CN116523266A - Flexible job shop scheduling method and device based on game evolution algorithm, electronic equipment and medium - Google Patents

Flexible job shop scheduling method and device based on game evolution algorithm, electronic equipment and medium Download PDF

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CN116523266A
CN116523266A CN202310713198.7A CN202310713198A CN116523266A CN 116523266 A CN116523266 A CN 116523266A CN 202310713198 A CN202310713198 A CN 202310713198A CN 116523266 A CN116523266 A CN 116523266A
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job shop
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葛艳
杨海根
刘佶鑫
曾凡玉
王爱民
王梅
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses a flexible job shop scheduling method, a device, electronic equipment and a medium based on a game evolution algorithm, which comprise the following steps: according to the acquired processing information of the flexible job shop, establishing a scheduling mathematical model of the flexible job shop; generating an initialization population according to the processing information, and setting related parameters for processing flexible workshop scheduling problems; and carrying out iterative solution on the scheduling mathematical model by utilizing a game evolution algorithm based on the initialized population and the related parameters to obtain an optimal solution of the scheduling scheme. The invention can quickly and effectively generate a reasonable scheduling scheme, effectively solve the problem of large-scale complex scheduling and greatly improve the production efficiency.

Description

Flexible job shop scheduling method and device based on game evolution algorithm, electronic equipment and medium
Technical Field
The invention relates to the technical field of production scheduling, in particular to a flexible job shop scheduling method, a flexible job shop scheduling device, electronic equipment and a flexible job shop scheduling medium based on a game evolution algorithm.
Background
The Flexible Job shop scheduling problem (FJSP) widely used in modern manufacturing is an extension of the classical Job shop scheduling problem (Job-Shop Scheduling Problem, JSP); compared with JSP, FJSP better reflects the actual requirements of current production, and particularly, each procedure can be processed on a plurality of optional and different devices. The traditional flexible job shop scheduling problem FJSP relates to a plurality of workpieces and a plurality of devices, each workpiece is processed by a series of working procedures with strict sequence, and each working procedure can be processed by one or a plurality of devices; thus, the traditional flexible job shop scheduling problem FJSP involves two sub-problems: equipment allocation problems and process sequencing; wherein: the equipment distribution problem is that a piece of processing equipment is distributed for each process; sequencing problem scheduling the processes on all equipment to obtain a more flexible and high quality scheduling solution to achieve maximum completion time C for the workpiece max Where C is minimized max The connotation of the target is consistent with the utilization rate of the maximized equipment and other resources.
Aiming at the scheduling problem of the flexible job shops, researchers at home and abroad have developed a great deal of researches; researchers have tended to study flexible job shop scheduling problems: aiming at the problem characteristics, the more complex and more practical FJSP problem solving is realized by improving a meta heuristic algorithm represented by an evolutionary algorithm. However, the traditional evolutionary algorithm design is initially directed to solving a general combination optimization problem, and the proposed population randomness mechanism based on the random selection of the father is derived, and more algorithm systems are formed from the general or common angle; this way of randomly selecting cross partners necessarily increases the randomness of the evolution way, and while bringing blindness, it is also easy to get into precocity and unfavorable to obtain global optimization results, which is also a prominent problem of the evolution algorithm in theoretical research and practical application.
With the continuous deep research of scheduling problems in flexible job shops and the increasingly urgent need of applying the research results of the scheduling problems to actual production, the scheduling problems which are closer to the actual production, larger in scale and have more complex constraint become the focus of research; whereas evolutionary algorithms have been difficult to cope with such large-scale complex scheduling problems due to their blind search characteristics.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a flexible job shop scheduling method, a device, electronic equipment and a medium based on a game evolution algorithm, which can quickly and effectively generate a reasonable scheduling scheme and greatly improve the production efficiency.
In order to achieve the above purpose, the invention is realized by adopting the following technical scheme:
in a first aspect, the invention provides a flexible job shop scheduling method based on a game evolution algorithm, which comprises the following steps:
according to the acquired processing information of the flexible job shop, establishing a scheduling mathematical model of the flexible job shop;
generating an initialization population according to the processing information, and setting related parameters for processing flexible workshop scheduling problems;
and carrying out iterative solution on the scheduling mathematical model by utilizing a game evolution algorithm based on the initialized population and the related parameters to obtain an optimal solution of the scheduling scheme.
In combination with the first aspect, preferably, the processing information includes the number of workpieces, the number of processes for each workpiece, the processing time for each process, and the number of processing apparatuses.
