CN102354311A - Balance method for reconfigurable assembly line customized on large scale - Google Patents

Balance method for reconfigurable assembly line customized on large scale Download PDF

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CN102354311A
CN102354311A CN2011102668413A CN201110266841A CN102354311A CN 102354311 A CN102354311 A CN 102354311A CN 2011102668413 A CN2011102668413 A CN 2011102668413A CN 201110266841 A CN201110266841 A CN 201110266841A CN 102354311 A CN102354311 A CN 102354311A
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assembly line
formula
balancing
assembly
job
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苑明海
许焕敏
纪爱敏
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Changzhou Campus of Hohai University
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Abstract

The invention relates to a balance method for a reconfigurable assembly line customized on a large scale. The method comprises the following steps of: establishing a mathematical model for balancing the reconfigurable assembly line customized on a large scale, encoding genes, performing genetic operation, selecting initial temperature, annealing, iterating repeatedly and the like. By the method, the number and loads of workstations and the efficiency of the assembly line can be considered comprehensively, and idle time of each workstation can be eliminated as far as possible so as to fulfill the aim of minimizing cost or maximizing output. Simultaneously, the invention also provides a mixed genetic algorithm for optimizing the balance of the assembly line. In the algorithm, by combining a simulation annealing algorithm and a genetic algorithm and adopting a self-adaption reconfiguration strategy of cross probability and mutation probability, the defects of local searching, low convergence and the like of the genetic algorithm in actual application can be effectively avoided, and the problems that the conditions of integral searching space is not known much and operation efficiency is low in the simulation annealing algorithm can be solved.

Description

Restructural assembly line balancing method towards mass customization
Technical field
The present invention relates to a kind of restructural assembly line balancing method, and can this arrange production, belong to production line control and areas of information technology automatically towards mass customization.
Background technology
Restructural assembly line towards mass customization is the assembly system for the complicacy that adapts to mass customization Assembling Production needs; Be based on the mixed-model assembly line of the dynamic need variation of order production; Characteristics such as have the customer demand variation, assembly technology is complicated, and data scale is big.For mixed-model assembly line, the balance of assembly line is that it needs problems of at first solving, and the restructural assembly line compares to traditional single variety assembly line and mixed-model assembly line, aspect difficulty, all has bigger different in the scale of problem.See from the document situation; Research for assembly line balancing at present mainly concentrates on single variety assembly line and mixed-model assembly line; For the research of restructural assembly line balancing but seldom; And the balance model that proposes assembly line is mostly from influencing assembly line balancing in a certain respect, considers equilibrium problem like the efficient of the quantity of workstation, pitch time, the load of machinery systems, assembly line.Yet the assembly line balancing process will receive the influence of many-sided factor, should do influence factor and take all factors into consideration.In addition; Assembly line balancing problem is a discrete type network mathematical optimization problem; It also is a typical NP-hard difficult problem; The demand optimum solution is difficulty relatively; Handle this type problem intelligent heuristics method commonly used; Like genetic algorithm, simulated annealing and tabu search algorithm etc., but shortcomings such as Local Search and the poor astringency of algorithm appear in genetic algorithm easily in practical application.Simulated annealing is understood few for the situation of whole search volume, operation efficiency is low, and the tabu search algorithm shortcoming is that not only it has stronger dependence to initial solution, and the process of search is serial, but not parallel search.Therefore, press for a kind of mixed-model assembly line that can satisfy the dynamic need variation of order production and solve the problem that faces at present.
Summary of the invention
The technical matters that the present invention will solve is to propose a kind of restructural assembly line balancing method towards mass customization; The mathematical model of the restructural assembly line balancing that this method proposes; Can take all factors into consideration workstation quantity; The factor of production efficiency three aspects of balancing the load degree and assembly line; Make it solve the deficiency that exists in the background technology; The line balancing that adapts to the restructural assembly line; Thereby can obtain than having the optimization method that various balance methods more adapt to now; For example can make the workstation minimum number; The production line balancing the load is best, and can enhance productivity greatly.
