CN111578961A - Optimization algorithm for solving uncertain condition vehicle path based on leader dolphin group - Google Patents
Optimization algorithm for solving uncertain condition vehicle path based on leader dolphin group Download PDFInfo
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- G06N3/004—Artificial life, i.e. computing arrangements simulating life
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Abstract
The invention discloses a leader dolphin group-based uncertain condition solving vehicle path optimization algorithm. The invention improves the original dolphin swarm algorithm DPA, and establishes a leader dolphin swarm algorithm by introducing the 'echo positioning' thought of the bat algorithm and adding the update equation of pulse loudness and emission rate in the optimal value iteration process. The method comprises the following specific steps: (1) initializing a population; (2) optimizing division of labor; (3) sharing information; (4) surrounding the food; (5) the dispensed food resumes a state. And converting uncertain conditions such as road congestion, traffic limitation, road quality, emergency, weather conditions and the like into constraint conditions for evaluating the optimal path by using the opportunistic fuzzy model, and further establishing an uncertain condition path planning model. Compared with other algorithms, the algorithm has obvious advantages of convergence precision, convergence speed and robustness.
Description
Technical Field
The invention belongs to the field of logistics transportation, and particularly relates to a leader-based dolphin group uncertain condition solving vehicle path optimization algorithm.
Background
The Vehicle Routing Problem (VRP), first proposed by Dantzing and Ramster in 1959, refers to one or more distribution centers that distribute goods to multiple customers with different needs to meet a series of objectives, such as minimum distance traveled, minimum cost, etc., while meeting constraints such as maximum number of vehicles, maximum one-way distance traveled, maximum payload, etc. In the logistics distribution process, the distribution company is often affected by many factors such as multiple weather changes, traffic congestion, uneven distribution of distribution network points and the like, and meanwhile, the time window requirement of a customer is met, and corresponding punishment needs to be carried out on the distribution company when the time required by the customer is exceeded. How to arrange the optimal distribution scheme becomes a key point and a difficult point in logistics distribution. By reasonably formulating the vehicle distribution route, the operation cost of an enterprise can be effectively saved, the service quality of the enterprise can be improved, and meanwhile, the comprehensive competitiveness of the enterprise can be enhanced.
Since the vehicle path problem is proposed, great attention has been paid to various disciplines such as operation research, logistics, management and the like. When the number of distributed points and the number of vehicles are too large, the scale of data processing is increased, the problem complexity is increased, and it is often difficult to obtain an accurate distribution result. Although the problem research on the vehicle path is very comprehensive, under the conditions of large scale, large number of vehicles and the like, the conventional algorithm cannot rapidly and accurately calculate the optimal path for distribution, the GA algorithm, the AA algorithm and the PSO algorithm show good global search capability on the VPR optimization problem, but have low convergence speed, are easy to fall into a local optimal solution and have high dependence on the initial solution; local optimization searching capabilities such as a simulated annealing algorithm (SA), a tabu search algorithm (TS) and the like are strong, the algorithm is easy to fall into the algorithm to be premature, even if the multiple algorithms are mixed, the best solution cannot be obtained perfectly, so that research on the VRP problem in the ten major problems in the world is continuous, the research on the algorithm enables the calculation time, the calculation precision and other performances to be improved, and is expected by a vehicle path researcher, a dolphin group algorithm published by professor Wuqi university in Zhejiang river in 2016 on foreign famous journal in foreign languages pulls a curtain on the research on the dolphin group algorithm, and a brand-new intelligent algorithm is obtained by simulating the fast and accurate food pounding of the dolphin group through the research on the life habits of the dolphin group.
The predation capacity of dolphins is not only surprising, but also the technical content is high. Their wisdom makes them the leader of all mammals except humans. They communicate and prey through echogenic localization, similar to the way bats prey. According to survey records, the frequency of echo location of dolphins by ultrasonic waves exceeds 200 and 350 kilohertz. The human hearing range is between 16-20 khz, so the human cannot hear the ultrasound waves emitted by the dolphin for echo location. The dolphin may use echo location to determine the distance, position, shape of the target. Echo location is a complex and highly evolved process in which dolphins create their own images of ambient sound by analyzing their own emitted ultrasound. By analyzing the echoes, dolphins can estimate the distance to nearby obstacles and find fish and other food for their predation. By means of the echo, the dolphin can tell the size, shape and direction of movement of the fish, which makes the predation very accurate.
