function:

Since the manufacturer's order can be fulfilled by both round-robin and cross-delivery shipping, the arrival time of the order of manufacturer g may be different, and the corresponding satisfaction may also be different. In order to solve this problem, this embodiment assigns a satisfaction weight related to the transportation volume to different transportation modes, because the vehicle with a larger transportation volume is more expected by the manufacturer to arrive on time, so w in formula (1) _kg and w _lg , respectively, can be calculated according to the following formulas:

Step S1.2, establishing constraints according to the objective function:

The objective function of the proposed model should satisfy various constraints, as shown below.

(1) Manufacturer g's order to supplier i can only be transported by one of round-robin or cross-delivery:

(2) The cargo loaded by the circulating transport vehicle k cannot exceed the capacity Q of the vehicle:

(3) The cargo loaded by an inbound vehicle transported from supplier i to cross-distribution center l cannot exceed the capacity Q of the vehicle, where the number of vehicles from supplier i to cross-distribution center l is _mil :

(4) The goods loaded by the outbound vehicle transported from the cross-distribution center l to the manufacturer g cannot exceed the capacity Q of the vehicle, where the number of vehicles from the cross-distribution center l to the manufacturer g is n _lg :

(5) For the order of manufacturer g transported by the circular transport vehicle k, its arrival time b _kg cannot exceed d _g :

b _kg ≤d _g , k∈K,g∈G (16)

(6) The arrival time f _lg of the order of manufacturer g transported through the cross distribution center l cannot exceed d _g :

f _lg ≤d _g , l∈L,g∈G (17)

(7) If the manufacturer has an order for supplier i, and the order is distributed through circular transportation, then there is a decision variable z _ikj of vehicle k from supplier i to the next node j as:

(8) If the order from manufacturer g to supplier i is distributed through circular transportation, then there is a decision variable z _ikg for vehicle k from supplier i to manufacturer g as:

(9) The decision variable z _ikg that vehicle k has only one route from supplier i to manufacturer g is:

(10) Set the range of decision variables:

x _ilg ∈ {0,1}, i∈S,l∈L,g∈G (21)

y _ikg ∈ {0,1}, i∈S, k∈K, g∈G (22)

z _ikj ∈{0,1}, i∈S,k∈K,j∈S∪G (23)

In the above constraints, since the transportation time is uncertain, and the arrival time and departure time are also uncertain, it is necessary to do fuzzy transportation time processing for the transportation time. The processing process is as follows:

同理得到到达时间b_kg的模糊数为

到达时间f_lg的模糊数为

故公式(16)、(17)可分别转化如下形式：First, convert the transit time tij of vehicle k from node i to node _j into a fuzzy number

Similarly, the fuzzy number of arrival time b _kg is obtained as

The fuzzy number of arrival time f _lg is

Therefore, formulas (16) and (17) can be respectively transformed into the following forms:

In order to deal with the uncertain variables in the optimization model, the present embodiment adopts the reliability theory, and compares the fuzzy variables with the fixed values to evaluate the uncertain values. Therefore, constraints (24) and (25) can also be transformed into the following form:

为到达时间b_kg的模糊随机变量，且

为到达时间f_lg的模糊随机变量，且

Cr^*表示风险承担的置信水平。in,

is a fuzzy random variable of arrival time b _kg , and

is a fuzzy random variable of arrival time f _lg , and

Cr ^* represents the confidence level of the risk-taking.

The higher the Cr ^* value, the larger the solution space, and the easier it is to obtain a better solution. However, the higher the Cr ^* value, the higher the risk of failure. In one embodiment, Cr ^* is set in the range [0.4, 0.6], within which the manufacturer can obtain the optimal satisfaction, and the fluctuation of the satisfaction of the manufacturer is small, and the failure risk level is also within an acceptable range.

The following present embodiment will adopt the representation method based on the block matrix and the EBBO algorithm to solve the route optimization model, and obtain the optimal transportation plan, including:

Step S2, initialize and obtain the solution of the path optimization model, that is, habitats, and use a block matrix to represent each habitat, calculate the suitability index value (HSI value) of each habitat, and determine the initial optimum value according to the suitability index value. optimal solution.

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 route optimization model, that is, the corresponding transportation scheme, can be regarded as a habitat. Since this application considers three sub-problems based on transportation mode, circular transportation sequence and cross-distribution center allocation at the same time, a block matrix is used to represent the transportation scheme under the condition of fuzzy transportation time.

