CN107909223B - Low-entropy layout and robust optimization method for complex workshop - Google Patents
Low-entropy layout and robust optimization method for complex workshop Download PDFInfo
- Publication number
- CN107909223B CN107909223B CN201711305854.0A CN201711305854A CN107909223B CN 107909223 B CN107909223 B CN 107909223B CN 201711305854 A CN201711305854 A CN 201711305854A CN 107909223 B CN107909223 B CN 107909223B
- Authority
- CN
- China
- Prior art keywords
- layout
- population
- workshop
- unit
- cells
- 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.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 49
- 238000005457 optimization Methods 0.000 title claims abstract description 43
- 229910052799 carbon Inorganic materials 0.000 claims abstract description 72
- 210000004027 cell Anatomy 0.000 claims description 110
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 claims description 47
- 210000000349 chromosome Anatomy 0.000 claims description 29
- 101150112906 fitm-2 gene Proteins 0.000 claims description 27
- 238000004519 manufacturing process Methods 0.000 claims description 27
- 230000008569 process Effects 0.000 claims description 25
- 101100083342 Mus musculus Picalm gene Proteins 0.000 claims description 23
- 101100018718 Rattus norvegicus Il1rl1 gene Proteins 0.000 claims description 23
- 230000001413 cellular effect Effects 0.000 claims description 9
- 238000010276 construction Methods 0.000 claims description 9
- 239000000463 material Substances 0.000 claims description 8
- 238000012163 sequencing technique Methods 0.000 claims description 8
- 238000013508 migration Methods 0.000 claims description 7
- 230000005012 migration Effects 0.000 claims description 7
- 238000012545 processing Methods 0.000 claims description 7
- 238000011156 evaluation Methods 0.000 claims description 6
- 230000006872 improvement Effects 0.000 claims description 6
- 238000004364 calculation method Methods 0.000 claims description 5
- 239000002245 particle Substances 0.000 claims description 5
- 238000012966 insertion method Methods 0.000 claims description 4
- 230000035772 mutation Effects 0.000 claims description 4
- 229910021409 T-carbon Inorganic materials 0.000 claims description 3
- 238000006243 chemical reaction Methods 0.000 claims description 3
- 238000006073 displacement reaction Methods 0.000 claims description 3
- 238000003780 insertion Methods 0.000 claims description 3
- 230000037431 insertion Effects 0.000 claims description 3
- 238000003763 carbonization Methods 0.000 abstract description 3
- 230000008859 change Effects 0.000 description 7
- 238000013461 design Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 238000011161 development Methods 0.000 description 2
- 230000009467 reduction Effects 0.000 description 2
- 230000006978 adaptation Effects 0.000 description 1
- 230000032823 cell division Effects 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000007405 data analysis Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000004134 energy conservation Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000002068 genetic effect Effects 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000005192 partition Methods 0.000 description 1
- 238000003672 processing method Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000010845 search algorithm Methods 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Images
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"
-
- 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
- G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
- G06Q50/04—Manufacturing
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/30—Computing systems specially adapted for manufacturing
Landscapes
- Engineering & Computer Science (AREA)
- Business, Economics & Management (AREA)
- Human Resources & Organizations (AREA)
- Economics (AREA)
- Strategic Management (AREA)
- Theoretical Computer Science (AREA)
- Tourism & Hospitality (AREA)
- General Physics & Mathematics (AREA)
- Marketing (AREA)
- General Business, Economics & Management (AREA)
- Physics & Mathematics (AREA)
- Operations Research (AREA)
- Quality & Reliability (AREA)
- Game Theory and Decision Science (AREA)
- Entrepreneurship & Innovation (AREA)
- Development Economics (AREA)
- Manufacturing & Machinery (AREA)
- Health & Medical Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Primary Health Care (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
A low-entropy layout and robust optimization method for a complex workshop comprises the following steps: constructing a low-carbon energy-saving objective function, constructing a complex workshop stable optimization model and a low-entropy layout model, and obtaining an optimal result by using an annular multi-cell hybrid optimization algorithm. Aiming at the characteristics of various complex workshop resources, strict geometric constraint of a workshop, complex relationship between logistics and non-logistics and close functional relationship between units. The method can effectively deal with various constraints of the complex workshop, and obtain the low-carbonization and high-robustness workshop layout under multiple constraint conditions and multiple dynamic disturbances; and an annular multi-cell mixed optimization algorithm combining a fuzzy clustering method and a parallel directed evolution method is designed, individual evolution rules in and among the cells of the population are designed, and the speed and quality of evolution can be effectively improved.
Description
Technical Field
The invention relates to a data processing method specially suitable for a prediction purpose, in particular to a low-entropy layout and robust optimization method for a complex workshop.
Background
The market demand of the manufacturing industry has the characteristics of continuity, relevance, variability and the like, the trend of diversified customer demands and dynamic fluctuation of orders is increasingly remarkable, and enterprises need more reasonable workshop layout to meet the requirements of high production flexibility, low manufacturing carbonization, low layout entropy and the like. The low-entropy layout and robust optimization of the workshop are a layout mode of a multi-processing unit group or an assembly unit group, and the low-entropy layout and robust optimization method has the advantages that the workshop layout has low-carbon, energy-saving and high-stability low-entropy characteristics on the premise that an enterprise does not increase cost or expand the area of the workshop.
