CN112488386A - Logistics vehicle distribution planning method and system based on distributed entropy multi-target particle swarm - Google Patents

Logistics vehicle distribution planning method and system based on distributed entropy multi-target particle swarm Download PDF

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CN112488386A
CN112488386A CN202011370056.8A CN202011370056A CN112488386A CN 112488386 A CN112488386 A CN 112488386A CN 202011370056 A CN202011370056 A CN 202011370056A CN 112488386 A CN112488386 A CN 112488386A
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刘切
王玙
杨桂彬
曾建学
柴毅
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Abstract

The invention discloses a logistics vehicle distribution planning method and a logistics vehicle distribution planning system based on distributed entropy multi-target particle swarm, which comprises the following steps: 1) obtaining the number M of destinations to be delivered, wherein the weight of delivered goods of the ith destination is qi(i 1, 2.. multidot.M), acquiring serial number information, geographical coordinate information and mutual distance information of objects to be matched; 2) constructing a logistics vehicle distribution path planning model of the multi-objective particle swarm under the condition that a plurality of logistics vehicles finish M customer distributions and with distribution time and transportation cost as optimization targets; 3) searching a global optimal solution of a logistics vehicle distribution path planning model of the multi-target particle swarm based on the distribution entropy to obtain an optimal logistics vehicle distribution path; the logistics vehicle path planning method plans the logistics vehicle path based on the distributed entropy multi-target particle swarm algorithm, and solves the better logistics vehicle pathThe route planning of (2) can reduce logistics cost and shorten delivery time.

Description

Logistics vehicle distribution planning method and system based on distributed entropy multi-target particle swarm
Technical Field
The invention relates to the field of vehicle path planning, in particular to a logistics vehicle distribution planning method and a logistics vehicle distribution planning system based on distribution entropy multi-target particle swarm.
Background
Automobile logistics is an important component in the field of logistics, has the characteristics different from other logistics types, is logistics activity with extremely high complexity, along with the rapid development of the automobile industry in China, today cost control becomes more and more important, cost control of automobile logistics also becomes the focus of people's attention increasingly, reducing logistics cost and shortening logistics time through resource summary integration become the problems that automobile enterprises must face and need to solve urgently, and the problem of reducing logistics cost and shortening logistics time through reasonably planning logistics transportation lines is a multi-objective optimization problem.
In recent years, multi-objective particle swarm optimization, multi-objective ant colony algorithm and multi-objective differential evolution algorithm are used to solve the multi-objective optimization problem. Among them, the multi-objective particle swarm optimization algorithm developed through the particle swarm optimization algorithm is one of the most popular optimization techniques at present. The particle swarm optimization algorithm has the remarkable characteristic of cooperation among all individuals in a colony, wherein each particle is attracted to the global optimum in the colony and the personal optimum of the particle, so that the particle swarm optimization algorithm can obtain better global development capability due to the cooperative search strategy.
However, in addition to archival maintenance in multi-objective particle swarm optimization, there are two problems to be further solved. The first one is global optimal and personal optimal updating, and in the multi-objective particle swarm optimization, different candidate objects can be selected from a non-dominant set according to different strategies of global optimal and personal optimal. However, the selection of global and personal optima results in different light orientations of the particles, which has a significant impact on the convergence and diversity of multi-objective particle swarm optimization. A second particular problem is rapid convergence at an early stage of the evolution process, which can lead to premature convergence or local optimization of multi-objective particle swarm optimization. In summary, the challenge of multi-objective particle swarm optimization is how to effectively and effectively manage convergence and diversity and obtain accurate, uniformly distributed and useful Pareto optimal leading edge approximation.
Disclosure of Invention
The invention aims to provide a logistics vehicle distribution planning method based on distribution entropy multi-target particle swarm, which can be used for planning logistics vehicle distribution paths.
The invention is realized by the technical scheme, which comprises the following steps:
1) data acquisition: obtaining the number M of destinations to be delivered, wherein the weight of delivered goods of the ith destination is qi(i 1, 2.. multidot.M), acquiring serial number information, geographical coordinate information and mutual distance information of objects to be matched;
2) constructing a model: constructing a logistics vehicle distribution path planning model of the multi-objective particle swarm under the condition that a plurality of logistics vehicles finish M customer distributions and with distribution time and transportation cost as optimization targets;
3) finding an optimal solution: and searching a global optimal solution of the logistics vehicle distribution path planning model of the multi-target particle swarm based on the distribution entropy to obtain an optimal logistics vehicle distribution path.
Further, the specific steps of constructing the model in step 2) are as follows:
2-1) constructing a transportation cost model:
Figure BDA0002805850510000021
in the formula (1), K is the number of delivery vehicles and the capacities are gk(K ═ 1,2,. K) and maxgi≥maxqk，
Figure BDA0002805850510000022
Representing the cost of vehicle travel per kilometer, DijIs the distance from client point i to j, if xijk1, the vehicle k is from i to j, G is an introduced penalty term, and C is a minimized target, namely the transportation cost of the vehicle, namely the transportation cost per kilometer plus the penalty term when the vehicle is overweight;
2-2) constructing a time cost model:
Figure BDA0002805850510000023
in the formula (2), vkFor each vehicle speed, T is the waiting time of the last dispatched customer, i.e. the total length of transportation of the vehicle. The calculation method is that the time sum of each distance is added with the penalty of overweight of the vehicle;
2-3) the constraint conditions of the vehicle route VRP are:
Figure BDA0002805850510000024
Figure BDA0002805850510000025
indicating that the load of each vehicle is greater than the sum of the demands of the customer sites it delivers;
Figure BDA0002805850510000026
Figure BDA0002805850510000027
indicating that each customer has one and only one vehicle to deliver;
Figure BDA0002805850510000028
Figure BDA0002805850510000029
indicating that each vehicle passes the customer site only once;
Figure BDA00028058505100000210
g is a penalty when the vehicle is delivering an overweight weight, where GkThe value of G is the weight ratio of the weight of the goods carried by the overweight vehicle to the maximum load of each vehicle; if yikAnd (1) indicating that the customer i is delivered by the vehicle K, introducing a penalty term G, and adding the penalty term into the objective function if the delivery vehicle is overloaded in the delivery process.
