CN108038339A - A kind of multiple target mixed flow two-sided assembly line balance method based on migratory bird optimization algorithm - Google Patents
A kind of multiple target mixed flow two-sided assembly line balance method based on migratory bird optimization algorithm Download PDFInfo
- Publication number
- CN108038339A CN108038339A CN201711493844.4A CN201711493844A CN108038339A CN 108038339 A CN108038339 A CN 108038339A CN 201711493844 A CN201711493844 A CN 201711493844A CN 108038339 A CN108038339 A CN 108038339A
- Authority
- CN
- China
- Prior art keywords
- task
- flying bird
- mrow
- assembly line
- algorithm
- 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
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- 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]
Landscapes
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- General Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Data Mining & Analysis (AREA)
- Biophysics (AREA)
- Biomedical Technology (AREA)
- Molecular Biology (AREA)
- Computing Systems (AREA)
- Computational Linguistics (AREA)
- Life Sciences & Earth Sciences (AREA)
- Mathematical Physics (AREA)
- Software Systems (AREA)
- Health & Medical Sciences (AREA)
- Computer Hardware Design (AREA)
- Geometry (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The present invention relates to a kind of multiple target mixed flow two-sided assembly line balance method, structure is minimizing station number, minimizing load balancing and minimizing mathematical model of the unit finished product totle drilling cost as target, multiple target mixing migratory bird algorithm is proposed to solve such MTALBP problems, devise the operation that corresponding flock of birds initializes, neck flying bird is evolved, evolves with flying bird and leads the processes such as flying bird replacement, and migratory bird algorithm is combined with multiple target greedy algorithm, the search capability of algorithm is further enhanced, faster to obtain more preferably Pareto solutions.
Description
Technical field
The present invention relates to machinery manufacturing technology field, and in particular to a kind of multiple target mixed flow based on migratory bird optimization algorithm is double
Side assembly line balancing method.
Background technology
Two-sided assembly line is that manufacturing field carries out producing the indispensable mode of production in enormous quantities, be widely used in car,
The assembling of the large products such as truck.From Bartholdi[1]Itd is proposed two-sided assembly line equilibrium problem (Two- first in 1993
SidedAssembly Line Balancing Problem, TALBP) since, attract more and more researchers to TALBP
Problem is studied.Compared to unilateral assembly line, two-sided assembly line can effectively shorten assembling line length, reduce assembling parts
Cost of transportation, improve utilization rate of mechanical equipment etc. on line.
In actual production assembling, it is often necessary to assemble the production of different cultivars at the same time on same two-sided assembly line
Product, to meet that the variation of product produces, that is, realize mixed-model assembly.With the diversified development of social demand, the bilateral dress of mixed flow
Distribution is increasingly welcome be subject to enterprise, mixed flow two-sided assembly line equilibrium problem (Mixed-model Two-sidedAssembly
Line Balancing Problem, MTALBP) also it is increasingly subject to the attention of researcher.
Mixed flow two-sided assembly line is mainly used on same two-sided assembly line while difference of the assembling with similar features
The product of kind, so as to fulfill the variation of assembly line product kind, meets in reality to the needs of product diversification production.Due to
There are many similar production features between different cultivars product, be placed on same assembly line and produce, product can be saved
Assembly cost, so as to fulfill the maximization of economic benefit.And problem of load balancing caused by mixed flow is consequently increased, face
New test.
2009,Deng[2]MTALBP models are established first and are solved using simulated annealing, together
Year, Simaria etc.[3]Multiple target MTALBOP is solved using ant group algorithm；2012, Chutima etc.[4]It is proposed has negative
The particle swarm optimization algorithm of knowledge, solves multiple target MTALBOP.Delice in 2014 etc.[5]With Yuan in 2015 etc.[6]
It is proposed that Modified particle swarm optimization algorithm and blending honey mating optimization algorithm solve MTALBP respectively.Then, 2016
Li Zi sound etc.[7]With Tang Qiuhua in 2017 etc.[8]It is proposed that Iterated Local Search algorithm and improvement Iterated Local Search algorithm are asked respectively
The problem is solved, and obtains preferable solution.The research for two-sided assembly line is concentrated mainly on single model TALBP at present, for multimode
The MTALBP of type is relatively fewer, and the research to multiple target is then more rare.
Compared to common assembly line balancing problem (Assembly Line Balancing Problem, ALBP),
MTALBP is increasingly complex NP-hard combinatorial optimization problems, solves the complexity of problems with the increase of problem scale
And exponentially increase.In the meta-heuristic algorithm applied in problems mentioned above, ant group algorithm, ant colony algorithm
Easily occur that local search ability is low in practical applications with particle cluster algorithm etc. and poor astringency etc., simulated annealing and repeatedly
The problems such as relatively low to the search efficiency in global search space is then shown for local search algorithm.Therefore, seek to be adapted to answer
Novel algorithm in this problem is most important.
Bibliography：
[1].J.J.Barthodi.Balancing two-sided assembly lines：a case study[J]
.International Journal ofProduction Research,1993,31(10):2447-2461.
[2]. U,TOKLU B.Balancing ofmixed-model two-sided assembly
lines[J].Computers&Industrial Engineering,2009,57(1):217-227.
[3].Simaria,A.S.and Vilarinho,P.M.2-ANTBAL:An ant colony optimisation
algorithm for balancing two-sided assembly lines[J].Computers and
IndustrialEngineering,2009,56:489-506.
[4].CHUTIMA P,CHIMKLAI P.Multi-objective two-sided mixed-model
assembly line balancing using particle swarm optimization with negative
knowledge[J].Computers&Industrial Engineering,2012,62(1):39-55.
[5].DELICE Y,E K,U,M.A modified particle
swarm optimization algorithm to mixedmodel two-sided assembly line balancing
[J].Journal of Intelligent Manufacturing,2014,DOI10.1007/s 10845-014-0959-7.
[6].YUAN Biao,ZHANG Chaoyong,SHAO Xinyu,JIANG Zhibin.An effective
hybrid honey bee mating optimization algorithm for balancing mixed-model two-
sided assemblylines[J].Computers&Operations Research,2015,53:32-41.