At present, the Dolphin swarm algorithm is not completely applicable to various fields no matter whether abroad or not, the Dolphin swarm algorithm is proposed by the Dolphin swarm algorithm published by the professor woodqi of Zhejiang university in 2016 and the precision and the practicability of the Dolphin swarm algorithm are tested by utilizing a test function. In 2018, the liberty professor announces control and decision-making to optimize the aerial target threat assessment of the grey neural network by using a dolphin swarm algorithm to improve the neural network and apply the algorithm to the aerial assessment. The Wang Meng Jiaojiao professor of northeast electric university in 2019 provides a jumping dolphin swarm algorithm on the basis of a basic dolphin swarm to improve the algorithm. Aiming at the defects of the dolphin group algorithm, the li-armor-xanth professor of northbound engineering university in 2019 provides an improved dolphin group algorithm based on information entropy, and the improved dolphin group algorithm is applied to optimization of a truss structure.
Disclosure of Invention
At present, the practicability research of the dolphin swarm algorithm at home and abroad is slightly lacked, and the invention aims to: on the basis of the basic dolphin group, the thoughts of the leaders are mixed and used for solving the problem of multi-target vehicle paths.
The invention discloses a leader-based Dolphin group uncertain condition solving vehicle path optimization algorithm, which is a bottom-up design method based on Artificial Dolphin (AD) as a main body and a collaborative search path structure based on responsibility division. The predation process of the dolphin group is finally completed according to the characteristics of the predation of dolphins, the sensitivity to the surrounding environment, the mutual transmission and sharing of information among dolphins and the behavior characteristics of the artificial dolphins in their own roles.
The invention is realized by the following technical scheme:
a leader dolphin group-based uncertain condition solving vehicle path optimization algorithm comprises the following steps:
(1) initializing a population
And (3) uniformly distributing each dolphin in the dolphin group in the definition domain of the target function, wherein the size of the dolphin group is N, the dimension of the search space is D, and then the position of the ith artificial dolphin is as follows:
Xi＝(xi1,…,xid,…xiD)
xid＝xmin+rand×(xmax-xmin)
wherein rand is in the interval [0,1 ]]A random number, x, uniformly distributed thereinmaxAnd xminRespectively corresponding to the upper limit and the lower limit of the search space;
(2) optimizing division of labor
In the dolphin predation space, any dolphin can be used as a 'guide' role, and the whole dolphin group is distributed in every position of the predation space according to a random distribution rule at first, if one dolphin finds food, said 'guide' can transfer the food information to correspondent other dolphins by means of 'echo positioning'; after obtaining the information, the dolphin group can search for the team members of the dolphin group to form a virtual team of the dolphin group;
defined as each dolphin Xi(i-1, 2, … n) as the center, dolphin X was calculated separatelyj(j ═ 1,2, … n) to dolphin XiDistance X ofijSorting the distances to each dolphin in ascending order, and selecting m dolphins closest to each dolphin to create a virtual team of the dolphin according to the sorting result;
wherein the calculation formula of the distance between dolphins is
In the whole dolphin group, more than one dolphin virtual team is provided, so that each virtual team has a local leader of the group, and team members judge the identity characteristics of the team members, the leader or common members through comparison of local optimal values of fitness functions; leaders of the whole group are generated from each virtual team, and in the process of gathering food, through continuous iteration, after the maximum iteration times are reached, a leader dolphin is selected, namely the global optimal value of the fitness function;
(3) information sharing
After the leader is selected, the leader carries out information exchange with the group members of the leader through sound to obtain the optimal positions and adaptive values of other members; after the information exchange is executed for a plurality of times, the dolphin with a better position is quickly detected by other dolphins; therefore, dolphins can approach food from top to bottom orderly under the guidance of the leader through information sharing, and form an enclosure gradually, and finally prey;
(4) surrounding food
After the leader dolphin obtains the food information of the 'guide' dolphin, other dolphins in the group are informed to surround through sound, and the other dolphins are unfolded and surrounded at the leader position;
as a common member, effective location updating is carried out, which becomes a key step in the predation link, and for the location updating, the number of the location updating is [0,1 ]]Internally generated random number rmIs generated if rmIf the ratio theta is smaller, the ith dolphin does not perform position updating, otherwise, the ith dolphin performs position updating by taking the leader dolphin as the center to surround food; theta is a preset threshold value;
the member position updating step is as follows:
updating the loudness A (i) and the emission rate R (i) of the pulses with the course of the optimization iteration;
the closer to the food, the lower the loudness of the pulse, the faster the emission rate, and a (i) of 0 means that dolphin i has just found a food and temporarily stops making any sound;
update equations for pulse loudness and transmission rate:
At+1(i)＝αAt
Rt+1(i)＝R0(i)×[1-exp(-γt)]
wherein, 0 < α < 1, gamma > 0, which are all constant, when t → ∞, At(i)＝0,Rt(i)＝R0(i) Setting the dolphin position at the t-th time as
The updated dolphin position
Is composed of
Wherein: is a group of [0,1]D-dimensional random vector of At(i) The loudness of the pulse at time t;
and (3) carrying out restoration processing on the updated position coordinates of the dolphin which is not in the predation space:
after the position of the dolphin leader is determined, the position and the fitness value of the dolphin leader are known by group members through information exchange, so that the group members continuously adjust the positions of the group members according to the fitness values of the group members to form an enclosure in order, the overall condition is optimized, and the most efficient predation is achieved;
(5) dispensing food recovery status
After the enclosure is formed, the enclosure is reduced through position updating, and finally the predation is carried out;
after the enclosing ring is formed, the dolphins in the optimal position and the local optimal position are stopped for a period of time, and the dolphins are preyed together after the subsequent dolphins are enclosed;
after the predation process is finished, the random state of the dolphin in the predation space is recovered, and the next predation is carried out.
