CN116109084A - Flexible job shop scheduling method considering transportation time and adjustment time - Google Patents
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Abstract
The invention relates to a flexible job shop scheduling method considering transportation time and adjustment time, which effectively solves the problems of long production period caused by low searching precision and slow convergence speed of the existing shop scheduling method; the technical scheme for solving the problems comprises the following steps: according to the scheme, the scheduling problem of the flexible job shop with the transportation time and the adjustment time is considered, a mathematical model which aims at minimizing the maximum finishing time, the total machine load, the key machine load and the delivery period punishment value of the workpiece is established, a Q learning algorithm in reinforcement learning is introduced into an improved ant colony algorithm to update pheromones secreted in the ant traversal process, the learning capability of the algorithm in the ant colony dynamic optimizing process is enhanced, and the searching precision and diversity of the algorithm are improved, so that the production period is further shortened.
Description
Technical Field
The invention belongs to the technical field of flexible job shop scheduling, and particularly relates to a flexible job shop scheduling method considering transportation time and adjustment time.
Background
The scheduling problem (Flexible Job Shop Scheduling Problem, FJSP) of the flexible job shop is an important combination optimization problem, in the actual production process, the transportation time and the adjustment time exist in indirect processing activities such as product carrying, machine tool die changing, cutter changing and the like (a plurality of processing procedures usually exist on workpieces, the operations need to be completed on different machines, and the conditions of workpiece transportation and machine adjustment exist in the middle of the working procedures), so that the production cycle is influenced;
although most scholars generally adopt heuristic algorithms when researching FJSP series problems, some scholars adopt group intelligent algorithms to solve flexible job shop scheduling problems, and the algorithms have the defects of low search precision, low convergence speed and the like to a certain extent;
at present, many scholars research FJSP considering transportation time or FJSP considering adjustment time, but research on the transportation time and adjustment time is less;
in view of the above, the present application provides a flexible job shop scheduling method that considers the transportation time and the adjustment time to solve the above-described problems.
Disclosure of Invention
Aiming at the situation, in order to overcome the defects of the prior art, the invention provides a flexible job shop scheduling method considering the transportation time and the adjustment time, and simultaneously, the flexible job shop scheduling problem of the transportation time and the adjustment time is considered, a mathematical model aiming at minimizing the maximum finishing time, the total machine load, the key machine load and the delivery period penalty value of a workpiece is established, a Q learning algorithm in reinforcement learning is introduced in an improved ant colony algorithm to update the pheromone secreted in the ant traversal process, the learning capability of the algorithm in the ant colony dynamic optimizing process is enhanced, and the searching precision and the diversity of the algorithm are improved, so that the production period is further shortened.
A flexible job shop scheduling method taking transport time and adjustment time into account, comprising the steps of:
s1: establishment of the problem: the method comprises the steps of machine allocation and procedure sequencing, and a feasible scheduling scheme is found so that an objective function is optimal;
s2: establishing a corresponding objective function and constraint conditions aiming at the target to be optimized;
s3: a distributed coding mode is implemented, a solution space is decomposed into a plurality of mutually independent areas, an ant colony algorithm is combined to search an optimal scheduling scheme of each optimization target in the areas, and machine allocation and procedure sequencing are continuously adjusted to obtain a final non-dominant solution set;
s4: simulation experiment analysis verifies the feasibility and effectiveness of the method.
The technical scheme has the beneficial effects that:
in the scheme, the flexible job shop scheduling problem of the transportation time and the adjustment time is considered simultaneously, a mathematical model which aims at minimizing the maximum finishing time, the total machine load, the key machine load and the delivery period punishment value of the workpiece is established, the Q learning algorithm in reinforcement learning is introduced into the improved ant colony algorithm to update the pheromone secreted in the ant traversal process, the learning capacity of the reinforcement algorithm in the ant colony dynamic optimizing process is improved, the searching precision and diversity of the algorithm are improved, and the production period is further shortened compared with the traditional shop scheduling method.
