CN109784604A - A kind of flexible job shop manufacturing recourses distribution method based on whale algorithm - Google Patents
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Abstract
The flexible job shop manufacturing recourses distribution method based on whale algorithm that the invention discloses a kind of, workshop manufacturing recourses assignment problem model is constructed first: including the description of workshop manufacturing recourses assignment problem, model hypothesis, then it establishes the mapping relations between the objective function of workshop manufacturing recourses assignment problem and whale algorithm fitness value function, i.e., objective function is generated to the original allocation disaggregation of workshop manufacturing recourses directly as fitness function and at random；The fitness function that distribution solution concentrates all individuals is calculated, finds and saves optimal solution S*；Directly using distribution disaggregation as the initial population of whale algorithm, keeping optimization S*Whale individual X corresponding with its*, and to the parameter initialization of whale algorithm；Judge whether the termination condition for meeting algorithm, finally exports optimal solution S*And its corresponding fitness function E, the present invention solve the problems, such as that flexible job shop manufacturing recourses existing in the prior art are difficult to reasonable distribution.
Description
Technical field
The invention belongs to job scheduling technical fields, and in particular to a kind of flexible job shop manufacture based on whale algorithm
Resource allocation methods.
Background technique
On current Flexible Job-shop Scheduling Problems, seldom consider in most products manufacture, technique process is all
Fixed situation, and reasonable distribution manufacturing recourses, make the lowest cost be only the final goal of enterprise, and present manufacturing industry is compeled
Need to solve job shop manufacturing recourses assignment problem with cutting, so as to preferably Instructing manufacture.
Summary of the invention
The flexible job shop manufacturing recourses distribution method based on whale algorithm that the object of the present invention is to provide a kind of solves
The problem of flexible job shop manufacturing recourses existing in the prior art are difficult to reasonable distribution.
The technical scheme adopted by the invention is that a kind of flexible job shop manufacturing recourses distribution side based on whale algorithm
Method is specifically implemented according to lower step:
Step 1, building workshop manufacturing recourses assignment problem model: including the description of workshop manufacturing recourses assignment problem, model
Assuming that；
Step 2 defines fitness function: the objective function and whale algorithm for establishing workshop manufacturing recourses assignment problem adapt to
Mapping relations between angle value function, i.e., by objective function directly as fitness function；
Step 3, the random original allocation disaggregation for generating workshop manufacturing recourses；
Step 4 calculates the fitness function that distribution solution concentrates all individuals, finds and saves optimal solution S*；
Step 5 will directly distribute disaggregation as the initial population of whale algorithm, keeping optimization S*Whale corresponding with its
Individual X*, and to the parameter initialization of whale algorithm；
Step 6 judges whether the termination condition for meeting algorithm, if not satisfied, with whale algorithm to all population at individual into
Row iteration updates, and by updated whale population by taking positive mode to be converted to distribution disaggregation, then executes step 4；
If satisfied, thening follow the steps 7；
Step 7, output optimal solution S*And its corresponding fitness function E.
The features of the present invention also characterized in that
Workshop manufacturing recourses assignment problem describes specific as follows in step 1:
Assuming that there is M platform equipment in workshop, every equipment is Mm, m=1,2..., M have P class product to need to process, every class product
PiDemand be Di, i=1,2..., P, product PiIt is needed altogether by niProcedure, i=1,2 ..., P, the per pass work of product
Sequence OijIt can be processed in one in more different equipment, wherein i=1,2 ..., P；J=1,2 ..., ni, resource allocation
Purpose be process meet resource capability constraint etc. constraint conditions under the premise of, with equipment processing cost and external coordination cost
Totle drilling cost is minimised as target, determines output, every class product every procedure of every every procedure of class product in every equipment
External coordination amount and every procedure process equipment.
Model hypothesis is specific as follows in step 1:
The demand of each product is not constrained successively between the process of different product it is known that the process sequence of each product determines；
Equipment can process working procedures, and distinct device processes time and the cost difference of certain process；
Every procedure can make by oneself or external coordination, and there is no dragging phase and inventory, makes by oneself and the common meet demand of external coordination
Amount.