Determining the optimal position of each team by comparing the adaptive value of each team, further determining the leader of each virtual team, and selecting the probability of each fitness value:
wherein, FiRepresenting fitness value, n, of each virtual teamiIndicating the size of the ith virtual team.
Due to the randomness of the dolphin group, individual dolphins with large fitness values may not necessarily appear in the next generation dolphin group, and the dolphin with the largest fitness value is iterated to the next generation by introducing an elite retention mechanism, and other groups are screened again.
The invention utilizes the echo positioning thought of bats to add the update equation of pulse loudness and emission rate in the optimal value iteration process on the basis of the original dolphin group algorithm, and establishes the leader dolphin group algorithm which is simpler and more convenient than the basic dolphin group algorithm, but has better optimization effect. The method overcomes the defects that the basic dolphin swarm algorithm is low in convergence speed and easy to fall into local optimum, and reduces blind search. Compared with other algorithms, the algorithm has obvious advantages of convergence precision, convergence speed and robustness.
Drawings
FIG. 1 is a flow chart of an LDHA algorithm for VRP problem under uncertain conditions;
FIG. 2 is a diagram of a dolphin predation model;
FIG. 3 is a diagram of the optimizing process of dolphin foraging;
FIG. 4 is an initial solution trajectory diagram of the delivery route;
FIG. 5 is a trace plot of 10 iterations;
FIG. 6 is a diagram of delivery trajectories after 200 iterations;
fig. 7 is a graph of algorithm convergence when the algorithm is iterated 200 times.
Detailed description of the invention
The following is a specific embodiment of the present invention, which will be further described with reference to the accompanying drawings.
The heuristic algorithm is applied to solve the problem of vehicle road stiffness, and the more mature is the ant colony algorithm (AA). With the gradual deepening of experts and scholars in various fields on the research of intelligent algorithms, the advantages of the AA algorithm optimization mechanism are gradually reduced in the aspect of solving the complex optimization problem, so that a plurality of experts and scholars are inspired in the field of bionics later, a plurality of new optimization mechanisms with good effects are generated, for example, heuristic bionic algorithms such as Genetic Algorithm (GA), wolf pack algorithm (WOA), monkey swarm algorithm (MA), particle swarm algorithm (PSO) and the like are adopted, and the defects of the AA algorithm in the complex path optimization problem are well overcome.
In the embodiment, by referring to a leader strategy, the concept of 'echo positioning' in the bat algorithm is introduced to simulate the predation of a dolphin group, so that group intelligent behaviors such as 'generation of leader', 'group gathering', 'information sharing' and 'enclosure food' are abstracted, and the defect that the intelligent algorithm is not free in the aspects of global and local over-optimization is well overcome. And a foundation is laid for solving the vehicle path model under the uncertain conditions.
Overview of logistics distribution model of vehicle path:
at present, the basic VRP logistics distribution model is mainly: for enterprises, a series of delivery locations and receiving locations are provided, a driving route network of the whole region is formed, vehicles can pass through the network orderly, and under the condition that certain constraint conditions (such as the demand of the receiving locations, the vehicle capacity, the delivery time, the driving time, the delivery mileage and the like) are met, the driving scheme reaches certain optimal conditions, such as the shortest time, the lowest cost, the fewest vehicles, the highest timeliness and the like.
The VRP problem includes multiple routes (typically determined by vehicle capacity or maximum distance traveled), each route is a complicated TSP problem (delivery loop), each delivery point can only be visited once, the total demand of the delivery points on each route is required to not exceed the maximum capacity of the delivery vehicle, or the length of each route does not exceed the maximum distance traveled, and the final optimization goal of VRP is to minimize transportation costs.
Uncertain condition of path:
on the basis of researching a large number of documents, the uncertain conditions of path optimization are mainly classified into the following categories: road congestion, traffic restrictions, road quality, emergency events, weather conditions, etc.