With reference to the first aspect, preferably, the related parameters include an initial population size, a maximum iteration number, and a variation probability.
With reference to the first aspect, preferably, establishing a scheduling mathematical model of the flexible job shop includes:
to minimize the maximum completion time C of all the processes max For the goal, a goal model of the flexible job shop scheduling problem is established:
wherein E is ij Indicating the completion time of the j-th process of the workpiece i,n represents the number of workpieces, G i The number of steps of the workpiece i;
establishing a resource constraint model of the flexible job shop scheduling problem through the formulas (2) to (5):
S ij +(1-B i′j′p-ijp )·L≥S i′j′ +AT i′j′ (5)
wherein, the formula (2) shows that at least one piece of processable equipment is needed for any one process, the formula (3) shows that only one piece of processable equipment for any one process is needed, and the formula (4) shows that the processable equipment for any one process is from a set of selectable processable equipment; equation (5) shows that each piece of equipment can only process one piece at the same time at mostA step of performing a step; x is X ijp 、U ijp And B i′j′p-ijp Are parameters each having a value of 0 or 1; x is X ijp Indicating whether the jth procedure of the workpiece i can be processed on the equipment p, wherein the energy value is 1, otherwise, the energy value is 0; u (U) ijp Indicating whether the jth procedure of the workpiece i is finally processed on the equipment p, if so, the value is 1, otherwise, the value is 0; b (B) i′j′p-ijp Indicating whether the jth process of the workpiece i is processed on the equipment p next to the jth process of the workpiece i', if so, the value is 1, otherwise, the value is 0;p.epsilon. (1, 2.. Multidot.m.), L is a constant;
establishing a process constraint model of the flexible job shop scheduling problem through a formula (6) and a formula (7):
wherein, the formula (6) shows the number relation of the processing starting time, the processing ending time and the processing man-hour of the working procedure; the formula (7) shows the process route constraint of workpiece processing, namely that any one process needs to be finished in the previous process under the process route constraint before the processing can be started; s is S ij 、E ij And T ij Respectively representing the processing starting time, the processing ending time and the processing duration of the jth procedure of the workpiece i; s is S i(j+1) The processing start time of the (j+1) th process of the workpiece i is shown.
With reference to the first aspect, preferably, the step of iteratively solving the scheduling mathematical model by using a game evolution algorithm includes:
population D to be used for the kth iteration k Dividing the decision-making party and the opposite party into decision-making parties and opposite parties with equal distribution of the good and bad degrees;
performing cross operation based on game theory on the decision-making party and the opposite party according to the k-1 th iterative updated game strategy to generate offspring;
performing mutation operation by randomly exchanging the positions of two procedures and corresponding processing equipment in one chromosome based on the offspring generated by the cross operation;
combining the individuals after cross mutation into a new offspring population Q k Merging the parent population D of the previous generation k And the new generation population Q k Generating a new parent population R k ＝D k ∪Q k ；
For new parent population R in order of fitness value from high to low k The individuals in the population D are sorted, and the first N individuals are selected from the sorted queue to form a new generation population D k+1 ；
Judging whether the iteration number k reaches the maximum iteration number, if not, enabling k=k+1, repeatedly executing the steps until the current iteration number reaches the maximum iteration number, stopping, and obtaining a population D at the moment k+1 And selecting an optimal solution as the optimal solution of the scheduling scheme.
With reference to the first aspect, preferably, the game policy is used for corresponding selection of the paired individuals by the counter party according to the selection probability of each current individual when the decision party generates one to-be-paired individual; the selection probability specifically comprises:
equally dividing a decision party into three categories of a superior individual DS, a medium individual DM and an inferior individual DI, equally dividing an individual of a counterpart party into three categories of a superior individual AS, a medium individual AM and an inferior individual AI, and respectively meeting the selection probabilities of nine pairing types:
P(AS|DS)+P(AM|DS)+P(AI|DS)＝1
P(AS|DM)+P(AM|DM)+P(AI|DM)＝1
P(AS|DI)+P(AM|DI)+P(AI|DI)＝1
where P (as|ds) represents the probability that the counterpart selects the superior individual AS when the decision-maker selects the superior individual DS; p (am|ds) represents the probability that the counterpart selects the medium individual AM when the decision-maker selects the high individual DS; p (ai|ds) represents the probability that the counterpart selects a disadvantaged individual AI when the decision-maker selects a disadvantaged individual DS; p (as|dm) represents the probability that the counterpart selects a superior individual AS when the decision-maker selects a medium individual DM; p (am|dm) represents the probability that the counterpart selects the medium individual AM when the decision-maker selects the medium individual DM; p (ai|dm) represents the probability that the counterpart selects an inferior individual AI when the decision-maker selects a medium individual DM; p (as|di) represents the probability that the counterpart selects a superior individual AS when the decision-maker selects a inferior individual DI; p (am|di) represents the probability that the counterpart selects a medium individual AM when the decision-maker selects a bad individual DI; p (ai|di) represents the probability that the counterpart selects the inferior individual AI when the decision-maker selects the inferior individual DI;
the initial values of the selection probabilities of the nine pairing types are all set to be 1/3, and the selection probabilities gradually evolve to be converged after repeated iterative updating.