The current intelligent optimization algorithm applied to workshop layout mainly focuses on Genetic Algorithm (GA), ant colony Algorithm (ACO), tabu search algorithm (TS) and the like, but when the algorithms are applied to solving the problem of complex workshop layout, the problems of large calculation amount, slow convergence, low efficiency and insufficient optimization capability exist.
At present, the targets of workshop layout consideration mainly focus on workshop logistics cost, carrying distance and the like, and low-carbon energy-saving and stable performance are used as the targets of workshop layout optimization. The method is characterized in that low-carbon green workshop layout is constructed by taking low-carbon energy-saving and sustainable development as targets, high-robustness workshop layout is constructed by taking entropy as a measurement index, and typical complex workshop layout design and optimization are carried out, so that the problem which needs to be solved urgently in the domestic manufacturing industry at present is solved.
A fuzzy clustering method and a parallel directed evolution method are combined to form a low-entropy layout and robust optimization method for a complex workshop of an annular multi-cell hybrid optimization algorithm, can effectively reduce carbon emission of the workshop and improve layout robustness, and belongs to the field of enterprise management engineering and intelligent manufacturing.
Disclosure of Invention
In order to overcome the defects of the prior art, a low-entropy layout and robust optimization method for a complex workshop is provided, so that the carbon emission of the workshop can be effectively reduced and the robust performance of the workshop is improved when the complex workshop layout is solved.
In order to achieve the purpose, the invention adopts the following technical scheme:
1. a low-entropy layout and robust optimization method for a complex workshop comprises the following steps:
step 1: low-carbon energy-saving objective function construction
1) Unit arrangement cost Q:
in the formula:
i-device number, representing device i;
j-element number, representing element j;
m is the total number of devices;
n is the total number of cells;
qi-cost of the equipment i;
F(ηj) -an aspect ratio evaluation function of cell j;
ηj-the aspect ratio of cell j;
hj-the height of the cell j;
wj-the width of cell j;
2) capacity per unit area T:
in the formula:
Tj-the capacity per unit area of unit j;
Pjk-the number of products k produced by unit j;
hj×wj-the area of cell j;
k is a product type label, which indicates a product k;
k is the total number of product types;
3) material flow distance product cost Z:
in the formula:
fjllogistics of functional units j to l in a plantAn amount;
cjl-unit transportation cost between functional units j and l;
djl-distance of functional units j and l;
l-Unit number, denoting Unit l;
4) layout/process robustness R:
in the formula:
Lk-representing the processing distance of the product k when it has passed through the complete process route;
5) layout flexibility F:
in the formula:
Okthe number of units passed during production of product k;
Ukj-representing the theoretical loading of unit j to produce product k;
6) the low-carbon energy-saving layout integrated optimization model comprises the following steps:
CE＝min(QνQ+CT+CZ+CRF) (formula 8)
CZ＝fZ×Z×pk (10)
CRF＝(1-R)fR+(1-F)fF(formula 11)
In the formula:
CE-Total carbon footprint;
CT-carbon emissions due to energy production;
CZcarbon emission caused by workshop workpiece transportation;
CRFexpected carbon emissions for future improvements due to robustness and flexibility;
vQ-arranging a cost carbon emission conversion factor;
fTj-carbon emission coefficient per unit area of unit j;
Fz-carbon deposit emission coefficient per unit volume distance;
Pk-the vehicle power for product k;
fZ-measuring the pitch carbon emission coefficient;
fR-a robust carbon emission coefficient;
fF-a flexible carbon emission coefficient;
step 2: complex workshop robust optimization model construction
In the formula:
h, the entropy of the workshop, which represents the measure index of the disturbance degree of the workshop;
A-Boltzmann constant;
n is the number of particles in the system, namely the product type in the workshop layout system;
a. b-System parameters;
wkthe energy owned in the system, i.e. the production cost of product k under this layout;
ck-the flow-volume product cost of product k;
w is the total cost of the layout;
α, β, γ, χ — a weighting factor, α + β + γ + χ ═ 1;
μ1-a unit area capacity cost conversion factor;
μ2-a layout/process robustness cost conversion factor;
μ3-laying out flexible cost conversion factors;
and step 3: complex workshop low-entropy layout model construction
In the formula:
CEmax-theoretical maximum carbon emission during layout of the plant;
CEmin-theoretical minimum carbon emission during plant layout;
and 4, step 4: the evolution steps of the circular multi-cell hybrid optimization algorithm are as follows:
step 41: chromosome coding/decoding, namely setting unit sequencing-segmentation mixed coding;
each chromosome is composed of a unit sequencing code and a unit dividing point code; the unit sequencing code consists of n unit symbols (n represents the number of workshop units), and represents the arrangement sequence of the units from left to right and from top to bottom in a workshop; the division point code consists of n-1 binary codes of 0-1, and the insertion space is distributed in the unit sequencing coding interval; 0 represents that the units are in the same column, and 1 represents that the unit is the unit arranged at the last of the column;
wherein, a1, a2, A3, a4, a5, and a6 represent cell numbers.