[7] Li Zi are rung, the Iterated Local Searchs such as Tang Qiuhua solve [J] the Machine Designs of two-sided assembly line equilibrium problem with
Manufacture, 2016 (3):54-57.
The such as [8] Tang Qiuhua, Rao Di improve Iterated Local Search Algorithm for Solving I class mixed flow two-sided assembly line equilibrium problem
[J] computer integrated manufacturing systems：1-14.(2017-04-15)[2017-08-20].
[9].Duman E,Uysal M,Alkaya AF.Migrating Birds Optimization:A new
metaheuristic approach and its performance on quadratic assignment problem
[J].Information Sciences,2012,217:65-77.
[10].Alkaya AF,Algin R,Sahin Y,Aksakalli MAV.Performance of migrating
birds optimization algorithm on continuous functions[J].Advances in Swarm
Intelligence Lecture Notes in Computer Science.2014,8795:452-459.
[11].Makas H,Yumusak N.New Cooperative and Modified Variants of the
Migrating Birds Optimization Algorithm.2013International Conference on
Electronices,Computer and Computation(ICECCO),2013,pp.176-179.
[12].Shen LW,Asmmuni H,Weng FC.A modified migrating bird optimization
for university course timetabling problem[J].Jurnal Teknologi(Science&
Engineering),2015,72(1):89-96.
[13].Pan QK,Dong Y.An improved migrating birds optimization for a
hybrid flowshop scheduling with total flowtime minimization[J].Information
Science,2014,277:643-655.
[14] thanks to limited buffer Flow Shop optimizing scheduling research [D] the Central China of Zhan Peng based on migratory bird optimization algorithm
University of Science and Technology, 2015.
[15].ROSHANI A,FATTAHI P.Cost-oriented teo-sided assembly line
balancing problem:a simulated annealing approach[J].International Journal of
Computer IntegratedManufacturing,2012,25(8):689-715.
[16].W.B.Helgeson,D.P.Birnie.Assembly line balancing using the ranked
positional weight technique[J].Journal of Industrial Engineering,1961(12):
394-397.
[17].TSENG H E.Guided genetic algorithms for solving alarger
constraint assembly problem[J].International Journal of Production Research,
2006,44(3):601-625.
The such as [18] Dashuang Lis, Zhang Chaoyong based on multiple target colonize Competitive Algorithms stochastic pattern two-sided assembly line [J] calculate
Machine integrated manufacturing system, 2014,20 (11):2774-2787.
The content of the invention
The present invention is directed to technical problem existing in the prior art, there is provided a kind of multiple target based on migratory bird optimization algorithm is mixed
Two-sided assembly line balance method is flowed, is built minimizing station number, minimizing load balancing and minimizing unit finished product totle drilling cost
For the mathematical model of target, multiple target mixing migratory bird algorithm is proposed to solve such MTALBP problems, devises corresponding flock of birds
The operation initialize, lead flying bird to evolve, evolved with flying bird and lead the processes such as flying bird replacement, and migratory bird algorithm is greedy with multiple target
Algorithm is combined, and further enhances the search capability of algorithm, faster to obtain more preferably Pareto solutions.
The technical solution that the present invention solves above-mentioned technical problem is as follows：A kind of multiple target mixed flow two-sided assembly line balance side
Method, comprises the following steps：
Step 1, according to mixed flow two-sided assembly line equilibrium problem feature, establish and station number is minimized with assembly line, is minimized
Load balancing and the mathematical model that minimum unit finished product totle drilling cost is target；
Step 2, the method being combined using the heuristic initialization of NEH and random initializtion carries out just the mathematical model
Beginningization, generates multigroup initial solution, and these solutions are ranked up using quick non-dominated ranking algorithm, obtains multiple boundary sets,
The characteristics of optimizing algorithm according to migratory bird, choosing the individual of crowding distance maximum in first boundary set becomes the neck flying bird of population,
Two individuals in each boundary set are chosen as population with flying bird according to the size of crowding distance successively；Maximum is set at the same time
The touring number G and touring number g=1 of initialization；
Step 3, neighbour structure is selected to produce neck flying bird and multiple neighbours with flying bird according to default selection strategy respectively
Domain solves, and carries out non-dominated ranking, and lookup can dominate neck flying bird or with the individual of flying bird and replace the neck flying bird or with flying bird,
Realize the neck flying bird and the evolution with flying bird；
Step 4, non-dominant disaggregation is updated, and each non-domination solution concentrated for non-domination solution uses multiple target iteration
Greedy algorithm carries out local search；
Step 5, if touring number g is less than maximum touring number G, g=g+1, and step 3 is jumped to, otherwise g=is set
1, and concentrate a selection individual to replace neck flying bird in current non-domination solution；
Step 6, judge whether to meet algorithm stop criterion, if not meeting, jump to step 3, otherwise, algorithm terminates,
Non-dominant disaggregation is exported, the non-dominant disaggregation is the optimal solution of mixed flow two-sided assembly line equilibrium problem.
The beneficial effects of the invention are as follows：Herein for mixed flow two-sided assembly line problem, construct to minimize station number, most
Smallization load balancing and minimum unit finished product totle drilling cost are the object and multi object mathematical model of target, and propose that multiple target mixes migratory bird
Optimization (MOHMBO) algorithm is solved.Migratory bird optimization algorithm realization it is simple, search capability is strong, robustness is good, migratory bird is calculated
Method is combined with multiple target greedy algorithm, further enhances the search capability of algorithm, faster to obtain more preferably Pareto solutions.
Brief description of the drawings
Fig. 1 is a kind of multiple target mixed flow two-sided assembly line balance method flow chart provided in an embodiment of the present invention；
Fig. 2 (a) is product A priority of task graphs of a relation；
Fig. 2 (b) is product B priority of task graphs of a relation；
Fig. 2 (c) is the Joint Task dominance relation figure of product A and product B；
Fig. 3 is the decoding process figure described in step 203；
Fig. 4 is neighbour structure schematic diagram；
Fig. 5 is multi-objective problem P65 and P148 parts case Pareto forward positions figure.
Embodiment
The principle of the present invention and feature are described below in conjunction with example, the given examples are served only to explain the present invention, and
It is non-to be used to limit the scope of the present invention.