With reference to the first aspect, preferably, the step of updating the game policy includes:
according to the offspring generated by the current iteration crossover operation, respectively counting the matching quantity of nine pairing types;
counting the number of the corresponding expected pairing from the matching number of the nine pairing types respectively; wherein, at least one of the filial generations generated after the two chromosomes are crossed is better than the parent, and the pairing of the current crossing is called as the pairing to be performed;
based on the matching number and the expected pairing of each matching type, combining the selection probability of the current iteration, and respectively calculating and updating the selection probability of nine matching types in the next iteration by using a Bayesian formula.
In a second aspect, the present invention provides a flexible job shop scheduling device based on a game evolution algorithm, the device comprising:
the building module is used for building a production scheduling mathematical model of the flexible job shop according to the acquired processing information of the flexible job shop;
the initialization module is used for generating an initialization population according to the processing information and setting related parameters for processing the scheduling problem of the flexible workshop;
and the iteration solving module is used for carrying out iteration solving on the scheduling mathematical model by utilizing a game evolution algorithm based on the initialized population and the related parameters to obtain an optimal solution of the scheduling scheme.
In a third aspect, the present invention provides an electronic device, including a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is configured to operate according to the instructions to perform the steps of the flexible job shop scheduling method based on the game evolution algorithm according to any one of the first aspect.
In a fourth aspect, the present invention provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the flexible job shop scheduling method based on the game evolution algorithm according to any one of the first aspects.
Compared with the prior art, the invention has the beneficial effects that:
the invention explores the directional control mechanism of population iteration by the designed game evolutionary algorithm on the basis of fully utilizing the integral advantages of the evolutionary algorithm, improves the optimizing effect of the algorithm, has the characteristics of strong adaptability, high instantaneity, high calculation speed and high reliability when facing the problem of large-scale complex scheduling, can quickly and effectively obtain a better scheduling scheme, realizes the optimal configuration of resources, greatly improves the production efficiency of a production line and saves the production cost.
Drawings
FIG. 1 is a schematic flow chart of a flexible job shop scheduling method based on a game evolution algorithm according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of encoding according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of decision-making party and counter-party partitioning strategies provided in an embodiment of the present invention;
FIG. 4 is a schematic diagram of nine pairing type selection probabilities provided in an embodiment of the invention;
fig. 5 is an iteration curve schematic diagram of an optimal solution obtained by solving case MK10 by using the game evolution algorithm and the conventional genetic algorithm according to the embodiment of the present invention.
Fig. 6 is a schematic block diagram of a flexible job shop scheduling device based on a game evolution algorithm according to an embodiment of the present invention.
Detailed Description
The following detailed description of the technical solutions of the present invention is made by the accompanying drawings and specific embodiments, and it should be understood that the specific features of the embodiments and embodiments of the present application are detailed descriptions of the technical solutions of the present application, and not limiting the technical solutions of the present application, and the technical features of the embodiments and embodiments of the present application may be combined with each other without conflict.
The term "and/or" is herein merely an association relationship describing an associated object, meaning that there may be three relationships, e.g., a and/or B, may represent: a exists alone, A and B exist together, and B exists alone. In addition, the character "/" herein generally indicates that the front and rear associated objects are an "or" relationship.
Embodiment one:
as shown in fig. 1, the embodiment of the invention introduces a flexible job shop scheduling method based on a game evolution algorithm, which specifically includes the following steps:
step 1: according to the acquired processing information of the flexible job shop, establishing a scheduling mathematical model of the flexible job shop;
the processing information comprises the number of workpieces, the number of working procedures of each workpiece, the processing time of each working procedure and the number of processing equipment;
step 2: generating an initialization population according to the processing information, and setting related parameters for processing flexible workshop scheduling problems;
the related parameters comprise initial population size, maximum iteration times and variation probability;
further, in the process of generating the initial population, coding is performed by using coding rules of the processing information process, wherein genes in the coding represent workpieces, and the times of occurrence of the same genes represent corresponding processes of the workpieces; as shown in fig. 2, the sequence of the coded representation is: the method comprises the steps of a first process of a workpiece 2, a first process of a workpiece 3, a first process of a workpiece 1, a second process of the workpiece 3, a second process of the workpiece 1, a third process of the workpiece 3, a second process of the workpiece 2 and a third process of the workpiece 1;
according to the embodiment, individuals in the population are decoded according to a decoding rule, and the fitness value of each individual is calculated according to a problem target; the scheduling problem of the flexible job shop mainly solves two sub-problems of sequence ordering and equipment selection, the coding can determine the sequence of sequence ordering, and the decoding mainly determines the processing equipment selection of the sequence; in the embodiment, the earliest starting rule is adopted as a decoding rule, namely, equipment which can be started earliest is selected for processing in each process; after the process arrangement is completed, the maximum finishing time of all the processes under the coding scheme can be obtained, namely the fitness value of the corresponding individual.
Step 3: and carrying out iterative solution on the scheduling mathematical model by utilizing a game evolution algorithm based on the initialized population and the related parameters to obtain an optimal solution of the scheduling scheme.
As an embodiment of the invention, the scheduling mathematical model established in step 1 includes:
a to minimize the maximum completion time C of all the processes max For the goal, a goal model of the flexible job shop scheduling problem is established:
wherein E is ij Indicating the completion time of the j-th process of the workpiece i,n represents the number of workpieces, G i The number of steps of the workpiece i;
b, establishing a resource constraint model of the scheduling problem of the flexible job shop through the formulas (2) to (5):
S ij +(1-B i′j′p-ijp )·L≥S i′j′ +AT i′j′ (5)
wherein, the formula (2) shows that at least one piece of processable equipment is needed for any one process, the formula (3) shows that only one piece of processable equipment for any one process is needed, and the formula (4) shows that the processable equipment for any one process is from a set of selectable processable equipment; equation (5) shows that each piece of equipment can only process one process at most at the same time; x is X ijp 、U ijp And B i′j′p-ijp Are parameters each having a value of 0 or 1; x is X ijp Indicating whether the jth procedure of the workpiece i can be processed on the equipment p, wherein the energy value is 1, otherwise, the energy value is 0; u (U) ijp Indicating whether the jth procedure of the workpiece i is finally processed on the equipment p, if so, the value is 1, otherwise, the value is 0; b (B) i′j′p-ijp Indicating whether the jth process of the workpiece i is processed on the equipment p next to the jth process of the workpiece i', if so, the value is 1, otherwise, the value is 0;p.epsilon. (1, 2.. Multidot.m.), L is a constant;
and C, establishing a process constraint model of the scheduling problem of the flexible job shop through a formula (6) and a formula (7):
wherein, the formula (6) shows the number relation of the processing starting time, the processing ending time and the processing man-hour of the working procedure; the formula (7) shows the process route constraint of workpiece processing, namely that any one process needs to be finished in the previous process under the process route constraint before the processing can be started; s is S ij 、E ij And T ij Respectively representing the processing starting time, the processing ending time and the processing duration of the jth procedure of the workpiece i; s is S i(j+1) The processing start time of the (j+1) th process of the workpiece i is shown.
As an embodiment of the present invention, in step 3, the step of iteratively solving the scheduling mathematical model by using a game evolution algorithm includes:
step 3.1: population D to be used for the kth iteration k Dividing the decision-making party and the opposite party into decision-making parties and opposite parties with equal distribution of the good and bad degrees;
referring to FIG. 3, a specific partitioning strategy is: and sequencing the individuals of the population according to the sequence from small to large of the fitness value, dividing the individuals with odd numbers into decision-making parties, and dividing the individuals with even numbers into corresponding parties.
Step 3.2: performing cross operation based on game theory on the decision-making party and the opposite party according to the k-1 th iterative updated game strategy to generate offspring;
step 3.3: performing mutation operation by randomly exchanging the positions of two procedures and corresponding processing equipment in one chromosome based on the offspring generated by the cross operation;
step 3.4: combining the individuals after cross mutation into a new offspring population Q k Merging the parent population D of the previous generation k And the new generation population Q k Generating a new parent population R k ＝D k ∪Q k ；
Step 3.5: for new parent population R in order of fitness value from high to low k The individuals in the population D are sorted, and the first N individuals are selected from the sorted queue to form a new generation population D k+1 ；
Step 3.6: judging whether the iteration number k reaches the maximum iteration number, if notLet k=k+1, repeatedly execute the above steps 3.1 to 3.5 until the current iteration number reaches the maximum iteration number, and stop the current iteration number until the population D is obtained at this time k+1 And selecting an optimal solution as the optimal solution of the scheduling scheme.
It should be noted that, in this embodiment, a new individual is generated by performing a crossover operation based on the game theory, and in fact, a crossover operator based on repeated games is designed, the operator references the idea of repeated games, and the process of searching for a pairing object and generating a child from individuals in a population is regarded as a game; by gradually summarizing the gaming results of the multiple rounds, the gaming strategy is continuously updated, and a suitable matching object is selected for each individual requiring cross pairing to produce excellent offspring, so that the algorithm gradually converges.
The method comprises the steps that a population is firstly divided into decision-making parties and counter-parties based on a cross operator of repeated games, then the decision-making parties sequentially and randomly generate individuals to be paired, and the counter-parties select one individual to be paired with the individual according to the individuals generated by the decision-making parties and a game strategy and generate offspring; and when all individuals of the decision-making party are paired, evaluating the crossing result of the time, and updating the selection probability of the game strategy for the crossing operation of the next iteration by using a Bayesian formula.
In order to facilitate the progress of game strategies, the embodiment of the invention is characterized in that a decision party is equally divided into three categories of a superior individual DS, a medium individual DM and an inferior individual DI, and an individual of a counterpart party is equally divided into three categories of a superior individual AS, a medium individual AM and an inferior individual AI, referring to the description of FIG. 4; as shown in fig. 4, three types of decision-making parties and three types of corresponding parties are combined pairwise to form nine pairing types; when a decision-making party selects a superior individual as an individual to be paired, the corresponding party selects the corresponding individual according to probability to be paired with the corresponding individual; and the selection probabilities of the nine pairing types respectively meet the following conditions:
P(AS|DS)+P(AM|DS)+P(AI|DS)＝1
P(AS|DM)+P(AM|DM)+P(AI|DM)＝1
P(AS|DI)+P(AM|DI)+P(AI|DI)＝1
where P (as|ds) represents the probability that the counterpart selects the superior individual AS when the decision-maker selects the superior individual DS; p (am|ds) represents the probability that the counterpart selects the medium individual AM when the decision-maker selects the high individual DS; p (ai|ds) represents the probability that the counterpart selects a disadvantaged individual AI when the decision-maker selects a disadvantaged individual DS; p (as|dm) represents the probability that the counterpart selects a superior individual AS when the decision-maker selects a medium individual DM; p (am|dm) represents the probability that the counterpart selects the medium individual AM when the decision-maker selects the medium individual DM; p (ai|dm) represents the probability that the counterpart selects an inferior individual AI when the decision-maker selects a medium individual DM; p (as|di) represents the probability that the counterpart selects a superior individual AS when the decision-maker selects a inferior individual DI; p (am|di) represents the probability that the counterpart selects a medium individual AM when the decision-maker selects a bad individual DI; p (ai|di) represents the probability that the counterpart selects the inferior individual AI when the decision-maker selects the inferior individual DI;
in the initial stage of the algorithm, in order to not lose generality, the initial values of the selection probabilities of the nine pairing types are all set to be 1/3, so that the nine pairing types iterate at a relatively fair starting point, and gradually evolve to achieve convergence of decision probabilities.
Further, the updating of the game strategy provided in this embodiment is based on a bayesian formula, and aims to generate more expected pairing, and when a decision maker generates a chromosome to be paired, the probability of the chromosome type to be selected by the decision maker is obtained through calculation; the specific updating steps of the game strategy comprise:
step a: according to the offspring generated by the current iteration crossover operation, respectively counting the matching quantity of nine pairing types;
step b: counting the number of the corresponding expected pairing from the matching number of the nine pairing types respectively; wherein, at least one of the filial generations generated after the two chromosomes are crossed is better than the parent, and the pairing of the current crossing is called as the pairing to be performed;
the specific statistics of step a and step b are shown in table 1:
table 1 statistics of results of crossover operations
The number of C in each parameter in table 1, the first subscript indicates the type of individual selected in the decision maker, and there are S, M, I; the second subscript indicates the type of paired individual selected from the counterpart, again three S, M, I; s, M, I represents a superior individual, an intermediate individual and an inferior individual, respectively; wherein Css represents the number of pairs of the decision maker of the superior individual and the counterpart of the superior individual, C SSE The number of expected pairs among the number of pairs of the decision maker of the superior individual and the counterpart of the superior individual is represented, and the meaning of the remaining parameters is similarly described, and will not be repeated here.
