CN108596403A - A kind of modeling of workshop multirow layout and method for solving - Google Patents
A kind of modeling of workshop multirow layout and method for solving Download PDFInfo
- Publication number
- CN108596403A CN108596403A CN201810438932.2A CN201810438932A CN108596403A CN 108596403 A CN108596403 A CN 108596403A CN 201810438932 A CN201810438932 A CN 201810438932A CN 108596403 A CN108596403 A CN 108596403A
- Authority
- CN
- China
- Prior art keywords
- functional areas
- formula
- layout
- workshop
- spacing
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
- G06Q10/043—Optimisation of two dimensional placement, e.g. cutting of clothes or wood
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/12—Computing arrangements based on biological models using genetic models
- G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Business, Economics & Management (AREA)
- Biophysics (AREA)
- Life Sciences & Earth Sciences (AREA)
- Health & Medical Sciences (AREA)
- Human Resources & Organizations (AREA)
- General Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Data Mining & Analysis (AREA)
- Evolutionary Biology (AREA)
- Bioinformatics & Computational Biology (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Software Systems (AREA)
- Mathematical Physics (AREA)
- Strategic Management (AREA)
- Computing Systems (AREA)
- Artificial Intelligence (AREA)
- Biomedical Technology (AREA)
- Economics (AREA)
- Computational Linguistics (AREA)
- Molecular Biology (AREA)
- Evolutionary Computation (AREA)
- General Health & Medical Sciences (AREA)
- Quality & Reliability (AREA)
- Game Theory and Decision Science (AREA)
- Development Economics (AREA)
- Entrepreneurship & Innovation (AREA)
- Marketing (AREA)
- General Business, Economics & Management (AREA)
- Operations Research (AREA)
- Tourism & Hospitality (AREA)
- Physiology (AREA)
- Genetics & Genomics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a kind of modeling of workshop multirow layout and method for solving, for workshop total arrangement problem, consider more restraint conditions, establishes the mathematical models for meeting practical layout situation, and solution is optimized using the genetic algorithm based on mixed coding technology.It is primarily based on the mixed-integer programming model of multirow layout, the actual features such as channel, spacing and vertical and horizontal placement is converted to constraints, builds mathematical models；Secondly mixed coding technology is used, is laid out using system method for arranging in the initial population of the embedded improved adaptive GA-IAGA of solution, rational parameter setting is carried out and selects suitable operation strategy, avoids algorithm from being absorbed in locally optimal solution, improves search capability and efficiency；Finally after iteration optimizing, more satisfied optimal location solution is obtained.The present invention be can get more ideal and more meet the actual workshop total arrangement of engineering by building accurate model and method for solving.
Description
Technical field
The present invention relates to plant layout's modeling and optimization field, the modeling of especially a kind of workshop multirow layout and solution side
Method.
Background technology
Plant layout's problem refers to that workshop appliance, road and other facilities etc. are laid out object in workshop space
Reasonable Arrangement is carried out as requested.Manufacture system enterprise produces in product, and the time of normal conditions 80% to 90% is in logistics
It carries and waits for, so select suitable layout designs target, plant layout is carried out according to relevant constraint and principle, it can be with
It reduces and carries logistics time and total flow amount, improve material circulation efficiency, logistics cost is made to decline 10% to 30%, for this purpose,
One good plant layout is particularly important for manufacturing enterprise.
In terms of plant layout's mathematical model, a large amount of scholar is studied, Literature [Kaku B K,
Thompson G L.An Exact Algorithm for the General Quadratic Assignment Problem
[J].European Journal of Operational Research,1986,23(3):382-390.] use for the first time it is mixed
It closes integer model (Mix Integer Programming, MIP) and handles layout of workshop facilities's problem.Plant layout's problem is in quilt
Simplify after taking out mathematical model, is still proved to belong to np hard problem, the problem generally use heuritic approach is to obtain at present
The approximate solution of dispersed problem is also such in plant layout's problem.Such as document [Haktanirlar Ulutas B,
Kulturel-Konak S.An artificial immune system based algorithm to solve unequal
area facility layout problem[J].Expert Systems with Applications,2012,39(5):
5384-5395.] based on artificial immune system solution unequal-area facility layout.
When establishing plant layout's mathematical model, usually model is simplified so as to optimizing, excessively simplified model is close
It is not high like spending, often cause between mathematical model and actual physics model that there are king-sized differences, for example, not considering unequal-side
The transverse and longitudinal of product facility layout place problem, it is interregional away from the practical site problems such as major trunk roads, what this to obtain after optimization
It is far often to deviate optimal solution after corresponding layout constraint is added for approximate solution.
Invention content
Technical problem to be solved by the invention is to provide a kind of modeling of workshop multirow layout and method for solving, consider more
Multiple constraint establishes the accurate workshop total arrangement mathematical model for more meeting produce reality, while being based on genetic algorithm, using mixing
Coding techniques is laid out in the initial population of the embedded improved adaptive GA-IAGA of solution using system method for arranging, carries out rational parameter and set
Suitable operation strategy is set and selected, search capability and efficiency are improved, realizes the solution of accurate placement model.