Model construction is specific as follows in step 1:
Step 1.1, defined parameters variable:
OijmWhether operated on equipment m for the process j of product i；XijmFor production of the process j on equipment m of product i
Amount；SijFor the quantity of the process j external coordination of product i；
P is planned production product category sum；M is the available equipment sum in workshop；niFor total process number of product i；iDi
For the demand of product i；The required time is processed on equipment m for the process j of product i；aijmExist for the process j of product i
The long-run cost rate processed on equipment m；δijFor the unit external coordination cost of the process j of product i；For the work energy of equipment m
Power.
Fitness function is specific as follows in step 2:
Mould is distributed it is assumed that constructing following job shop manufacturing recourses according to the description and Model Condition in the step 1
Type fitness function:
The target of the model is the processing capacity and external coordination amount when determining to produce certain demand product in every equipment, so that
The sum of the equipment processing cost and external coordination cost that are related in production process minimum, wherein formula (2-1) is indicated with totle drilling cost
Minimum objective function, totle drilling cost are equal to the sum of processing cost and external coordination cost of equipment, and formula (2-2) to formula (2-3) is
The constraint condition of model, wherein formula (2-2) indicate for each procedure workshop self-control output and external coordination amount it
It is constrained with the numerical value that need to meet product consumption；Formula (2-3) indicates that in process of production all quantity for being related to product is i.e. certainly
Plan variable is the numerical value constraint of positive integer；Formula (2-4) indicates always to process each equipment within the production and processing period
Time is no more than the manufacturing resource capability constraint of given net cycle time；
A vector for collectively constituting all decision variable, that is, outputs and external coordination amount in step 4 is as a whale
The position vector X of body, random initializtion whale body position, is randomly formed in the value range that output meets constraint condition
Whale population generates one group of Resource Allocation Formula at random under the conditions of meeting constraint function, including number of groups N, maximum change
Generation number M, logarithmic spiral shape constant b, current iteration number t and algorithm termination condition, specific as follows:
The target function value that each distribution solution is calculated using the fitness function of formula (2-1), is as corresponded to each initial
The fitness value of whale individual finds and saves the whale individual X of optimal adaptation angle value in current whale population*(t) and its it is right
The optimum allocation solution S answered*。
Whale population number is set as 40.
Step 6 is specific as follows:
Step 6.1, hypothesis algorithm termination condition are t >=M, if not satisfied, t=t+1 is then enabled to execute step 6.2；If meeting
Then follow the steps 7；
Step 6.2 will directly distribute disaggregation as whale population at individual, be solved using whale algorithm, specific as follows:
Step 6.2.1, whale random search iterative formula is executed, i.e., A, C is coefficient vector, and value range is [0,1], is iterated update to whale population at individual,
By updated whale population by taking positive mode to be converted to distribution disaggregation, step 4 is then executed；
Step 6.2.2, it is no to judge that A > 1 is set up, executes step 6.2.1 if setting up and going to；It is invalid, judge p < 0.5
Set up it is no, if set up, go to execute step 6.2.3, it is invalid, go to execute step 6.2.4,
Step 6.2.3, whale is executed around predation formula: i.e.To whale population at individual
It is iterated update, by updated whale population by taking positive mode to be converted to distribution disaggregation, then executes step
4；
Step 6.2.4, it executes whale foam screen and attacks formula:Its
In,Update is iterated to whale population at individual, by updated whale population by taking just
Mode be converted to distribution disaggregation, then execute step 4.
The invention has the advantages that a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm, i.e.,
One by one by the whale individual position vector in decision variable and whale algorithm required in job shop manufacturing recourses assignment problem
It is mapped, due to the uniqueness of whale algorithm, it can be directly by whale body position and discrete workshop manufacturing recourses point
It is mapped with problem, a kind of method for devising initialization population, it is ensured that the quality and diversity of population do not need it
His shifts to new management mechanisms.Whale algorithm bionic be whale predation mechanism, this algorithm logic is succinct, thus ensure that solution knot
The validity of fruit, and significant the solving speed for improving algorithm and solving job shop manufacturing recourses assignment problem.