Drawings
FIG. 1 is a schematic diagram of a machine for selecting individual expression information according to the present invention;
FIG. 2 is a schematic diagram of an ant selection process according to the present invention;
FIG. 3 is a graph showing the concentration of pheromones according to the present invention;
FIG. 4 is a schematic diagram of a dominant rank selection process in accordance with the present invention;
FIG. 5 is a schematic diagram of the mutation operation of the present invention;
FIG. 6 is a schematic view of the Hamming distance of the present invention;
fig. 7 is a flowchart of an improved hybrid multi-objective ant colony algorithm according to the present invention;
FIG. 8 is a schematic diagram of the mean-principal-effect;
FIG. 9 is a schematic diagram of a Pareto optimal front face of a 10×6 example of the invention;
FIG. 10 is a graph showing the convergence of the operation of the improved HMACO algorithm of the present invention;
FIG. 11 is a 10X 6 example Gantt chart of the present invention.
Detailed Description
The foregoing and other features, aspects and advantages of the present invention will become more apparent from the following detailed description of embodiments of the present invention when taken in conjunction with the accompanying drawings, wherein like reference characters refer to the same parts throughout the several views.
1 FJSP with transport time and adjustment time
The scheme is based on the traditional flexible job shop scheduling problem (Flexible Job Shop SchedulingProblem, FJSP), and simultaneously considers the transportation time and the adjustment time, namely, the flexible job shop scheduling problem (FJSP with Transportation andSetup Time, FJSP_T/S) with the transportation time and the adjustment time;
1.1 description of the problem
Flexible job shop scheduling problems with transport time and adjustment time can be described as: there are n mutually independent workpieces to be processed, which form a workpiece set j= { J1, J2, …, ji, …, jn }; there are M machines available for machining, which constitute the set of machines m= { M1, M2, …, mj, …, mm }.
The procedure of processing Ji is to pass through hi channel to give priority order constraint
I.e. the same work-piece processes must be performed in a specified order, e.g. the processing Oi,2 must be started after Oi,1 is completed. Each process has a designated set of optional machines +.>
(obviously->
) The processing time of which depends on the selected processingA machine. In the working procedure machining gap, the transportation time and the adjustment time exist;
the difference is that there is a transport time between adjacent processes of the same workpiece and there is an adjustment time between adjacent processes on the same machine. The adjustment time is also related to the processing sequence, namely, when two adjacent working procedures on the same machine belong to the same workpiece, the adjustment time between the two working procedures is 0;
the objective is to find a viable scheduling scheme to optimize the objective function. The scheduling of the problem involves two sub-problems of machine allocation and process ordering;
machine allocation refers to the allocation of each process to an appropriate machine, and process sequencing refers to the prioritization of process processing on each machine.
The FJSP_T/S problem herein has the following assumptions:
(1) All machines are available at time 0;
(2) All the workpieces are released at the moment 0;
(3) The transportation time of the first working procedure of all workpieces is ignored;
(4) The process preemption operation is forbidden at any time, i.e. all the processes cannot be interrupted once the processes are started;
(5) The same working procedure can only be processed by one machine at the same time;
(6) Each machine can process only one process at a time.
1.2 mathematical model
Decision variables in this context are
And delta ijk Wherein->
For determining a selection relationship between the process and the machine tool; delta ijk For determining whether there is an adjustment and transportation time for the process;
the relevant variable symbols and definitions herein are shown in table 1:
table 1 variable description
In the FJSP study with transportation time and adjustment time, 4 targets are comprehensively considered, and a mathematical model is established, wherein four objective function calculation formulas and constraint conditions of the model are as follows:
minf 1 ＝max i C i i＝1,...,n(3)
constraint conditions:
wherein (3) - (6) are four optimization objectives, f 1 The processing end time of the last procedure; f (f) 2 On all machines for the whole production processThe sum of the processing time, the transport time and the adjustment time spent; f (f) 3 The sum of the processing time, the transportation time and the adjustment time spent on the machine which takes the most time; f (f) 4 Finishing time CJ for workpiece i i 
Not within a specified delivery period [ DS i ，DE i ]The loss caused by the method requires a certain storage cost when the method is finished in advance, alpha s To advance the storage fee per unit time, if the expiration is completed, the default fee, alpha, is paid e To delay the surprise charge spent per unit time.
(7) Ensuring that each process is assigned to one and only one eligible machine.
(8) Representing a priority relationship between successive operations of the same job.
2 improving hybrid multi-objective ant colony algorithm to solve FJSP_T/S
The method comprises the steps of providing an improved hybrid multi-objective ant colony algorithm to solve FJSP_T/S, designing a distributed coding mode by a coding part, firstly determining machine allocation, then decomposing a solution space into a plurality of mutually independent areas, searching an optimal scheduling scheme of each optimization objective in the areas by combining the ant colony algorithm, and finally obtaining a final non-dominant solution set by continuously adjusting the machine allocation and the procedure sequencing.