In order to solve the above technical problems, the technical solution adopted by the present invention is：
A kind of modeling of workshop multirow layout and method for solving, include the following steps：
Step 1：The workshop total arrangement modeling of MIP models based on multirow layout
Using three-layer type layout method, multiple constraint and rule of the third layout layer according to scene, structure majorized function is simultaneously
It solves, object function is：
In formula：fijFor the carrying frequency of functional areas i to functional areas j, cijFor functional areas i to functional areas j unit carry at
This, αi、βiIt is the x and y coordinates of the functional areas i centre of moments, αj、βjIt is the x and y coordinates of the functional areas j centre of moments；
Step 2：It is solved using the genetic algorithm based on mixed coding technology, specially：
1) chromosome coding is carried out
Gene code mode is put in order by functional areas, spacing, 3 parts of placement are constituted anyhow, and uses mixed coding
Use integer coding, spacing that real coding, vertical and horizontal place is used to use binary encoding when structure, i.e. functional areas sort；
2) initial population is generated
The section layout scheme that initial population is obtained by system arrangement, along with random population is constituted；
3) it evaluates population, carry out selection operation；
4) crossover operation
Functional areas sequence layer is integer coding, using partial mapped crossover；Spacing layer is real coding, is handed over using counting
Fork；It is binary coding that layer, which is arranged, in functional areas anyhow, using two-point crossover；
5) mutation operation
Gene section selection basic bit mutation operator is arranged in functional areas anyhow；Functional areas sequence gene section, which then selects to reverse, to make a variation
Operator, i.e., randomly generate position at 2 in gene section, then this genic value at 2 on position is interchangeable；Spacing uses
Real coding finds change point according to mutation probability first, in [Wmin,Wmax] section randomly generates k functional areas distance values, and
The distance values for replacing change point respectively calculate the fitness value of these chromosomes, use fitness to obtain k chromosome
Highest distance values replace original distance values；
6) it evolves and terminates
The maximum evolution iterations for reaching setting then terminate iteration；
7) decoding output optimal location solution.
Further, in the workshop total arrangement mathematical models that step 1 is established, constraints is：
Wi l≤Yi″-Yi′≤Wi u, Yi', Yi″≥0 (3)
(Xi″-Xi′)(Yi″-Yi')=Ai (4)
0≤Xi′≤Xi″≤Bx (5)
0≤Yi′≤Yi″≤By (6)
αi=0.5Xi′+0.5Xi″ αi≥0 (7)
βi=0.5Yi′+0.5Yi″ βi≥0 (8)
Xi″,Xi′≥Tj1 or Xi″,Xi′≤Tj2 (9)
Li=1 or 0 (14)
In formula：For the length limit and lower limit of functional areas i,It is the width upper and lower bound of functional areas i,
Xi′、Xi" it is respectively the x coordinate of functional areas the right and left, Yi′、Yi" y-coordinate of the functional areas tops i and bottom edge, Bx、ByRefer to workshop
Length, A are measured along x, y-axisiFor the area of functional areas i, αi、βiIt is the x and y coordinates of the functional areas i centre of moments, M is penalty function, Tj1、
Tj2The left and right coordinate of respectively vertical major trunk roads x-axis, decision variableIndicate that functional areas i is strictly limited at the right side of functional areas j
Side, otherwiseDecision variableFunctional areas i is strictly limited at the top of functional areas j, otherwiseSijFor function
Spacing between area；Minimum safe spacing between functional areas；Decision variable Li=1 expression functional areas i is placed vertically, Li
=0 indicates that functional areas i is laterally disposed；
Constraint formula (2) and (3) are respectively used to ensure that the long wide direction of each functional areas does not exceed specified range, formula (4)
The nonlinear restriction relationship between each functional areas coordinate points and area is expressed, formula (5) and formula (6) limit each function position
In in workshop, x, the y-coordinate of formula (7) and the specified functional areas centre of moment of formula (8), formula (9) assurance function area layout avoid vertical trunk
Road；Constraint formula (10) showsWhen, Xj″≤Xi', i.e., functional areas i must be necessarily arranged at the right of proximity association functional areas j, formula
(11) it is for the constraint of the proximity association functional areas in the directions y, formula (12) avoids any two functional areas on the direction x, y
Interference, formula (13) ensure that the spacing between minimum functional areas, formula (14) indicate that functional areas can be anyhow to placement.
Further, in evaluating population process, fitness function therein is designed using penalty function method.
Further, when carrying out selection operation, the mode for choosing wheel disc stake alternatively operates.
Compared with prior art, the beneficial effects of the invention are as follows：
1) transverse and longitudinal for considering functional areas or layout units places problem.Due to containing multiple lathes inside functional areas
Unit, transverse and longitudinal Layout Problem directly affect logistics cost.For this purpose, just needing to consider functional areas transverse and longitudinal cloth in optimization process
It sets, to obtain more excellent placement scheme.Consider major trunk roads and each functional areas region pitch problems.In actual workshop and factory,
Major trunk roads are designed according to workshop size, and require to reserve enough volume spacing between each region, and during optimizing often
Ignore this point, interchannel is being added away from rear in the solution obtained after optimization, and target function value changes greatly, and often deviates optimal solution.