The block matrix includes the choice of transportation mode, the sequence of vehicle circulation and the choice of cross-distribution center, which expands the one-dimensional habitat representation in the traditional BBO algorithm to a two-dimensional habitat representation, thereby solving the proposed vehicle routing optimization model.

Each habitat consists of a block matrix T = [T _g ], where g represents the manufacturer g, the columns of the block matrix represent the supplier, and the rows represent the manufacturer, and the elements of the block matrix T are composed of many small matrices T _g ;

Among them, the matrix T _g contains three rows, the first row is an integer between 0 and M, 0 indicates that the goods are transported by cross-delivery, M indicates the number of vehicles transported in a circular manner, and the integer E∈{0,M} indicates the corresponding supplier The goods are distributed by the E-th vehicle through cyclic transportation; the second row of the matrix T _g is a random real number between 0 and 1, which represents the order of cyclic transportation vehicles. The larger the random real number, the earlier the corresponding supplier is traversed , and the random real number 0 indicates that the goods of the corresponding supplier are not delivered by cyclic transportation; the third row of the matrix T _g is a random integer between 0 and n, 0 indicates that the goods of the corresponding supplier are not delivered by cross-distribution, n Represents the number of cross-distribution centers, and a random integer F∈{0,n} indicates that the goods of the corresponding supplier are transported through the F-th cross-distribution center.

The method for representing habitats by a block matrix is further described below through embodiments.

Example 1:

Table 1 Habitat representation based on block matrix

Table 1 provides an example of a transportation scenario (habitat) based on a tiled matrix representation with six suppliers, three manufacturers, 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 these two suppliers are transported in a circular manner by Vehicle 2 to Supplier 1. The second row of the matrix indicates that vehicle 2 visits supplier 2 first and continues to visit supplier 5 if the vehicle is not overloaded. 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 who do not participate in round-robin shipping will ship the goods through cross-shipping. Here, the goods of suppliers 3 and 4 are transported to the manufacturer 1 through the cross-distribution center 2.

Step S3, calculate the in-migration rate and the out-migration rate of the population, and judge whether to carry out the in-migration or out-migration operation to the habitat according to the in-migration rate and the out-migration rate. The block matrix corresponding to the habitat performs vector substitution to realize the in-or-out operation of the habitat.

During the migration phase, the higher the HSI value of a habitat, the easier it is for that habitat to share its characteristics with habitats with lower HSI values. In this application, the HSI value of each habitat is calculated according to formula (1). The change in each solution (i.e. habitat) is determined by the mobility. Mobility rates are used to probabilistically select habitats for out- and in-migration operations when selecting a solution to change. The in-migration and out-migration rates are calculated as follows:

Among them, k _i is the ranking order of the i-th solution after all solutions are sorted in descending order of their HSI values, n represents the number of solutions, I represents the maximum in-migration rate, and E represents the maximum in-migration rate.

The suitability vector (SIV) in the habitat is represented by a column in the block matrix T. When the habitat is moved in or out, the outgoing column of the habitat to be emigrated is used to replace the one of the habitat to be emigrated. Move in columns, complete vector substitution.

The following examples further describe the habitat migration operation of the present application.

Example 2:

被栖息地j中的第三列

代替。这里，栖息地i中的向量((2,0.78,0)-(1,0.34,0))被栖息地j中的向量((1,0.42,0)–(0,0,2))所代替，完成迁移。As shown in Figure 2, in a vehicle routing optimization, four suppliers, two manufacturers and two cross distribution centers are included. where the second column of SIVs in habitat i migrated out of that habitat, and the third column of SIVs in habitat j migrated into habitat i. So the second column in habitat i

by the third column in habitat j

replace. Here, the vector ((2,0.78,0)-(1,0.34,0)) in habitat i is divided by the vector ((1,0.42,0)-(0,0,2)) in habitat j Instead, complete the migration.

Step S4: Calculate the mutation rate of the population by using the adaptive mutation probability and the secondary mutation probability, select corresponding habitats to perform mutation operations according to the adaptive mutation probability and the secondary mutation probability, and update the optimal solution.