Step 42: fuzzy clustering generates a plurality of population cells:
in the formula:
Fma clustering objective function, which represents the minimum comprehensive dissimilarity degree of all clustering characteristic factors of different population cells;
u(x)IJ-membership functions of layout scheme J in class I;
i-population index, which represents population unit cell I;
j-chromosome number, representing chromosome J;
g-clustering factor label, representing clustering factor G;
g is a population label which represents a population cell g;
cIcluster centers of population I, i.e. representative chromosomes in the set;
cgcluster centers of population g, i.e. representative chromosomes in the set;
xJ-chromosome J in the population;
NI-the number of population cells;
NJ-the number of chromosomes in the population of cells;
NG-the number of clustering factors;
f-blur parameter greater than 1;
step 43: and (3) fitness evaluation:
Fit1＝QνQ+CT+CZ+CRF(formula 19)
Step 44: matching rules of population cells: completing fuzzy clustering and fitness calculation to obtain a plurality of groups of population cells, wherein each cell is a similar chromosome set; in order to ensure the diversity in the cooperative evolution process of the population to the maximum extent, all the cells are arranged in a descending order by taking the fitness Fit1 as a target, the cells are arranged by adopting an insertion method and form a ring-shaped topological structure, the pairing operation among the population cells is carried out, and the ring-shaped evolutionary topological structure matched with each other in pairs is formed; the operation ensures that the two matched cells have difference, and the difference values are relatively close; step 45: chromosome selection: designing a secondary displacement algorithm for selection; adopting a direct competition mode of the children and the father, wherein the competition content comprises a carbon emission value and an entropy value; the algorithm proceeds as follows:
randomly selecting two father individuals p1 and p2 from the matched population cellgroup in a replacement mode;
performing crossover and mutation to generate offspring c1 and c 2;
calculating fitness values Fit1 and Fit2 according to the fitness function:
if Fit1(c) < Fit1(p), then
If Fit2(c1) < Fit2(p1), then replace p1 with c1, otherwise retain p 1;
if Fit2(c1) < Fit2(p2), then replace p2 with c1, otherwise retain p 2;
if Fit2(c2) < Fit2(p1), then replace p1 with c2, otherwise retain p 1;
if Fit2(c2) < Fit2(p2), then replace p2 with c2, otherwise retain p 2;
wherein Fit1(c) < Fit1(p) indicates that the fitness Fit1 of any child is smaller than that of the parent;
step 46: and (3) performing collaborative evolution of the population:
matching mixed cross operation among cells;
independent variation operation in each cell;
thirdly, immigration operation among the ring topology structure population cells: completing selection, crossing and variation operations, designing a certain migration topology among population cells, and determining the individual exchange mode among the sets; for adjacent cells, a chromosome migration path is designed as A, B: copying a certain proportion of optimal individuals in the cellular A to migrate to a neighborhood cellular B according to a path, and simultaneously removing the worst individuals with the same proportion from the cellular B; sequentially operating all the cells and the neighbor cells thereof; the immigration strategy can keep the diversity of the population and play a guiding role in the population evolution; step 47: termination conditions
After population initialization, performing fuzzy clustering, selection, intersection, variation, immigration and the like in a circulating manner, and when N Pareto solution sets are generated and the entropy value H is always within a theoretically controllable range, ending the circulating process and outputting an optimal result.
The invention has the advantages that: 1) due to the fact that complex workshops are rich in resources, the geometrical constraint of the workshops is strict, the logistics and non-logistics relations are complex, and the functional relations among units are close. The low-carbon layout model, the robust optimization model and the integrated low-entropy workshop layout model provided by the invention can effectively deal with all constraints of the complex workshop to obtain the workshop layout with low carbonization and high robustness under multiple constraint conditions and multiple dynamic disturbances; 2) an annular multi-cell mixed optimization algorithm combining a fuzzy clustering method and a parallel directed evolution method is designed, individual evolution rules in and among the cells of the population are designed, and the speed and quality of evolution are effectively improved.
The complex workshop described by the invention is a multi-product, multi-process and multi-functional area integrated production workshop which is realized by large-scale customized enterprises and large-scale agent enterprises under industrial clusters on the basis of a unit cluster manufacturing mode to meet the market requirements of multiple varieties and small batches. The production process shows the diversity of forms and states more and more prominently on the levels of orders, equipment, processes, batches, bottlenecks and the like, and the requirements on flexibility, robustness and dynamics of the layout are gradually enhanced.
A complex shop layout problem description may be described as having N products that need to be assembled in M functional units. Each product is constrained by the immediate relation of the functional areas, and needs to complete the corresponding functional process on the functional units which must pass through, and the functional processes cannot be changed or omitted. The layout process is constrained by multiple conditions such as unit shape, logistics cost, product technology, layout flexibility and the like, and overall optimization of the layout of the workshop is sought.
Drawings
FIG. 1 is a diagram of plant robustness versus entropy.
FIG. 2 is a schematic diagram of a matching combination of a circular multi-cell hybrid optimization algorithm.
FIG. 3 is a diagram of a shop layout according to an example of the present invention.
Fig. 4 is a graph of carbon emissions during optimization of the layout.
FIG. 5 is a graph of entropy change between vehicles during the optimization layout process.
FIG. 6 is a comparison graph of the change of each index before and after the low-carbon energy-saving target.
FIG. 7 is a comparison graph of the change before and after layout robustness and flexibility indexes.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples.