(1) Road congestion: with the rapid development of urban economy and the gradual increase of private vehicles, traffic jam of roads in urban centers is frequent, and enterprises usually intentionally avoid the roads which are often jammed (although the routes are shortest) when planning distribution driving routes. Meanwhile, the delivery cost and the punishment cost of delivery delay are also considered, so that the proper departure time is selected.
(2) Traffic limitation: different cities have different traffic restrictions, such as single and double traffic restrictions in Beijing, time and weight restrictions for Wuhan Changjiang bridge trucks, and restriction of the trucks' travel by Harbin in the morning and evening peaks. When an enterprise formulates a distribution driving path scheme, whether to consider avoiding the traffic control road sections can have great influence on the result of vehicle path optimization.
(3) The quality of the road can affect the normal running speed and safety of the distribution vehicle; in addition, uncertain factors such as security accidents and weather conditions can also influence the selection of the route.
When solving the VRP problem, if the above-mentioned uncertain conditions are not considered, the optimization result will be significantly affected, and the transportation budget cost of the enterprise will be exceeded, so the optimization solution needs to be reconsidered according to the actual situation.
Considering the requirement of the customer on the delivery time of the enterprise commodity and the above considered conditions, the time window factor is added in the embodiment when the VRP model is established, and the following three cases are mainly included:
(1) hard time window:
the distributor sends the commodity to the appointed position in the appointed time according to the client requirement, and the penalty function of setting the hard time window is as follows:
wherein, P (T)i) Representing a penalty value over a specified time, M representing a positive number, TiRepresenting the time of arrival of the delivery vehicle at the customer-specified location, aiRepresenting the customer-specified earliest time of arrival, biRepresenting the latest arrival time specified by the customer, the value between the latest arrival time and the latest arrival time is the time window of the customer, and if the latest arrival time exceeds the time window specified by the customer, a large penalty value is given (the latest arrival time is used when the delivery requirement of the customer or a company is very large).
(2) Soft time window:
the distributor preferably distributes the commodity to the position specified by the customer within the time range specified by the customer, the distribution time is allowed to be delayed or advanced, but corresponding penalty values are borne, and the specific penalty function is as follows:
wherein, P (T)i) Representing a penalty value, T, over a specified timeiRepresenting the time of arrival of the delivery vehicle at the customer-specified location, aiOn behalf of the customer-specified earliest time of arrival,birepresenting the latest arrival time, P, specified by the clientlPenalty factor, P, representing early arrival at a delivery pointePenalty factor, P, indicating late arrival at a delivery pointl、PeA number between 0 and 1. Under the condition of a soft time window, the distributor is allowed to reach a specified place beyond the time specified by the customer, and corresponding penalty values are given.
(3) Mixing time window:
in the enterprise commodity distribution process, some customers' time windows are soft time windows, and some are hard time windows, and this needs to set up the time windows according to different situations, and then forms mixed time windows.
Establishing a model:
in the embodiment, when the VRP model is established, the total target is set to be the minimum driving distance, the minimum delivery time and the maximum customer satisfaction (i.e. the minimum penalty value), so that a multi-target VRP path planning model is established for evaluating the optimal delivery path.
Optimization objective of total travel of delivery vehicle:
wherein x isijk1 denotes that the k-th vehicle travels from the delivery point with the serial number i to the delivery point with the serial number j, otherwise xijk＝0；dijIndicating the distance from the delivery point with the serial number i to the delivery point with the serial number j; n represents the number of customer delivery points, and M represents the number of delivery vehicles.
The optimization goals of the minimum transit time are:
wherein, tijRepresents the delivery time, t, of the vehicle traveling from the delivery point with the number i to the delivery point with the number j0Indicating the time that the k-th vehicle dwells at the delivery point. In the actual solution process, since it is assumed that each delivery vehicle has only one travel route, i.e.
Being a constant, it can be omitted during path optimization.
Minimum penalty target:
wherein, TiRepresenting the time of arrival of the delivery vehicle at the customer-specified location, aiRepresenting the customer-specified earliest time of arrival, biRepresenting the latest arrival time, P, specified by the clientlPenalty factor, P, representing early arrival at a delivery pointeA penalty factor indicating late arrival at the delivery point.
When three objective functions are satisfied, certain constraint conditions need to be satisfied:
first, the deliverer needs to complete the transportation task under the constraint of the vehicle:
wherein, giThe demand with serial number i as the distribution point, q0Maximum capacity per vehicle;
the delivery task completed by the kth vehicle is then:
wherein, y ik1 means that i delivery point is transported by k-th vehicle, otherwise yik＝0。
One customer can only be transported by one vehicle:
all vehicles are required to start from the distribution center:
X＝(xijk)∈S S＝{(xijk)|∑∑xijk≤|r|-1,r＝1,2,3…N；k＝1,2,3…M}
this approach avoids routes that are not connected to the distribution center.