Detailed description of the invention
Fig. 1 is that respectively generation adapts to embodiment 2 in a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm
Spend optimal value convergence curve figure.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The present invention a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm, specifically according to lower step
Implement:
Step 1, building workshop manufacturing recourses assignment problem model: including the description of workshop manufacturing recourses assignment problem, model
Assuming that, wherein workshop manufacturing recourses assignment problem describes specific as follows:
Assuming that there is M platform equipment in workshop, every equipment is Mm, m=1,2..., M have P class product to need to process, every class product
PiDemand be Di, i=1,2..., P, product PiIt is needed altogether by niProcedure, i=1,2 ..., P, the per pass work of product
Sequence OijIt can be processed in one in more different equipment, wherein i=1,2 ..., P；J=1,2 ..., ni, resource allocation
Purpose be process meet resource capability constraint etc. constraint conditions under the premise of, it is total with equipment processing cost and external coordination cost
Cost minimization turns to target, determines output of every every procedure of class product in every equipment, every every procedure of class product
The process equipment of external coordination amount and every procedure；
Model hypothesis is specific as follows:
The demand of each product is not constrained successively between the process of different product it is known that the process sequence of each product determines；
Equipment can process working procedures, and distinct device processes time and the cost difference of certain process；
Every procedure can make by oneself or external coordination, and there is no dragging phase and inventory, makes by oneself and the common meet demand of external coordination
Amount；
Model construction is specific as follows:
Step 1.1, defined parameters variable:
OijmWhether operated on equipment m for the process j of product i；XijmFor production of the process j on equipment m of product i
Amount；SijFor the quantity of the process j external coordination of product i；
P is planned production product category sum；M is the available equipment sum in workshop；niFor total process number of product i；iDi
For the demand of product i；The required time is processed on equipment m for the process j of product i；aijmExist for the process j of product i
The long-run cost rate processed on equipment m；δijFor the unit external coordination cost of the process j of product i；For the work energy of equipment m
Power；
Step 2 defines fitness function: the objective function and whale algorithm for establishing workshop manufacturing recourses assignment problem adapt to
Mapping relations between angle value function, i.e., specific as follows by objective function directly as fitness function:
Mould is distributed it is assumed that constructing following job shop manufacturing recourses according to the description and Model Condition in the step 1
Type fitness function:
The target of the model is the processing capacity and external coordination amount when determining to produce certain demand product in every equipment, so that
The sum of the equipment processing cost and external coordination cost that are related in production process minimum, wherein formula (2-1) is indicated with totle drilling cost
Minimum objective function, totle drilling cost are equal to the sum of processing cost and external coordination cost of equipment, and formula (2-2) to formula (2-3) is
The constraint condition of model, wherein formula (2-2) indicate for each procedure workshop self-control output and external coordination amount it
It is constrained with the numerical value that need to meet product consumption；Formula (2-3) indicates that in process of production all quantity for being related to product is i.e. certainly
Plan variable is the numerical value constraint of positive integer；Formula (2-4) indicates always to process each equipment within the production and processing period
Time is no more than the manufacturing resource capability constraint of given net cycle time；
Step 3, the random original allocation disaggregation for generating workshop manufacturing recourses；
Step 4 calculates the fitness function that distribution solution concentrates all individuals, finds and saves optimal solution S*, wherein by institute
Position vector X of the vector for thering is decision variable i.e. output and external coordination amount to collectively constitute as a whale individual, in life
Yield meets random initializtion whale body position in the value range of constraint condition, is randomly formed whale population, that is, is meeting
One group of Resource Allocation Formula, including number of groups N, maximum number of iterations M, logarithmic spiral shape are generated under the conditions of constraint function at random
Shape constant b, current iteration number t and algorithm termination condition, specific as follows:
The target function value that each distribution solution is calculated using the fitness function of formula (2-1), is as corresponded to each initial
The fitness value of whale individual finds and saves the whale individual X of optimal adaptation angle value in current whale population*(t) and its it is right