A company is a manufacturing enterprise with a vacuum cleaner as a main product, and the current production assembly shop still meets the order requirement of customers in a large-scale and repeated production operation mode. The total area of the plant was 100 × 100(m2), including 15 functional unit areas as shown in table 1. The unit flow volume product cost per unit is shown in table 2, and the functional unit constraint of the product is shown in table 3. The minimum distance between the specified distance and the boundary of the workshop is 4.5m in the length direction, 2.5m in the width direction and 5 m.
TABLE 1 cell size and number
TABLE 2 cost of material flow between units (Yuan)
TABLE 3 product functional Unit constraints
A low-entropy layout and robust optimization method for a complex workshop comprises the following specific steps:
1. low-carbon energy-saving objective function construction
Enterprises hope to reduce the equipment or unit arrangement cost and logistics cost, improve the area utilization rate, guarantee sufficient robustness and layout flexibility, reduce carbon emission caused by fixed cost and variable cost, and achieve the purposes of low-carbon energy-saving and sustainable development of workshops. According to the key target of green layout, a low-carbon energy-saving objective function of complex workshop layout is provided:
1) unit arrangement cost Q:
the unit arrangement cost refers to variation in the arrangement shape of the functional units due to consideration of different device layout modes, which causes variation in the unit arrangement cost. The introduced cell aspect ratio evaluates the merits of the cell arrangement shape, and for any cell, an appropriate aspect ratio characterizes a reasonable cell shape, and an excessively large or small aspect ratio causes an increase in the arrangement cost. Coupling the aspect ratio with the layout cost allows ignoring the effect of cell placement problems, either horizontally or vertically, on the encoding.
In the formula:
Q-Unit Placement cost;
i-device number, representing device i;
j-element number, representing element j;
m is the total number of devices;
n is the total number of cells;
qi-cost of the equipment i;
F(ηj) -an aspect ratio evaluation function of cell j;
ηj-the aspect ratio of cell j;
hj-the height of the cell j;
wj-the width of cell j;
2) capacity per unit area T:
under the background of shortage of land resources and overhigh land cost, the workshop area is fully utilized, the positions of all units are reasonably arranged, the production requirement is met, the high-yield requirement under the low land cost is realized, and the method is a problem to be urgently solved by enterprises.
When various types of products are produced in a workshop, the comprehensive capacity can be used for measuring the unit production capacity. The unit area capacity represents the ratio of the comprehensive capacity of a certain unit of the workshop to the unit area.
In the formula:
Tj-the capacity per unit area of unit j;
Pjk-the number of products k produced by unit j;
hj×wj-the area of cell j.
k is a product type label, which indicates a product k;
k is the total number of product types;
3) material flow distance product cost Z:
the product of the mass flow moment and the distance moment is the mass flow moment product cost. In complex plants, different types of products involve different material flow paths and material flow rates. The quality of the workshop layout determines the complexity and the crossing frequency of the logistics route. The reduction of the distance between the object flow and each functional unit in the workshop is a direct means for reducing the product cost of the object flow and the moment, and is also the visual embodiment of the green index.
In the formula:
z-the flow volume versus product cost, see Table 2;
fjl-the flow of objects to the functional units j to l in the plant;
cjl-unit transportation cost between functional units j and l;
djl-distance of functional units j and l;
l-Unit number, denoting Unit l;
4) layout/process robustness R:
the customer demand changes rapidly, the robustness is dynamic change aiming at the production condition, and the robustness of the layout to the product process is reflected on the stability of the product processing distance. The process routes and the processing distances of different products are different, the stability of the processing distance can be ensured, the production stability can be ensured, and the change cost can be reduced. The robustness is taken as a workshop target and is an important index of excellent workshop performance.
In the formula:
r-layout/process robustness;
Lkthe processing distance of the product k through the complete process route is represented.
5) Layout flexibility F:
the layout flexibility embodies the self-adjusting capability of the layout system. Due to the variability of customer orders and the uncertainty of manufacturing environment, enterprises need to change layouts frequently to meet production requirements, and complex workshops integrating multiple products, multiple functions and multiple processes need high layout flexibility. Its main influencing factors are the number of selectable paths, the working efficiency of the paths, the object flow, the number of variable units, the unit load capacity, etc.
In the formula:
f, layout flexibility;
Okthe number of units passed during production of product k;
Ukj-representing the theoretical loading of unit j to produce product k; 6) the low-carbon energy-saving layout integrated optimization model comprises the following steps:
according to the low-carbon energy-saving index of the workshop layout, the workshop layout carbon emission model is composed of four parts, namely unit layout carbon emission, logistics carbon emission, production carbon emission and expected layout carbon emission. The expected carbon emissions refer to the potential carbon emissions of future layout improvement processes due to layout robustness and flexibility, with higher robustness and flexibility characterizing a layout more stable and lower expected improvement costs. Designing a low-carbon energy-saving layout integrated optimization model:
CE＝min(QνQ+CT+CZ+CRF) (formula 8)
CZ＝fZ×Z×pk (10)
CRF＝(1-R)fR+(1-F)fF(formula 11)
In the formula:
CE-Total carbon footprint;
CT-carbon emissions due to energy production;
CZcarbon emission caused by workshop workpiece transportation;
CRFexpected carbon emissions for future improvements due to robustness and flexibility;
vQ-arranging a cost carbon emission conversion factor;
fTj-carbon emission coefficient per unit area of unit j;
Fz-carbon deposit emission coefficient per unit volume distance;
Pk-the vehicle power for product k;
fZ-measuring the pitch carbon emission coefficient;
fR-a robust carbon emission coefficient;
fF-a flexible carbon emission coefficient;
2. complex workshop robust optimization model construction
The structure of the complex system is a fragile structure with potential collapse tendency, and the layout robust optimization model based on the fragile abstraction takes the physical entropy as a measure robustness index, so that the requirement of the system for continuous improvement can be well met.