Each customer delivery point is in the route:
xijk∈{0,1}i,j＝1,2,3…N；k＝1,2,3…M
each delivery vehicle has only one travel route:
yijk∈{0,1}i,j＝1,2,3…N；k＝1,2,3…M
the transit time for the kth vehicle to reach the jth delivery point is:
establishing an uncertain condition vehicle path model:
in the whole logistics distribution process of an enterprise, traffic congestion, emergencies, weather changes and the like can cause the running speed of vehicles to change, so that the final time optimization target can be influenced. Therefore, the delivery time of each delivery point cannot be simply defined as a constant, but is considered as a variable subject to a certain probability distribution. The method can obtain the probability information about the passing speed of the vehicle according to the congestion condition of the urban traffic road section, the experience of a distributor, the traffic data of a third party and the like.
The demonstration finds that the method is a random optimization theory (random planning problem) under the uncertain condition, is mainly provided by Liu Bao Xuan professor, and is mainly divided into three models, namely an expected value model, an opportunity constraint model, a related opportunity planning model and the like. On the basis of the research of the method, the method adopts the opportunistic fuzzy model to solve the VRP problem under the uncertain condition.
VRP summary of fuzzy constraint planning:
because of the difficulty in collecting different traffic information, the resulting information may be a fuzzy evaluation. On the basis of random planning, due to the contingency, the traffic condition cannot be accurately predicted, and the ambiguity mainly expresses on the result of the occurrence of an event, and the road condition can be evaluated from different angles only by using some ambiguity sentences.
Meanwhile, for the VRP model based on fuzzy transit time, it is continuously assumed that other parameters than transit time are known. In addition, the VRP problem of fuzzy time constraint can represent the time information collected in the commodity distribution process by triangular fuzzy numbers, and further reflect the change of the driving time under different traffic conditions, namely the original path passing time tijFuzzy number by triangle
Represents:
establishing a fuzzy constraint programming (VRP) model:
for the change of the transportation time, the VRP model under the uncertain condition is improved, and the specific model is as follows:
an objective function:
constraint conditions are as follows:
∑xijk＝yjki,j＝1,2,3…N；k＝1,2,3…M
X＝(xijk)∈S S＝{(xijk)|∑∑xijk≤|r|-1,r＝1,2,3…N；k＝1,2,3…M}
xijk∈{0,1}i,j＝1,2,3…N；k＝1,2,3…M
yijk∈{0,1}i,j＝1,2,3…N；k＝1,2,3…M
the method comprises the following steps of (1) realizing a multi-target vehicle path optimization algorithm based on a leader dolphin group of a VRP model under an uncertain condition:
with reference to fig. 1 to 7, based on the concept of the dolphin group predation algorithm, a multi-objective vehicle path optimization algorithm based on a leader dolphin group is used to solve a VRP model under an uncertain condition, and the specific implementation steps are as follows:
step1: initializing dolphin groups
At this stage, the goal is to have each dolphin in the dolphin population evenly distributed within the definition domain of the objective function. The dolphin group size is N, the dimension of the search space is D, and then the position of the ith artificial dolphin is:
Xi＝(xi1,…,xid,…xiD)
xid＝xmin+rand×(xmax-xmin)
wherein rand is in the interval [0,1 ]]A random number, x, uniformly distributed thereinmaxAnd xminRespectively corresponding to the upper and lower limits of the search space.
Determining the maximum number of iterations maxth while checking the delivery vehicles
And is
In addition, dolphins which do not satisfy the time window, the transportation time, and the transportation route is too long are eliminated, and the rest dolphins are used as the initial dolphin group. For the size of the dolphin group size N, if the value of N is too large, the search quality of the uncertain condition vehicle path optimization algorithm based on the leader dolphin group can be improved, premature maturation is prevented, but larger N can affect the evaluation and selection of the group and slow down the convergence speed, and the value of a problem within 10 distribution points can be 50-200 in general.
Step2: optimizing division of labor and determining fitness function
In the dolphin predation space, any dolphin can be used as "guide", and at first, the whole dolphin group is distributed in every position of the predation space according to the random distribution rule, if one dolphin finds food, said "guide" can transfer the food information to correspondent other dolphins by means of "echo positioning".
After obtaining the information, the dolphin group will find its own team members to form its own virtual teami(i-1, 2, … n) as the center, dolphin X was calculated separatelyj(j ═ 1,2, … n) to dolphin XiDistance X ofij(the distance can be calculated from the two dolphin position formula). The distances to each dolphin are sorted in ascending order. For each dolphin, the results are sorted, and the m dolphins closest to the results are selected to create a virtual team of the dolphins.