Step c: based on the matching number and expected pairing of each matching type, combining the selection probability of the current iteration, respectively calculating the selection probability of the nine matching types in the next iteration by using a Bayes formula (8) -formula (16)):
wherein P (AS|DS) k And P (AS|DS) k+1 Respectively represent the probabilities of the kth and the kth+1th updates when the decision-maker selects the superior individual DS and the counterpart selects the superior individual AS; the meaning of the remaining parameters is the same and will not be described in detail here.
Further, in order to verify the effectiveness of the game evolutionary algorithm designed by the present invention in solving the scheduling problem of the flexible job shop, in this embodiment, ten test problems MK1-MK10 designed by Brandimarte (Brandimarte P. Routing and Scheduling in aFlexible Job Shop by Tabu Search [ J ]. Annals of Operations Research,1993,41 (3): 157-183 ]) are taken as cases, the verification table 2 shows detailed information of the cases, wherein nop represents the value range of the number of processes contained in each workpiece, meq represents the number of optional processing devices in each process, and proc represents the value range of the processing man-hours in each process.
TABLE 2
Adopting Visual C# programming to realize game evolutionary algorithm, running on a personal computer with a processor of i5-2400 CPU, a main frequency of 3.1GHz and a memory of 4GB, and solving the 10 cases; the maximum number of iterations of the algorithm was set to 220 by crossover experiments.
In the selection probability updating stage, the population scale of the algorithm is set to 6000, the iteration times are 20, and the initial values of the selection probabilities are equal and are 1/3; in the optimization solving stage, the population scale of the algorithm is set to 120, the iteration number is set to 200, and the experimental results after 20 continuous runs are shown in table 3; wherein, A1 is a game evolutionary algorithm provided in this embodiment; a2 is a traditional genetic algorithm; a3 is the algorithm proposed by Ho and Tay (Ho N B, tay J C. An efficient cultural algorithm for solving the flexible job-shop program. In: proceedings of 2004Congress on Evolutionary Computation,Piscataway,IEEE,2004,2:1759-1766.); a4 is an improved genetic algorithm proposed by highlighting and the like (Zhang Guohui, highlighting, li Peigen, et al. Improved genetic algorithm solves flexible job shop scheduling problem [ J ]. Mechanical engineering report, 2009 (07): 151-157); a5 is a bidirectional tabu search algorithm proposed by Brandimarte; cmax represents the optimal value calculated by the algorithm; AV (CPU) is the average run time in s for the algorithm to run 20 times in succession.
TABLE 3 Table 3
Note that: n/a indicates that the data is not provided in the literature, indicating the current optimum value
From the results shown in Table 3, it can be seen that:
(1) The game evolution algorithm provided by the invention obtains the current optimal solutions of five cases MK1, MK3, MK4, MK8 and MK 9.
(2) Because the basic information of the case has greater flexibility, for the same case, there may be a large difference in the number of procedures, the man-hours of the procedures, the optional equipment set of the procedures, and other attributes in the order generated by each operation of the algorithm.
(3) Compared with the traditional genetic algorithm (A2), the game evolution algorithm provided by the invention obtains better optimal solutions in all cases, which illustrates the superiority of the crossover operator based on repeated games in the aspect of global optimization; to more intuitively demonstrate the global search performance of both algorithms; FIG. 5 shows an iterative plot of the optimal solution obtained by solving case MK10 with a game evolutionary algorithm (A1) and a traditional genetic algorithm (A2), and as can be seen from FIG. 5, the game evolutionary algorithm has better convergence and obtains a better final solution; in the whole iteration stage, particularly in the initial stage of iteration, the optimal fitness value of the population of the game evolutionary algorithm has a larger descending speed, and the guiding effect of the game evolutionary algorithm on the evolution direction of the population is well reflected.
(4) Compared with the traditional genetic algorithm, under the condition that the algorithm parameter settings are the same, the evolution algorithm consumes more running time when solving cases; this aspect is due to the fact that traditional genetic algorithms tend to fall into early maturity, leading to premature algorithm termination conditions; on the other hand, the repeated game-based crossover operation in the game evolution algorithm has higher time complexity due to the addition of crossover evaluation, selection probability updating and other steps; however, for all cases, the running time of the multi-expenditure of the game evolution algorithm is still within an acceptable range compared with the traditional genetic algorithm; the scheduling scheme obtained by the game evolution algorithm is better, and is more beneficial to realizing the optimal configuration of resources when facing the large-scale complex scheduling problem, and the production efficiency is further improved.