1 mixed flow two-sided assembly line equilibrium problem
1.1 problems describe
Mixed flow two-sided assembly line is generally used for a set product of the assembling with similar production feature, and each product has oneself
Priority of task ordinal relation, the priority of task graph of a relation of all products can be merged into a priority of task graph of a relation.Fig. 2
(a) the priority of task graph of a relation of product A and product B are represented respectively with Fig. 2 (b), the joint that Fig. 2 (c) is product A and product B is appointed
Business dominance relation figure.Wherein, a task in each circle representative products, numeral and letter on circle in square brackets are then divided
Operating time and the operative orientation (L- left bits, R- right bits, E- arbitrary orientations) of task are not expressed as, and arrow then represents task
Between precedence relationship.The operating time of each task of identical product is fixed, the operation of the same task of different product
Time can be different, and the same task of different product has identical operative orientation attribute.When a kind of product need not assemble certain
During one task, the operating time of the task is arranged to 0.Based on above-mentioned attribute, the Joint Task of product A and product B can obtain
Shown in dominance relation figure such as Fig. 2 (c), which contains all operation tasks of product A and product B.
According to priority of task relation, all tasks of each product of hybrid precast are assigned to each operation position of assembly line
In, operating time of every kind of product in station is satisfied by pitch time constraint, priority constraint and operative orientation constraint.
Processing for the operating time of task on mixed flow two-sided assembly line, since non-weighting scheme is requiring every kind of product
Each task meet beat constraint while, more highlight load total amount of every kind of product in each station and be less than
Pitch time, is advantageously implemented the load balance of each station on assembly line, during herein using nonweighted mode to task operating
Between handled.
Assuming that the yield of product is P, the yield of model m is Dm, then the pitch time CT of two-sided assembly line and model m institutes are right
The assembling accounting q answeredmIt can be determined by following formula：
1.2 mathematical model
I class mixed flow two-sided assembly line is exactly given productive temp, is meeting that beat constrains, operative orientation constrains and preferential
On the premise of ordinal relation constrains, paired station quantity and chief engineer's bit quantity are minimized.Herein, construct with minimum chemical industry
Digit, minimize load balancing and minimize the mathematical model that unit finished product totle drilling cost is target, solves multiple target MTALBP.Number
Learn model and object function is as follows：
(1) mathematical model
Its each constraint equation is as follows：
Formula (2) ensures that each task is only assigned to a station.Formula (3) is then that dominance relation constrains, between guarantee task
Dominance relation constraint be met.Formula (4) is pitch time constraint, deadline of each task will pitch time it
It is interior.Formula (5)-(7) control the influence of priority of task relation pair task completion time in each product model, for every a pair of of task
(i, h), if task h is the precedence activities of task i, and two tasks are dispensed in same station j in pairs, then formula
(5) work, i.e., If there is no dominance relation constraint between two tasks, and they
It is assigned in identical station (j, k), then using formula (6) and (7)；When task i distribution more early than task p, formula (6) is changed into Otherwise formula (7) is changed intoFormula (8) and (9) are
Integrity constraint.Formula (10) then ensures that the deadline of each task is greater than the operating time equal to the task.
Symbol implication is as follows in formula：
I, p, h, r task
The paired station of j, g
M product types
The orientation of k operation positions
Set of tasks in I joint dominance relation figures, I={ 1,2 ..., i ..., nt
The paired station set of J, J={ 1,2 ..., j ..., nm }
M product model set, M={ 1,2 ..., m ..., np }
The precedence activities set of P (i) tasks i
Pa(i) all preamble set of tasks of task i
The successor activities set of S (i) tasks i
Sa(i) all postorder set of tasks of task i
P0Set of tasks without precedence activities,
timThe operating time of the i tasks of m type products
One very big integer
Set of tasks opposite with task i operation positions C (i),
The optional operation position set of K (i) tasks i,
CT pitch times
xijkIt is otherwise 0 for 1 if task i is assigned to station (j, k)
The deadline of the task i of m type products
zipIf task i is first distributed than p in same station, it is worth for 1, is otherwise 0
(2) object function
In actual production process, the situation that assembly line faces in design and producing is more complicated, it usually needs same
When consider plurality of target in the hope of reaching the balance of production, these targets be probably it is compatible be also likely to be conflicting.At this
Wen Zhong, it will be considered that minimize station number, minimize load balancing and minimize unit finished product three targets of totle drilling cost.
Typically for minimizing shown in the processing such as following formula (11) of station number, the object function is by paired station number and always
Station number considers together, and assigns different weights, while both are optimized, and assembly line will be caused by minimizing station number
Length and required operative employee's number are minimum.
min wnm×nm+wns×ns (11)
Wherein：Nm and ns is expressed as to station quantity and chief engineer's bit quantity, wnmAnd wnsRepresent corresponding weighting coefficient, one
As be set to 2 and 1.
It is to reduce load difference to minimize load balancing, considers mixed flow characteristic, is divided into two parts：Loaded between standing equal
Weigh BbWith load balancing B in stationw.Wherein BbIt is in order to enable the free time of each station is equal as far as possible, so that each behaviour
It is as equal as possible to make the task amount that worker is undertaken, BwThen ensure that each work station handles roughly the same workload, and from
The limitation of the product type produced[3]。
Wherein ns is station number, and nm is paired station number, and np is model quantity, and WIT is weighting free time and sjkFor work
Stand (j, k) free time and, sjkmIt is as follows in the free time of work station (j, k), calculation formula for model m：
When the free time of assembly line being equal to the free time of one of station, Bb1 is maximized, works as all working
It is minimized when station evenly distributes as 0；The B when the free time of each work station only having a kind of model to producewIt is maximized 1,
When all models are minimized as 0 when each work station evenly distributes.