2.1 distributed encoding and initialization
The improved hybrid multi-objective ant colony algorithm is different from the traditional two-section coding and decoding search framework, and a distributed coding mode is provided by combining the problems and the algorithm characteristics. According to the scheduling problem characteristics of the flexible job shop, the distributed codes are divided into machine selection information and procedure ordering information, an initial information list of a machine selection part is firstly initialized and generated, and the initial information list of the procedure ordering part is generated by an improved hybrid multi-objective ant colony algorithm.
In the process of initializing and selecting the machines, in order to ensure the quality of initial solutions and the diversity of search spaces, the machine with the shortest process for processing the j-th working procedure of the workpiece i is selected with 50 percent probability, the machine with the shortest process for processing the j-th working procedure of the workpiece i can be selected with 30 percent probability, and the machine with the earliest process for processing the j-th working procedure of the workpiece i can be selected with 20 percent probability at random. Through three different machine selection modes, the space for selecting the machine can be increased, the diversity is improved, and the traversing path of ants is wider.
The information expression mode of machine selection is shown in figure 1, each machine selection information is a series of integers, the length is L, L is the number of all working procedures, O ij Representing the jth process of workpiece i, by the initialization process described above, we create a machine string in which each integer represents the serial number of the alternative processing machine for the corresponding process, e.g., integer 2 in the first pale yellow box of the machine string in FIG. 1, representing the number of O that can be processed in two 11 In the machine (M) 1 、M 3 ) Selecting a second machine M 3 To O 11 Processing and analogizing the workpiece J 1 Three processes O of (2) 11 、O 12 、O 13 Respectively select M 3 、M 3 、M 6 Three machines for processing.
2.2 improved ant colony Algorithm
The ant colony algorithm (Ant Colony Optimization, ACO), a probabilistic algorithm for finding an optimized path in the graph, is inspired by the foraging behavior of ants in nature. During ant foraging, the ant colony can always find an optimal path from the ant nest and the food source. When the FJSP problem is solved by using an ant colony algorithm, the ants start from the node 0 at the beginning, traverse L nodes until the node at the end, select one workpiece from the optional workpiece processing set of each node for processing, and the obtained sequence of procedures is a solution of the problem. In the figure, a first ant selects a workpiece 1 to process in an optional processing workpiece set of a node 1, selects a workpiece 3 to process at a node 2, selects a workpiece 5 to process at a node 3, and L nodes represent the number of all working procedures, as shown in the figure 2, and are schematic diagrams of ant selection working procedures;
the improved ant colony algorithm is adopted, individuals in the machine selection population are sequentially searched, under the machine selection scheme,optimal procedure ordering schemes on four targets of maximum finishing time, total machine load, key machine load and delivery period penalty value of workpieces are obtained, optimal scheduling schemes on four different targets are obtained, and a selection population of the machine is traversed, so that 4N can be obtained pop Scheduling scheme (N) pop Is the population number);
the main steps of the single ant colony are as follows:
(1) Firstly initializing a pheromone concentration table, wherein the concentration is C init 。
(2) The sequence of the process of each ant is determined according to the roulette method. Taking the pheromone concentration of fig. 3 as an example, the number of lines is the number of work pieces, the number of columns is the number of steps, and the numerical value on each cell indicates that the pheromone of the work piece is selected at the time of processing the corresponding step. For example, the value on the (j, k) th cell is a work step of selecting the work j as the kth processing. When determining the kth processing procedure of ants, firstly determining a set of workpieces to be processed, and then calculating the fitness value P of each workpiece by adopting a formula (9) k ij The obtained fitness value of each workpiece is planned to be a whole turntable, each workpiece is distributed on the turntable according to the fitness value, each time the turntable rotates, the arrow points to one workpiece, but the single mode of selecting the workpiece according to the fitness value can lead to premature convergence of an algorithm to be sunk into local optimum, so after the fitness value of each candidate procedure is obtained, 70% of ants are bet by adopting a turntable to select the next workpiece, and 30% of ants select the next workpiece in a random selection mode. Not only can the workpiece with larger fitness value be selected, but also the workpiece with smaller fitness value can be selected with opportunity, so that the search space is further enlarged, and the diversity of solutions is increased;
in formula (9), i is the last determined workpiece and j is allowed k Work pieces τ in a collection ij (k) At k, the concentration of pheromone, eta from work piece i to work piece j ij (k) Distance d from workpiece i to workpiece j at k k ij Inverse of (d) in fact d k ij The size of the machine idle gap generated by processing the workpiece j when k is reflected, and if the gap is 0, the arrangement of the processing workpiece j can improve the local production efficiency. Since 0 cannot be denominator, d k ij Minimum 0.1 is taken. d, d k ij The calculation formula of (2) is shown as formula (10):
wherein S is M For the allowed start time of the machine S J Is the allowable start time for the workpiece.