Embodiment two:
as shown in fig. 6, an embodiment of the present invention provides a flexible job shop scheduling device based on a game evolution algorithm, which may be used to implement the method described in the first embodiment, where the device includes:
the building module is used for building a production scheduling mathematical model of the flexible job shop according to the acquired processing information of the flexible job shop;
the initialization module is used for generating an initialization population according to the processing information and setting related parameters for processing the scheduling problem of the flexible workshop;
and the iteration solving module is used for carrying out iteration solving on the scheduling mathematical model by utilizing a game evolution algorithm based on the initialized population and the related parameters to obtain an optimal solution of the scheduling scheme.
The flexible job shop scheduling device based on the game evolutionary algorithm provided by the embodiment of the present invention and the flexible job shop scheduling method based on the game evolutionary algorithm provided by the first embodiment of the present invention are based on the same technical concept, and can produce the beneficial effects described in the first embodiment, and the details of the descriptions in the first embodiment can be seen from the first embodiment.
Embodiment III:
the embodiment of the invention provides electronic equipment, which comprises a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is operative according to instructions to perform steps of a method according to any one of the embodiments.
Embodiment four:
an embodiment of the invention provides a computer-readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method as in any of the embodiments.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.

Claims (10)

1. A flexible job shop scheduling method based on a game evolution algorithm, the method comprising:
according to the acquired processing information of the flexible job shop, establishing a scheduling mathematical model of the flexible job shop;
generating an initialization population according to the processing information, and setting related parameters for processing flexible workshop scheduling problems;
and carrying out iterative solution on the scheduling mathematical model by utilizing a game evolution algorithm based on the initialized population and the related parameters to obtain an optimal solution of the scheduling scheme.
2. The flexible job shop scheduling method according to claim 1, wherein the processing information includes the number of workpieces, the number of processes for each workpiece, the processing time for each process, and the number of processing apparatuses.
3. The flexible job shop scheduling method according to claim 1, wherein the related parameters include initial population size, maximum number of iterations, and probability of variation.
4. A flexible job shop scheduling method based on a game evolution algorithm according to any one of claims 1 to 3, wherein building a scheduling mathematical model of the flexible job shop comprises:
to minimize the maximum completion time C of all the processes max For the goal, a goal model of the flexible job shop scheduling problem is established:
wherein E is ij Indicating the completion time of the j-th process of the workpiece i,n represents the number of workpieces, G i The number of steps of the workpiece i;
establishing a resource constraint model of the flexible job shop scheduling problem through the formulas (2) to (5):
S ij +(1-B i′j′p-ijp )·L≥S i′j′ +AT i′j′ (5)
wherein, the formula (2) shows that at least one piece of processable equipment is needed for any one process, the formula (3) shows that only one piece of processable equipment for any one process is needed, and the formula (4) shows that the processable equipment for any one process is from a set of selectable processable equipment; equation (5) shows that each piece of equipment can only process one process at most at the same time; x is X ijp 、U ijp And B i′j′p-ijp Are parameters each having a value of 0 or 1; x is X ijp Indicating whether the jth procedure of the workpiece i can be processed on the equipment p, wherein the energy value is 1, otherwise, the energy value is 0; u (U) ijp Indicating whether the jth procedure of the workpiece i is finally processed on the equipment p, if so, the value is 1, otherwise, the value is 0; b (B) i′j′p-ijp Indicating whether the jth process of the workpiece i is processed on the equipment p next to the jth process of the workpiece i', if so, the value is 1, otherwise, the value is 0;l is a constant;
establishing a process constraint model of the flexible job shop scheduling problem through a formula (6) and a formula (7):
wherein, the formula (6) shows the number relation of the processing starting time, the processing ending time and the processing man-hour of the working procedure; the formula (7) shows the process route constraint of workpiece processing, namely that any one process needs to be finished in the previous process under the process route constraint before the processing can be started; s is S ij 、E ij And T ij Respectively represent the first of the workpieces ij working procedures of processing starting time, processing ending time and processing duration; s is S i(j+1) The processing start time of the (j+1) th process of the workpiece i is shown.