The optimum allocation solution S answered*；
Whale population number is set as 40；
Step 5 will directly distribute disaggregation as the initial population of whale algorithm, keeping optimization S*Whale corresponding with its
Individual X*, and to the parameter initialization of whale algorithm；
Step 6 judges whether the termination condition for meeting algorithm, if not satisfied, with whale algorithm to all population at individual into
Row iteration updates, and by updated whale population by taking positive mode to be converted to distribution disaggregation, then executes step 4；
If satisfied, 7 are thened follow the steps, it is specific as follows:
Step 6.1, hypothesis algorithm termination condition are t >=M, if not satisfied, t=t+1 is then enabled to execute step 6.2；If meeting
Then follow the steps 7；
Step 6.2 will directly distribute disaggregation as whale population at individual, be solved using whale algorithm, specific as follows:
Step 6.2.1, whale random search iterative formula is executed, i.e., A, C is coefficient vector, and value range is [0,1], is iterated update to whale population at individual,
By updated whale population by taking positive mode to be converted to distribution disaggregation, step 4 is then executed；
Step 6.2.2, it is no to judge that A > 1 is set up, executes step 6.2.1 if setting up and going to；It is invalid, judge p < 0.5
Set up it is no, if set up, go to execute step 6.2.3, it is invalid, go to execute step 6.2.4,
Step 6.2.3, whale is executed around predation formula: i.e.To whale population at individual
It is iterated update, by updated whale population by taking positive mode to be converted to distribution disaggregation, then executes step
4；
Step 6.2.4, it executes whale foam screen and attacks formula:Its
In,Update is iterated to whale population at individual, by updated whale population by taking just
Mode be converted to distribution disaggregation, then execute step 4；
Step 7, output optimal solution S*And its corresponding fitness function E.
The present invention a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm, according to the whale constructed
Fish algorithm solves the model of workshop manufacturing recourses assignment problem, now with the distribution of the job shop manufacturing recourses of certain machining enterprise
For problem, the practicability and validity of model and algorithm are verified, and is the job shop manufacturing recourses of the machining enterprise point
Optimal allocation plan is provided with problem:
1. initial data is as follows:
Certain machining enterprise now needs to process P1, P2, P3, P4 class product within the production cycle, and every class product corresponds to specific
Manufacturing procedure.In the production cycle, the demand and relevant cost parameter of product are as shown in table 1 below.The Operation Van of the enterprise
Between existing 10 production equipments, wherein M1-M3For special equipment, a small number of specific processes can be processed；M4-M10For common apparatus,
It can be processed a variety of different processes, but its processing efficiency difference.Every equipment corresponds to the process time of different processes, processing
The working ability of cost and every equipment is as shown in table 2 below:
1 product consumption of table, unit external coordination cost parameter
2 equipment process time of table, processing cost and working ability parameter
2. calculated result is as follows:
After the algorithm routine of the corresponding parameters input programming of model, the convergence for obtaining each generation fitness optimal value is bent
Line is as shown in Figure 1.The running environment of algorithm is 7 Ultimate of Window, 64 bit manipulation system, AMD E1-1200APU with
Software is realized in the programming of Radeon (tm) HD Graphics 1.40GHz processor, the installation memory (RAM) of 4.00GB, algorithm
For MATLAB R2016a.As seen from Figure 1, curve finally tends to restrain, it is obtained in convergence state in the production cycle
Interior, the optimal case of workshop manufacturing recourses assignment problem is as shown in table 3.
When the manufacturing shop of the enterprise produces four kinds of products, i.e., P1, P2, P3, P4 when, iteration updates 500 times each
For adaptive optimal control degree function convergence curve as shown in Figure 1, the optimal case of its corresponding workshop manufacturing recourses assignment problem such as
Shown in the following table 3:
3 workshop manufacturing recourses allocation plan of table
It is solved in the workshop manufacturing recourses allocation plan obtained above-mentioned according to algorithm, the value of all parameters is big
In the natural number for being equal to 0；And for every procedure of each workpiece, meet equation Qij+SiJ=Di；It is set for each
For standby, meet inequality:
Analyze case calculated result, it was demonstrated that whale algorithm is solving the superiority in workshop manufacturing recourses assignment problem:
It can be seen that the resource of WOA optimization distribution for the manufacturing recourses that example allocation processes four ten procedures of workpiece
Scheme is as shown in table 4, according to convergence figure it is found that the time used in iteration 500 times be 48.522s, algorithm at the 327th time more
Optimal value, optimal value 2906 are obtained when new.
All be by the target function value image that algorithm known to convergence curve is formed it is convergent, finally tend towards stability, stabilization
In optimal value, i.e., the smallest totle drilling cost.Although piece count increases from the point of view of Practical Project verification result, operation quantity increases,
Individual vector dimension increases, and with 110 dimensions that the dimension of problem to be optimized increases to four workpiece from the 55 of two workpiece, solves
Difficulty increases with it, but WOA algorithm has good exploitation and exploration ability, obtains preferable effect of optimization, restrains
Speed is fast, and convergence precision is high.
From allocation plan as can be seen that production is mainly undertaken by self-control, this is because this solution only considered equipment and add
Work cost and external coordination cost, and homemade cost is lower than the cost of external coordination, therefore the allocation plan after optimization can be by big portion
Point even all of output is placed on equipment self part, and is actually consistent.
Claims (8)
1. a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm, which is characterized in that specifically according to lower step
It is rapid to implement:
Step 1, building workshop manufacturing recourses assignment problem model: including the description of workshop manufacturing recourses assignment problem, model hypothesis；
Step 2 defines fitness function: establishing the objective function and whale algorithm fitness value of workshop manufacturing recourses assignment problem
Mapping relations between function, i.e., by objective function directly as fitness function；
Step 3, the random original allocation disaggregation for generating workshop manufacturing recourses；
Step 4 calculates the fitness function that distribution solution concentrates all individuals, finds and saves optimal solution S*；
Step 5 will directly distribute disaggregation as the initial population of whale algorithm, keeping optimization S*Whale individual corresponding with its
X*, and to the parameter initialization of whale algorithm；
Step 6 judges whether the termination condition for meeting algorithm, if not satisfied, being changed with whale algorithm to all population at individual
In generation, updates, and by updated whale population by taking positive mode to be converted to distribution disaggregation, then executes step 4；If full
Foot, thens follow the steps 7；
Step 7, output optimal solution S*And its corresponding fitness function E.
2. a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm according to claim 1, special
Sign is that workshop manufacturing recourses assignment problem describes specific as follows in the step 1:
Assuming that there is M platform equipment in workshop, every equipment is Mm, m=1,2..., M have P class product to need to process, every class product Pi's
Demand is Di, i=1,2..., P, product PiIt is needed altogether by niProcedure, i=1,2 ..., P, every procedure O of productijEnergy
An enough processing in more different equipment, wherein i=1,2 ..., P；J=1,2 ..., ni, the purpose of resource allocation is
Under the premise of process meets the constraint conditions such as resource capability constraint, most with equipment processing cost and external coordination cost totle drilling cost
It is small to turn to target, determine the external coordination amount of output of every every procedure of class product in every equipment, every every procedure of class product
And the process equipment of every procedure.
3. a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm according to claim 2, special
Sign is that model hypothesis is specific as follows in the step 1:
The demand of each product is not constrained successively between the process of different product it is known that the process sequence of each product determines；
Equipment can process working procedures, and distinct device processes time and the cost difference of certain process；
Every procedure can make by oneself or external coordination, and there is no dragging phase and inventory, makes by oneself and the common meet demand amount of external coordination.
4. a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm according to claim 3, special
Sign is that model construction is specific as follows in the step 1:
Step 1.1, defined parameters variable:
OijmWhether operated on equipment m for the process j of product i；XijmFor output of the process j on equipment m of product i；Sij
For the quantity of the process j external coordination of product i；
P is planned production product category sum；M is the available equipment sum in workshop；niFor total process number of product i；iDiTo produce
The demand of product i；The required time is processed on equipment m for the process j of product i；aijmIt is being set for the process j of product i
The long-run cost rate processed on standby m；δijFor the unit external coordination cost of the process j of product i；For the ability to work of equipment m.