For solving the problems of the technologies described above, the technical scheme that the present invention adopts is:
A kind of restructural assembly line balancing method towards mass customization is characterized in that described restructural assembly line balancing method carries out according to following steps:
(1) foundation is towards the restructural assembly line balancing model of mass customization
1) set up the idle status evaluation index of assembly line:
The idle situation of whole production line can be measured with following index:
Figure 370956DEST_PATH_IMAGE001
（1）
Formula (1) in
Figure 2011102668413100002DEST_PATH_IMAGE002
for a given assembly line of maximum working hours, are
Figure 2011102668413100002DEST_PATH_IMAGE004
workstations working hours,
Figure 437580DEST_PATH_IMAGE005
is the number of workstations;
2) set up the balancing the load evaluation index of assembly line:
Assembly line can utilize the evaluation index of the standard deviation of each workstation load as balancing the load;
（2）
Formula (2) in the for a given assembly line beats,
Figure 638197DEST_PATH_IMAGE003
are
Figure 2011102668413100002DEST_PATH_IMAGE008
workstations working hours,
Figure 106829DEST_PATH_IMAGE005
is the number of workstations;
3) set up the production efficiency evaluation index of assembly line:
As far as the restructural assembly line, the demand of production is that the order by the client spurs, and can consider the production efficiency of assembly line with the production cycle of order requirements;
Figure 164784DEST_PATH_IMAGE009
（3）
Wherein: T is the production cycle of order requirements;
Figure 958296DEST_PATH_IMAGE005
as the number of workstations;
a boolean decision variable, when the first
Figure 469437DEST_PATH_IMAGE004
jobs element is used = 1, otherwise
Figure 210046DEST_PATH_IMAGE010
= 0;
Figure 860994DEST_PATH_IMAGE011
for the first
Figure 2011102668413100002DEST_PATH_IMAGE012
The number of products;
Figure 274527DEST_PATH_IMAGE013
for the first
Figure 640786DEST_PATH_IMAGE004
a job elements operating time;
the number of types of products;
Figure 496003DEST_PATH_IMAGE015
is the total number of elements in the job;
4) set up the mathematical model of restructural assembly line balancing:
Comprehensive step 1), 2), 3) promptly obtain the mathematical model of restructural assembly line balancing, be shown below:
Figure 2011102668413100002DEST_PATH_IMAGE016
（4）
Formula (4) in the weight values
Figure 123162DEST_PATH_IMAGE017
can according to the actual situation in the assembly line or expert judgment method to get; formula (4) in the
Figure 2011102668413100002DEST_PATH_IMAGE018
reaction assembly line idle state,
Figure 964387DEST_PATH_IMAGE019
reaction assembly line load balance,
Figure 2011102668413100002DEST_PATH_IMAGE020
reaction assembly line production efficiency; due
Figure 490046DEST_PATH_IMAGE021
The same dimensionless through different weight values
Figure 959073DEST_PATH_IMAGE017
, by linear combination of the three parts, the assembly line can be considered a minimum idle time, load balancing and assembly lines maximum production efficiency three objectives, in order to evaluate the entire balance of reconfigurable assembly line, the adaptation function value is smaller, the better the balance of the assembly line;
Satisfy constraint condition simultaneously:
Figure 2011102668413100002DEST_PATH_IMAGE022
（5）
Figure 709248DEST_PATH_IMAGE023
（6）
Figure 2011102668413100002DEST_PATH_IMAGE024
（7）
If
Figure 526900DEST_PATH_IMAGE025
(8)
Formula (5) for the occurrence of constraint to ensure that any job elements can only be assigned to a workstation that can not repeat the same job elements assigned to multiple workstations; formula (6) to ensure that all job elements are assigned; formula (5) and Formula (6) Guarantee element set into mutually exclusive and completeness; formula (7) for the beat constraint, which means that all assigned to either a workstation operating time of job elements and must be no larger than the beat
Figure 870681DEST_PATH_IMAGE007
; formula (8) is Operating element takes precedence relation constraints, ensure job elements assigned to meet assembly precedence relations, there is no element is assigned to a job than their previous job yuan;
(2) gene code
Encoded using genetic algorithms in the form of real numbers, each bit represents a job elements gene, chromosome length is equal to the number of job elements, store them in the order of priority to meet the assembly sequence constraint relationships, and in subsequent operations to meet each job elements The serial number can not be repeated; assembly first sequence diagram with priority matrix
Figure 2011102668413100002DEST_PATH_IMAGE026
said that in order to accelerate the convergence speed, in order to meet the first assembly diagram based on the use of heuristic rules and random search sorting method to generate the initial population;
(3) genetic manipulation
Select two chromosomes as parents from population at random, and select a mating zone thereon arbitrarily, obtain two new child chromosome; Because parent is feasible solution, the filial generation after therefore intersecting also is a feasible solution, and simultaneously, this method still can produce variation effect to a certain degree under the identical situation of two father's chromosomes, and this has certain effect to keeping variation certain in the colony;
In line balancing, since the assembly sequence constraint legal solutions in order to increase the number of mutation, using the displacement variation and combination of swap mutation, crossover probability
Figure 2454DEST_PATH_IMAGE027
and mutation probability
Figure 2011102668413100002DEST_PATH_IMAGE028
The impact of genetic algorithm selection is the key to behavior and performance a direct impact on convergence of the algorithm; in the standard genetic algorithm,
Figure 607135DEST_PATH_IMAGE027
and
Figure 408738DEST_PATH_IMAGE028
general rule of thumb is taken as a fixed value, establishes a crossover probability and mutation probability adaptive reconfiguration strategy;
Figure 784356DEST_PATH_IMAGE029
(10)
Figure 2011102668413100002DEST_PATH_IMAGE030
(11)
Formula (10), (11) in, is a constant, whose value is (0,1);
Figure 2011102668413100002DEST_PATH_IMAGE032
is the largest population fitness value,
Figure 190726DEST_PATH_IMAGE033
for every generation population average fitness value;
Figure 428810DEST_PATH_IMAGE018
want to cross two individuals larger fitness value;
Figure 2011102668413100002DEST_PATH_IMAGE034
for the population variance of the individual to the fitness value;
(4) the temperature operation is selected and moved back to initial temperature
The initial temperature selection
Figure 793188DEST_PATH_IMAGE035
in the form of optional
Figure 2011102668413100002DEST_PATH_IMAGE036
= 10,20,100 ... other test values; wherein
Figure 266764DEST_PATH_IMAGE032
as the initial population of the largest objective function value,
Figure 721403DEST_PATH_IMAGE037
as the initial population of the smallest objective function value; retreat temperature commonly used functions
Figure 2011102668413100002DEST_PATH_IMAGE038
form, where
Figure 255022DEST_PATH_IMAGE039
;
(5) iterate
If, then repeating the operating process of (2)-(5) less than the predefined algebraically that falls, can accomplish subalgebra.
After using the above technical scheme of the present invention over the prior art has obvious advantages, the proposed mass customization of reconfigurable assembly line balancing method takes into account the number of workstations, workstation loading and assembly line efficiency three factors that can make possible to eliminate idle time on each workstation, to minimize costs or maximize output, while an optimized assembly line balancing hybrid genetic algorithm, simulated annealing and genetic algorithms are combined and used crossover probability and The adaptive mutation probability reconstruction strategy, can effectively avoid the application of genetic algorithms prone local search and convergence defects and poor; but also can solve the simulated annealing conditions for the entire search space is poorly understood, the operation inefficient issue.
Description of drawings
Fig. 1 is a genetic algorithm process flow diagram of the present invention;
Fig. 2 preferentially schemes for the assembling of uniting of product.