The workshop is regarded as an unordered open system, unit equipment, materials and the like are regarded as particles in the system, and the movement of the particles generates different states. The plant entropy generated by different states of the layout is essentially the total cost fluctuation caused by different states, the entropy value is increased, and even the plant is stopped and crashed. And (3) constructing a stable optimization model of the workshop layout according to the definition of an entropy formula:
in the formula:
h, the entropy of the workshop, which represents the measure index of the disturbance degree of the workshop;
A-Boltzmann constant;
n is the number of particles in the system, namely the product type in the workshop layout system;
a. b-System parameters;
wkthe energy owned in the system, i.e. the production cost of product k under this layout;
ckthe product k flow product cost, see table 2;
w is the total cost of the layout;
α, β, γ, χ — a weighting factor, α + β + γ + χ ═ 1;
μ1-a unit area capacity cost conversion factor;
μ2-a layout/process robustness cost conversion factor;
μ3-laying out flexible cost conversion factors;
3. complex workshop low-entropy layout model construction
The proposed low-entropy layout is a low-entropy robust layout in a low-carbon context. Therefore, the model comprises two parts of low-carbon energy conservation meeting the energy resource constraint and robust optimization meeting the low physical entropy. The carbon emissions CE are normalized and mapped to a [0-1] range. H is an entropy value in the range of [0-1 ]. Integrating a low-entropy layout optimization model:
in the formula:
CEmax-theoretical maximum carbon emission during layout of the plant;
CEmin-theoretical minimum carbon emission during plant layout;
4. design of annular multi-cellular hybrid optimization algorithm
And designing an annular multi-cell hybrid optimization algorithm combining a fuzzy clustering method and a parallel directed evolution method. The fuzzy clustering method replaces random division with population clustering division to generate a plurality of groups of population cells, each population cell is composed of a plurality of similar individuals, a ring topology structure is formed according to rules, cooperation crossing and immigration among various population cells are carried out, and population-oriented evolution is enhanced.
The evolution steps of the circular multi-cell hybrid optimization algorithm are as follows:
1) and (4) chromosome coding/decoding, namely setting unit sequencing-segmentation mixed coding.
Each chromosome is composed of a unit sequencing code and a unit partition point code. The unit sequencing code consists of n unit symbols (n represents the number of workshop units), and represents the arrangement sequence of the units from left to right and from top to bottom in a workshop; the division point code is composed of n-1 binary codes 0-1, and the insertion space is distributed in the unit sequencing coding interval. 0 indicates that the cells are in the same column, and 1 indicates that the cell is the last cell in the column. As shown in Table 1, the 0-1 cell division point codes are randomly generated by sequentially designating the cells numbered 1-15 by letters A-O.
TABLE 4 Unit code symbols
| Numbering | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Encoding | A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | A14 | A15 |
2) Fuzzy clustering generates a plurality of population cells: setting a clustering characteristic factor: the unit layout cost Q, the unit area productivity T, the material flow distance product cost Z, the layout/process robustness R and the layout flexibility F are used, and the fuzzy clustering operation is carried out on all chromosomes by taking the comprehensive membership degree of the 5 characteristics as an index. The layout problem is complicated and variable, and the same layout scheme is allowed to be in multiple classifications at the same time. And completing fuzzy clustering operation, wherein the initial population is divided into a plurality of population cells, and each cell is a chromosome set with similar characteristics.
In the formula:
Fma clustering objective function, which represents the minimum comprehensive dissimilarity degree of all clustering characteristic factors of different population cells;
u(x)IJ-membership functions of layout scheme J in class I;
i-population index, which represents population unit cell I;
j-chromosome number, representing chromosome J;
g-clustering factor label, representing clustering factor G;
g is a population label which represents a population cell g;
cIcluster center of population I, i.e. the value of the 5 cluster features of the representative solution in the set;
cgcluster center of population g, i.e. the value of 5 cluster features of the representative solution in the set;
xJ-chromosome J in the population;
NIthe number of cells in the population, in the case NI＝8；
NJ-the number of chromosomes in the population of cells;
NG——number of clustering factors, in case NG＝5；
f is a fuzzy parameter which is larger than 1, and the value of f is 2;
3) and (3) fitness evaluation: the low-entropy layout model is a multi-objective function formed by low-entropy steady optimization in a controllable range with minimum carbon emission, the two functions are in a nonlinear relation, the carbon emission index factors have a mutual competition relation, in order to obtain a balanced solution meeting all targets and facilitate chromosome selection, a chromosome Pareto fitness solution set is calculated by using a double function, and a layout scheme with low carbon emission and low entropy in the controllable range is obtained. Through typical complex workshop layout case research and data analysis of more than ten enterprises, the entropy value H of the workshop robustness index is controlled within the range of [0.3-0.8], so that the low entropy requirement can be ensured, and the high robustness requirement that the entropy value is controlled within a reasonable range can be obtained.