5. a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm according to claim 4, special
Sign is that fitness function is specific as follows in the step 2:
It is fitted according to the description and Model Condition in the step 1 it is assumed that constructing following job shop manufacturing recourses distribution model
Response function:
XijmSij>=0 and be integer
The target of the model is the processing capacity and external coordination amount when determining to produce certain demand product in every equipment, so that production
The sum of the equipment processing cost and external coordination cost that are related in the process minimum, wherein formula (2-1) is indicated with totle drilling cost minimum
For objective function, totle drilling cost is equal to the sum of processing cost and external coordination cost of equipment, and formula (2-2) to formula (2-3) is model
Constraint condition, wherein formula (2-2) indicate for each procedure workshop self-control the sum of output and external coordination amount need to expire
The numerical value of sufficient product consumption constrains；Formula (2-3) indicate in process of production, all quantity for being related to product i.e. decision variable
It is the numerical value constraint of positive integer；Formula (2-4) indicates for each equipment, and total elapsed time is not within the production and processing period
Manufacturing resource capability more than given net cycle time constrains；
6. a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm according to claim 5, special
Sign is that a vector for collectively constituting all decision variable, that is, outputs and external coordination amount in the step 4 is as a whale
The position vector X of fish individual, the random initializtion whale body position in the value range that output meets constraint condition, at random
Whale population is formed, i.e., generates one group of Resource Allocation Formula, including number of groups N at random under the conditions of meeting constraint function, most
Big the number of iterations M, logarithmic spiral shape constant b, current iteration number t and algorithm termination condition, specific as follows:
The target function value that each distribution solution is calculated using the fitness function of formula (2-1), as corresponds to each initial whale
The fitness value of individual, finds and saves the whale individual X of optimal adaptation angle value in current whale population*(t) and its it is corresponding
Optimum allocation solution S*。
7. a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm according to claim 6, special
Sign is that the whale population number is set as 40.
8. a kind of flexible job shop manufacturing recourses distribution method based on whale algorithm according to claim 7, special
Sign is that the step 6 is specific as follows:
Step 6.1, hypothesis algorithm termination condition are t >=M, if not satisfied, t=t+1 is then enabled to execute step 6.2；It is held if meeting
Row step 7；
Step 6.2 will directly distribute disaggregation as whale population at individual, be solved using whale algorithm, specific as follows:
Step 6.2.1, whale random search iterative formula is executed, i.e.,
A, C is coefficient vector, and value range is [0,1], update is iterated to whale population at individual, by updated whale kind
Then group executes step 4 by taking positive mode to be converted to distribution disaggregation；
Step 6.2.2, it is no to judge that A > 1 is set up, executes step 6.2.1 if setting up and going to；It is invalid, judge that p < 0.5 is set up
It is no, if set up, goes to and execute step 6.2.3, it is invalid, it goes to and executes step 6.2.4,
Step 6.2.3, whale is executed around predation formula: i.e.Whale population at individual is carried out
Iteration updates, and by updated whale population by taking positive mode to be converted to distribution disaggregation, then executes step 4；
Step 6.2.4, it executes whale foam screen and attacks formula:
Wherein,Whale population at individual is carried out
Iteration updates, and by updated whale population by taking positive mode to be converted to distribution disaggregation, then executes step 4.
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| CN112783172A (en) * | 2020-12-31 | 2021-05-11 | 重庆大学 | AGV and machine integrated scheduling method based on discrete whale optimization algorithm |
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| CN110531716A (en) * | 2019-08-12 | 2019-12-03 | 陕西科技大学 | The method for solving low-carbon Job-Shop problem based on discrete whale algorithm |
| CN112070418A (en) * | 2020-09-21 | 2020-12-11 | 大连大学 | Weapon target allocation method of multi-target whale optimization algorithm |
| CN112163808A (en) * | 2020-09-23 | 2021-01-01 | 贵州工程应用技术学院 | Method for solving logistics center addressing problem by self-adaptive whale algorithm based on opponent learning |
| CN112163808B (en) * | 2020-09-23 | 2022-04-01 | 贵州工程应用技术学院 | Method for solving logistics center addressing problem by self-adaptive whale algorithm based on opponent learning |
| CN112783172A (en) * | 2020-12-31 | 2021-05-11 | 重庆大学 | AGV and machine integrated scheduling method based on discrete whale optimization algorithm |
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