(3) When the ants have selected all the workpieces, four target values of the ant corresponding scheme are calculated according to formulas (3) - (6). The time information of each work procedure is calculated in the selection process, and the encoding and decoding operations are not required to be repeated.
(4) And recording a scheduling scheme corresponding to the optimal individual in the ant colony.
(5) Updating the pheromone; after the ants complete one-time path selection, the pheromone concentration of the ants passing through a certain path changes, the higher the pheromone concentration of the path becomes the optimal path, and meanwhile, the pheromone concentration volatilizes according to a certain coefficient. The key method is to map the pheromone concentration table in the ant colony algorithm into the Q table in the Q learning and map the pheromone into the Q value in the Q learning. Q learning is a value-based learning method, and is not based on a state transformation model, and a method for solving a reinforcement learning problem by using time sequence difference is introduced, so that the learning capacity of an algorithm in a dynamic environment is reinforced, the accuracy of the ant colony algorithm is improved, and the convergence rate of the algorithm is accelerated;
local pheromone update rules:
τ ij (t+1)＝(1-P rho )τ ij (t)+Δτ ij (t) (11)
τ in the above ij (t+1) represents the pheromone concentration of ant at the (i, j) position at time t+ 1, Δτ ij (t) represents the pheromone increment of the ant passing (i, j) at the moment t, P rho For the pheromone evaporation rate, P is the added value at the corresponding position of the pheromone concentration table when the ant passes through (i, j).
Global pheromone update rules: the updated formula for Q learning is as follows
Q t+1 (s,a)＝(1-δ)Q t (s,a)+δ(r t+1 +γmaxQ(S t+1 ,a)) (13)
Q in t (s, a) is the return value of the selected action a in the s state, delta is the learning rate, and the magnitude is generally 0,1]Between, r t+1 Taking action a from state s at time t+ 1, wherein gamma is the discount rate;
if the pheromone concentration of the ant colony algorithm is mapped to the Q value of Q learning, the pheromone updating rule in the ant colony algorithm is as follows:
τ ij (t+1)＝(1-P rho )τ ij (t)+P rho (Δτ ij (t)+γmax(τ ij (t))) (14)
in Deltaτ ij (t) global pheromone delta, maxQ (S) t+1 A) is the maximum pheromone concentration at time t+ 1, P rho For the evaporation rate of pheromone, deltaτ ij The calculation formula of (t) is as follows:
actually Deltaτ ij (t) represents the pheromone rewarding value of the optimal path after each ant of a single population selects the path, L is the additional pheromone rewarding increasing value of the optimal path, 1 is to avoid the evaporation of the pheromone to be 0, and the pheromone increasing value of the whole road is explored for each population, and is easy to cause the accumulation and sinking of the pheromone under the influence of the increment of the global pheromoneTo solve the problem of early search stagnation, limiting the pheromone of ant selection path by using maximum and minimum ant system, and setting a maximum value of the pheromone concentration table
And a minimum value +.>
When->
When in use, let->
When->
When in use, let->
(6) Judging whether the ant colony algorithm is terminated or not, judging whether the algorithm is terminated or not according to the setting of the algorithm termination condition in the parameters, and outputting the current optimal solution if the algorithm is terminated; otherwise, the algorithm has not been terminated, and the execution returns to (2) to continue.