The traditional BBO algorithm evolves through the two operations of migration and mutation, and shows good search ability when solving different types of optimization problems. However, habitats with higher HSI values were only slightly improved by mutation operations, and the evolutionary probability of habitats with higher HSI values was very small due to the small value of the initial maximum mutation rate. In order to solve this problem, this embodiment introduces a new adaptive mutation probability and quadratic mutation operation to improve the diversity of the population. in

The adaptive mutation probability m _i1 is:

表示所有栖息地中的HSI值的最大值；此处的HSI值的中间值应理解为将栖息地根据HSI值从大到小排列之后，选取位于中间的栖息地的HSI值。例如：若有3个栖息地，从大到小排列后的HSI值分别为3、2、1，则中间值为2；若有4个栖息地，从大到小排列后它们的HSI值分别为4、3、2、1，则中间值为2.5。where f _i represents the HSI value of the ith habitat, f _mid represents the median of the HSI values of all habitats,

Represents the maximum value of HSI value in all habitats; the median value of HSI value here should be understood as the HSI value of the habitat located in the middle after the habitats are arranged from large to small according to the HSI value. For example: if there are 3 habitats, and the HSI values after ranking from largest to smallest are 3, 2, and 1, the median value is 2; if there are 4 habitats, their HSI values after ranking from largest to smallest are respectively 4, 3, 2, 1, then the median value is 2.5.

The quadratic mutation probability m _i2 is:

表示中间70％的栖息地中的HSI值的最大值；此处的中间70％的栖息地应理解为将栖息地根据HSI值递减排列之后，去除前面和后面的各15％的数量的栖息地，选取位于中间70％的数量的栖息地，且向后选取。例如：若栖息地有100个，则取第16～85个；若栖息地有10个，则向后选取，取第3～9个。where f _i represents the HSI value of the ith habitat, f _mid represents the median of the HSI values of all habitats,

Represents the maximum value of HSI value in the middle 70% of the habitats; the middle 70% of the habitats here should be understood as the habitats in the descending order of the HSI value, and the front and rear 15% of the habitats are removed , select habitats that are in the middle 70% of the population, and select backwards. For example: if there are 100 habitats, take the 16th to 85th; if there are 10 habitats, select backward and take the 3rd to 9th.

First, all habitats are selected as the primary mutation target, and the corresponding habitats in the primary mutation target are mutated for the first time according to the adaptive mutation probability m _i1 , and the habitats after the first mutation are selected according to the results of the first mutation. The habitats whose HSI value is in the middle 70% are used as the secondary mutation target, and the corresponding habitats in the secondary mutation target are subjected to secondary mutation according to the secondary mutation probability m _i2 .

The adaptive mutation probability m _i1 proposed in this application makes both habitats with a lower HSI value and a higher HSI value have a higher probability to evolve into a better solution. And, in order to overcome the limitation that habitats with intermediate HSI values still have a smaller probability to evolve into better solutions, a quadratic mutation operation is introduced to improve the mutation probability of habitats with intermediate HSI values.

The following examples further describe the variation operations of the present application on habitats.

Example 3:

从0变为随机数0.35，

相应地从2变为0。同理，因为供应商3到厂商2的货物运输方式由循环运输变为交叉配送，所以

从随机数0.72变为0，并且

相应地从0变为2。即在变异操作中，栖息地i第三列即((0,0,2)-(1,0.72,0))被新的列即((1,0.35,0)-(0,0,2))所替代。Figure 3 shows an example of mutation operation based on the proposed hybrid vehicle routing model, which contains four suppliers, two manufacturers, and two cross-distribution centers. In this example, since the mode of transportation of goods from supplier 3 to manufacturer 1 has changed from cross-delivery to round-robin, so

from 0 to a random number 0.35,

Change from 2 to 0 accordingly. In the same way, because the transportation mode of goods from supplier 3 to manufacturer 2 has changed from circular transportation to cross-distribution, so

from a random number 0.72 to 0, and

Change from 0 to 2 accordingly. That is, in the mutation operation, the third column of habitat i i.e. ((0,0,2)-(1,0.72,0)) is replaced by the new column i.e. ((1,0.35,0)-(0,0,2 )) is replaced.

Step S5, judge whether the preset number of iterations is reached, and if the number of iterations is reached, output the optimal solution, that is, the optimal transportation plan; otherwise, go to Step S3 to continue the iteration.

In this embodiment, when the number of iterations is preset, it is set according to the number of manufacturers. If the number of manufacturers N _g among the participants in the vehicle routing optimization is 1≤N _g <4, the preset number of iterations is 300; if the vehicle routing optimization The number of manufacturers N _g in the participating parties is N _g ≥ 4, and the preset number of iterations is 500.

For example: if the participants in vehicle routing optimization involve 1 manufacturer, 10 suppliers and 2 cross-distribution centers, the preset number of iterations is 300; if the participants in vehicle routing optimization involve 4 manufacturers and 30 suppliers and 5 cross distribution centers, the preset number of iterations is 500.

In order to verify the superiority and feasibility of a vehicle route optimization method based on block matrix and fuzzy transit time of the present invention, an improved biogeographical optimization algorithm (EBBO) of the present invention and a standard BBO algorithm (BBO) are selected through examples. , Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Variable Neighborhood Search (VNS) are compared.

Example 4:

In order to obtain a reasonable population size, this example first uses a small vehicle path including 10 suppliers, 1 manufacturer and 2 cross distribution centers to test the performance of different algorithms when the population size ranges from 30 to 100. For each population size, this example is run 50 times under the same conditions to calculate the average optimal manufacturer satisfaction, and the maximum number of iterations for each run is set to 300. The calculation results are shown in Figure 4.

As shown in Figure 4, within a given population size range, the average manufacturer's optimal satisfaction obtained by using the EBBO algorithm is higher than the average manufacturer's optimal satisfaction obtained by the other four algorithms. In addition, as the population size increased from 30 to 100, the manufacturer satisfaction curve obtained by using the EBBO algorithm remained relatively stable, and the manufacturer satisfaction curve obtained by using the PSO algorithm showed a weak growth trend. However, the manufacturer satisfaction curves obtained using the BBO and GA algorithms are fluctuating and remain stable until the population size exceeds 80. The vendor satisfaction curve obtained using the VNS algorithm is also volatile and less stable. When the population size is about 80, the VNS algorithm is used to obtain the optimal manufacturer satisfaction. Therefore, in the subsequent experiments, the population size of the five algorithms is set to be 80 to ensure the fairness of the comparison of the five algorithms.

Further verify the validity of the algorithm of the present invention (EBBO):

First, a small vehicle routing case involving 10 suppliers, 1 manufacturer, and 2 cross-distribution centers was selected to compare manufacturer satisfaction.

As shown in Figure 5, when the Cr* value is 0.4 and the number of iterations is 300, the manufacturer satisfaction obtained by using the EBBO algorithm is superior to the other four algorithms. The main reason is that EBBO introduces adaptive mutation probability and quadratic mutation operation, which increases population diversity and improves the global search ability of the algorithm.

In order to further prove the effectiveness of the EBBO algorithm of the present invention, a large vehicle routing case including 30 suppliers, 4 manufacturers and 5 cross-distribution centers is selected in this embodiment to compare the satisfaction of manufacturers.

As shown in Figure 6, when the Cr* value is 0.4 and the number of iterations is 500, the EBBO algorithm of the present invention also shows better performance than the other four algorithms in solving the large-scale mixed vehicle routing problem. The reason why the EBBO algorithm shows weak convergence when solving large-scale vehicle routing problems is that when the problem size becomes larger, the time required to find the global optimal solution also needs to increase accordingly. In addition, the EBBO algorithm introduces a quadratic mutation operation, resulting in a slower convergence rate. However, the EBBO algorithm has better global search ability when solving large-scale mixed vehicle routing problems, and is superior to the other four algorithms in finding the global optimal solution.

Further verify the feasibility of the algorithm of the present invention (EBBO):

Suppose a logistics company is assigned the task of transporting parts from six different auto parts suppliers producing clutches, brake discs, steering gears, valves, oil pumps, and mufflers to a certain car manufacturer. In order to centralize the delivery time, the time window for the car manufacturer to receive the goods is [11:10, 12:50].

Since the Cr* value will affect the optimal solution obtained, the performance of the EBBO algorithm under different Cr* values is first tested according to the above hypothetical tasks. For each Cr* value, the experiment was run 50 times, and the maximum number of iterations per run was set to 300. The calculation results are shown in Figure 7.

In the figure, when the Cr* value range is [0.4, 0.9], the curve is relatively stable. Since the lower the Cr*, the higher the risk of failure, the most reasonable Cr* value is 0.9. Therefore, Cr* was set to 0.9 for further study.

Under the above task, when Cr* is set to 0.9, the fitness curve as shown in Figure 8 is obtained. According to the figure, as the number of iterations increases, the manufacturer satisfaction obtained by the EBBO algorithm is higher than that obtained by the other four algorithms. manufacturer satisfaction.