Due to BbAnd BwValue range be [0,1], and the value of station number then changes with the difference of problem scale
Become, for more optimization of the visual representation to station number, select the permanent weighting line efficiency WLE for [0,1] of value range as most
The performance indicator of small chemical industry digit carries out objective optimization, and ns is chief engineer's digit：
In order to more efficient acquisition preferably task allocative decision, guaranteeing to optimize B at the same timeb、BwBefore WLE
Put, it is as follows to be merged into formula into a minimum target by nonlinear combination by three：
3rd target is to minimize unit finished product totle drilling cost Cost, is broadly divided into labor cost and cost of investment (bag
Include mechanical equipment cost and transporting equipment cost).Labor cost is by distributing the average wage rate of task on each station
Determine, the labor rate (w of taski) paid by pitch time, mechanical equipment cost is determined by chief engineer's digit, transporting equipment cost by
Line length is assembled to determine.In conclusion according to Roshani in the formula provided in 2012, the meter of unit finished product totle drilling cost is drawn
It is as follows to calculate formula[15]：
C in formulaSSCAnd CMSCThe corresponding mechanical equipment cost of single station is represented respectively and single station is corresponding sets in pairs
Standby cost of transportation, herein, for benchmark problem P65, P148 and P205, CSSCAnd CMSCValue and Dashuang Li text in data
Unanimously[13], it is set to 500 and 800.
2 multiple targets mixing migratory bird optimization Algorithm for Solving multiple target mixed flow two-sided assembly line equilibrium problem
Migratory bird optimization (Migrating Birds Optimization) algorithm is Duman etc.[9]Itd is proposed first in 2011
A kind of meta-heuristic algorithm inspired naturally, be a kind of emerging algorithm based on neighborhood search, by simulating migratory bird moving mistake
V-shape (chevron shaped) flight formation is kept to be optimized to reduce energy expenditure in journey.The step of migratory bird optimization algorithm, is divided into
Initialization, neck flying bird evolve, evolve with flying bird and lead flying bird to replace.To solve multi-objective problem, optimize algorithm in migratory bird herein
Middle addition Pareto optimal solutions thought and multiple target greedy algorithm are combined into multiple target mixing migratory bird optimization algorithm (Multi-
objectiveHybridMigrating Birds Optimization,MOHMBO)。
2.1 quick non-dominated ranking algorithms
In the multi-objective Algorithm based on the non-dominant disaggregation of Pareto, non-dominant disaggregation will be updated per a generation,
Pareto disaggregation is established using quick non-dominated ranking algorithm herein.Quick non-dominated ranking algorithm can be divided into two steps：The
One step calculate population in each individual i by domination individual amount niWith the individual collections S dominated by individual ii；Second step is
All individuals are divided into each boundary set P1, P2..., Pm.Wherein PiFor the individual collections for being i-1 by domination number of individuals.
Population is divided into m boundary set by quick non-dominated ranking, and the wherein small boundary set of sequence number dominates the big border of sequence number
Collection.So we can distinguish the quality between boundary set, and for the individual in same boundary set, then taken with focusing distance
House.The density that the big individual of focusing distance is solved around it is small, and in order to keep the diversity and the distributivity that are solved in population, we are general
Selective focus is apart from big individual.Shown in the calculation formula of focusing distance following (20)：
Dis [i]=(dis [i+1] * f1-dis[i-1]*f1)+(dis[i+1]*f2-dis[i-1]*f2) (20)
In formula, dos [i] represents the focusing distance of individual i in population, f1, f2Represent respectively with Combinedfintess and
Cost is two object functions of target.For the individual at boundary set both ends, focusing distance is set to infinitely great.
In the evolutionary process of population, small of boundary set sequence number is selected when two positions are in different boundary sets
Body, and selective focus is apart from big individual when positioned at same boundary set.
2.2 initialization
Migratory bird optimization algorithm is similar with genetic algorithm, and a kind of colony's optimization algorithm based on population, in population
Body becomes " migratory bird ", represents the possibility solution of combinatorial optimization problem.Each task is combined into one according to task finite relationship figure
The process of task sequence is known as encoding, and decoding is then to select the task in sequence successively and be assigned in corresponding station.
2.2.1 the heuristic initialization of NEH
In order to improve the quality of algorithm initial solution and accelerate algorithm search speed, the heuristic initial methods of NEH are designed,
Its main thought is：Coding mode based on priority, according to classification position power (RPW)[16]Obtain the initial priority of each task
Weights, then arrange to obtain task sequence according to the size descending of priority valve.Due between each task there are priority about
Beam, to meet that priority constrains, using TSENG[17]The y-bend tree adjustment method of proposition is not to meeting the task of sequence constraint
Sequence is adjusted.Heuritic approach step is as follows：
Step 1：Weigh to obtain task sequence SEQ (SEQ={ task based on classification position1, task2... taskn})；
Step 2：I=1 is set；
Step 3：By i-th of task taskiRemoving, the task sequence after removal is SEQ ', and by taskiIt is inserted into SEQ '
Each position obtain new task sequence, decoded, be replaced if more excellent than current solution；I=i+1；
Step 4：If i≤n, repeat step 3, otherwise algorithm termination.
2.2.2 coding/decoding method
, it is necessary to consider the pitch time constraint of task, dominance relation constraint and operative orientation constraint during decoding.For operation
Orientation is the task of E, and a station is randomly choosed if identical between at the beginning of the station of left and right, otherwise, is assigned to relatively early open
The station of beginning.In selection operation station it should be noted that if left and right station is not belonging to same paired station, meeting to save
On the premise of clapping the time, the station small to station sequence number is first chosen to.Decoding process is as shown in Figure 3：
2.2.3 flock of birds initializes
In order to ensure the quality of initial flock of birds, NEH algorithms are used herein using the Combinedfintess of formula (18) as target
An initial solution is produced, then produces an initial solution by target of the Cost of formula (19).In order to ensure the distribution of initial flock of birds
Property, we randomly generate one group of initial solution again, i.e., task sequence is produced by the way of generating at random is encoded, and adjust task
Decoded after sequence.These solutions of generation are put into a set, these solutions are ranked up using quick non-dominated ranking,
Obtain boundary set.Two solutions are randomly selected from each boundary set and form the initial flock of birds that we need.In first boundary set
The individual of middle crowding distance maximum becomes neck flying bird.
Encoded and decoding process obtains a feasible solution.These solutions are put into a set, using quick non-dominant
Sort algorithm is ranked up these solutions, obtains boundary set.Two solutions are randomly selected from each boundary set to form needed for us
The initial flock of birds wanted.The individual of focusing distance maximum becomes neck flying bird in first boundary set.