Fit1＝QνQ+CT+CZ+CRF(formula 19)
4) Matching rules of population cells: and completing fuzzy clustering and fitness calculation to obtain a plurality of groups of population cells, wherein each cell is a similar chromosome set. In order to ensure the diversity of the population in the process of cooperative evolution to the maximum extent, all the cells are arranged in a descending order by taking the fitness Fit1 as a target, the cells are arranged by an insertion method and form a ring topology structure, and the pairing operation among the population cells is carried out. From 2), knowing that the number of the cells is 8, the matching arrangement rule is shown in figure 2: assuming that 8 population cells are arranged in sequence from high to low according to fitness values, the numbers of the cells are 1, 2, 3, 4, 5, 6, 7 and 8, the cell 1 is optimal in adaptation, the cells are 2 times, and the like, the cell 8 is worst, the cells 1, 2, 3 and 4 are arranged firstly by an insertion method, then the cell 5 is arranged between the cells 1 and 2, the cells 6, 3 and 4 are arranged between the cells 2 and 3, the cell 7 is arranged between the cells 3 and 4, and finally the cell 8 is arranged, connected in a head-to-tail manner to form a ring structure, and matched with cell combinations. And forming pairwise matched annular evolutionary topological structures. This operation ensures that there is a difference between the two matched cells, and the difference values are relatively close.
5) Chromosome selection: and designing a secondary displacement algorithm for selection. And adopting a direct competition mode of the children and the parents, wherein the competition contents comprise a carbon emission value and an entropy value. The algorithm proceeds as follows:
randomly selecting two father individuals p1 and p2 from the matched population cellgroup in a replacement mode;
performing crossover and mutation to generate offspring c1 and c 2;
calculating fitness values Fit1 and Fit2 according to the fitness function:
if Fit1(c) < Fit1(p), then
If Fit2(c1) < Fit2(p1), then replace p1 with c1, otherwise retain p 1;
if Fit2(c1) < Fit2(p2), then replace p2 with c1, otherwise retain p 2;
if Fit2(c2) < Fit2(p1), then replace p1 with c2, otherwise retain p 1;
if Fit2(c2) < Fit2(p2), then replace p2 with c2, otherwise retain p 2;
where Fit1(c) < Fit1(p) indicates that the fitness Fit1 of any child is less than that of the parent.
6) And (3) performing collaborative evolution of the population:
matching mixed cross operation among cells;
independent variation operation in each cell;
thirdly, immigration operation among the ring topology structure population cells: the selection, crossing and mutation operations are completed, a certain migration topology is appointed among the population cells, and the individual exchange mode among the sets is determined. For the adjacent cell, as A, B, the migration path is designed: and transferring a certain proportion of optimal individuals in the copied cellular A to the adjacent cellular B according to the path, and simultaneously removing the same proportion of worst individuals from the cellular B. All cells and their neighbor cells are operated in sequence. The immigration strategy can keep the diversity of the population and play a guiding role in the population evolution. The design migration path is shown in FIG. 2.
7) Termination conditions
After population initialization, performing fuzzy clustering, selection, intersection, variation, immigration and the like in a circulating mode, and when 50 Pareto solution sets are generated and the entropy value H is always within a theoretical controllable range [0.3-0.8], ending the circulation and outputting an optimal result.
After the model and the algorithm are applied to the specific implementation of the case, the obtained partial effective solutions are shown in table 5. The solution with sequence number 1 is selected as the optimal solution of the example layout, and the optimal chromosome code is as follows:
TABLE 5 Pareto solution set
The layout of the workshop in this embodiment is shown in fig. 3, the carbon emission and entropy change curve of the workshop is shown in fig. 4 and 5, and the comparison graph before and after optimization of each sub-target obtained by calculation is shown in fig. 6. The layout cost eventually converges to 16751.33 dollars, which is a 15.45% reduction in the overall cost of the layout compared to 19813 dollars for the original layout. For a complex workshop, the layout scheme obtained by applying the method can obviously reduce the total layout cost, and the workshop layout with low carbon emission and high robustness is obtained.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.