The vehicle route optimization method based on block matrix and fuzzy transportation time provided by the present invention comprehensively considers the selection of suppliers, manufacturers, transportation methods, vehicle circulation transportation sequence and selection of cross distribution centers, and proposes a A block matrix-based representation method to represent the transportation scheme in a more intuitive, reasonable and efficient way; the one-dimensional habitat representation in the traditional BBO algorithm is extended to a two-dimensional habitat representation to solve 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, an adaptive mutation probability calculation method is proposed, so that both high-quality and low-quality habitats have a higher probability to evolve into a better solution, and at the same time Cooperate with the proposed quadratic mutation operation to improve the evolutionary probability of intermediate quality habitats.

The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity, all possible combinations of the technical features in the above-described embodiments are not described. However, as long as there is no contradiction between the combinations of these technical features, All should be regarded as the scope described in this specification.

The above-mentioned embodiments only represent several embodiments of the present invention, and the descriptions thereof are more specific and detailed, but should not be construed as a limitation on the scope of the invention patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present invention, several modifications and improvements can be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should 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:

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 is_kgIs satisfied by the manufacturer g and the order of the manufacturer is transported by a circulating transport vehicle k, w_kgIs 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, r_lgIs satisfied by the manufacturer g and the order of the manufacturer is transported through the cross-distribution centre l, w_lgIs 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,d_g]Time window required by manufacturer g, D_igFor the order of the manufacturer g to the supplier i, D_gOrders for vendor g for all suppliers;

y in the objective function_ikgAnd x_ilgIs a decision variable, and

b in the objective function_kg1、b_kg2And b_kg3Fuzzy time of arrival of order of manufacturer g transported by circulating transport vehicle k, the fuzzy time being b_kgFuzzy number of (b)_kgFor the time that the vehicle k reaches the manufacturer g through the circulation transportation, and

b_kg＝b_ki+st_ki+t_ig

wherein K belongs to K, G belongs to G, i belongs to S, b_kiFor circulating the time of arrival of the transport vehicle k at the supplier i, st_kiFor circulating the service time, t, of the transport vehicle k at the supplier i_igIs the transit time from supplier i to vendor g, and

st_ki＝γD_igy_ikg

where γ is the unit product loading or unloading time, D_igFor the order of the manufacturer g to the supplier i, y_ikgIs a decision variable;

f in the objective function_lg1、f_lg2And f_lg3Fuzzy time of arrival of order for manufacturer g passing through cross-distribution center l, f_lgFuzzy number of f_lgFor the time of arrival of the vehicle at the manufacturer g through the cross distribution center l, and

f_lg＝a_lg+t_lg

wherein L is belonged to L, G is belonged to G, a_lgTime of departure, t, from the Cross distribution center l for the order of the manufacturer g_lgFor the transit time from the cross-distribution center l to the manufacturer g, and

where γ is the unit product loading or unloading time, T_ilgFor the initialization time of the transport of vehicles through the cross-distribution centre l to the manufacturer g, q being the manufacturer q, D_iqFor orders of manufacturer q to supplier i, x_ilqAnd x_ilgAs decision variables, t_ilFor the transit time of the supplier i to the cross-distribution centre l, D_igAn 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:

setting that the goods loaded by the circulating transport vehicle k cannot exceed the capacity Q of the vehicle:

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 vehicle_il：

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 vehicle_lg：

Setting the order of the manufacturer g transported by the circulating transport vehicle k, the arrival time b thereof_kgMust not exceed d_gWherein the arrival timeb_kgIs a fuzzy number of

Confidence level of risk exposure is Cr^*：

Setting the order of manufacturer g transported through the cross-distribution center l and the arrival time f_lgMust not exceed d_gWherein the arrival time f_lgIs a fuzzy number of

Confidence level of risk exposure is Cr^*：

Setting the range of decision variables:

x_ilg∈{0,1}，i∈S,l∈L,g∈G

y_ikg∈{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 m_i1Comprises the following steps:

in the formula (f)_iDenotes the HSI value, f, of the ith habitat_midRepresents the median of the HSI values for all habitats,

represents the maximum value of HSI values in all habitats;

probability of quadratic variation m_i2Comprises the following steps:

in the formula (f)_iDenotes the HSI value, f, of the ith habitat_midRepresents the median of the HSI values for all habitats,

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 m_i1Performing 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 m_i2And 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 ═ T_g]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 T_gComposition is carried out;

wherein, the matrix T_gThe 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 T_gRepresents 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 T_gThe 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 optimized_gIs 1. ltoreq. N_gIf 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 optimized_gIs N_gAnd if the number of iterations is more than or equal to 4, the preset number of iterations is 500.

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