Further, the specific steps of finding the optimal solution in step 3) are as follows:
3-1) initialization particles: initializing the number of particles in the population and the scale of an external file, setting a polynomial variation distribution index, the positions and the speeds of the particles, and adding the particles into the external file;
3-2) partitioning the evolution state: calculating the particle distribution entropy in the current external file, calculating the difference entropy according to the distribution entropy and dividing the evolution state;
3-3) selecting a global optimal solution: selecting a global optimal solution according to the current evolution state and the diversity convergence of the particles;
3-4) updating the individual optimal solution: updating the speed of the particles, limiting the speed of the particles, updating the positions of the particles, calculating a target value, and updating the individual optimal solution according to the domination relationship;
3-5) local disturbance: locally perturbing the position of the particle using polynomial variation;
3-6) updating external files: adding the updated particles into an external file, and maintaining the external file;
3-7) iterative judgment: if the maximum iteration number is not reached, turning to 3-2), and if the maximum iteration number is reached, outputting the external file.
Further, the specific steps of calculating the particle distribution entropy in the current external archive in the step 3-2), calculating the difference entropy and dividing the evolution state are as follows:
3-2-1) calculating the distribution entropy of the particles: defining the density function of each solution as a set of influence functions of all other solutions, the influence function between each two solutions can be well fitted with a gaussian function as follows:
Figure BDA0002805850510000031
in equation (4), r is the euclidean distance between any two particles, σ is the standard deviation, and is selected to be one third of the target number, and the density function of the particles is defined according to the influence function as follows:
Figure BDA0002805850510000032
in the formula (5), q is the number of particles in the external file;
the final particle distribution entropy is calculated from the density function as follows:
Figure BDA0002805850510000033
3-2-2) calculating the difference entropy Δ H:
△H＝H(t)-H(t-1) (7)
when the external file changes, the time difference entropy also changes, and the larger the Delta H is, more particles in the external file are replaced, so that the population can be judged to be in a development state, otherwise, the more stable the Delta H is, the population can be judged to tend to a mining state, and the diversity of solution sets is increased by replacing a single solution in the external file;
setting the threshold u, u for Δ H as the case of replacing a single solution: when the solutions in all the external files are very close, one solution is replaced to the solution with the rest
Figure BDA0002805850510000041
When all solutions are close, they can be approximately considered as being equidistant from each other; the distribution entropy at this time is:
H1≈ln(q) (8)
the density function values of the remaining solutions can be approximately calculated as:
Figure BDA0002805850510000042
the density function value for a single solution is calculated as:
Figure BDA0002805850510000043
the following can be obtained:
Figure BDA0002805850510000044
Figure BDA0002805850510000045
Figure BDA0002805850510000046
the distribution entropy of the population after the particle replacement is:
Figure BDA0002805850510000047
the difference entropy at this time is:
Figure BDA0002805850510000048
3-2-3) partitioning the evolution state according to the difference entropy: classifying the population evolution state according to the ratio of the delta H to the threshold u:
(1) if |. DELTA.H | ≧ u: indicating that the population is in a development state, accelerating convergence and positioning to a solution space at the moment, and selecting a global optimal solution to focus on the convergence of the particles at the moment;
(2) if | Δ H | < u and | a | < N: representing that the population is in a mining stage, the particles are exploring a potential solution space, and the global optimal solution emphasizes the diversity of the particles;
(3) if | Δ H | < u and | a | ═ N: indicating that the population is in a stagnant phase, diversity and convergence are equally weighted.
Further, in step 3-3), the specific steps of selecting the global optimal solution according to the evolution state and the diversity and convergence of the particles are as follows:
3-3-1) calculating the diversity of the particles: the distance is estimated using normalized displacement-based density to define the diversity of the particles:
PD(pi)＝(SDE(pi)-SDEmin)/(SDEmax-SDEmin) (16)
in formula (16), SDEmax,SDEminThe maximum value and the minimum value of the SDE distance of the species group are respectively, the larger the SDE distance is, the more dispersed the particles are, the better the diversity is, and the calculation method of the SDE distance is as follows:
Figure BDA0002805850510000051
Figure BDA0002805850510000052
in formulae (17) and (18), f'k(pi) Is piNormalizing the target value on the kth target;
3-3-2) calculating convergence of the particles:
Figure BDA0002805850510000053
Figure BDA0002805850510000054
in the formulae (19) and (20), m is the target number dis (p)i) The distance between the particles and an ideal reference point in a target space is represented, and the larger the value of the PC is, the closer the particles are to the ideal reference point, the better the convergence capability of the particles is;
3-3-3) selecting a global optimal solution: and (3) selecting a global optimal solution according to the evolutionary state and the diversity convergence of the particles:
(1) if the population is in a development state: the global optimal solution focuses on convergence, and one particle is randomly selected as the global optimal solution from a set consisting of M-1 particles with the maximum diversity and M +1 particles with the maximum convergence;
(2) if the population is in a mining state: the global optimal solution focuses on diversity, and one particle is randomly selected as the global optimal solution from a set consisting of M +1 particles with the maximum diversity and M-1 particles with the maximum convergence;
(3) if the population is in a stagnant state: the global optimal solution considers both convergence and diversity, and one particle is randomly selected from a set consisting of M particles with the maximum diversity and M particles with the maximum convergence to serve as the global optimal solution.