Wherein the calculation formula of the distance between dolphins is
There is more than one such dolphin virtual team in the overall dolphin population, so that each virtual team has a local leader of the population. The team members judge the identity characteristics (leaders or common members) of the team members through comparison of local optimal values of fitness functions. Leaders of the whole group are generated from each virtual team, and the dolphin leader (namely the global optimal value of the fitness function) is selected after the maximum iteration times are reached through continuous iteration in the process of gathering food.
For the vehicle path optimization problem established in the embodiment under the uncertain condition, the targets conflict and offset with each other, so that a good optimization effect cannot be generated, and the optimal solution of all the targets does not necessarily exist. In the embodiment, a weight is given to each objective function in the optimization process to form a fitness evaluation function, so that the smaller the fitness value of an individual is, the better the optimization effects of the three objective functions are, that is:
F＝G1+λ1G2+λ2G3
wherein G isi(i ═ 1,2,3) represents the three objective functions modeled above.
In the aspect of weight dereferencing, multiple attempts are needed, and finally the optimal fitness function value is judged, wherein lambda can be determined3Should be a large positive number because the overall goal is as little as possible against the customer's requirements.
Step3: information sharing
After the leader is selected, the leader can communicate with the members of the group by sound to obtain the optimal positions and adaptive values of other members, the communication can be executed for a plurality of times, and the dolphin with the better position can be quickly detected by other dolphins. Therefore, the dolphins can approach the food from top to bottom orderly under the guidance of the leader through information sharing, so as to gradually form a surrounding ring and finally prey.
According to the generated initialization dolphin group, creating virtual teams of dolphins by using a distance formula, then determining the optimal position of each team by comparing the fitness value of each team, further determining the leader of each virtual team, and selecting the probability of each fitness value as follows:
wherein, FiRepresenting the fitness of each virtual teamValue niIndicating the size of the ith virtual team.
In addition, due to the randomness of the dolphin group, individual dolphins with large fitness values may not necessarily appear in the next-generation dolphin group, and in the embodiment, the dolphin with the largest fitness value is iterated to the next generation by introducing an elite retention mechanism, and other groups are screened again, so that although the convergence speed is slowed down, the optimization effect of the model can be effectively ensured.
Step4: the group follows and surrounds the food
After the leader dolphin obtains the food information of the "guide" dolphin, the other dolphin in the group is notified by sound to surround, and the other dolphin is spread out to surround with the leader position. As a general member, effective location update is carried out, which becomes a key step in the predation link, and for the location update, the number of the location update is [0,1 ]]Internally generated random number rmIf rmIf the ratio is smaller than theta (a preset threshold), the ith dolphin does not perform position update, otherwise, the ith dolphin performs position update with the leader dolphin as the center to surround the food. Here, the loudness and rate of the pulses are introduced[26]The loudness a (i) and the emission rate r (i) of the pulses are updated with the process of the optimization iteration. In general, the closer to the food, the lower the loudness of the pulse, and the faster the emission rate, and when a (i) is 0, it means that dolphin i has just found a food and temporarily stops emitting any sound, and the following formula is an update equation of the loudness of the pulse and the emission rate:
At+1(i)＝αAt
Rt+1(i)＝R0(i)×[1-exp(-γt)]
wherein, 0 is more than α and less than 1, gamma is more than 0, and all are constant and can be easily found, and when t → ∞, At(i)＝0,Rt(i)＝R0(i) Setting the dolphin position at the t-th time as
The updated dolphin position
Is composed of
Wherein: is a group of [0,1]D-dimensional random vector of At(i) The loudness of the pulse at time t.
For the position of the common dolphin, the position may not be in the predation space, so the position coordinates of the updated food surrounded by the dolphin group are repaired:
after the position of the dolphin leader is determined, the position and the fitness value of the dolphin leader are known by group members through information exchange, so that the group members continuously adjust the positions of the group members according to the fitness value of the group members, and an enclosure is formed in order, so that the overall condition reaches the optimal and most-efficient predation.
Processing the iteration border-crossing condition of the common dolphin through a position coordinate formula, and iterating the group members again through a position updating formula to form a predation enclosure, determining a local optimal solution, and performing the next position updating.
Step5: group renewal, distribution of food
After the enclosure is formed, the enclosure is reduced through position updating, and finally the predation is carried out. The dolphin group is not designed to distribute food according to the amount of labor, but is designed to be caught by a subsequent dolphin after the enclosure is formed, such as a pause for a certain period of time.
And after one iteration is finished, screening out the local optimal solution of each virtual team, judging whether the maximum iteration times is met, exiting the loop and recording the result, otherwise, jumping to Step 2.
Case solving:
in the embodiment, a MATLAB2014a is used for writing a program for solving, a model established by algorithm solving is verified, company C has 51 customer distribution points in city B, the demand of each customer needs to be quantified according to distribution sample data, the demand is respectively 120kg, 150kg, 200kg, 50kg and 160kg … 230kg, the total demand is about 13000kg, the load capacity (neglecting commodity shape) of each vehicle distribution vehicle is 8000kg, and about 2 trucks are needed to complete a transportation task. The spacing between each delivery point and delivery center is given in the following table:
distance between each delivery point and delivery center (km)
Departure time of 2 cars was 8 in the morning: 00, time in the model is treated as 0, and so forth for later arrival times. Assuming that the time to arrive at a delivery point from the delivery center satisfies the positive distribution function, the travel time between the delivery points is shown in the following table:
two by two travel time (about min) of each customer delivery point
Solving result of VRP model
And solving the VRP multi-target path optimization model by using a multi-target vehicle path optimization algorithm based on the leader dolphin group under an uncertain condition, wherein an initial dolphin group n is 250, and the maximum iteration number maxth is 200. Tests show that when the fixed loudness and the rate A (i) R (i) are 0.65, the convergence speed and the calculation accuracy are optimal, and the running speed of each individual is set to be [ -0.5,0.5 [ -0.5 []In the meantime. After many times of comparison and test, the weight of the fitness function is finally set as: lambda [ alpha ]1＝0.3，λ10.4. The specific algorithm convergence iteration graph and the search path change are shown in figures 4, 5 and 6.
According to the initial trajectory diagram 4 and the trajectory diagram 5 iterated for 10 times, it is found that the trajectory improvement is not obvious and still messy, and although the convergence rate is high, the accuracy is not high, and the solution cannot be used as a final optimization solution. It can be seen from fig. 5 and fig. 6 that after 90 iterations, the algorithm tends to converge, the optimization result reaches a stable state, the trajectory graph becomes more concise, and the algorithm convergence speed is higher.
By the above solution, the optimal adaptive value is 18325.887, and the evaluation degree of the optimization effect of the path at this time is the best. The path at this time is:
1→27→8→14→25→18→4→16→41→40→19→42→44→17→47→ 12→37→15→45→33→39→40→30→38→11→32→16→9→49→5→46 →51→24→43→26→31→28→3→36→35→20→29→21→34→50→16→ 2→22→8→26→7→23→48→1。
at this point, the total path length is about: 138.00km, total travel time: 360 minutes, without violating the client's time window limit, the program run time is: 22.43800 s.
The result of the solution shows that the algorithm can obtain the optimal distance and the optimal driving time under the condition of not violating the time window limit.
Further, through experiments, if only the shortest path is considered, the length thereof is 125.00km, but the travel time is increased to 400 minutes, and a case where a customer time window is violated occurs. Through comparison, although the stroke is increased, the other two conditions can be better met, and the effect is ideal overall. Algorithms can also be used to make vehicle routing problems for local delivery.
The DPA algorithm is more suitable for global and local iteration of function optimization by improving the DPA of the original dolphin swarm algorithm, introducing the concept of 'echo positioning' of the bat algorithm and adding an update equation of pulse loudness and emission rate in the process of optimal value iteration, and the vehicle path optimization algorithm based on uncertain conditions of the dolphin swarm of a leader has the characteristics of high convergence speed, high precision, good robustness and the like. The method can save a large amount of cost for the transport company and improve the customer satisfaction, so that the dolphin swarm algorithm based on the leader can be used for guiding practice.
Claims (3)
1. A leader dolphin group-based uncertain condition solving vehicle path optimization algorithm is characterized by comprising the following steps of:
step1 initializing population
And (3) uniformly distributing each dolphin in the dolphin group in the definition domain of the target function, wherein the size of the dolphin group is N, the dimension of the search space is D, and then the position of the ith artificial dolphin is as follows:
Xi＝(xi1,…,xid,…xiD)
xid＝xmin+rand×(xmax-xmin)
wherein rand is in the interval [0,1 ]]A random number, x, uniformly distributed thereinmaxAnd xminRespectively corresponding to the upper limit and the lower limit of the search space;
step2 optimizing division of labor
In the dolphin predation space, any dolphin can be used as a 'guide' role, and the whole dolphin group is distributed in every position of the predation space according to a random distribution rule at first, if one dolphin finds food, said 'guide' can transfer the food information to correspondent other dolphins by means of 'echo positioning'; after obtaining the information, the dolphin group can search for the team members of the dolphin group to form a virtual team of the dolphin group;
defined as each dolphin Xi(i-1, 2, … n) as the center, dolphin X was calculated separatelyj(j ═ 1,2, … n) to dolphin XiDistance X ofijSorting the distances to each dolphin in ascending order, and selecting m dolphins closest to each dolphin to create a virtual team of the dolphin according to the sorting result;
wherein the calculation formula of the distance between dolphins is
In the whole dolphin group, more than one dolphin virtual team is provided, so that each virtual team has a local leader of the group, and team members judge the identity characteristics of the team members, the leader or common members through comparison of local optimal values of fitness functions; leaders of the whole group are generated from each virtual team, and in the process of gathering food, through continuous iteration, after the maximum iteration times are reached, a leader dolphin is selected, namely the global optimal value of the fitness function;
step3 information sharing
After the leader is selected, the leader carries out information exchange with the group members of the leader through sound to obtain the optimal positions and adaptive values of other members; after the information exchange is executed for a plurality of times, the dolphin with a better position is quickly detected by other dolphins; therefore, dolphins can approach food from top to bottom orderly under the guidance of the leader through information sharing, and form an enclosure gradually, and finally prey;
step4 surrounding food
After the leader dolphin obtains the food information of the 'guide' dolphin, other dolphins in the group are informed to surround through sound, and the other dolphins are unfolded and surrounded at the leader position;
as a common member, effective location updating is carried out, which becomes a key step in the predation link, and for the location updating, the number of the location updating is [0,1 ]]Internally generated random number rmIs generated if rmIf the ratio theta is smaller, the ith dolphin does not perform position updating, otherwise, the ith dolphin performs position updating by taking the leader dolphin as the center to surround food; theta is a preset threshold value;
the member position updating step is as follows:
updating the loudness A (i) and the emission rate R (i) of the pulses with the course of the optimization iteration;
the closer to the food, the lower the loudness of the pulse, the faster the emission rate, and a (i) of 0 means that dolphin i has just found a food and temporarily stops making any sound;
update equations for pulse loudness and transmission rate:
At+1(i)＝αAt
Rt+1(i)＝R0(i)×[1-exp(-γt)]
wherein, 0 < α < 1, gamma > 0, which are all constant, when t → ∞, At(i)＝0,Rt(i)＝R0(i) Setting the dolphin position at the t-th time as
The updated dolphin position
Is composed of
Wherein: is a group of [0,1]D-dimensional random vector of At(i) The loudness of the pulse at time t;
and (3) carrying out restoration processing on the updated position coordinates of the dolphin which is not in the predation space:
after the position of the dolphin leader is determined, the position and the fitness value of the dolphin leader are known by group members through information exchange, so that the group members continuously adjust the positions of the group members according to the fitness values of the group members to form an enclosure in order, the overall condition is optimized, and the most efficient predation is achieved;
step5 restoration State of assigned food
After the enclosure is formed, the enclosure is reduced through position updating, and finally the predation is carried out;
after the enclosing ring is formed, the dolphins in the optimal position and the local optimal position are stopped for a period of time, and the dolphins are preyed together after the subsequent dolphins are enclosed;
after the predation process is finished, the random state of the dolphin in the predation space is recovered, and the next predation is carried out.
2. The leader dolphin group-based solution to uncertain condition vehicle path optimization algorithm of claim 1, wherein: determining the optimal position of each team by comparing the adaptive value of each team, further determining the leader of each virtual team, and selecting the probability of each fitness value:
wherein, FiRepresenting fitness value, n, of each virtual teamiIndicating the size of the ith virtual team.
3. The leader-dolphin-based group-solving uncertain condition vehicle path optimization algorithm according to any of claims 1 or 2, characterized by: due to the randomness of the dolphin group, individual dolphins with large fitness values may not necessarily appear in the next generation dolphin group, and the dolphin with the largest fitness value is iterated to the next generation by introducing an elite retention mechanism, and other groups are screened again.
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| CN114723106A (en) * | 2022-03-16 | 2022-07-08 | 西南交通大学 | Inter-station goods train cooperative flow distribution method based on fixed-point aggregation mode under mixed condition |
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| CN112733272A (en) * | 2021-01-13 | 2021-04-30 | 南昌航空大学 | Method for solving vehicle path problem with soft time window |
| CN114723106A (en) * | 2022-03-16 | 2022-07-08 | 西南交通大学 | Inter-station goods train cooperative flow distribution method based on fixed-point aggregation mode under mixed condition |
| CN114723106B (en) * | 2022-03-16 | 2023-04-18 | 西南交通大学 | Inter-station goods train cooperative flow distribution method based on fixed-point aggregation mode under mixed condition |
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