5. The flexible job shop scheduling method according to claim 4, wherein the step of iteratively solving the scheduling mathematical model using the game evolution algorithm comprises:
population D to be used for the kth iteration k Dividing the decision-making party and the opposite party into decision-making parties and opposite parties with equal distribution of the good and bad degrees;
performing cross operation based on game theory on the decision-making party and the opposite party according to the k-1 th iterative updated game strategy to generate offspring;
performing mutation operation by randomly exchanging the positions of two procedures and corresponding processing equipment in one chromosome based on the offspring generated by the cross operation;
combining the individuals after cross mutation into a new offspring population Q k Merging the parent population D of the previous generation k And the new generation population Q k Generating a new parent population R k ＝D k ∪Q k ；
For new parent population R in order of fitness value from high to low k The individuals in the population D are sorted, and the first N individuals are selected from the sorted queue to form a new generation population D k+1 ；
Judging whether the iteration number k reaches the maximum iteration number, if not, enabling k=k+1, repeatedly executing the steps until the current iteration number reaches the maximum iteration number, stopping, and obtaining a population D at the moment k+1 And selecting an optimal solution as the optimal solution of the scheduling scheme.
6. The flexible job shop scheduling method based on the game evolution algorithm according to claim 5, wherein the game strategy is used for the counter party to select the corresponding matched individuals according to the selection probability of the current individuals when the decision party generates an individual to be matched; the selection probability specifically comprises:
equally dividing a decision party into three categories of a superior individual DS, a medium individual DM and an inferior individual DI, equally dividing an individual of a counterpart party into three categories of a superior individual AS, a medium individual AM and an inferior individual AI, and respectively meeting the selection probabilities of nine pairing types:
P(AS|DS)+P(AM|DS)+P(AI|DS)＝1
P(AS|DM)+P(AM|DM)+P(AI|DM)＝1
P(AS|DI)+P(AM|DI)+P(AI|DI)＝1
where P (as|ds) represents the probability that the counterpart selects the superior individual AS when the decision-maker selects the superior individual DS; p (am|ds) represents the probability that the counterpart selects the medium individual AM when the decision-maker selects the high individual DS; p (ai|ds) represents the probability that the counterpart selects a disadvantaged individual AI when the decision-maker selects a disadvantaged individual DS; p (as|dm) represents the probability that the counterpart selects a superior individual AS when the decision-maker selects a medium individual DM; p (am|dm) represents the probability that the counterpart selects the medium individual AM when the decision-maker selects the medium individual DM; p (ai|dm) represents the probability that the counterpart selects an inferior individual AI when the decision-maker selects a medium individual DM; p (as|di) represents the probability that the counterpart selects a superior individual AS when the decision-maker selects a inferior individual DI; p (am|di) represents the probability that the counterpart selects a medium individual AM when the decision-maker selects a bad individual DI; p (ai|di) represents the probability that the counterpart selects the inferior individual AI when the decision-maker selects the inferior individual DI;
the initial values of the selection probabilities of the nine pairing types are all set to be 1/3, and the selection probabilities gradually evolve to be converged after repeated iterative updating.
7. The flexible job shop scheduling method based on the game evolution algorithm according to claim 6, wherein the updating step of the game strategy comprises:
according to the offspring generated by the current iteration crossover operation, respectively counting the matching quantity of nine pairing types;
counting the number of the corresponding expected pairing from the matching number of the nine pairing types respectively; wherein, at least one of the filial generations generated after the two chromosomes are crossed is better than the parent, and the pairing of the current crossing is called as the pairing to be performed;
based on the matching number and the expected pairing of each matching type, combining the selection probability of the current iteration, and respectively calculating and updating the selection probability of nine matching types in the next iteration by using a Bayesian formula.
8. A flexible job shop scheduling device based on a game evolution algorithm, the device comprising:
the building module is used for building a production scheduling mathematical model of the flexible job shop according to the acquired processing information of the flexible job shop;
the initialization module is used for generating an initialization population according to the processing information and setting related parameters for processing the scheduling problem of the flexible workshop;
and the iteration solving module is used for carrying out iteration solving on the scheduling mathematical model by utilizing a game evolution algorithm based on the initialized population and the related parameters to obtain an optimal solution of the scheduling scheme.
9. An electronic device, comprising a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is operative according to the instructions to perform the steps of the flexible job shop scheduling method based on a game evolution algorithm according to any one of claims 1 to 7.
10. A computer readable storage medium having stored thereon a computer program, which when executed by a processor, implements the steps of a flexible job shop scheduling method based on a game evolution algorithm according to any one of claims 1 to 7.
CN202310713198.7A 2023-06-15 2023-06-15 Flexible job shop scheduling method and device based on game evolution algorithm, electronic equipment and medium Pending CN116523266A (en)

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