Claims (1)
1. A low-entropy layout and robust optimization method for a complex workshop is characterized by comprising the following steps:
step 1: low-carbon energy-saving objective function construction
1) Unit arrangement cost Q:
in the formula:
i-device number, representing device i;
j-element number, representing element j;
m is the total number of devices;
n is the total number of cells;
qi-cost of the equipment i;
F(ηj) -an aspect ratio evaluation function of cell j;
ηj-the aspect ratio of cell j;
hj-the height of the cell j;
wj-the width of cell j;
2) capacity per unit area T:
in the formula:
Tj-the capacity per unit area of unit j;
Pjk-the number of products k produced by unit j;
hj×wj-the area of cell j;
k is a product type label, which indicates a product k;
k is the total number of product types;
3) material flow distance product cost Z:
in the formula:
fjl-the flow of objects to the functional units j to l in the plant;
cjl-unit transportation cost between functional units j and l;
djl-distance of functional units j and l;
l-Unit number, denoting Unit l;
4) layout/process robustness R:
in the formula:
Lk-representing the processing distance of the product k when it has passed through the complete process route;
5) layout flexibility F:
in the formula:
Okthe number of units passed during production of product k;
Ukj-representing the theoretical loading of unit j to produce product k;
6) the low-carbon energy-saving layout integrated optimization model comprises the following steps:
CE＝min(Q×vQ+CT+CZ+CRF) (formula 8)
CZ＝fZ×Z×pk(formula 10)
CRF＝(1-R)fR+(1-F)fF(formula 11)
In the formula:
CE-Total carbon footprint;
CT-carbon emissions due to energy production;
CZcarbon emission caused by workshop workpiece transportation;
CRFexpected carbon emissions for future improvements due to robustness and flexibility;
vQ-arranging a cost carbon emission conversion factor;
fTj-carbon emission coefficient per unit area of unit j;
Fz-carbon deposit emission coefficient per unit volume distance;
Pk-the vehicle power for product k;
fZ-measuring the pitch carbon emission coefficient;
fR-a robust carbon emission coefficient;
fF-a flexible carbon emission coefficient;
step 2: complex workshop robust optimization model construction
In the formula:
h, the entropy of the workshop, which represents the measure index of the disturbance degree of the workshop;
A-Boltzmann constant;
n is the number of particles in the system, namely the product type in the workshop layout system;
a. b-System parameters;
wkthe energy owned in the system, i.e. the production cost of product k under this layout;
ck-the flow-volume product cost of product k;
w is the total cost of the layout;
α, β, γ, χ — a weighting factor, α + β + γ + χ ═ 1;
μ1-a unit area capacity cost conversion factor;
μ2-a layout/process robustness cost conversion factor;
μ3-laying out flexible cost conversion factors;
and step 3: complex workshop low-entropy layout model construction
In the formula:
CEmax-theoretical maximum carbon emission during layout of the plant;
CEmin-theoretical minimum carbon emission during plant layout;
and 4, step 4: the evolution steps of the circular multi-cell hybrid optimization algorithm are as follows:
step 41: chromosome coding/decoding, namely setting unit sequencing-segmentation mixed coding;
each chromosome is composed of a unit sequencing code and a unit dividing point code; the unit sorting code consists of n unit symbols, wherein n represents the number of workshop units and represents the arrangement sequence of the units from left to right and from top to bottom in a workshop; the division point code consists of n-1 binary codes of 0-1, and the insertion space is distributed in the unit sequencing coding interval; 0 represents that the units are in the same column, and 1 represents that the unit is the unit arranged at the last of the column;
wherein, a1, a2, A3, a4, a5, a6 represent unit numbers;
step 42: fuzzy clustering generates a plurality of population cells:
in the formula:
Fma clustering objective function, which represents the minimum comprehensive dissimilarity degree of all clustering characteristic factors of different population cells;
u(x)IJ-membership functions of layout scheme J in class I;
i-population index, which represents population unit cell I;
j-chromosome number, representing chromosome J;
g-clustering factor label, representing clustering factor G;
g is a population label which represents a population cell g;
cIcluster centers of population I, i.e. representative chromosomes in the set;
cgcluster centers of population g, i.e. representative chromosomes in the set;
xJ-chromosome J in the population；
NI-the number of population cells;
NJ-the number of chromosomes in the population of cells;
NG-the number of clustering factors;
f-blur parameter greater than 1;
step 43: and (3) fitness evaluation:
Fit 1＝Q×vQ+CT+CZ+CRF(formula 19)
Step 44: matching rules of population cells: completing fuzzy clustering and fitness calculation to obtain a plurality of groups of population cells, wherein each cell is a similar chromosome set; in order to ensure the diversity in the cooperative evolution process of the population to the maximum extent, all the cells are arranged in a descending order by taking the fitness Fit1 as a target, the cells are arranged by adopting an insertion method and form a ring-shaped topological structure, the pairing operation among the population cells is carried out, and the ring-shaped evolutionary topological structure matched with each other in pairs is formed; the operation ensures that the two matched cells have difference, and the difference values are relatively close;
step 45: chromosome selection: designing a secondary displacement algorithm for selection; adopting a direct competition mode of the children and the father, wherein the competition content comprises a carbon emission value and an entropy value; the algorithm proceeds as follows:
randomly selecting two father individuals p1 and p2 from the matched population cellgroup in a replacement mode;
performing crossover and mutation to generate offspring c1 and c 2;
calculating fitness values Fit1 and Fit2 according to the fitness function:
if Fit1(c) < Fit1(p), then
If Fit2(c1) < Fit2(p1), then replace p1 with c1, otherwise retain p 1;
if Fit2(c1) < Fit2(p2), then replace p2 with c1, otherwise retain p 2;
if Fit2(c2) < Fit2(p1), then replace p1 with c2, otherwise retain p 1;
if Fit2(c2) < Fit2(p2), then replace p2 with c2, otherwise retain p 2;