Further, the specific steps of updating the speed of the particles and limiting the speed of the particles in the step 3-4), updating the positions of the particles, calculating the target values, and updating the individual optimal solution according to the dominating relationship are as follows:
3-4-1) update the velocity and position of the particle:
Figure BDA0002805850510000055
in the formula (21), xi＝[xi1,xi2,...,xin]∈RnIs a position, vi＝[vi1,vi2,...,vin]∈RnIs velocity, t is the number of iterations, ω is the inertial weight, c1,c2An acceleration coefficient, r, of greater than 01,r2Is at [0,1 ]]Random number of (1), pbestiFor the optimal solution of particle history arrival, gbestiBest position, ω and c, representing the entire population1、c2Influence the searching ability of the algorithm;
3-4-2) limiting the velocity of the particles:
Figure BDA0002805850510000061
Figure BDA0002805850510000062
in the formula (22), χ is a velocity limiting coefficient, the velocity of the particle after iteration is multiplied by χ, and then whether the particle reaches the boundary is judged, so that the purpose of limiting the velocity of the particle is achieved;
3-4-3) updating the individual optimal solution: updating the individual optimal solution according to the domination relationship, and replacing the old solution with the new solution if the new solution and the old solution are not dominated mutually; for any two vectors a, b ∈ X, it is said that a dominates b, and if and only if equation (20) holds, it is written as
Figure BDA0002805850510000065
Figure BDA0002805850510000063
Further, the specific method for locally perturbing the position of the particle by using the polynomial variation in step 3-5) is as follows:
for x ═ x1,x2,..,xn) In the j-th dimension of (d), in its value range [ u ]j,zj]In, the value in the original dimension is x'jInstead, calculate x'jThe method comprises the following steps:
x'j＝xj+δ(zj-uj) (25)
wherein δ is:
Figure BDA0002805850510000064
in the formula (26), beta1＝(xj-uj)/(zj-uj),β2＝(zj-xj)/(zj-uj) Alpha is [0,1 ]]η is a distribution index, and the larger η is, the closer the value after the variation is to the value before the variation is.
Further, the specific method for adding the updated particles into the external file in the step 3-6) and maintaining the external file is as follows:
when the external file is full, if the iteration is not finished, the new solution at the moment and the solution searched by the previous iteration are chosen, wherein A is the external file to be updated; z is the maximum capacity of the external file; p is a new solution obtained by the evolutionary algorithm; a' is the updated external file, then:
(1) if it is
Figure BDA0002805850510000071
Then a '═ { P }, return to a'; when the external file has no solution, the new solution directly enters the external file;
(2) if P is dominated by any member of a, a' ═ a; that is, when the updated solution is dominated by the original solution, the updated solution does not enter the external archive.
(3) If for any one particle AiE.g. A if AiIf P predominates, A is A/{ AiAU { P }; that is, when the new solution dominates the old solution, the old solution is removed from the external archive and added to the new solution.
(4) If the new solution and the old solution do not dominate each other, B ═ AU { P }, maintenance is performed based on the evolution state calculated in 2) and the convergence and diversity of the particles calculated in 3): if the population is in the development state, the solution with the worst convergence is deleted. If the population is in the mining state, the solution with the worst diversity is deleted. And if the population is in a stagnation state, the strategy is the same as the mining state strategy.
The invention further aims to provide a logistics vehicle distribution planning system based on the distribution entropy multi-target particle swarm, which can be used for planning logistics vehicle distribution paths.
The invention is realized by the technical scheme, which comprises the following modules:
a data acquisition module: obtaining the number M of destinations to be delivered, wherein the weight of delivered goods of the ith destination is qi(i 1, 2.. multidot.M), acquiring serial number information, geographical coordinate information and mutual distance information of objects to be matched;
constructing a model module: constructing a logistics vehicle distribution path planning model of the multi-objective particle swarm under the condition that a plurality of logistics vehicles finish M customer distributions and with distribution time and transportation cost as optimization targets;
and an optimal solution searching module: and searching a global optimal solution of the logistics vehicle distribution path planning model of the multi-target particle swarm based on the distribution entropy to obtain an optimal logistics vehicle distribution path.
Further, the module for finding the optimal solution comprises the following sub-modules:
initializing a particle module: initializing the number of particles in the population and the scale of an external file, setting a polynomial variation distribution index, the positions and the speeds of the particles, and adding the particles into the external file;
an evolution state division module: calculating the particle distribution entropy in the current external file, calculating the difference entropy according to the distribution entropy and dividing the evolution state;
selecting a global optimal solution module: selecting a global optimal solution according to the current evolution state and the diversity convergence of the particles;
an update individual optimal solution module: updating the speed of the particles, limiting the speed of the particles, updating the positions of the particles, calculating a target value, and updating the individual optimal solution according to the domination relationship;
a local disturbance module: locally perturbing the position of the particle using polynomial variation;
updating an external file module: adding the updated particles into an external file, and maintaining the external file;
an iteration judgment module: and if the maximum iteration times are not reached, adding the updated particles into the external file to continue the iteration, and if the maximum iteration times are reached, outputting the external file.
Due to the adoption of the technical scheme, the invention has the following advantages:
1. according to the logistics vehicle route planning method, the logistics vehicle route is planned based on the distributed entropy multi-target particle swarm algorithm, better route planning is solved, logistics cost can be reduced, and distribution time can be shortened; 2. according to the method, the particle difference entropy in the current external file is calculated, the evolution state is divided, the global optimal solution is selected according to the current evolution state and the diversity convergence of the particles, and the diversity and the algorithm convergence of the final solution set can be effectively considered.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof.
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Detailed Description
The invention is further illustrated by the following figures and examples.
Example 1:
a logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm comprises the following steps:
1) data acquisition: the number of destinations to be distributed is 14, the weight and related information of the goods to be distributed of the destinations are shown in table 1, and the coordinates of the warehouse are (143,242);
table 1 delivery destination information table
Figure BDA0002805850510000081
Figure BDA0002805850510000091
2) Constructing a model: constructing a logistics vehicle distribution path planning model of multi-objective particle swarm under the condition that 7 logistics vehicles complete the distribution of 14 distribution destinations, the vehicle information is shown in table 2, and the distribution time and the transportation cost are taken as optimization targets; the method comprises the following specific steps:
TABLE 2 vehicle information
Figure BDA0002805850510000092
2-1) constructing a transportation cost model:
Figure BDA0002805850510000093
in the formula (27), K is the number of delivery vehicles, and the capacities are gk(K ═ 1,2,. K) and maxgi≥maxqk，
Figure BDA0002805850510000094
Representing the cost of vehicle travel per kilometer, DijIs the distance from client point i to j, if xijk1, the vehicle k is from i to j, G is an introduced penalty term, and C is a minimized target, namely the transportation cost of the vehicle, namely the transportation cost per kilometer plus the penalty term when the vehicle is overweight;
2-2) constructing a time cost model:
Figure BDA0002805850510000095
in the formula (28), vkFor each vehicle speed, T is the waiting time of the last dispatched customer, i.e. the total length of transportation of the vehicle. The calculation method is that the time sum of each distance is added with the penalty of overweight of the vehicle;
2-3) the constraint conditions of the vehicle route VRP are:
Figure BDA0002805850510000101
Figure BDA0002805850510000102
indicating that the load of each vehicle is greater than the sum of the demands of the customer sites it delivers;
Figure BDA0002805850510000103
Figure BDA0002805850510000104
indicating that each customer has one and only one vehicle to deliver;
Figure BDA0002805850510000105
Figure BDA0002805850510000106
indicating that each vehicle passes the customer site only once;
Figure BDA0002805850510000107
g is a penalty when the vehicle is delivering an overweight weight, where GkThe value of G is the weight ratio of the weight of the goods carried by the overweight vehicle to the maximum load of each vehicle; if yikThe method is characterized in that 1 represents that a client i is delivered by a vehicle K, a penalty item G is introduced, and if the delivery vehicle is overloaded in the delivery process, the penalty item is added into an objective function, so that the problem becomes an unconstrained multi-objective optimization problem.
3) Finding an optimal solution: searching a global optimal solution of a logistics vehicle distribution path planning model of the multi-target particle swarm based on the distribution entropy to obtain an optimal logistics vehicle distribution path, and specifically comprising the following steps:
3-1) initialization particles: initializing the number of particles in a population, the scale of an external file, setting the maximum iteration number to be 100, setting the cross rate of an evolutionary algorithm to be 0.9, setting the distribution index to be 20, initializing the positions and the speeds of the particles, and adding the particles into the external file;
3-2) partitioning the evolution state: calculating the particle distribution entropy in the current external file, calculating the difference entropy according to the distribution entropy and dividing the evolution state; the method comprises the following specific steps:
3-2-1) calculating the distribution entropy of the particles: defining the density function of each solution as a set of influence functions of all other solutions, the influence function between each two solutions can be well fitted with a gaussian function as follows:
Figure BDA0002805850510000108
in equation (30), r is the euclidean distance between any two particles, σ is the standard deviation, and is selected to be one third of the target number, and the density function of the particles is defined according to the influence function as follows:
Figure BDA0002805850510000109
in the formula (31), q is the number of particles in the external file;
the final particle distribution entropy is calculated from the density function as follows:
Figure BDA0002805850510000111
3-2-2) calculating the difference entropy Δ H:
△H＝H(t)-H(t-1) (33)
when the external file changes, the time difference entropy also changes, and the larger the Delta H is, more particles in the external file are replaced, so that the population can be judged to be in a development state, otherwise, the more stable the Delta H is, the population can be judged to tend to a mining state, and the diversity of solution sets is increased by replacing a single solution in the external file;
setting the threshold u, u for Δ H as the case of replacing a single solution: when the solutions in all the external files are very close, one solution is replaced to the solution with the rest
Figure BDA0002805850510000112
When all solutions are close, they can be approximately considered as being equidistant from each other; the distribution entropy at this time is:
H1≈ln(q) (34)
the density function values of the remaining solutions can be approximately calculated as:
Figure BDA0002805850510000113
the density function value for a single solution is calculated as:
Figure BDA0002805850510000114
the following can be obtained:
Figure BDA0002805850510000115
Figure BDA0002805850510000116
Figure BDA0002805850510000117
the distribution entropy of the population after the particle replacement is:
Figure BDA0002805850510000118
the difference entropy at this time is:
Figure BDA0002805850510000121
3-2-3) partitioning the evolution state according to the difference entropy: classifying the population evolution state according to the ratio of the delta H to the threshold u:
(1) if |. DELTA.H | ≧ u: indicating that the population is in a development state, accelerating convergence and positioning to a solution space at the moment, and selecting a global optimal solution to focus on the convergence of the particles at the moment;
(2) if | Δ H | < u and | a | < N: representing that the population is in a mining stage, the particles are exploring a potential solution space, and the global optimal solution emphasizes the diversity of the particles;
(3) if | Δ H | < u and | a | ═ N: indicating that the population is in a stagnant phase, diversity and convergence are equally weighted.
3-3) selecting a global optimal solution: selecting a global optimal solution according to the current evolution state and the diversity convergence of the particles; the method comprises the following specific steps:
3-3-1) calculating the diversity of the particles: the distance is estimated using normalized displacement-based density to define the diversity of the particles:
PD(pi)＝(SDE(pi)-SDEmin)/(SDEmax-SDEmin) (42)
in formula (42), SDEmax,SDEminThe maximum value and the minimum value of the SDE distance of the species group are respectively, the larger the SDE distance is, the more dispersed the particles are, the better the diversity is, and the calculation method of the SDE distance is as follows:
Figure BDA0002805850510000122
Figure BDA0002805850510000123
in formulae (43) and (44), fk'(pi) Is piNormalizing the target value on the kth target;
3-3-2) calculating convergence of the particles:
Figure BDA0002805850510000124
Figure BDA0002805850510000125
in the formulae (45) and (46), m is the target number dis (p)i) The distance between the particles and an ideal reference point in a target space is represented, and the larger the value of the PC is, the closer the particles are to the ideal reference point, the better the convergence capability of the particles is;
3-3-3) selecting a global optimal solution: and (3) selecting a global optimal solution according to the evolutionary state and the diversity convergence of the particles:
(1) if the population is in a development state: the global optimal solution focuses on convergence, and one particle is randomly selected as the global optimal solution from a set consisting of M-1 particles with the maximum diversity and M +1 particles with the maximum convergence;
(2) if the population is in a mining state: the global optimal solution focuses on diversity, and one particle is randomly selected as the global optimal solution from a set consisting of M +1 particles with the maximum diversity and M-1 particles with the maximum convergence;
(3) if the population is in a stagnant state: the global optimal solution considers both convergence and diversity, and one particle is randomly selected from a set consisting of M particles with the maximum diversity and M particles with the maximum convergence to serve as the global optimal solution.
3-4) updating the individual optimal solution: updating the speed of the particles, limiting the speed of the particles, updating the positions of the particles, calculating a target value, and updating the individual optimal solution according to the domination relationship; the method comprises the following specific steps:
3-4-1) update the velocity and position of the particle:
Figure BDA0002805850510000131
in the formula (47), xi＝[xi1,xi2,...,xin]∈RnIs a position, vi＝[vi1,vi2,...,vin]∈RnIs velocity, t is the number of iterations, ω is the inertial weight, c1,c2An acceleration coefficient, r, of greater than 01,r2Is at [0,1 ]]Random number of (1), pbestiFor the optimal solution of particle history arrival, gbestiBest position, ω and c, representing the entire population1、c2Influence the searching ability of the algorithm;
3-4-2) limiting the velocity of the particles:
Figure BDA0002805850510000132
Figure BDA0002805850510000133
in the formula (48), χ is a velocity limiting coefficient, the velocity of the particle after iteration is multiplied by χ, and then whether the particle reaches the boundary is judged, so that the purpose of limiting the velocity of the particle is achieved;
3-4-3) updating the individual optimal solution: updating the individual optimal solution according to the domination relationship, and replacing the old solution with the new solution if the new solution and the old solution are not dominated mutually; for any two vectors a, b ∈ X, it is said that a dominates b, and if and only if equation (20) holds, it is written as
Figure BDA0002805850510000135
Figure BDA0002805850510000134
3-5) local disturbance: locally perturbing the position of the particle using polynomial variation; the specific method comprises the following steps:
for x ═ x1,x2,..,xn) In the j-th dimension of (d), in its value range [ u ]j,zj]In, the value in the original dimension is x'jInstead, calculate x'jThe method comprises the following steps:
x'j＝xj+δ(zj-uj) (51)
wherein δ is:
Figure BDA0002805850510000141
in the formula (52), β1＝(xj-uj)/(zj-uj),β2＝(zj-xj)/(zj-uj) Alpha is [0,1 ]]Eta is distribution index, the larger eta is, the closer the value after variation is to the value before variationThe value is obtained.
3-6) updating external files: adding the updated particles into an external file, and maintaining the external file; the specific method comprises the following steps:
when the external file is full, if the iteration is not finished, the new solution at the moment and the solution searched by the previous iteration are chosen, wherein A is the external file to be updated; z is the maximum capacity of the external file; p is a new solution obtained by the evolutionary algorithm; a' is the updated external file, then:
(1) if it is
Figure BDA0002805850510000142
Then a '═ { P }, return to a'; when the external file has no solution, the new solution directly enters the external file;
(2) if P is dominated by any member of a, a' ═ a; that is, when the updated solution is dominated by the original solution, the updated solution does not enter the external archive.
(3) If for any one particle AiE.g. A if AiIf P predominates, A is A/{ AiAU { P }; that is, when the new solution dominates the old solution, the old solution is removed from the external archive and added to the new solution.
(4) If the new solution and the old solution do not dominate each other, B ═ AU { P }, maintenance is performed based on the evolution state calculated in 2) and the convergence and diversity of the particles calculated in 3): if the population is in the development state, the solution with the worst convergence is deleted. If the population is in the mining state, the solution with the worst diversity is deleted. And if the population is in a stagnation state, the strategy is the same as the mining state strategy.
3-7) iterative judgment: if the maximum iteration number is not reached, the process goes to 3-2), if the maximum iteration number is reached, an external file is output, and the vehicle path plan is shown in the table 3.
TABLE 3 vehicle Path planned by the method proposed by the present invention
Figure BDA0002805850510000143
Figure BDA0002805850510000151
TABLE 4 optimization results of the method proposed by the present invention
Figure BDA0002805850510000152
The invention plans the vehicle path by utilizing the MOPSO algorithm, sets the population scale to be 50, sets the iteration times to be 100, and solves the vehicle path planning scheme and the price cost as shown in tables 5 and 6.
TABLE 5 vehicle Path planned by MOPSO Algorithm
Figure BDA0002805850510000153
TABLE 6 optimization results of MOPSO method
Figure BDA0002805850510000154
Experimental results show that the solution scheme obtained by the algorithm has advantages over the solution obtained by the MOPSO algorithm in both the transportation cost and the user waiting time entropy, has larger advantages on the transportation cost target and has smaller advantages on the user waiting time. It can be seen that these two goals are contradictory, with shipping costs increasing when customer wait times are short and customer costs slightly decreasing when customer wait times are long. In conclusion, in practical application, compared with the MOPSO algorithm, the algorithm provided by the invention can provide better path planning.
Example 2:
a logistics vehicle distribution planning system based on distributed entropy multi-target particle swarm comprises the following modules:
a data acquisition module: the number of destinations to be distributed is 14, the weight and related information of the goods to be distributed of the destinations are shown in table 1, and the coordinates of the warehouse are (143,242);
constructing a model module: constructing a logistics vehicle distribution path planning model of multi-objective particle swarm under the condition that 7 logistics vehicles complete the distribution of 14 distribution destinations, the vehicle information is shown in table 2, and the distribution time and the transportation cost are taken as optimization targets;
and an optimal solution searching module: and searching a global optimal solution of the logistics vehicle distribution path planning model of the multi-target particle swarm based on the distribution entropy to obtain an optimal logistics vehicle distribution path.
The optimal solution finding module comprises the following sub-modules:
initializing a particle module: initializing the number of particles in the population and the scale of an external file, setting a polynomial variation distribution index, the positions and the speeds of the particles, and adding the particles into the external file;
an evolution state division module: calculating the particle distribution entropy in the current external file, calculating the difference entropy according to the distribution entropy and dividing the evolution state;
selecting a global optimal solution module: selecting a global optimal solution according to the current evolution state and the diversity convergence of the particles;
an update individual optimal solution module: updating the speed of the particles, limiting the speed of the particles, updating the positions of the particles, calculating a target value, and updating the individual optimal solution according to the domination relationship;
a local disturbance module: locally perturbing the position of the particle using polynomial variation;
updating an external file module: adding the updated particles into an external file, and maintaining the external file;
an iteration judgment module: and if the maximum iteration times are not reached, adding the updated particles into the external file to continue the iteration, and if the maximum iteration times are reached, outputting the external file.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (10)

1. A logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm is characterized by comprising the following steps:
1) data acquisition: obtaining the number M of destinations to be delivered, wherein the weight of delivered goods of the ith destination is qi(i 1, 2.. multidot.M), acquiring serial number information, geographical coordinate information and mutual distance information of objects to be matched;
2) constructing a model: constructing a logistics vehicle distribution path planning model of the multi-objective particle swarm under the condition that a plurality of logistics vehicles finish M customer distributions and with distribution time and transportation cost as optimization targets;
3) finding an optimal solution: and searching a global optimal solution of the logistics vehicle distribution path planning model of the multi-target particle swarm based on the distribution entropy to obtain an optimal logistics vehicle distribution path.
2. The logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm as claimed in claim 1, wherein the specific steps of constructing the model in step 2) are as follows:
2-1) constructing a transportation cost model:
Figure FDA0002805850500000011
in the formula (1), K is the number of delivery vehicles and the capacities are gk(K ═ 1,2,. K) and maxgi≥maxqk，Ck pRepresenting the cost of vehicle travel per kilometer, DijIs the distance from client point i to j, if xijk1, vehicle k is represented from i to j, G is the penalty term introduced, and C is the minimum target-vehicle transportCost, i.e. the transport cost per kilometer plus penalty term when the vehicle is overweight;
2-2) constructing a time cost model:
Figure FDA0002805850500000012
in the formula (2), vkFor each vehicle speed, T is the waiting time of the last dispatched customer, i.e. the total length of transportation of the vehicle. The calculation method is that the time sum of each distance is added with the penalty of overweight of the vehicle;
2-3) the constraint conditions of the vehicle route VRP are:
Figure FDA0002805850500000013
indicating that the load of each vehicle is greater than the sum of the demands of the customer sites it delivers;
Figure FDA0002805850500000014
indicating that each customer has one and only one vehicle to deliver;
Figure FDA0002805850500000015
indicating that each vehicle passes the customer site only once;
Figure FDA0002805850500000021
g is a penalty when the vehicle is delivering an overweight weight, where GkThe value of G is the weight ratio of the weight of the goods carried by the overweight vehicle to the maximum load of each vehicle; if yikAnd (1) indicating that the customer i is delivered by the vehicle K, introducing a penalty term G, and adding the penalty term into the objective function if the delivery vehicle is overloaded in the delivery process.
3. The logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm as claimed in claim 2, wherein the specific step of finding the optimal solution in step 3) is as follows:
3-1) initialization particles: initializing the number of particles in the population and the scale of an external file, setting a polynomial variation distribution index, the positions and the speeds of the particles, and adding the particles into the external file;
3-2) partitioning the evolution state: calculating the particle distribution entropy in the current external file, calculating the difference entropy according to the distribution entropy and dividing the evolution state;
3-3) selecting a global optimal solution: selecting a global optimal solution according to the current evolution state and the diversity convergence of the particles;
3-4) updating the individual optimal solution: updating the speed of the particles, limiting the speed of the particles, updating the positions of the particles, calculating a target value, and updating the individual optimal solution according to the domination relationship;
3-5) local disturbance: locally perturbing the position of the particle using polynomial variation;
3-6) updating external files: adding the updated particles into an external file, and maintaining the external file;
3-7) iterative judgment: if the maximum iteration number is not reached, turning to 3-2), and if the maximum iteration number is reached, outputting the external file.
4. The logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm as claimed in claim 3, wherein the specific steps of calculating the particle distribution entropy in the current external archive in step 3-2), calculating the difference entropy and dividing the evolution state are as follows:
3-2-1) calculating the distribution entropy of the particles: defining the density function of each solution as a set of influence functions of all other solutions, the influence function between each two solutions can be well fitted with a gaussian function as follows:
Figure FDA0002805850500000022
in equation (4), r is the euclidean distance between any two particles, σ is the standard deviation, and is selected to be one third of the target number, and the density function of the particles is defined according to the influence function as follows:
Figure FDA0002805850500000023
in the formula (5), q is the number of particles in the external file;
the final particle distribution entropy is calculated from the density function as follows:
Figure FDA0002805850500000031
3-2-2) calculating the difference entropy Δ H:
△H＝H(t)-H(t-1) (7)
when the external file changes, the time difference entropy also changes, and the larger the Delta H is, more particles in the external file are replaced, so that the population can be judged to be in a development state, otherwise, the more stable the Delta H is, the population can be judged to tend to a mining state, and the diversity of solution sets is increased by replacing a single solution in the external file;
setting the threshold u, u for Δ H as the case of replacing a single solution: when the solutions in all the external files are very close, one solution is replaced to the solution with the rest
Figure FDA0002805850500000032
When all solutions are close, they can be approximately considered as being equidistant from each other; the distribution entropy at this time is:
H1≈ln(q) (8)
the density function values of the remaining solutions can be approximately calculated as:
Figure FDA0002805850500000033
the density function value for a single solution is calculated as:
Figure FDA0002805850500000034
the following can be obtained:
Figure FDA0002805850500000035
Figure FDA0002805850500000036
Figure FDA0002805850500000037
the distribution entropy of the population after the particle replacement is:
Figure FDA0002805850500000038
the difference entropy at this time is:
Figure FDA0002805850500000041
3-2-3) partitioning the evolution state according to the difference entropy: classifying the population evolution state according to the ratio of the delta H to the threshold u:
(1) if |. DELTA.H | ≧ u: indicating that the population is in a development state, accelerating convergence and positioning to a solution space at the moment, and selecting a global optimal solution to focus on the convergence of the particles at the moment;
(2) if | Δ H | < u and | a | < N: representing that the population is in a mining stage, the particles are exploring a potential solution space, and the global optimal solution emphasizes the diversity of the particles;
(3) if | Δ H | < u and | a | ═ N: indicating that the population is in a stagnant phase, diversity and convergence are equally weighted.
5. The logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm as claimed in claim 4, wherein in step 3-3), the specific steps of selecting the global optimal solution according to the evolution state and the diversity and convergence of the particles are as follows:
3-3-1) calculating the diversity of the particles: the distance is estimated using normalized displacement-based density to define the diversity of the particles:
PD(pi)＝(SDE(pi)-SDEmin)/(SDEmax-SDEmin) (16)
in formula (16), SDEmax,SDEminThe maximum value and the minimum value of the SDE distance of the species group are respectively, the larger the SDE distance is, the more dispersed the particles are, the better the diversity is, and the calculation method of the SDE distance is as follows:
Figure FDA0002805850500000042
Figure FDA0002805850500000043
in formulae (17) and (18), f'k(pi) Is piNormalizing the target value on the kth target;
3-3-2) calculating convergence of the particles:
Figure FDA0002805850500000044
Figure FDA0002805850500000045
in the formulae (19) and (20), m is the target number dis (p)i) The larger the value of PC, which represents the distance of the particle from the ideal reference point in the target spaceThe closer the particle is to the ideal reference point, the better the convergence ability of the particle is;
3-3-3) selecting a global optimal solution: and (3) selecting a global optimal solution according to the evolutionary state and the diversity convergence of the particles:
(1) if the population is in a development state: the global optimal solution focuses on convergence, and one particle is randomly selected as the global optimal solution from a set consisting of M-1 particles with the maximum diversity and M +1 particles with the maximum convergence;
(2) if the population is in a mining state: the global optimal solution focuses on diversity, and one particle is randomly selected as the global optimal solution from a set consisting of M +1 particles with the maximum diversity and M-1 particles with the maximum convergence;
(3) if the population is in a stagnant state: the global optimal solution considers both convergence and diversity, and one particle is randomly selected from a set consisting of M particles with the maximum diversity and M particles with the maximum convergence to serve as the global optimal solution.
6. A logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm as claimed in claim 5, wherein the specific steps of updating the speed of the particles and limiting the speed of the particles in step 3-4), updating the positions of the particles, calculating the target values, and updating the individual optimal solution according to the dominating relationship are as follows:
3-4-1) update the velocity and position of the particle:
Figure FDA0002805850500000051
in the formula (21), xi＝[xi1,xi2,...,xin]∈RnIs a position, vi＝[vi1,vi2,...,vin]∈RnIs velocity, t is the number of iterations, ω is the inertial weight, c1,c2An acceleration coefficient, r, of greater than 01,r2Is at [0,1 ]]Random number of (1), pbestiFor the optimal solution of particle history arrival, gbestiPresentation wholeBest position of the population, ω and c1、c2Influence the searching ability of the algorithm;
3-4-2) limiting the velocity of the particles:
Figure FDA0002805850500000052
Figure FDA0002805850500000053
in the formula (22), χ is a velocity limiting coefficient, the velocity of the particle after iteration is multiplied by χ, and then whether the particle reaches the boundary is judged, so that the purpose of limiting the velocity of the particle is achieved;
3-4-3) updating the individual optimal solution: updating the individual optimal solution according to the domination relationship, and replacing the old solution with the new solution if the new solution and the old solution are not dominated mutually; for any two vectors a, b ∈ X, a is called to dominate b, if and only if equation (20) holds, it is written that a > b;
Figure FDA0002805850500000054
7. a logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm as claimed in claim 6, wherein the specific method for locally perturbing the positions of the particles by utilizing polynomial variation in step 3-5) is as follows:
for x ═ x1,x2,..,xn) In the j-th dimension of (d), in its value range [ u ]j,zj]In, the value in the original dimension is x'jInstead, calculate x'jThe method comprises the following steps:
x'j＝xj+δ(zj-uj) (25)
wherein δ is:
Figure FDA0002805850500000061
in the formula (26), beta1＝(xj-uj)/(zj-uj),β2＝(zj-xj)/(zj-uj) Alpha is [0,1 ]]η is a distribution index, and the larger η is, the closer the value after the variation is to the value before the variation is.
8. The logistics vehicle distribution planning method based on distributed entropy multi-target particle swarm as claimed in claim 1, wherein the specific method for adding the updated particles into the external file in step 3-6) and maintaining the external file is as follows:
when the external file is full, if the iteration is not finished, the new solution at the moment and the solution searched by the previous iteration are chosen, wherein A is the external file to be updated; z is the maximum capacity of the external file; p is a new solution obtained by the evolutionary algorithm; a' is the updated external file, then:
(1) if it is
Figure FDA0002805850500000062
Then a '═ { P }, return to a'; when the external file has no solution, the new solution directly enters the external file;
(2) if P is dominated by any member of a, a' ═ a; that is, when the updated solution is dominated by the original solution, the updated solution does not enter the external archive.
(3) If for any one particle AiE.g. A if AiIf P predominates, A is A/{ AiAU { P }; that is, when the new solution dominates the old solution, the old solution is removed from the external archive and added to the new solution.
(4) If the new solution and the old solution do not dominate each other, B ═ AU { P }, maintenance is performed based on the evolution state calculated in 2) and the convergence and diversity of the particles calculated in 3): if the population is in the development state, the solution with the worst convergence is deleted. If the population is in the mining state, the solution with the worst diversity is deleted. And if the population is in a stagnation state, the strategy is the same as the mining state strategy.
9. The logistics vehicle distribution planning system based on the distributed entropy multi-target particle swarm is characterized by comprising the following modules:
a data acquisition module: obtaining the number M of destinations to be delivered, wherein the weight of delivered goods of the ith destination is qi(i 1, 2.. multidot.M), acquiring serial number information, geographical coordinate information and mutual distance information of objects to be matched;
constructing a model module: constructing a logistics vehicle distribution path planning model of the multi-objective particle swarm under the condition that a plurality of logistics vehicles finish M customer distributions and with distribution time and transportation cost as optimization targets;
and an optimal solution searching module: and searching a global optimal solution of the logistics vehicle distribution path planning model of the multi-target particle swarm based on the distribution entropy to obtain an optimal logistics vehicle distribution path.
10. The logistics vehicle distribution planning system based on distributed entropy multi-target particle swarm of claim 9, wherein the module for finding the optimal solution comprises the following sub-modules:
initializing a particle module: initializing the number of particles in the population and the scale of an external file, setting a polynomial variation distribution index, the positions and the speeds of the particles, and adding the particles into the external file;
an evolution state division module: calculating the particle distribution entropy in the current external file, calculating the difference entropy according to the distribution entropy and dividing the evolution state;
selecting a global optimal solution module: selecting a global optimal solution according to the current evolution state and the diversity convergence of the particles;
an update individual optimal solution module: updating the speed of the particles, limiting the speed of the particles, updating the positions of the particles, calculating a target value, and updating the individual optimal solution according to the domination relationship;
a local disturbance module: locally perturbing the position of the particle using polynomial variation;
updating an external file module: adding the updated particles into an external file, and maintaining the external file;
an iteration judgment module: and if the maximum iteration times are not reached, adding the updated particles into the external file to continue the iteration, and if the maximum iteration times are reached, outputting the external file.
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