2.3 flocks of birds are evolved
Flock of birds is evolved and with flying bird evolution into neck flying bird is divided into.Wherein flying bird is led to evolve by itself neighborhood solution, and with
Flying bird is then evolved by the combination of sets of itself neighborhood solution and the untapped neighborhood solution for coming its bird generation in front.Using four kinds
Neighbour structure：Exchange, be forwardly inserted, being inserted back into and backward.We are by producing a random number R, according to the scope of R to neighbour
Domain structure makes choice.The schematic diagram of four kinds of neighbour structures is as shown in Figure 4.
Flying bird is led to evolve by following strategy：K neighborhood solution is produced, to these neighborhood solutions progress non-dominated ranking, obtains the
The individual of focusing distance maximum in one boundary set.Then by this individual compared with leading flying bird, if the individual dominates
Flying bird is led, then replaces neck flying bird with the individual, otherwise, neck flying bird is constant.The more excellent neighborhood solution that x of high-ranking military officer flying bird do not use passes
To next individual.
In order to which algorithm is absorbed in local optimum too early, following evolution strategy is taken with flying bird：For every with flying bird, produce
K-x neighborhood solution, the x neighborhood solution transmitted with individual above are merged into a set, carry out non-dominated ranking, equally find
The individual of focusing distance maximum in first boundary set, if the individual is dominated with flying bird, is replaced, otherwise, under
Formula calculates acceptance probability：
Wherein,WithIt is the neighborhood solution using Combinedfintess as the object function of target respectively
And primitive solution；WithMake respectively to minimize neighbours of the unit finished product totle drilling cost Cost as the object function of target
Domain solves and primitive solution.
2.4 local searching strategy
In the MOHMBO algorithms of this paper, in order to further enhance the search capability of algorithm, a kind of multiple target iteration is added
Greedy (Multi-objective Iterated Greedy, MOIG) algorithm, which acts only on updated in every generation
Non-dominant disaggregation.The step of MOIG algorithms, is as follows：
Step 1：Each non-domination solution concentrated for non-domination solution, performs step 2-7；
Step 2：Random erasure task sequence SEQiIn d task, and by these tasks deposit task sequence SEQdIn,
SEQiDelete the task sequence SEQ after d taskrRepresent.
Step 3：The non-dominant disaggregation of part task sequence is represented with NDS, starts only SEQ in NDSr；I=1 is set；
Step 4：By each task sequence SEQdIn each task insertion NDS in it is all individual all possible
Position, obtains r+1 task sequence, carries out quick non-dominated ranking to them, obtains new non-dominant disaggregation NWS；
Step 5：NDS=NWS, empties NWS, if i such as d, i++, and return to step 4；
Step 6：Export the non-dominant disaggregation NDS of complete series of tasks.
2.5 neck flying birds are replaced
Due to neck flying bird, awing suffered air drag is maximum, leads flying bird to occur after flight a period of time tired
Labor, at this moment needs other migratory birds to replace becoming new neck flying bird, and front neck flying bird falls back on tail of the queue and becomes with flying bird.It is right herein
Lead the replacement processing of flying bird as follows：After touring number is reached, neck flying bird will be replaced, and randomly choose current non-dominant disaggregation
In an individual to neck flying bird be replaced.
2.6 MOHMBO algorithm flows
MOHMBO algorithm flows proposed in this paper, as shown in Figure 1, comprising the following steps：
Step 1：Initialization.Set parameters and algorithm stop criterion.Initial method in 2.2 sections carries out
Initialization.NEH algorithms are used to produce an initial solution by target of the Combinedfintess of formula (18), then with formula (19)
Cost for target produce an initial solution, we randomly generate one group of initial solution again.These solutions of generation are put into a collection
Close, these solutions are ranked up using quick non-dominated ranking, the individual of crowding distance maximum becomes in first boundary set
Flying bird is led, taking out two individuals successively from each boundary set becomes with flying bird.Touring number counter g=1 is set；
Step 2：Flying bird is led to evolve.Selection strategy selection neighbour structure in 2.3 sections produces the k neighborhood of neck flying bird
These neighborhood solutions are carried out non-dominated ranking, the individual of focusing distance maximum in first boundary set are obtained, then by this by solution
Individual is compared with leading flying bird, if the individual can dominate neck flying bird, with its replacement neck flying bird, otherwise, neck flying bird protects
Hold constant.Untapped x preferably neighborhood solutions are inserted into PlAnd Pr, the PlAnd PrThe respectively left queue of migratory bird population and right team
The neighborhood disaggregation of row.
Step 3：Evolve with flying bird.According to the method introduced in 2.3 sections, for left queue LlIn each solution S ∈ Ll, press
The k-x neighborhood solution S of S is produced according to selection strategy selection neighbour structure1, S2..., Sk-x}.To set N={ S1, S2..., Sk-x}
∪PlIn individual carry out non-dominated ranking, equally find the individual of focusing distance maximum in first boundary set, if this
Body is dominated with flying bird, then is replaced with flying bird, otherwise calculate acceptance probability by formula (21), connect if the random number produced is less than
Then replaced by probability, otherwise without replacing.Empty Pl, untapped x in set N preferably solutions are inserted into Pl；
Step 4：For right queue LrIn each solution S ∈ Lr, k-x of S are produced according to selection strategy selection neighbour structure
Solve { S1, S2..., Sk-x}.To set N={ S1, S2..., Sk-x}∪PrIn individual carry out non-dominated ranking, equally find first
The individual of focusing distance maximum in a boundary set, if the individual is dominated with flying bird, is replaced with flying bird, otherwise by formula
(21) acceptance probability is calculated, is replaced if the random number produced is less than acceptance probability, otherwise without replacing.Empty Pr, will
Untapped x preferably solutions insert P in set Nr；
Step 5：Update non-dominant disaggregation；
Step 6：Local search is carried out to non-dominant disaggregation using the MOIG algorithms in 2.4 sections；
Step 7：If counter g for example touring number G, g=g+1, recall to step 2.Otherwise, g=1 is set, according in 2.5 sections
The method of introduction, concentrates a random selection individual to replace neck flying bird in current non-domination solution；
Step 8：If not yet meeting algorithm stop criterion, step 2 is recalled to.Otherwise, algorithm terminates, and exports non-dominant disaggregation.
3 sample calculation analysis
To verify the validity of MOHMBO, Example Verification will be carried out to two base cases of P65 and P148 herein.Target is
Composite object Combinedfitness is solved with formula (18), unit finished product totle drilling cost Cost is solved with formula (19).For each
The data source of the labor rate of task is in the document of 2012 such as Roshani[15], the labour cost of each station is by the station institute
The average wage rate for getting task determines.Iterations for benchmark problem P65 and P148 is respectively 200 and 300.For into
The iterations for the quick non-dominated sorted genetic algorithm (NSGA- II) that row compares also is set to consistent with this algorithm.All cases
Calculate 10 times.
This paper all problems are programmed using C Plus Plus, and volume is used as using MicrosoftVisual Studio 2010
Cheng Pingtai, is transported on the personal computer of Intel (R) Core (TM) i3-2350M CPU 2.3HZ 2.29GHZ, 6GB memories
OK.The parameter setting of MOHMBO algorithms is as follows：The individual amount S=51 of initial flock of birds, the neighborhood solution of each individual need it is total
Number k=3, each individual are transmitted to next individual neighborhood solution quantity x=1, touring number G=10, remove and reconstructed operation
Parameter d=8.
In order to compare two multi-objective Algorithms as a result, with reference to Dashuang Li etc.[18], using the average specific of Pareto optimal solutions
The quantization means method of rate as a result.Use P1And P2Represent that mixing improves CCA and II algorithms of NSGA- calculate gained respectively
Pareto optimal solution sets, P represent P1And P2Union, i.e. comprise only non-domination solution in P.Therefore PiIn Pareto optimal solutions not
It is by the probability that the unlock in P dominates：
Y ＞ X represent that solution X is dominated by solution Y in formula.Rate value R (Pi) is more big, illustrates that algorithm is better.Two benchmark cases
Result of calculation it is as shown in the table：
1 multiple target example result of calculation of table
From table 3 it can be seen that all ratios that MOHMBO algorithms calculate gained are all higher than NSGA- II, except the CT381 of P65
Case makes an exception, and the required rate value of all case problems is all higher than 0.75, and has multiple solutions to reach 1.00, and the ratio of NSGA- II
Below 0.40, illustrate that MOHMBO algorithms possess very strong optimal solution search ability.Fig. 5 will provide several specific case row
Pareto forward positions figure.As shown in figure 5, the obtained point of MOHMBO Algorithm for Solving is located substantially on below NSGA- II, i.e.,
The solution performance of MOHMBO algorithms is better than NSGA- II.
Test result indicates that MOHMBO algorithms possess stronger search capability, asked applied to mixed flow two-sided assembly line balance
In the solution of topic, effectively and stablize.
Herein for mixed flow two-sided assembly line problem, construct to minimize station number, minimize load balancing and minimum
Change unit finished product totle drilling cost and be the object and multi object mathematical model of target, and propose multiple target mixing migratory bird optimize (MOHMBO) algorithm into
Row solves, and is the validity of verification algorithm, and P65 and the extensive problems of P148 two solved, and with quickly non-dominant row
Sequence heredity (NSGA- II) algorithm is contrasted, the results showed that the validity and stability of MOHMBO algorithms.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all the present invention spirit and
Within principle, any modification, equivalent replacement, improvement and so on, should all be included in the protection scope of the present invention.
Claims (8)
1. a kind of multiple target mixed flow two-sided assembly line balance method, it is characterised in that comprise the following steps：
Step 1, according to mixed flow two-sided assembly line equilibrium problem feature, establish and station number is minimized with assembly line, minimizes load
Mathematical model balanced and that minimum unit finished product totle drilling cost is target；
Step 2, the method being combined using the heuristic initialization of NEH and random initializtion carries out the mathematical model initial
Change, generate multigroup initial solution, and these solutions are ranked up using quick non-dominated ranking algorithm, obtain multiple boundary sets, root
The characteristics of optimizing algorithm according to migratory bird, choosing the individual of crowding distance maximum in first boundary set becomes the neck flying bird of population, root
Two individuals in each boundary set are chosen successively as population with flying bird according to the size of crowding distance；Maximum is set to patrol at the same time
The round trip number G and touring number g=1 of initialization；
Step 3, neighbour structure is selected to produce neck flying bird and multiple neighborhood solutions with flying bird according to default selection strategy respectively,
And non-dominated ranking is carried out, lookup can dominate neck flying bird or with the individual of flying bird and replace the neck flying bird or with flying bird, realize
The neck flying bird and the evolution with flying bird；
Step 4, non-dominant disaggregation is updated, and it is greedy using multiple target iteration for each non-domination solution that non-domination solution is concentrated
Algorithm carries out local search；
Step 5, if touring number g is less than maximum touring number G, g=g+1, and step 3 is jumped to, otherwise g=1 is set, and
A selection individual is concentrated to replace neck flying bird in current non-domination solution；
Step 6, judge whether to meet algorithm stop criterion, if not meeting, jump to step 3, otherwise, algorithm terminates, output
Non-dominant disaggregation, the non-dominant disaggregation are the optimal solution of mixed flow two-sided assembly line equilibrium problem.
A kind of 2. multiple target mixed flow two-sided assembly line balance method according to claim 1, it is characterised in that institute in step 2
That states initializes the mathematical model using NEH initialization and random initializtion method, generates multigroup initial solution, wraps
Include：
First, using the heuristic initial methods of NEH, an initial solution is produced as target to minimize composite object, then with
Minimize unit finished product totle drilling cost and produce an initial solution for target, then randomly generate one group of initial solution, i.e., using random generation
Mode produce task sequence and encoded, decoded after adjusting task sequence.
3. a kind of multiple target mixed flow two-sided assembly line balance method according to claim 2, it is characterised in that described
The heuristic initial method steps of NEH are as follows：
Step 201, the coding mode based on priority, weighs to obtain the initial priority weights of each task, then according to classification position
Size descending according to priority valve arranges to obtain task sequence SEQ (SEQ={ task1, task2... taskn})；
Step 202, i=1 is set；
Step 203, by i-th of task taskiRemoving, the task sequence after removal is SEQ ', and by taskiIt is inserted into SEQ's '
Each position obtains new task sequence, is decoded, and is replaced if more excellent than current solution；I=i+1；
Step 204, if i≤n, repeat step 3, otherwise algorithm termination, exports task sequence.
A kind of 4. multiple target mixed flow two-sided assembly line balance method according to claim 3, it is characterised in that the step
Rapid 203 include：, it is necessary to consider the pitch time constraint of task, dominance relation constraint and operative orientation constraint during decoding.
A kind of 5. multiple target mixed flow two-sided assembly line balance method according to claim 4, it is characterised in that the step
Rapid 203 specifically include：The operative orientation includes left bit L, right bit R and arbitrary orientation E；It it is appointing for E for operative orientation
Business, randomly chooses a station if identical between at the beginning of the station of left and right, otherwise, is assigned to the station more early started；
During selection operation station, if left and right station is not belonging to same paired station, on the premise of pitch time is met, preferential choosing
It is selected to the station small to station sequence number.
A kind of 6. multiple target mixed flow two-sided assembly line balance method according to claim 1, it is characterised in that the step 3
Including：
For neck flying bird：For exchange, be forwardly inserted, be inserted back into four kinds of neighbour structures of backward, pass through random number R selection appoint
A kind of neighbour structure, produces the k neighborhood solution of neck flying bird, carries out non-dominated ranking to these neighborhood solutions, obtains first border
The individual of focusing distance maximum is concentrated, then by the individual compared with leading flying bird, if the individual dominates neck flying bird, is used
The individual replaces neck flying bird, and otherwise, neck flying bird is constant；The x of the high-ranking military officer flying bird more excellent neighborhood solutions do not used be transmitted to it is next each and every one
Body；
For with flying bird：For exchange, be forwardly inserted, be inserted back into four kinds of neighbour structures of backward, pass through random number R selection appoint
A kind of neighbour structure, produces the k-x neighborhood solution with flying bird, and the x neighborhood solution transmitted with an above individual is merged into one
A set, carries out dominated Sorting, equally finds the individual of focusing distance maximum in first boundary set, if individual domination with
Flying bird, then be replaced.
A kind of 7. multiple target mixed flow two-sided assembly line balance method according to claim 6, it is characterised in that the step 3
In, for flying bird, after the individual of focusing distance maximum in finding first boundary set, if the individual can not be dominated with flying
Bird, then：
Acceptance probability is calculated according to the following formula, prevents algorithm to be absorbed in local optimum too early：
<mrow>
<mi>p</mi>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msubsup>
<mi>f</mi>
<mn>1</mn>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>b</mi>
<mi>o</mi>
<mi>r</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>f</mi>
<mn>1</mn>
<mrow>
<mi>o</mi>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msubsup>
<mi>f</mi>
<mn>2</mn>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>b</mi>
<mi>o</mi>
<mi>r</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>f</mi>
<mn>2</mn>
<mrow>
<mi>o</mi>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>/</mo>
<mn>100</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,WithRespectively to minimize the neighborhood solution of the object function of composite object and primitive solution；WithRespectively to minimize neighborhood solution and primitive solution of the unit finished product totle drilling cost as the object function of target；
The composite object is the composite object for combining load balancing and assembly line efficiency.
A kind of 8. multiple target mixed flow two-sided assembly line balance method according to claim 1, it is characterised in that institute in step 4
That states carries out local search for each non-domination solution that non-domination solution is concentrated using multiple target iteration greedy algorithm, including：
Step 401：Random erasure task sequence SEQiIn d task, and by these tasks deposit task sequence SEQdIn,
SEQiDelete the task sequence SEQ after d taskrRepresent；
Step 402：The non-dominant disaggregation of part task sequence is represented with NDS, starts only SEQ in NDSr；I=1 is set；
Step 403：By each task sequence SEQdIn each task insertion NDS in all individual all possible positions
Put, obtain r+1 task sequence, quick non-dominated ranking is carried out to them, obtains new non-dominant disaggregation NWS；
Step 404：NDS=NWS, empties NWS, if i such as d, i++, and return to step 403；
Step 405：Export the non-dominant disaggregation NDS of complete series of tasks.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711493844.4A CN108038339A (en) | 2017-12-31 | 2017-12-31 | A kind of multiple target mixed flow two-sided assembly line balance method based on migratory bird optimization algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711493844.4A CN108038339A (en) | 2017-12-31 | 2017-12-31 | A kind of multiple target mixed flow two-sided assembly line balance method based on migratory bird optimization algorithm |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN108038339A true CN108038339A (en) | 2018-05-15 |
Family
ID=62099291
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201711493844.4A Pending CN108038339A (en) | 2017-12-31 | 2017-12-31 | A kind of multiple target mixed flow two-sided assembly line balance method based on migratory bird optimization algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108038339A (en) |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109635510A (en) * | 2019-01-15 | 2019-04-16 | 西南交通大学 | The parallel repair line setting method of railway freight-car |
| CN111400868A (en) * | 2020-02-24 | 2020-07-10 | 山东师范大学 | Distributed workshop scheduling optimization method and system with order and robot carrying functions |
| CN112605988A (en) * | 2020-11-27 | 2021-04-06 | 辽宁石油化工大学 | Random multi-product robot disassembly line balance control method |
| CN112632776A (en) * | 2020-12-22 | 2021-04-09 | 华中科技大学 | Assembly line balancing method and system for I-type problems of bilateral assembly line of household appliance products |
| CN112731888A (en) * | 2021-01-07 | 2021-04-30 | 浙江工业大学 | Improved migrant bird optimization method for scheduling problem of batch flow mixed flow shop |
| CN113766131A (en) * | 2021-09-15 | 2021-12-07 | 广州市明美光电技术有限公司 | Multi-target-point focusing method and application thereof |
| CN115310353A (en) * | 2022-07-26 | 2022-11-08 | 明珠电气股份有限公司 | Power transformer design method based on rapid multi-objective optimization |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040143352A1 (en) * | 2003-01-17 | 2004-07-22 | Julius Gyorfi | Balancing workloads in an electronics assembly factory |
| CN103714395A (en) * | 2013-12-18 | 2014-04-09 | 华中科技大学 | Cost-oriented mixed-model two-sided assembly line balancing method |
| CN107316107A (en) * | 2017-06-15 | 2017-11-03 | 南京理工大学 | A kind of tricot machine assembly line balancing method towards multiple-objection optimization |
-
2017
- 2017-12-31 CN CN201711493844.4A patent/CN108038339A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040143352A1 (en) * | 2003-01-17 | 2004-07-22 | Julius Gyorfi | Balancing workloads in an electronics assembly factory |
| CN103714395A (en) * | 2013-12-18 | 2014-04-09 | 华中科技大学 | Cost-oriented mixed-model two-sided assembly line balancing method |
| CN107316107A (en) * | 2017-06-15 | 2017-11-03 | 南京理工大学 | A kind of tricot machine assembly line balancing method towards multiple-objection optimization |
Non-Patent Citations (5)
| Title |
|---|
| ANA S. SIMARIA等: "2-ANTBAL: An ant colony optimisation algorithm for balancing two-sided assembly lines", 《COMPUTERS & INDUSTRIAL ENGINEERING》 * |
| 张三强: "整车混流装配线平衡和优化排序的研究与应用", 《万方数据》 * |
| 李大双: "基于混合殖民竞争算法的双边装配线平衡问题研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
| 李梓响等: "迭代局部搜索求解双边混流装配线平衡问题", 《机械设计与制造》 * |
| 谢展鹏: "基于候鸟优化算法的有限缓冲区流水车间调度优化研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
Cited By (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109635510B (en) * | 2019-01-15 | 2022-08-26 | 西南交通大学 | Method for setting parallel overhaul lines of railway freight cars |
| US20200346675A1 (en) * | 2019-01-15 | 2020-11-05 | Southwest Jiaotong University | Arrangement of parallel maintenance lines for railway wagons |
| CN109635510A (en) * | 2019-01-15 | 2019-04-16 | 西南交通大学 | The parallel repair line setting method of railway freight-car |
| CN111400868A (en) * | 2020-02-24 | 2020-07-10 | 山东师范大学 | Distributed workshop scheduling optimization method and system with order and robot carrying functions |
| CN111400868B (en) * | 2020-02-24 | 2023-04-07 | 山东师范大学 | Distributed workshop scheduling optimization method and system with order and robot carrying functions |
| CN112605988A (en) * | 2020-11-27 | 2021-04-06 | 辽宁石油化工大学 | Random multi-product robot disassembly line balance control method |
| CN112632776B (en) * | 2020-12-22 | 2023-02-10 | 华中科技大学 | Assembly line balancing method and system for I-type problems of bilateral assembly line of household appliance products |
| CN112632776A (en) * | 2020-12-22 | 2021-04-09 | 华中科技大学 | Assembly line balancing method and system for I-type problems of bilateral assembly line of household appliance products |
| CN112731888B (en) * | 2021-01-07 | 2022-07-01 | 浙江工业大学 | Improved migrant bird optimization method for scheduling problem of batch flow mixed flow shop |
| CN112731888A (en) * | 2021-01-07 | 2021-04-30 | 浙江工业大学 | Improved migrant bird optimization method for scheduling problem of batch flow mixed flow shop |
| CN113766131A (en) * | 2021-09-15 | 2021-12-07 | 广州市明美光电技术有限公司 | Multi-target-point focusing method and application thereof |
| CN113766131B (en) * | 2021-09-15 | 2022-05-13 | 广州市明美光电技术有限公司 | Multi-target point focusing method and digital slice scanner applying same |
| CN115310353A (en) * | 2022-07-26 | 2022-11-08 | 明珠电气股份有限公司 | Power transformer design method based on rapid multi-objective optimization |
| CN115310353B (en) * | 2022-07-26 | 2024-02-20 | 明珠电气股份有限公司 | Power transformer design method based on rapid multi-objective optimization |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108038339A (en) | A kind of multiple target mixed flow two-sided assembly line balance method based on migratory bird optimization algorithm | |
| CN109190857B (en) | Optimization algorithm based on multi-target resource limited project scheduling model | |
| Van Veldhuizen et al. | Multiobjective evolutionary algorithm research: A history and analysis | |
| Sivanandam et al. | Genetic algorithm optimization problems | |
| Nie et al. | A GEP-based reactive scheduling policies constructing approach for dynamic flexible job shop scheduling problem with job release dates | |
| Wu et al. | Modified the performance of differential evolution algorithm with dual evolution strategy | |
| CN108846570A (en) | A method of solving resource constrained project scheduling problem | |
| CN113225370B (en) | Block chain multi-objective optimization method based on Internet of things | |
| Wang et al. | Evolutionary multitasking for semantic web service composition | |
| Dalirinia et al. | Lotus effect optimization algorithm (LEA): a lotus nature-inspired algorithm for engineering design optimization | |
| Fakhrzad et al. | A new multi-objective job shop scheduling with setup times using a hybrid genetic algorithm | |
| CN106127332A (en) | Base station resource configuration based on optimal spatial coupling and planing method | |
| Bhattacharjee et al. | A binary cuckoo search algorithm for knapsack problems | |
| CN105069517B (en) | Power distribution network multiple target fault recovery method based on hybrid algorithm | |
| CN107153889A (en) | Water quality sampling cruise ship path planning optimal method | |
| CN108108554B (en) | Multi-material vehicle body assembly sequence planning and optimizing method | |
| Elahi et al. | An evolutionary algorithm for multi-objective optimization of freshwater consumption in textile dyeing industry | |
| Rajeswary | A survey on efficient evolutionary algorithms for web service selection | |
| Dominik | Solving multi-objective job shop problem using nature-based algorithms: new Pareto approximation features | |
| Wu et al. | A genetic-ant-colony hybrid algorithm for task scheduling in cloud system | |
| CN106406082A (en) | System control method and device, controller and control system | |
| Chen et al. | Research on ant colony optimization Tabu search and genetic fusion algorithm | |
| Kapsalis et al. | A unified paradigm for parallel genetic algorithms | |
| Grine et al. | A new efficient metaheuristic for solving the uncapacitated single allocation p-hub median problem | |
| Dou et al. | A genetic algorithm with path-relinking for operation sequencing in CAPP |
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 |
Application publication date: 20180515 |
|
| RJ01 | Rejection of invention patent application after publication |