Conversely, just considering the two practical problems in optimization process, the optimal location scheme to tally with the actual situation can get.
2) present invention takes genetic algorithm to solve plant layout's problem, and using integer coding, real coding and binary system
The mixed coding technology of coding is laid out using what system method for arranging acquired in the initial population of the embedded improved adaptive GA-IAGA of solution,
It carries out rational parameter setting and selects suitable operation strategy, wherein intersecting and being intersected using segmentation in mutation operation, become
Exclusive-OR operator carries out segmentation intersection and variation, avoids algorithm from being absorbed in locally optimal solution, while improving search capability and efficiency.
Description of the drawings
Fig. 1 is workshop total arrangement genetic algorithm flow chart in the present invention；
Fig. 2 is plant layout's result figure in the present invention.
Specific implementation mode
The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.A kind of workshop of the present invention is more
The modeling of row layout and method for solving, include the following steps：
Step 1：Workshop total arrangement modeling based on MMIP
In order to reduce calculation scale, using document " the multi-level formula layout of aircraft structure processing workshop and optimizing research "
(Chen Chunpeng, Wang Ruoxin, fourth national wealth, sword automated manufacturings, 2017,39 (02):The three-layer type cloth proposed in 138-141.)
Office's method.Wherein third layer location problem, i.e. the workshop total arrangement of unequal-area functional areas are a most complicated layout layers.
Multiple constraint and rule of the layout according to scene, build majorized function and solve, to meet minimum logistics capacity, most short logistics road
The indexs such as diameter obtain the optimal solution for best suiting field condition.
In the practical total arrangement of functional areas, usually it is arranged across situation according to workshop point, functional areas can be with transverse and longitudinal
It to being placed on the both sides in horizontal trun road, while should be ensured that the safe distance in function section, and cannot exceed and to be laid out
Workshop range, thus using multirow mixed integer programming (the Multi-row Mix Integer under based on multiple constraint
Programming, MMIP) accurate model.The model is structure optimization mesh on the basis of linear and non-linear decision variable
Each line width is arranged according to the width of most wide equipment in scalar functions, is divided in every a line to carrying out not decile, forms different width
The rectangle of degree, then match area not etc. need place function area, selection function area it is vertical and horizontal to it to be arranged in each row one by one
In rectangle.Colleague waits for that the middle ordinate in place function area is obviously consistent, and each functional areas are described with rectangle, adjacent rows
Centreline space horizontal trun road is arranged, and avoids adjacent rows functional areas from interfering, each work(away from being arranged according to the scheduled distance of workshop
Also enough safe distances can should be reserved between area and workshop wall, while functional areas layout needs to avoid vertical arterial highway.Mathematics
Model is as follows：
Object function：
Multiple constraint condition：
Wi l≤Yi″-Yi′≤Wi u, Yi', Yi″≥0 (3)
(Xi″-Xi′)(Yi″-Yi')=Ai (4)
0≤Xi′≤Xi″≤Bx (5)
0≤Yi′≤Yi″≤By (6)
αi=0.5Xi′+0.5Xi″ αi≥0 (7)
βi=0.5Yi′+0.5Yi″ βi≥0 (8)
Xi″,Xi′≥Tj1 or Xi″,Xi′≤Tj2 (9)
Li=1 or 0 (14)
In formula：fijFor the carrying frequency of functional areas i to functional areas j, cijFor functional areas i to functional areas j unit carry at
This, αi、βiIt is the x and y coordinates of the functional areas i centre of moments, αj、βjIt is the x and y coordinates of the functional areas j centre of moments.
For the length limit and lower limit of functional areas i,It is the width upper and lower bound of functional areas i, Xi′、
Xi" it is respectively the x coordinate of functional areas the right and left, Yi′、Yi" y-coordinate of the functional areas tops i and bottom edge, Bx、ByRefer to workshop along x, y
Axis measures length, AiFor the area of functional areas i, M is penalty function, Tj1、Tj2The left and right coordinate of respectively vertical major trunk roads x-axis, certainly
Plan variableIndicate that functional areas i is strictly limited at the right of functional areas j, otherwiseDecision variableFunctional areas i
It is strictly limited at the top of functional areas j, otherwiseSijSpacing between functional areas；Minimum between functional areas
Safe spacing；Decision variable Li=1 expression functional areas i is placed vertically, Li=0 indicates that functional areas i is laterally disposed.
Formula (1) is the material landed cost object function based on distance and carrying frequency, and constraint formula (2) and (3) is used respectively
Long wide direction in each functional areas of guarantee does not exceed specified range, and formula (4) expresses each functional areas coordinate points and area
Between nonlinear restriction relationship, formula (5) and formula (6) limit each functional areas and be located in workshop, formula (7) and the specified work(of formula (8)
X, the y-coordinate of the energy area centre of moment, formula (9) assurance function area layout avoid vertical major trunk roads.Constraint formula (10) showsWhen, Xj″
≤Xi', i.e. functional areas i must be necessarily arranged at the right of proximity association functional areas j, and formula (11) is the proximity association work(for the directions y
Can area constraint, formula (12) avoids the interference of any two functional areas on the direction x, y, formula (13) ensure minimum functional areas it
Between spacing, formula (14) indicate functional areas can be anyhow to placement.Formula (1)-(14) establish while considering major trunk roads, spacing and put
Set the workshop total arrangement mathematical models of the actual conditions such as direction.
Step 2：It is solved using the genetic algorithm based on mixed coding technology
Genetic algorithm searches for the side of optimal solution using iterative cycles iteration by the process of the entire biological evolution of simulation
Method, the present invention solve the problems, such as that workshop total arrangement, basic procedure are as shown in Figure 1 using the algorithm：1) chromosome coding, 2) is carried out
It generates initial population, 3) evaluates population, 4) selection operation, 5) crossover operation, 6) mutation operation, 7) evolution and termination, 8) decoding
Export optimal location solution.
In order to solve multiple constraint plant layout model, the gene code mode of genetic algorithm is arranged by functional areas in the present invention
Sequentially, spacing, 3 parts of vertical and horizontal placement constitute, and use mixed coding structure, i.e., using integer volume when functional areas are sorted
Code, spacing use real coding, vertical and horizontal place to use binary encoding.This coding techniques is simple and efficient, but due to base
Because code is especially long, the problem of causing the operating difficulties such as to intersect, make a variation and select in genetic algorithm.
Plant layout's problem is typical discrete optimization problems of device, it is necessary first to find the best function area for meeting constraints
The arrangement of layout, therefore integer coding is most suitable.Such as when multirow functional areas are laid out, [5,3, Isosorbide-5-Nitrae, 2] indicate functional areas certainly
Number consecutively sequence left-to-right, from bottom to top；Can be more than to set in advance after the last one functional areas is discharged into if on certain row
When the maximum width set, then enters a new line to the functional areas, be aligned to lastrow.Actual spacing is a real number range, institute
To use floating-point encoding more efficient, such as [2.3,1.6,2.1,1.2,1.1] indicate from left to right, function from bottom to top
Area and a upper functional areas or the spacing of wall.Using the vertical and horizontal placement in binary coding expressive function area, such as [0,1,1,0,0] table
Show the 3rd and the 1st functional areas are vertically arranged, other layout units lateral arrangements.
Initial population is the section layout scheme obtained by system arrangement, adds two part structures of random population
At.Through overtesting, assignment is carried out to the initial parameter of genetic algorithm, optimisation strategy is selected.Fitness function uses and penalizes letter
Number method is designed so that poor individual has relatively low fitness.The mode for choosing wheel disc stake alternatively operates, individual quilt
The fitness value of the probability of selection and its individual itself is closely bound up, and the fitness value the big, the probability remained by selection
It is bigger.Due to the coding containing different structure in chromosome, functional areas sequence is integer coding, and selected section mapping intersects,
Spacing is real coding, selects the intersection that counts, setting is binary coding anyhow for functional areas, selects two-point crossover.
In genetic algorithm mutation operation, segmentation variation is carried out.Wherein functional areas are arranged gene section selection basic bit and become anyhow
Exclusive-OR operator, and functional areas sequence gene section then selects to reverse mutation operator, that is, position at 2 is randomly generated in gene section,
The genic value by this at 2 on position is interchangeable again.Since spacing uses real coding, mutation process is more complex, first
Change point is first found according to mutation probability, in [Wmin,Wmax] section randomly generates k functional areas distance values, and replaces become respectively
The distance values of dissimilarity calculate the fitness value of these chromosomes to obtain k chromosome, with fitness highest distance values
To replace original distance values.
The method of the present invention and advantageous effect are verified below by specific example.
Certain enterprise prepares to build new workshop, and 90 meters of length is 60 meters wide；According to prediction and analysis, market department provides 5 years from now on
Production outline, and the device type and quantity of workshop configuration are cooked up, the subregion of functional areas is distributed according to group technology such as 1 institute of table
Show.According to processing technology and functions of the equipments area situation, carrying out logistics analysis can obtain to table, while empirically, setting peace
Full distance.
1 functional areas information table of table
Concrete operations：It builds majorized function according to the multiple constraint at scene and rule first against example and solves, with
Meet and minimize logistics landed cost index, obtains the optimal solution for best suiting field condition.Its object function is：
Constraints is：
Wi l≤Yi″-Yi′≤Wi u, Yi', Yi″≥0 (3)
(Xi″-Xi′)(Yi″-Yi')=Ai (4)
0≤Xi′≤Xi″≤90 (5)
0≤Yi′≤Yi″≤60 (6)
αi=0.5Xi′+0.5Xi″ αi≥0 (7)
βi=0.5Yi′+0.5Yi″ βi≥0 (8)
Xi″,Xi′≥Tj1 or Xi″,Xi′≤Tj2 (9)
Li=1 or 0 (14)
Target function value is solved using the genetic algorithm based on mixed coding technology.Initial parameter is set first：
Maximum evolution iterative algebra chose for 200 generations, and Population Size chooses 50, and crossover probability Pc chooses 0.8, and mutation probability chooses 0.08.
1) chromosome coding is carried out：The gene code mode of genetic algorithm is put in order by functional areas, spacing, is placed anyhow
What 3 parts were constituted, and mixed coding structure is used, there are 16 functional areas in this example, then be encoded to [5,3, Isosorbide-5-Nitrae, 2,9,
12,14,7,10,15,8,6,16,11,13；1.3,1.2,1.1,1.2,1.1,0.3,0.9,0.4,1.2,0.3,0.5,0.6,
1.2,1.5,0.6,0.6；0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0].Integer coding is used when i.e. functional areas are sorted,
Spacing uses real coding, vertical and horizontal place to use binary encoding.Such as when multirow functional areas are laid out [5,3, Isosorbide-5-Nitrae, 2,9,
12,14,7,10,15,8,6,16,11,13] the number consecutively sequence of functional areas from left to right, from bottom to top is indicated；If at certain
On row, after the last one functional areas is discharged into, when can be more than pre-set maximum width, then enters a new line, arrange to the functional areas
Arrange lastrow.Actual spacing is a real number range, thus it is more efficient using floating-point encoding, such as [1.3,1.2,
1.1,1.2,1.1,0.3,0.9,0.4,1.2,0.3,0.5,0.6,1.2,1.5,0.6,0.6] it indicates from left to right, from bottom to top
Functional areas and a upper functional areas or wall spacing.Using the vertical and horizontal placement in binary coding expressive function area, such as [0,1,1,
0,0,1,1,1,0,0,0,1,0,1,1,0] indicate that the functional areas that number is 3,1,9,12,14,8,16,11 are vertically arranged, other
Place function area unit transverse arrangement.
2) initial population is generated：The initial population of genetic algorithm is the section layout scheme obtained by system arrangement,
Along with two parts of random population are constituted.
3) population is evaluated：Wherein fitness function is designed using penalty function method so that poor individual has relatively low suitable
Response.
4) selection operation：The mode for choosing wheel disc stake alternatively operates.
5) crossover operation：Due to the coding containing different structure in chromosome, in crossover operation of genetic algorithms, it is segmented
Intersect, functional areas sequence layer is integer coding, and using partial mapped crossover, spacing layer is real coding, is intersected using counting, work(
It is binary coding that floor, which is arranged, in energy area anyhow, using two-point crossover.
6) mutation operation：In genetic algorithm mutation operation, segmentation variation is carried out, gene Duan Xuan is arranged in wherein functional areas anyhow
Basic bit mutation operator is selected, and functional areas sequence gene section then selects to reverse mutation operator, that is, produced at random in gene section
Position at raw 2, then this genic value at 2 on position is interchangeable.Since spacing uses real coding, mutation process multiple
It is more miscellaneous, change point is found according to mutation probability first, in [Wmin,Wmax] section randomly generates k functional areas distance values, and divides
Not Ti Huan the distance values of change point calculate the fitness value of these chromosomes to obtain k chromosome, most with fitness
High distance values replace original distance values.
7) it evolves and terminates：In loop iteration, maximum 200 generation of evolution iterations until reaching setting, then terminate iteration.
8) decoding output optimal location solution.
5 kinds of experimental strategies are designed, experiment 1 does not consider channel when optimizing, consider that spacing is placed with vertical and horizontal, after optimization again by force
Channel is added；Do not consider spacing when 2 optimization of experiment, consider channel and place anyhow, spacing is added in optimization by force again；Experiment 3 is then
Do not consider that functional areas are arranged anyhow, considers channel and spacing；Experiment 4 considers spacing, channel, vertical and horizontal placement simultaneously, but uses and pass
Genetic algorithm optimization of uniting solves；Experiment 5 is identical as 4 strategies of experiment, but using the something lost of system method for arranging (SLP) build initial solution
Propagation algorithm optimizes solution.The optimum results of 5 experiments are shown in Table 2.
Table 2 optimizes data comparison table
The optimum results explanation of experiment 1 does not consider that channel optimizes, although the Optimized model after simplifying obtains desired value
It is minimum in 5 experiments, but after channel really is added, realistic objective value but increases 22%, illustrates that channel greatly influences
The optimal solution of model；Experiment 2 optimum results explanation do not consider that spacing optimizes, obtain desired value be also it is smaller,
But after spacing to be added, realistic objective value but increases 15%, illustrates that influence of the spacing to model optimal solution is also very prodigious；
The data result of contrast experiment 3 and experiment 4, it is seen that the precision that optimal solution is placed in consideration functional areas anyhow can be improved 6% or so, together
When convergence rate improve, it is easier to obtain optimal solution；The data result of contrast experiment 4 and experiment 5, it is seen that obtain SLP methods
Scheme as part initial solution, can be easier to obtain more satisfying excellent solution, and further increase convergence rate.Experiment
5 final functional areas layout result is shown in that Fig. 2, desired value are smaller by 13%, 17% than the realistic objective value of experiment 1, experiment 2, as a result
Most preferably.
Claims (4)
1. modeling and the method for solving of a kind of workshop multirow layout, which is characterized in that include the following steps：
Step 1：The workshop total arrangement modeling of MIP models based on multirow layout
Using three-layer type layout method, multiple constraint and rule of the third layout layer according to scene build majorized function and solve,
Its object function is：
In formula：fijFor the carrying frequency of functional areas i to functional areas j, cijFor the unit landed cost of functional areas i to functional areas j,
αi、βiIt is the x and y coordinates of the functional areas i centre of moments, αj、βjIt is the x and y coordinates of the functional areas j centre of moments；
Step 2：It is solved using the genetic algorithm based on mixed coding technology, specially：
1) chromosome coding is carried out
Gene code mode is put in order by functional areas, spacing, 3 parts of placement are constituted anyhow, and uses mixed coding structure,
Use integer coding, spacing that real coding, vertical and horizontal place is used to use binary encoding when i.e. functional areas are sorted；
2) initial population is generated
The section layout scheme that initial population is obtained by system arrangement, along with random population is constituted；
3) it evaluates population, carry out selection operation；
4) crossover operation
Functional areas sequence layer is integer coding, using partial mapped crossover；Spacing layer is real coding, is intersected using counting；Work(
It is binary coding that floor, which is arranged, in energy area anyhow, using two-point crossover；
5) mutation operation
Gene section selection basic bit mutation operator is arranged in functional areas anyhow；Functional areas sequence gene section then selects that variation is reversed to calculate
Son, i.e., randomly generate position at 2 in gene section, then this genic value at 2 on position is interchangeable；Spacing uses reality
Number encoder finds change point according to mutation probability first, in [Wmin,Wmax] section randomly generates k functional areas distance values, and divides
Not Ti Huan the distance values of change point calculate the fitness value of these chromosomes to obtain k chromosome, most with fitness
High distance values replace original distance values；
6) it evolves and terminates
The maximum evolution iterations for reaching setting then terminate iteration；
7) decoding output optimal location solution.
2. modeling and the method for solving of a kind of workshop multirow layout as described in claim 1, which is characterized in that built in step 1
In vertical workshop total arrangement mathematical models, constraints is：
Wi l≤Yi″-Yi′≤Wi u, Yi', Yi″≥0 (3)
(Xi″-Xi′)(Yi″-Yi')=Ai (4)
0≤Xi′≤Xi″≤Bx (5)
0≤Yi′≤Yi″≤By (6)
αi=0.5Xi′+0.5Xi″ αi≥0 (7)
βi=0.5Yi′+0.5Yi″ βi≥0 (8)
Xi″,Xi′≥Tj1 or Xi″,Xi′≤Tj2 (9)
Li=1 or 0 (14)
In formula：For the length limit and lower limit of functional areas i, Wi u、Wi lIt is the width upper and lower bound of functional areas i, Xi′、
Xi" it is respectively the x coordinate of functional areas the right and left, Yi′、Yi" y-coordinate of the functional areas tops i and bottom edge, Bx、ByRefer to workshop along x, y
Axis measures length, AiFor the area of functional areas i, αi、βiIt is the x and y coordinates of the functional areas i centre of moments, M is penalty function, Tj1、Tj2Respectively
For the left and right coordinate of vertical major trunk roads x-axis, decision variableIndicate that functional areas i is strictly limited at the right of functional areas j, it is no
ThenDecision variableFunctional areas i is strictly limited at the top of functional areas j, otherwiseSijFor functional areas it
Between spacing；Minimum safe spacing between functional areas；Decision variable Li=1 expression functional areas i is placed vertically, Li=0
Then indicate that functional areas i is laterally disposed；
Constraint formula (2) and (3) are respectively used to ensure that the long wide direction of each functional areas does not exceed specified range, formula (4) expression
Nonlinear restriction relationship between each functional areas coordinate points and area, formula (5) and formula (6) limit each functional areas and are located at factory
In room, x, the y-coordinate of formula (7) and the specified functional areas centre of moment of formula (8), formula (9) assurance function area layout avoid vertical major trunk roads；About
Beam formula (10) showsWhen, Xj″≤Xi', i.e. functional areas i must be necessarily arranged at the right of proximity association functional areas j, and formula (11) is
For the constraint of the proximity association functional areas in the directions y, formula (12) avoids the interference of any two functional areas on the direction x, y,
Formula (13) ensures that the spacing between minimum functional areas, formula (14) indicate that functional areas can be anyhow to placement.
3. modeling and the method for solving of a kind of workshop multirow layout as described in claim 1, which is characterized in that in evaluation population
In the process, fitness function therein is designed using penalty function method.
4. modeling and the method for solving of a kind of workshop multirow layout as described in claim 1, which is characterized in that selected
When operation, the mode for choosing wheel disc stake alternatively operates.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810438932.2A CN108596403A (en) | 2018-05-09 | 2018-05-09 | A kind of modeling of workshop multirow layout and method for solving |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810438932.2A CN108596403A (en) | 2018-05-09 | 2018-05-09 | A kind of modeling of workshop multirow layout and method for solving |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN108596403A true CN108596403A (en) | 2018-09-28 |
Family
ID=63636083
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810438932.2A Pending CN108596403A (en) | 2018-05-09 | 2018-05-09 | A kind of modeling of workshop multirow layout and method for solving |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108596403A (en) |
Cited By (15)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109917754A (en) * | 2019-03-14 | 2019-06-21 | 湘潭大学 | A kind of robotic asssembly unit multiple target layout optimization method based on Estimation of Distribution Algorithm on multiple populations |
| CN110399629A (en) * | 2019-05-29 | 2019-11-01 | 北京工业大学 | A kind of tower crane type selecting and layout optimization modeling method based on mixing shaping planning |
| CN111079273A (en) * | 2019-12-03 | 2020-04-28 | 北京新学堂网络科技有限公司 | Automatic layout design method and device |
| CN111090898A (en) * | 2019-11-07 | 2020-05-01 | 郑州大学 | Building indoor layout design method |
| CN111191304A (en) * | 2019-11-27 | 2020-05-22 | 中国地质大学（武汉） | Construction site plane arrangement method based on random strategy and multi-objective optimization algorithm |
| CN111583055A (en) * | 2020-05-09 | 2020-08-25 | 电子科技大学 | Product grouping method under multiple process paths based on genetic algorithm |
| CN111950060A (en) * | 2020-08-11 | 2020-11-17 | 中国民航大学 | Multi-objective optimization method for plane layout of airport flight area |
| CN112084704A (en) * | 2020-08-19 | 2020-12-15 | 浙江工业大学 | Multi-process route and layout combined optimization method for flexible workshop |
| CN112085368A (en) * | 2020-09-02 | 2020-12-15 | 西南交通大学 | Equipment energy production configuration and layout optimization method based on immune genetic algorithm |
| CN112464309A (en) * | 2020-11-24 | 2021-03-09 | 中天众达智慧城市科技有限公司 | Equipment arrangement method of smart city data center |
| CN112464310A (en) * | 2020-11-24 | 2021-03-09 | 中天众达智慧城市科技有限公司 | Equipment arrangement method of smart city data center |
| CN112699548A (en) * | 2020-12-25 | 2021-04-23 | 珠海格力电器股份有限公司 | Method and device for generating electric cabinet layout scheme and electronic equipment |
| CN113111523A (en) * | 2021-04-21 | 2021-07-13 | 西南交通大学 | Meta-heuristic method for solving intelligent layout of multi-constraint double-layer aisle |
| CN116127584A (en) * | 2023-03-13 | 2023-05-16 | 西南交通大学 | Dynamic aisle arrangement method |
| CN116502752A (en) * | 2023-04-24 | 2023-07-28 | 西南交通大学 | Free line feed strategy solving method for workshop multi-line layout |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040019850A1 (en) * | 2002-07-23 | 2004-01-29 | Xerox Corporation | Constraint-optimization system and method for document component layout generation |
| CN106875071A (en) * | 2017-03-31 | 2017-06-20 | 华南理工大学 | A kind of workshop appliance multiple-objection optimization layout method of self-adapted genetic algorithm |
-
2018
- 2018-05-09 CN CN201810438932.2A patent/CN108596403A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040019850A1 (en) * | 2002-07-23 | 2004-01-29 | Xerox Corporation | Constraint-optimization system and method for document component layout generation |
| CN106875071A (en) * | 2017-03-31 | 2017-06-20 | 华南理工大学 | A kind of workshop appliance multiple-objection optimization layout method of self-adapted genetic algorithm |
Non-Patent Citations (3)
| Title |
|---|
| 周娜 等著: "基于遗传算法的车间布局多目标优化", 《工业工程》 * |
| 孙焰 等著: "基于最短路多种群遗传算法的物流园区内部布局研究", 《物流科技》 * |
| 赵川 等著: "基于混合遗传算法的制造车间布局设计", 《重庆理工大学学报（自然科学）》 * |
Cited By (20)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109917754A (en) * | 2019-03-14 | 2019-06-21 | 湘潭大学 | A kind of robotic asssembly unit multiple target layout optimization method based on Estimation of Distribution Algorithm on multiple populations |
| CN110399629A (en) * | 2019-05-29 | 2019-11-01 | 北京工业大学 | A kind of tower crane type selecting and layout optimization modeling method based on mixing shaping planning |
| CN110399629B (en) * | 2019-05-29 | 2023-06-20 | 北京工业大学 | Tower crane model selection and layout optimization modeling method based on hybrid shaping planning |
| CN111090898B (en) * | 2019-11-07 | 2023-03-10 | 郑州大学 | Building indoor layout design method |
| CN111090898A (en) * | 2019-11-07 | 2020-05-01 | 郑州大学 | Building indoor layout design method |
| CN111191304A (en) * | 2019-11-27 | 2020-05-22 | 中国地质大学（武汉） | Construction site plane arrangement method based on random strategy and multi-objective optimization algorithm |
| CN111079273A (en) * | 2019-12-03 | 2020-04-28 | 北京新学堂网络科技有限公司 | Automatic layout design method and device |
| CN111583055A (en) * | 2020-05-09 | 2020-08-25 | 电子科技大学 | Product grouping method under multiple process paths based on genetic algorithm |
| CN111950060A (en) * | 2020-08-11 | 2020-11-17 | 中国民航大学 | Multi-objective optimization method for plane layout of airport flight area |
| CN112084704A (en) * | 2020-08-19 | 2020-12-15 | 浙江工业大学 | Multi-process route and layout combined optimization method for flexible workshop |
| CN112085368A (en) * | 2020-09-02 | 2020-12-15 | 西南交通大学 | Equipment energy production configuration and layout optimization method based on immune genetic algorithm |
| CN112464309A (en) * | 2020-11-24 | 2021-03-09 | 中天众达智慧城市科技有限公司 | Equipment arrangement method of smart city data center |
| CN112464310A (en) * | 2020-11-24 | 2021-03-09 | 中天众达智慧城市科技有限公司 | Equipment arrangement method of smart city data center |
| CN112464310B (en) * | 2020-11-24 | 2024-04-26 | 中天众达智慧城市科技有限公司 | Equipment arrangement method for smart city data center |
| CN112464309B (en) * | 2020-11-24 | 2024-04-30 | 中天众达智慧城市科技有限公司 | Equipment arrangement method for smart city data center |
| CN112699548A (en) * | 2020-12-25 | 2021-04-23 | 珠海格力电器股份有限公司 | Method and device for generating electric cabinet layout scheme and electronic equipment |
| CN113111523A (en) * | 2021-04-21 | 2021-07-13 | 西南交通大学 | Meta-heuristic method for solving intelligent layout of multi-constraint double-layer aisle |
| CN116127584A (en) * | 2023-03-13 | 2023-05-16 | 西南交通大学 | Dynamic aisle arrangement method |
| CN116127584B (en) * | 2023-03-13 | 2024-05-14 | 西南交通大学 | Dynamic aisle arrangement method |
| CN116502752A (en) * | 2023-04-24 | 2023-07-28 | 西南交通大学 | Free line feed strategy solving method for workshop multi-line layout |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108596403A (en) | A kind of modeling of workshop multirow layout and method for solving | |
| CN110363344A (en) | Probability integral parameter prediction method based on MIV-GP algorithm optimization BP neural network | |
| Onwunalu | Optimization of field development using particle swarm optimization and new well pattern descriptions | |
| CN109165778B (en) | Cantilever beam type stereoscopic warehouse goods space distribution method applied to long material storage | |
| CN109271320A (en) | A kind of upper multiple target priorities of test cases sort method | |
| CN1450493A (en) | Nerve network system for realizing genetic algorithm | |
| CN116090788B (en) | Batch scheduling planning method for flexible assembly job shop | |
| CN101256648A (en) | Genetic operation operator based on indent structure for producing quening system | |
| CN113953685A (en) | Planar plate laser cutting path planning method | |
| Gu et al. | A discrete particle swarm optimization algorithm with adaptive inertia weight for solving multiobjective flexible job-shop scheduling problem | |
| CN105739304A (en) | Multi-UCAV on-line striking target allocation method of opposition-based genetic algorithm(GA) | |
| CN116957177A (en) | Flexible workshop production line planning method, system, equipment and medium | |
| CN109917754B (en) | Multi-population distribution estimation algorithm-based robot assembly unit multi-target layout optimization method | |
| Kim et al. | Field development optimization using a cooperative micro-particle swarm optimization with parameter integration schemes | |
| Qin et al. | Multi-objective multi-verse optimizer for multi-robotic u-shaped disassembly line balancing problems | |
| CN104281917A (en) | Fuzzy job-shop scheduling method based on self-adaption inheritance and clonal selection algorithm | |
| Shang et al. | Complete coverage path planning for horticultural electric tractors based on an improved genetic algorithm | |
| Fang | [Retracted] An Effective Hybrid Multiobjective Flexible Job Shop Scheduling Problem Based on Improved Genetic Algorithm | |
| Opalach et al. | Stacking optimization of 3D printed continuous fiber layer designs | |
| CN110400068B (en) | Artificial fish reef scale effect evaluation method | |
| CN103164554B (en) | A kind of method determining metamaterial modular construction | |
| Pei et al. | A multi-objective hybrid differential optimization algorithm for flow-shop scheduling problem | |
| CN103810322B (en) | Integrated circuit layout method based on best fit heuristic sequence and organizational evolutionary algorithms | |
| Askari-Nasab et al. | Creating mining-cuts using hierarchical clustering and tabu search algorithms | |
| CN113419489B (en) | Multi-cavity component rough machining cutter optimization selection method based on genetic algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20180928 |