wherein Fit1(c) < Fit1(p) indicates that the fitness Fit1 of any child is smaller than that of the parent;
step 46: and (3) performing collaborative evolution of the population:
matching mixed cross operation among cells;
independent variation operation in each cell;
thirdly, immigration operation among the ring topology structure population cells: completing selection, crossing and variation operations, designing a certain migration topology among population cells, and determining the individual exchange mode among the sets; for adjacent cells, a chromosome migration path is designed as A, B: copying a certain proportion of optimal individuals in the cellular A to migrate to a neighborhood cellular B according to a path, and simultaneously removing the worst individuals with the same proportion from the cellular B; sequentially operating all the cells and the neighbor cells thereof; the immigration strategy can keep the diversity of the population and play a guiding role in the population evolution;
step 47: termination conditions
After population initialization, performing fuzzy clustering, selection, intersection, variation, immigration and the like in a circulating manner, and when N Pareto solution sets are generated and the entropy value H is always within a theoretically controllable range, ending the circulating process and outputting an optimal result.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711305854.0A CN107909223B (en) | 2017-12-11 | 2017-12-11 | Low-entropy layout and robust optimization method for complex workshop |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711305854.0A CN107909223B (en) | 2017-12-11 | 2017-12-11 | Low-entropy layout and robust optimization method for complex workshop |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107909223A CN107909223A (en) | 2018-04-13 |
| CN107909223B true CN107909223B (en) | 2020-11-13 |
Family
ID=61865259
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201711305854.0A Active CN107909223B (en) | 2017-12-11 | 2017-12-11 | Low-entropy layout and robust optimization method for complex workshop |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107909223B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108764741B (en) * | 2018-06-01 | 2019-10-18 | 英特尔产品（成都）有限公司 | For determining the method and device of the layout of the production equipment in factory set region |
| CN110472765B (en) * | 2019-06-25 | 2021-05-11 | 浙江工业大学 | Low-entropy collaborative optimization method for workshop layout scheduling |
| CN113536712B (en) * | 2021-07-29 | 2023-04-25 | 软通智慧信息技术有限公司 | Method, device, equipment and storage medium for optimally designing automobile appearance parameters |
| CN113761623A (en) * | 2021-08-30 | 2021-12-07 | 浙江工业大学 | Reconfigurable low-entropy-based intelligent workshop layout modeling and optimizing method |
-
2017
- 2017-12-11 CN CN201711305854.0A patent/CN107909223B/en active Active
Non-Patent Citations (4)
| Title |
|---|
| An effective artificial bee colony algorithm for the flexible job-shop scheduling problem;Ling Wang;《The International Journal of Advanced Manufacturing Technology》;20110902;第60卷(第1-4期);全文 * |
| 复杂车间低熵布局建模与稳健优化;陶维栋;《中国优秀硕士论文电子期刊网》;20190415;全文 * |
| 考虑布局熵的多态性车间布局稳健优化模型与算法;陈勇; 程子文; 姜枞聪; 王亚良; 王成; 郦仕云;《中国机械工程》;20190831;第30卷(第15期);全文 * |
| 面向低熵的一类多态性作业车间布局智能建模;陈勇; 许雅斌; 王成; 王亚良; 励秀宇;《浙江工业大学学报》;20170430;第45卷(第2期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107909223A (en) | 2018-04-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107909223B (en) | Low-entropy layout and robust optimization method for complex workshop | |
| Elsayed et al. | An improved self-adaptive differential evolution algorithm for optimization problems | |
| Bas et al. | A modified genetic algorithm for forecasting fuzzy time series | |
| Shang et al. | A multi-population cooperative coevolutionary algorithm for multi-objective capacitated arc routing problem | |
| CN109636043B (en) | Adaptive optimization method and system for power generation dispatching of cascade hydropower system | |
| CN106131862B (en) | Optimization covering method based on multi-objective Evolutionary Algorithm in a kind of wireless sensor network | |
| CN100582262C (en) | Copper flash smelting operation parameter optimization method | |
| Fan et al. | Angle-based constrained dominance principle in MOEA/D for constrained multi-objective optimization problems | |
| Jolai et al. | A variable neighborhood binary particle swarm algorithm for cell layout problem | |
| CN109460859A (en) | A kind of plant layout's optimization method | |
| CN105469118B (en) | The rare category detection method of fusion Active Learning and non-half-and-half supervision clustering based on kernel function | |
| Luo et al. | A hybrid algorithm combining genetic algorithm and variable neighborhood search for process sequencing optimization of large-size problem | |
| CN113052537A (en) | Logistics vehicle low-carbon route planning method based on heuristic particle swarm optimization | |
| Rajabalipour Cheshmehgaz et al. | Effective local evolutionary searches distributed on an island model solving bi-objective optimization problems | |
| Tavakkoli-Moghaddam et al. | Solving a dynamic cell formation problem with machine cost and alternative process plan by memetic algorithms | |
| Huang et al. | Competitive and cooperative-based strength Pareto evolutionary algorithm for green distributed heterogeneous flow shop scheduling | |
| CN103164487B (en) | A kind of data clustering method based on density and geological information | |
| Yu et al. | Multipopulation management in evolutionary algorithms and application to complex warehouse scheduling problems | |
| Li et al. | Optimizing combination of aircraft maintenance tasks by adaptive genetic algorithm based on cluster search | |
| Jain et al. | Solving travelling salesman problem using greedy genetic algorithm GGA | |
| Liu et al. | Optimization algorithm for rectangle packing problem based on varied-factor genetic algorithm and lowest front-line strategy | |
| Wu et al. | Intelligent automated control of life support systems using proportional representations | |
| CN107203805A (en) | A kind of many group's bi-directional drive collaborative searching algorithms under big data environment | |
| Farahmand et al. | Load balanced energy-aware genetic algorithm clustering in wireless sensor networks | |
| Ji et al. | Optimization and Integration of Logistics Facilities Resources Based on Genetic-Simulated Annealing Hybrid 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 | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |