CN108267954B - Cutter punctual delivery path planning algorithm with hard time window - Google Patents

Cutter punctual delivery path planning algorithm with hard time window Download PDF

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CN108267954B
CN108267954B CN201810033444.3A CN201810033444A CN108267954B CN 108267954 B CN108267954 B CN 108267954B CN 201810033444 A CN201810033444 A CN 201810033444A CN 108267954 B CN108267954 B CN 108267954B
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张维
杨洋洋
吴燕
马志华
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Northwestern Polytechnical University
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Abstract

The invention provides a cutter punctual delivery path planning algorithm with a hard time window. Firstly, by considering that the cutter requirements of stations are separable, arranging a distribution time window for each process of the stations, and establishing an optimization function taking the average satisfaction degree of the processes and the number of distributed vehicles as targets, the actual situation in the vehicle path distributed by the cutter on time in a workshop is more accurately reflected, so that the distribution scheme made based on the method is more reliable; then, a genetic algorithm is adopted to carry out model solution, a plurality of solutions in a search space are evaluated, the risk that a traditional optimization algorithm is easy to fall into a local optimal solution is reduced, and a probabilistic transition rule is adopted to guide the search direction, so that the algorithm has self-learning and self-adaptability.

Description

Cutter punctual delivery path planning algorithm with hard time window
Technical Field
The invention belongs to the technical field of logistics path planning control, and particularly relates to a cutter punctual delivery path planning algorithm with a hard time window in a production workshop.
Background
With the rise and development of the domestic and foreign logistics distribution industry at present, the application and development of related technologies of logistics distribution of workshops are more and more emphasized. The cutter is an extremely important production resource in a numerical control workshop, the distribution of the cutter is also an important component of a workshop production logistics system, the distribution and production process is logistics activity along with the production process in an enterprise, and the on-time and efficient distribution of the cutter is an important guarantee for stable and efficient production operation.
At present, most discrete manufacturing enterprises have original cutter distribution path technologies and low informatization degree in production workshops, and the production workshops of most of the enterprises do not adopt an advanced intelligent distribution system. In the tool distribution process of the workshop, generally, a distributor distributes all tools required by the workshop to each work station before the work station starts according to the production operation schedule, and the tool overstock beside the work station is caused. With the proposal of the punctual production mode, in order to reduce the waste caused by the overstocked cutter beside the station in the production process, the enterprise requires the working procedure to produce the required product according to the required quantity only when the working procedure is required. The tool distribution in the workshop should therefore also be such that the tools required for a work station are only distributed to that work station when the work process requires it.
Vehicle Routing Problem (VRP) was first introduced by Dantzig and Ramser in 1959, and a general description of the Vehicle Routing Problem (VRP) for general logistics is: a certain number of customers, each having a different number of goods, are provided with goods by a distribution center, a fleet of vehicles is responsible for distributing the goods and organizing appropriate driving routes, the goal is to meet the customer's needs and to achieve the goals of shortest route, minimum cost, minimum time consumption and the like under certain constraints.
However, the problem of the workshop cutter distribution path is different from the problem of most social logistics VRP, most of the current researches on the workshop cutter distribution path are directly applied with mathematical models belonging to the social logistics VRP, only the algorithm is improved, and the actual workshop cutter distribution process is ignored.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a cutter on-time distribution path planning algorithm with a hard time window. The method comprises the steps of combing a workshop cutter distribution process, comparing different points of the workshop cutter distribution problem with a general VRP problem, considering that the cutter requirement of a station can be split, adding a service hard time window for each process of the station, establishing a model with a hard time window for cutter on-time distribution path planning, taking the highest average satisfaction degree of the processes and the minimum quantity of distribution vehicles as optimization targets, considering the time window in a constraint condition, enabling each process in one task to be served by only one trolley, enabling the type and the quantity of cutters required by each process to be known, and solving the established model by using a genetic algorithm.
A cutter punctual delivery path planning algorithm with a hard time window is characterized by comprising the following steps:
step 1: the method comprises the following steps of knowing the start time and the requirement of each process of a station in a tool warehouse center, the hard time window of each process and the closed vehicle path, wherein each process only has one vehicle for distribution, and determining decision variables according to the following formula:
Figure BDA0001547196410000021
Figure BDA0001547196410000022
wherein x isijkVariables representing the sequence of travel between the processes and the delivery carriages, yikIn order to indicate which vehicle the process is distributed from, i and j indicate the process number, i is 1,2, …, N, j is 1,2, …, N is the total number of the process, K indicates the number of the vehicle, K is 1,2, …, K is the total number of the vehicle;
step 2: the inequality constraints are respectively established according to the following formulas:
tid＜ti＜tiu(3)
Figure BDA0001547196410000023
Figure BDA0001547196410000024
Figure BDA0001547196410000025
Figure BDA0001547196410000026
Figure BDA0001547196410000027
wherein, tidRepresents the lower limit of the time window, t, of step iiuRepresents the upper limit of the time window, t, of step iiThe time of the delivery vehicle reaching the station corresponding to the working procedure i is shown;
and step 3: according to
Figure BDA0001547196410000028
Establishing an optimization objective function, wherein muiFor satisfaction of Process i, according to
Figure BDA0001547196410000031
Calculation of tieRepresenting a desired cart service time for process i;
and 4, step 4: randomly generating popsize individuals as an initial population, wherein each individual is a full array of natural numbers of all process numbers, namely process number codes, and the popsize is a genetic algorithm initialization parameter with the value range of 10-200;
and 5: according to the time window requirement of each process, each individual is decoded respectively, namely, the process number code is converted into a station code, and the method specifically comprises the following steps:
step a: initializing the departure time of the trolley to be 11min before the departure time of the earliest procedure, aiming at an individual, firstly inserting 0 into the first coding position of the station code, traversing the individual procedure number code from left to right, finding out the station where the procedure can be reached in a time window according to the travel time between the distribution center and the station corresponding to the procedure number, if the station can be found, putting the station number into the station code, and removing the procedure number from the procedure number code, wherein at the moment, the travel time of the trolley is the departure time of the trolley plus the travel time of the distribution center to reach the station corresponding to the procedure number, and turning to the step b; otherwise, changing the departure time of the trolley as the starting time of the procedure corresponding to the first coding position of the procedure number code minus 11min, traversing the procedure number code from left to right, finding the station where the procedure can be reached in the time window according to the running time between the distribution center and the station corresponding to the procedure number, putting the station number into the procedure number, removing the procedure number from the procedure number code, and turning to the step b when the running time of the trolley is the departure time of the trolley plus the running time of the distribution center reaching the station corresponding to the procedure number;
step b: traversing the process number codes from left to right based on the running time of the trolley, searching the stations where the processes can arrive in the time window according to the running time between the stations corresponding to the process numbers, putting the station numbers into the process number codes, removing the process numbers from the process number codes, and updating the running time of the trolley into the running time of the previous trolley plus the running time between the stations corresponding to the process numbers. Repeating the step until the working procedure meeting the conditions can not be found, and turning to the step c;
step c: adding 0 at the last position of the station code, judging whether the length of the process number code is 0 at the moment, and if so, ending the decoding; otherwise, returning to the step a;
step 6: calculating a fitness value of each individual according to a value (i), wherein the value (i) is the sum of the process average satisfaction value of the ith individual and the reciprocal of the vehicle number value, and the process average satisfaction refers to the average of the satisfaction values of the processes corresponding to all codes other than 0 in the station codes; the vehicle quantity value is the quantity of 0 in the station code minus 1;
and 7: selecting the initial population by adopting a proportion selection method according to the fitness value calculated in the step 6 to obtain a parent population consisting of individuals with high fitness;
and 8: with a certain cross probability PcCrossing the individuals selected in step 7 by a partial matching method to obtain a progeny population, PcThe value range of (a) is 0.4-0.99;
and step 9: with a certain mutation probability PmAnd (4) carrying out variation on the filial generation population obtained in the step (8) by adopting an inverse variation algorithm to obtain a next generation temporary population, PmThe value range of (a) is 0.0001-0.1;
step 10: recording the individual with the highest fitness value in the temporary population, and judging whether the maximum iteration number N is reacheddIf so, ending, finding out the individual with the maximum fitness value from the set formed by the recorded individuals with the maximum fitness value of each generation, and obtaining the path decoded by the individual with the maximum fitness value as the optimal cutter distribution path; otherwise, taking the temporary population obtained in the step 9 as an initial population, returning to the step 5, adding 1 to the iteration number, wherein the initial value of the iteration number is 1, and the maximum iteration number N isdThe value range of (1) is 100-500.