2.3 non-dominant ordering selection
Because the conflict exists among four optimization targets and cannot be compared, it is difficult to find a solution so that all objective functions are optimal at the same time, and thus the scale obtained by the improved ant colony algorithm is 4N pop Fast non-dominant ordering of a set of scheduling schemes [15] . Carrying out weight assignment on the target value through an entropy weight method, calculating the comprehensive score of the scheduling scheme, and then layering and sequencing the population individuals;
the basic idea of the entropy weight method is to determine objective weights according to the size of index variability. Generally, the smaller the entropy value of a certain index, the greater the degree of variation of the index, the greater the amount of information provided, and the greater the function that can be played in the overall evaluation, and the greater the weight thereof. The entropy weighting method is an objective weighting method, and can deeply reflect the distinguishing capability of indexes so as to determine weights. The entropy weight method comprises the following specific steps:
(1) Normalizing the target value by using the formula (16):
wherein x is ij The original value of the jth index data of the ith object, y ij The j-th index value for the i-th object, i=1, 2, …, N, n=4×n pop ；
(2) Calculating the proportion Y of the ith object to the jth index by adopting a formula (17) ij ：
(3) Calculating entropy value e of j-th index j And information utility value d j The calculation formulas are shown in formulas (18) and (19):
d j ＝1-e j (19)
(4) The weight W of the index value of the j items can be obtained j As shown in formula (20):
(5) Calculate the composite score F as shown in equation (21):
F＝∑W j y ij (21)
after obtaining the comprehensive score of each solution, non-dominant ordering is carried out on each solution, and the solution set is divided into different dominant layers such as F 1 、F 2 、F 3 Etc.;
sequentially selecting solutions of different dominant layers until F n When in layer, the number of the selected solutions is greater than or equal to N pop If the number of solutions selected is exactly equal to N pop Will F 1 The machine selection information of the solutions in (a) is extracted to form a population F 1 ，F 2 ～F n The machine selection information of the solutions in (a) is extracted to form a population F 2n . Otherwise, the solution of the first n-1 layer (|F) 1 |+|F 2 |+…+|F n-1 |＜N pop ，|F 1 |+|F 2 |+…+|F n |＞N pop ) Are selected and the solutions with the top comprehensive scores in the nth layer are selected until the number of the selected solutions reaches N pop Extracting the machine selection information of the selected solutions to obtain populations F 1 And population F 2n In which a non-dominant ranking selection process is schematically shown in figure 4.
2.4 mutation and closing
The mutation and the approaching are operations of information exchange among individuals, so that the information of excellent individuals can be reserved to the next generation, and the searching precision of an algorithm is improved. The mutation and closing operation is directed to only the machine selection portion of the individual.
For selected population F 1 The mutation operation is carried out on the individual in the step (2), as shown in a mutation operation schematic diagram of figure 3, the mutation position (2) and the position (6) of the individual are randomly selected, the mutation position (2) and the position (6) of the individual are converted into any number of selectable machine numbers in the position, 3 in the position (2) is converted into 1 after mutation, 2 in the position (6) is converted into 3, and a new information individual is generated, as shown in figure 5;
for selected population F 2n Individual execution to population F 1 Is to first calculate each F 2n Individuals in (B) and F 1 The Hamming distance d of the individual is the number of different corresponding positions in the two individuals, and as shown in fig. 4, the information of the 1 st, 2 nd and 4 th positions of the individual 1 and the individual 2 are different, so that the Hamming distance of the individual 1 and the individual 2 is equal to 3. Then F 2n Each individual in the layer randomly goes to 1 nearest F 1 The middle individuals are closed, and the machine part is closed by adopting a multi-point cross variation modeRandomly generating a plurality of intersecting positions, F 1 Replacement of individual information in a layer to a corresponding F to be brought together 2n On individuals in (F) 1 The information on the rest of the individual remains unchanged.
Combining the two information lists after mutation and closing operation to obtain 2N pop The new generation information list of individual information is calculated, the optimal solution of the individual in the information list is recorded, the optimal individual in the list is compared with the current optimal solution, if the objective function value is smaller than the current optimal solution, the current optimal solution is replaced to be the optimal individual in the list, otherwise, the current optimal solution is unchanged;
the algorithm flow when the FJSP_T/S is solved by the improved hybrid multi-objective ant colony algorithm in the scheme is shown in figure 7.
3. Simulation experiment analysis
3.1 parameter settings
Simulation experiments are carried out on the calculation example by using Matlab 2017b, and the running environments are Intel Core i7 CPU2.2GHz and 8GB RAM. The improved HMACO algorithm parameters presented herein are specifically set as: population size N pop Number of iterations n=50 iter =50, mutation probability P mutr =0.5, maximum number of iterations of ant colony N ACO-iter Number of ants n=20 ant =10, initial pheromone concentration C init =1, target value f 4 Punishment coefficient alpha of the lining s ＝1、α e =5, for pheromone evaporation rate P rho Three parameters, namely a local pheromone increment P and a global pheromone increment L, are subjected to multi-factor orthogonal experiments by using a field method and Minitab software, the parameter level table is shown as a table 2, each parameter has 3 levels, and 9 different combinations of the three parameters can be seen in the parameter combination orthogonal table of the table 3.
The HV (Hypervolume) index is adopted to evaluate different parameter combinations, HV accuracy has a great relation with reference point selection, the reference set of the parameter experiment is a solution set obtained by screening results obtained by 5 experiments of the HMACO algorithm under the parameter combination of the sequence number 3 in the table 3 through non-dominant sorting and crowding degree sorting, and the solution obtained under different parameter combinations is evaluated through the reference set.
HV is used to represent the volume of the hypercube enclosed by the individual in the solution and the reference point in the target space. The convergence and distribution of the solution set S is evaluated by calculating HV values, which are defined as in equation 22.
S is an approximate solution set of the optimal Pareto front, P is a reference point corresponding to the real Pareto front, v (S, P) represents the super volume of a space formed between the solution S and the reference point P in the non-dominant solution set S, and the larger HV represents the better diversity of the solution set S.
The average main effect diagram obtained by field analysis of the parameter combination orthogonal table is shown in figure 8 to obtain the pheromone evaporation rate P rho The three parameters of the local pheromone increment P and the global pheromone increment L are respectively selected from 0.2, 4 and 10.
Table 2 parameter levels
TABLE 3 parameter combination orthogonal tables
3.2 Algorithm self-loop effectiveness experiment
In order to verify the effectiveness of the improved ant colony algorithm proposed herein, comprising the proposed mutation, closing operation and a pheromone updating mode based on Q learning, the BRdata dataset is utilized to compare the variation expansion experiment of the HMACO algorithm. We define HMACOtk as the comparison algorithm 1 after no mutation and approach operation, and HMACOQ as the comparison algorithm 2 that does not employ the Q-learning based pheromone update approach presented herein but employs the normal update approach.
The evaluation index adopted in the experiment is Set Coverage (SC), andalgorithm 10 sets of experiments were performed for each example and the average of the results was compared. SC is a set of approximate optimal solutions S for two Pareto in a multi-objective problem 1 And S is 2 Comparing the relative coverage, i.e. calculating S 2 Is at least S 1 The ratio of the weak dominance of the solution in (c) is measured by defining the degree of coincidence between the two solution sets as in equation 23.
|S 2 I represents the set S 2 The number of individuals in (C) (S) 1 ,S 2 ) =1 represents the binding set S 2 All solutions in (1) are S 1 Is governed by at least one solution, C (S 1 ,S 2 ) =0 denotes set S 2 Not all solutions in (a) are S 1 Is governed by any one of the solutions, C (S 1 ,S 2 )＝C(S 2 ,S 1 ) =0.5 represents set S 1 Sum set S 2 If the mass of C (S) 1 ,S 2 )>C(S 2 ,S 1 ) Representing solution set S 1 Quality is better than solution set S 2 And vice versa.
TABLE 4 comparison of variant experiment SC values
In table 4 we can find that except in the examples Mk06 and Mk08, C (HMACO, HMAC OQ) < C (HMACO q, HMACO), in other examples all C (HMACO, HMACO q) > C (HMACO q, HMACO), and in all examples C (HMACO ) > C (HMACO ott, HMACO), most of C (HMACO, HMACO q) > C (HMACO q, HMACO tk), i.e. the quality of the HMACO solution is superior to HMACO and HMACO q, HMACO tk is inferior to HMACO, HMACO q the most times, indicating that HMACO is overall superior to the other two comparison algorithms. Thus, it was verified that the Q-learning based pheromone update approach presented herein plays an important role in HMACO, whereas the mutation and closing operation can further increase the diversity and quality of solutions, and that the two improvement approaches presented herein are effective in combination.
3.3 Algorithm comparison experiment
To test the performance of the improved HMACO algorithm, the benchmark examples employed were from Brandimarte [16] The transit time and the adjustment time in the examples were randomly generated and compared with the modified HMACO herein using the modified genetic algorithm (Improved Genetic Algorithm, IGA), the Non-dominant ordered genetic algorithm II (Non-dominated Sorting Genetic Algorithm-II, NSGA-II). Due to the uncertainty of the algorithm, all experiments were repeated 10 times and evaluated by the average of the indices, table 5 shows the comparison of the three algorithms.
Table 5 comparison of the results of the three algorithms
The bolded fonts in table 5 represent improved results for the HMACO algorithm solution over the other two algorithms. As can be seen from Table 5, on MK01, f is found by three algorithms 1 The values are the same, but the other three target values obtained by improving the HMACO algorithm are better than those obtained by the IGA algorithm and the NSGA-II algorithm; in 10 reference examples, the f obtained by the HMACO algorithm is improved 1 Examples of values better than the other two algorithms are 7, f found by MO-HSIOA algorithm 2 Examples of values better than the other two algorithms are 7, and f obtained by improving the HMACO algorithm is improved 3 Examples of values superior to the other two algorithms are 10, f obtained by improving the HMACO algorithm 4 There are 9 examples of values that are superior to the other two algorithms, thus indicating that the improved HMACO algorithm presented herein is viable and effective.
3.4 real-world example experiment
In addition to performing the algorithm effectiveness test on the baseline dataset, the actual flexible job shop scheduling problem, considering the transit time and the adjustment time, is solved with the modified HMACO algorithm. This example is a 10 x 6 FJSP with transit time and trim time from a plant manufacturing plant in zheng state, with the data for the example shown in table 6 and table 7 as the transit schedule. The IGA algorithm, NSGA-II algorithm and the improved HMACO algorithm are used for solving, and the optimal values of the targets in the solution set obtained by the three algorithms are shown in Table 8.
Table 6 example data table
Table 7 transportation schedule
Table 8 8 ×6 example three algorithm target optimum value comparison results
On solving the scheduling problem of the 10 multiplied by 6 flexible job shop with the transportation time and the adjustment time, comprehensively comparing the improved HMACO algorithm proposed herein with other two algorithms, wherein the optimal values of the four obtained target values are 92, 419, 77 and 171 respectively;
FIG. 9 is a Pareto optimal front view obtained by improving the HMACO algorithm, FIG. 10 is a calculation convergence curve of the improved HMACO algorithm, FIG. 11 is a Pareto solution set f obtained by improving the HMACO algorithm 1 The Gantt chart of optimal solution is adjusted before machining the workpiece, wherein all light brown boxes in the Gantt chart represent the machine adjustment time for machining the process, such as the first light brown box of 101 processes machined on machine 1, and the workpiece needs to be transported in the middle of machining on different machinesIn the figure, all bluish boxes are transportation time corresponding to the process, such as the third bluish box of the 101 process, and the green box in the middle of the two boxes is processing time of the 101 process.
In summary, experiments are carried out, the FJSP_T/S problem is solved by providing an improved hybrid multi-objective ant colony algorithm, the improved ant colony algorithm and a non-dominant sorting method are combined, four target values of maximum finishing time, total machine load, key machine load and delivery period penalty value of a workpiece are optimized, 10 reference problems and production example problems are subjected to experimental analysis, the improved HMACO algorithm is compared with two different algorithms, and it is verified that the FJSP_T/S problem can be effectively solved by the algorithm provided herein.
The above description is only for the purpose of illustrating the invention, and it should be understood that the invention is not limited to the above embodiments, but various modifications consistent with the idea of the invention are within the scope of the invention.
Claims (5)
1. A flexible job shop scheduling method taking transport time and adjustment time into account, comprising the steps of:
s1: establishment of the problem: the method comprises the steps of machine allocation and procedure sequencing, and a feasible scheduling scheme is found so that an objective function is optimal;
s2: establishing a corresponding objective function and constraint conditions aiming at the target to be optimized;
s3: a distributed coding mode is implemented, a solution space is decomposed into a plurality of mutually independent areas, an ant colony algorithm is combined to search an optimal scheduling scheme of each optimization target in the areas, and machine allocation and procedure sequencing are continuously adjusted to obtain a final non-dominant solution set;
s4: simulation experiment analysis verifies the feasibility and effectiveness of the method.
2. The flexible job shop scheduling method according to claim 1, wherein the distributed code in S3 includes machine selection information and process ordering information, comprising the steps of:
s3-1: initializing an initial information list of a machine selection part, selecting a machine with the shortest process of the jth process for processing the workpiece i with 50% probability, selecting a machine with the 30% probability that can start the jth process for processing the finished workpiece i earliest, and randomly selecting the machine with the 20% probability;
s3-2: generating an initial information list of a procedure ordering part by adopting an improved ant colony algorithm;
s3-3: determining an optimal procedure ordering scheme of a target to be optimized under a machine selection scheme to obtain an optimal scheduling scheme of the target to be optimized;
s3-4: and carrying out rapid non-dominant sorting on a plurality of scheduling scheme sets obtained by an improved ant colony algorithm: and carrying out weight assignment on the target value by an entropy weight method, calculating the comprehensive score of the corresponding scheduling scheme, and carrying out non-dominant sorting on each solution after obtaining the comprehensive score of each solution.
3. A flexible job shop scheduling method taking account of transportation time and adjustment time according to claim 1, wherein the optimization objective in S2 comprises:
(1)f 1 the corresponding objective function is as follows:
minf 1 ＝mai＝1,...,n(3)；
(2)f 2 the sum of the processing time, the transportation time and the adjustment time spent on all machines in the whole production process corresponds to the objective function:
(3)f 3 for the sum of the processing time, the transportation time and the adjustment time spent on the machine with the most time, the corresponding objective function is:
(4)f 4 finishing time (CJ i =max) is not within the prescribed delivery period [ DS i The resulting loss, its corresponding objective function is:
the constraint conditions include:
(1) Ensuring that each process is allocated to one and only one qualified machine, the corresponding function formula is:
(2) The priority relation between the continuous operation of the same job is represented, and the corresponding function formula is as follows:
4. the flexible job shop scheduling method according to claim 2, wherein the individual ant colony algorithm steps in S3-4 are as follows:
(1) Firstly initializing a pheromone concentration table, wherein the concentration is C init ；
(2) Determining the sequence of the ants according to a roulette method;
(3) When the ants select all the workpieces, calculating four target values of the ant corresponding scheme according to formulas (3) - (6);
(4) Recording a scheduling scheme corresponding to an optimal individual in the ant colony;
(5) Updating the pheromone;
(6) Judging whether the ant colony algorithm is terminated or not, judging whether the algorithm is terminated or not according to the setting of the algorithm termination condition in the parameters, and outputting the current optimal solution if the algorithm is terminated;
otherwise, the algorithm has not been terminated, and the execution returns to (2) to continue.
5. The flexible job shop scheduling method considering transportation time and adjustment time according to claim 4, wherein in the step (5), the secret pheromone secreted in the ant traversal process is updated by adopting a Q learning algorithm based on reinforcement learning, the pheromone concentration table in the ant colony algorithm is mapped to a Q table in the Q learning algorithm, the pheromone is mapped to a Q value in the Q learning, and the secret pheromone comprises a local pheromone updating rule and a global pheromone updating rule;
wherein the local pheromone update rule comprises the following formula:
τ ij (t+1)＝(1-P rho )τ ij (t)+Δτ ij (t) (11)
τ ij (t+1) represents the pheromone concentration of ant at the (i, j) position at time t+1, Δτ ij (t) represents the pheromone increment of the ant passing (i, j) at the moment t, P rho The evaporation rate of the pheromone is that P is an added value at a corresponding position of the pheromone concentration table when ants pass through the (i, j);
the global pheromone updating rule comprises the following formula:
Q t+1 (s,a)＝(1-δ)Q t (s,a)+δ(r t+1 +γmaxQ(S t+1 ,a)) (13)
Q t (s, a is the return value of the selected action a in the state of s, delta is the learning rate, and the magnitude is generally 0,1]Between, r t+1 Taking action a from state s at time t+1, wherein gamma is the discount rate; and mapping the pheromone concentration of the ant colony algorithm to the Q value of Q learning, wherein the pheromone updating rule in the ant colony algorithm is as follows:
τ ij (t+1)＝(1-P rho )τ ij (t)+P rho (Δτ ij (t)+γmax(τ ij (t))) (14)
Δτ ij (t) global pheromone delta, maxQ (S) t+1 A) is the maximum pheromone concentration at time t+1, P rho For the evaporation rate of pheromone, deltaτ ij The calculation formula of (t) is as follows:
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