The invention has the beneficial effects that: due to the fact that the cutter requirements of the stations are considered to be detachable, the distribution time window is arranged for each process of the stations, the optimization function with the average satisfaction degree of the processes and the number of the distributed vehicles as the target is established, the actual situation in the vehicle path distributed by the cutter on time in the workshop is reflected more accurately, and the distribution scheme made based on the method is more reliable; the maximum average satisfaction degree of the working procedures and the minimum number of the delivered vehicles are taken as fitness functions, so that the adaptability to a hard time window can be better met; because the genetic algorithm is adopted to carry out model solution, a plurality of solutions in a search space are evaluated, the risk that the traditional optimization algorithm is easy to fall into the local optimal solution is reduced, and the search direction is guided by the transition rule of probability, so that the algorithm has self-learning property and self-adaptability.
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FIG. 1 is a flow chart of an on-time tool distribution path planning algorithm with a hard time window according to the present invention
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
As shown in FIG. 1, the invention provides a cutter on-time distribution path planning algorithm with a hard time window, which mainly comprises two parts of establishing a path planning mathematical model and solving the model by using a genetic algorithm. The specific process is as follows:
1. and establishing a mathematical model of the cutter on-time distribution path planning with hard time window constraint.
The tool delivery path planning problem can be described as: a tool warehouse center of a production workshop is provided with a plurality of trolleys, and tools are distributed to each procedure of each station on time according to the production operation schedule of an enterprise. Delivery time window [ t ] for Process iid,tie,tiu]，tidRepresents the lower limit of the time window, tiuRepresents the upper limit of the time window, tieRepresenting the expected arrival time and in a fuzzy reservation time window tid,tie,tiu]Satisfaction mu of the inner considered processi. And the tool distribution vehicle starts from the tool warehouse center, serves stations and returns to the distribution center after completing distribution tasks. The vehicles and the running paths are required to be reasonably arranged, and the maximum average satisfaction degree of the working procedures and the minimum number of the delivered vehicles are required under the condition that the constraint is met. The present invention is based on the following assumptions: a tool warehouse center, wherein the start time of each process of the station is known, and the requirement of each process is known; a closed vehicle path; each process can be delivered by only one vehicle, and each process can be ensured to be met; the time window for each process is known and is a hard time window.
(1) The decision variables are determined as follows:
Figure BDA0001547196410000051
Figure BDA0001547196410000052
wherein x isijkVariables representing the sequence of travel between the processes and the delivery carriages, yikIn order to indicate which vehicle the process is distributed from, i and j indicate the process number, i is 1,2, …, N, j is 1,2, …, N is the total number of the process, K indicates the number of the vehicle, K is 1,2, …, K is the total number of the vehicle;
(2) an inequality constraint is established according to the following formula:
tid＜ti＜tiu(11)
Figure BDA0001547196410000053
Figure BDA0001547196410000054
Figure BDA0001547196410000055
Figure BDA0001547196410000056
Figure BDA0001547196410000061
wherein, tiIndicating deliveryAnd (5) the time when the vehicle reaches the station corresponding to the working procedure i. Equation (11) indicates that the time for the delivery vehicle to start servicing the process being performed must be within the time window; equation (12) indicates that each process can only be serviced by one delivery cart in a single delivery job; formulas (13) - (14) show that the distribution trolley starts from the distribution center and finally returns to the distribution center; the expressions (15) to (16) represent the variable xijkAnd yikIs constrained by the relationship of (1).
(3) Determining an optimization objective and establishing an objective function
The average satisfaction degree of the process is the maximum, namely:
Figure BDA0001547196410000062
Figure BDA0001547196410000063
the number of delivery trolleys is minimized, namely:
Figure BDA0001547196410000064
from the optimization perspective, the method is a multi-objective optimization problem, and a weighted combination method can be adopted to convert the multi-objective problem into a single-objective problem so as to optimize two objective functions. Converting the two objective functions into a single objective function as follows:
Figure BDA0001547196410000065
wherein α is a weight coefficient, and α + β is 1, according to practical experience, the average satisfaction degree of the working procedure is more important than the number of the distribution trolleys, according to the sequence relation analysis method, α is more than β, and omega is set1＝α，ω2＝β，
Figure BDA0001547196410000066
By
Figure BDA0001547196410000071
Known as ω2＝(1+γ2)-10.38, then ω10.61, then rounded off, α -0.6, β -0.4.
In summary, the optimization objective function is:
Figure BDA0001547196410000072
2. and solving the established model by using a genetic algorithm.
(1) Constructing individuals to generate an initial population
Natural number coding is used, i.e. each individual is a full permutation of natural numbers for all process numbers, wherein each natural number corresponds to a process number in the distribution system. Randomly generating popsize individuals as an initial population, wherein the sequence of natural numbers in each individual is the access sequence of the algorithm to the process. The popsize is an initialization parameter of a genetic algorithm, and the value range is 10-200.
(2) Decoding each individual
And (3) decoding each individual according to the time window requirement of each process, namely converting the process number code into a station code, inserting 0(0 represents a distribution center) into the station code to form a specific vehicle distribution route, wherein the operation starting point and the operation ending point of the transport vehicle are both the distribution center, namely, the transport vehicle starts from the distribution center each time, and returns to the distribution center after completing a distribution task.
The specific process is as follows:
step a: initializing the departure time of the trolley to be 11min before the departure time of the earliest procedure, aiming at an individual, firstly inserting 0 into the first coding position of the station code, traversing the individual procedure number code from left to right, finding out the station where the procedure can be reached in a time window according to the travel time between the distribution center and the station corresponding to the procedure number, if the station can be found, putting the station number into the station code, and removing the procedure number from the procedure number code, wherein at the moment, the travel time of the trolley is the departure time of the trolley plus the travel time of the distribution center to reach the station corresponding to the procedure number, and turning to the step b; otherwise, changing the departure time of the trolley as the starting time of the procedure corresponding to the first coding position of the procedure number code minus 11min, traversing the procedure number code from left to right, finding the station where the procedure can be reached in the time window according to the running time between the distribution center and the station corresponding to the procedure number, putting the station number into the procedure number, removing the procedure number from the procedure number code, and turning to the step b when the running time of the trolley is the departure time of the trolley plus the running time of the distribution center reaching the station corresponding to the procedure number;
step b: traversing the process number codes from left to right based on the running time of the trolley, searching the stations where the processes can arrive in the time window according to the running time between the stations corresponding to the process numbers, putting the station numbers into the process number codes, removing the process numbers from the process number codes, and updating the running time of the trolley into the running time of the previous trolley plus the running time between the stations corresponding to the process numbers. Repeating the step until the working procedure meeting the conditions can not be found, and turning to the step c;
step c: adding 0 at the last position of the station code, judging whether the length of the process number code is 0 at the moment, and if so, ending the decoding; otherwise, returning to the step a;
(3) calculating a fitness value
The fitness function, i 1,2, popsize, is used to calculate the fitness value of each individual i.
value (i) is the sum of the process average satisfaction value of the ith individual and the reciprocal of the vehicle quantity value, and is calculated by the following steps: firstly, calculating the satisfaction degree of the vehicles except the distribution center to reach the station from left to right of the genes of the individuals, and then calculating the average satisfaction degree; secondly, traversing the codes of the individuals, calculating the number of distribution centers, and subtracting 1 to obtain the number of distribution vehicles; and thirdly, adding the inverse values evaluated in the first step and the second step to obtain the value (i).
(4) Selecting
According to the fitness value calculated in the above steps, selection operator operation is carried out on the initial population, and the individuals with high fitness value are selected as parents. The specific operation is as follows:
firstly, according to the fitness value of each individual, calculating the probability of each individual being inherited to the next generation group:
Figure BDA0001547196410000081
then, the cumulative probability for each individual is calculated:
Figure BDA0001547196410000082
then, a random number r which is uniformly distributed is generated in the interval of [0, 1], if r is less than q (1), an individual 1 is selected, otherwise, if q (k-1) < r < q (k), an individual k is selected, and the process of popsize is repeated for times to complete the selection.
(5) Crossing
With a certain cross probability PcCrossing the selected individuals by partial matching method to obtain filial generation population PcThe value range of (A) is 0.4-0.99.
First, the individuals in the population are randomly combined with each other two by two, and then the combined combination is randomly generated to be [0,1]And then judging whether the random number of the combined object is less than the cross probability PcIf it is less than PcPerforming cross operation; taking two parents (12345678) and (2468531) as an example, the specific process of the partial matching method is as follows: two crossing points are randomly selected, the first point is added as position 4, the second crossing position is 6, then the position between the two points will be crossed, and the other positions are copied or replaced by matching numbers. In this embodiment, 456 of the first parent is selected and 875 of the second parent is selected. Then 4Matching 8, 5 with 7, 6 with 5. First, add 456 and 875 to the corresponding positions in child 2 and child 1, respectively, copy the number in other positions directly to the corresponding child, if the number already exists in the child, replace it with the corresponding matching rule, for example, when 7 is copied in child 1, 7 is found to already exist in the child, find 7 matches 5 by looking up the corresponding matching rule, then copy 5, find 5 also exists in the child, find 5 matches 6 by looking up the matching rule, copy 6, and do not exist in the child, so 6 can be copied in, and so on until the number of workstations in the child reaches the defined length, and the creation of the child is completed.
(6) Variation of
With a certain mutation probability PmCarrying out variation on the obtained filial generation population by adopting an inverse variation algorithm to obtain a next generation temporary population PmThe value range of (a) is 0.0001-0.1.
The specific process of the reverse mutation method is as follows: each individual randomly generates [0, 1]]The random number in between, whether the random number is less than the mutation probability P is judgedmIf it is less than PmCarrying out mutation operation on individuals; assuming that the code of any one individual in the population is "1, 2, 3, 4, 5, 6, 7, 8, 9", two variation points 2 and 6 are randomly generated, namely "1, 2, 3, 4, 5, 6, 7, 8, 9" to reverse the variation segment into a new individual "1, 6, 3, 4, 5, 2, 7, 8, 9".
(7) Determination of cessation of evolution Condition
Recording the individual with the highest fitness value in the temporary population, and judging whether the maximum iteration number N is reacheddIf so, ending, finding out the individual with the maximum fitness value from the set formed by the recorded individuals with the maximum fitness value of each generation, and obtaining the path decoded by the individual with the maximum fitness value as the optimal cutter distribution path; otherwise, taking the temporary population obtained in the step 9 as an initial population, returning to the step 5, adding 1 to the iteration number, wherein the initial value of the iteration number is 1, and the maximum iteration number N isdThe value range of (1) is 100-500.
The specific simulation data and results of this example are as follows:
table 1 shows the information of each station, wherein the actual start time of production is from 8:00 earliest, and for the convenience of calculation, the actual start time of production is changed from 0min earliest, and the start times of other processes are pushed backwards. Table 2 shows the travel time between stations. The process sequence is iterated for 200 times through the genetic algorithm, and the optimal solution is output. The number of the initial population is 50, the cross probability is 0.6, and the mutation probability is 0.001. Table 3 shows the results calculated using the algorithm of the present invention. Compared with the method that all the tools of each station are required to be delivered at one time, the method has the advantages that the hard time window is added to each process of each station, and then each process is delivered one by one, so that the method can better reflect that the tools required by the stations are delivered to the stations only when the processes are required to be processed in the on-time production, and the delivery on-time performance is improved.
TABLE 1
Figure BDA0001547196410000101
Figure BDA0001547196410000111
TABLE 2
Figure BDA0001547196410000112
Figure BDA0001547196410000121
TABLE 3
Figure BDA0001547196410000122

Claims (1)

1. A cutter punctual delivery path planning algorithm with a hard time window is characterized by comprising the following steps:
step 1: the method comprises the following steps of knowing the start time and the requirement of each process of a station in a tool warehouse center, the hard time window of each process and the closed vehicle path, wherein each process only has one vehicle for distribution, and determining decision variables according to the following formula:
Figure FDA0002212812030000011
Figure FDA0002212812030000012
wherein x isijkVariables representing the sequence of travel between the processes and the delivery carriages, yikIn order to indicate which vehicle the process is distributed from, i and j indicate the process number, i is 1,2, …, N, j is 1,2, …, N is the total number of the process, K indicates the number of the vehicle, K is 1,2, …, K is the total number of the vehicle;
step 2: the inequality constraints are respectively established according to the following formulas:
tid＜ti＜tiu(3)
Figure FDA0002212812030000013
Figure FDA0002212812030000014
Figure FDA0002212812030000015
Figure FDA0002212812030000016
Figure FDA0002212812030000017
wherein, tidRepresents the lower limit of the time window, t, of step iiuTo representUpper time window limit of step i, tiThe time of the delivery vehicle reaching the station corresponding to the working procedure i is shown;
and step 3: according to
Figure FDA0002212812030000018
Establishing an optimization objective function, wherein muiFor satisfaction of Process i, according to
Figure FDA0002212812030000021
Calculation of tieRepresenting a desired cart service time for process i;
and 4, step 4: randomly generating popsize individuals as an initial population, wherein each individual is a full array of natural numbers of all process numbers, namely process number codes, and the popsize is a genetic algorithm initialization parameter with the value range of 10-200;
and 5: according to the time window requirement of each process, each individual is decoded respectively, namely, the process number code is converted into a station code, and the method specifically comprises the following steps:
step a: initializing the departure time of the trolley to be 11min before the departure time of the earliest procedure, aiming at an individual, firstly inserting 0 into the first coding position of the station code, traversing the individual procedure number code from left to right, finding out the station where the procedure can be reached in a time window according to the travel time between the distribution center and the station corresponding to the procedure number, if the station can be found, putting the station number into the station code, and removing the procedure number from the procedure number code, wherein at the moment, the travel time of the trolley is the departure time of the trolley plus the travel time of the distribution center to reach the station corresponding to the procedure number, and turning to the step b; otherwise, changing the departure time of the trolley as the starting time of the procedure corresponding to the first coding position of the procedure number code minus 11min, traversing the procedure number code from left to right, finding the station where the procedure can be reached in the time window according to the running time between the distribution center and the station corresponding to the procedure number, putting the station number into the procedure number, removing the procedure number from the procedure number code, and turning to the step b when the running time of the trolley is the departure time of the trolley plus the running time of the distribution center reaching the station corresponding to the procedure number;
step b: traversing the process number codes from left to right on the basis of the running time of the trolley, searching the stations where the processes can reach in a time window according to the running time between the stations corresponding to the process numbers, putting the station numbers into the station codes, removing the process numbers from the process number codes, updating the running time of the trolley into the running time of the previous trolley plus the running time between the stations corresponding to the process numbers, repeating the step until the process meeting the conditions cannot be found, and turning to a step c;
step c: adding 0 at the last position of the station code, judging whether the length of the process number code is 0 at the moment, and if so, ending the decoding; otherwise, returning to the step a;
step 6: calculating a fitness value of each individual according to a value (i), wherein the value (i) is the sum of the process average satisfaction value of the ith individual and the reciprocal of the vehicle number value, and the process average satisfaction refers to the average of the satisfaction values of the processes corresponding to all codes other than 0 in the station codes; the vehicle quantity value is the quantity of 0 in the station code minus 1;
and 7: selecting the initial population by adopting a proportion selection method according to the fitness value calculated in the step 6 to obtain a parent population consisting of individuals with high fitness;
and 8: with a certain cross probability PcCrossing the individuals selected in step 7 by a partial matching method to obtain a progeny population, PcThe value range of (a) is 0.4-0.99;
and step 9: with a certain mutation probability PmAnd (4) carrying out variation on the filial generation population obtained in the step (8) by adopting an inverse variation algorithm to obtain a next generation temporary population, PmThe value range of (a) is 0.0001-0.1;
step 10: recording the individual with the highest fitness value in the temporary population, and judging whether the maximum iteration number N is reacheddIf yes, ending the process, and recording the most adaptability value of each generationFinding out the individual with the maximum fitness value from the set consisting of the high individuals, wherein the path obtained by decoding the individual with the maximum fitness value is the optimal cutter distribution path; otherwise, taking the temporary population obtained in the step 9 as an initial population, returning to the step 5, adding 1 to the iteration number, wherein the initial value of the iteration number is 1, and the maximum iteration number N isdThe value range of (1) is 100-500.
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