Embodiment
Below in conjunction with accompanying drawing and embodiment the present invention is done further detailed explanation:
A special vehicle assembly line with certain special vehicle manufacturing enterprise is an example; In this assembly line, mainly accomplish certain special vehicle chassis general assembly, its main assembly process has: the ground plate rail is reached the standard grade, wire harness and auxiliary stand are installed, fall to adorning front axle assy, fall to adorning rear axle assy, the mounted engine assembly that falls, oil bunkering case, adorn each auxilitary unit, wheel assembling, fall to adorning pilothouse, dress rotation axis assembly, chair mounted etc.Three kinds of products of existing order requirements assembling, the basic function module of these three kinds of products is identical, and different demands is just arranged in some aspects, therefore can be regarded as mass customization production, realizes through the restructural assembly line.
The assembling of uniting of three kinds of products is preferentially schemed, shown in accompanying drawing 2.The production cycle of order is 3 days, and calculated by 8 hours every day, and the order volume of three kinds of products does, A=5 spare, and B=10 spare, C=10 spare, productive temp is decided to be 265s.Require to seek a kind of more excellent operation element assembled scheme, make that workstation minimum number, workstation load balancing, the production line efficiency of assembly line are higher.The present invention can be made by using reconfigurable assembly line balance model (equation (4) in the weight values according to the actual situation of the factory from each 1/3) and mixed heritage algorithm (written using VC + +6.0), the problem is solved Select the initial temperature coefficient
Figure 2011102668413100002DEST_PATH_IMAGE040
, back temperature coefficient
Figure 654167DEST_PATH_IMAGE041
, crossover and mutation probability coefficient
Figure 2011102668413100002DEST_PATH_IMAGE042
= 0.45, = 0.03,
Figure 2011102668413100002DEST_PATH_IMAGE044
= 0.65,
Figure 478128DEST_PATH_IMAGE045
= 0.5.Population size
Figure 2011102668413100002DEST_PATH_IMAGE046
= 80, if successive iterations 40 times the minimum evolutionary population objective function value
Figure 182648DEST_PATH_IMAGE037
no change, then the algorithm terminates.
Concrete solution procedure is following:
(1) gene code
Coding adopts the form of real number; Each gene position is represented an operation element; Chromosomal length equals the operation element prime number, and its order of depositing will satisfy the precedence constraint relation of assembling sequence, and the sequence number that will satisfy each operation element in operation subsequently can not repeat to occur.Assembly first sequence diagram with priority matrix
Figure 210034DEST_PATH_IMAGE026
said that in order to accelerate the convergence speed, in order to meet the first assembly diagram based on the use of heuristic rules and random search sorting method to generate the initial population.
The random search ranking method produces the process of initial population:
Step1: The priority matrix
Figure 900778DEST_PATH_IMAGE026
form an initial set of job elements, called ordered set ; generate a new, empty set, called the free set ;
Step2: Set the sort
Figure 939852DEST_PATH_IMAGE047
the job elements listed as 0 (pre-order elements, or those who do not have pre-order elements, but pre-order elements have been assigned to the workstation those elements) into free collection
Figure 186025DEST_PATH_IMAGE048
in;
Step3: Randomly from a free set
Figure 680461DEST_PATH_IMAGE048
select a job elements for allocation;
Step4: Updated Sort collection
Figure 774319DEST_PATH_IMAGE047
crossed the
Figure 696007DEST_PATH_IMAGE047
has been assigned the row and column elements;
Step5: if the middle All Jobs element of ordering collection
Figure 432406DEST_PATH_IMAGE047
is assigned with finish, just finish; Otherwise change Step2.
(2) genetic decoding
The process of decoding is exactly that operation element is assigned to workstation and is arranged in the process on the assembly line.To the characteristics of assembly line balancing, to satisfy following principle during decoding:
1) gene order in the coding will satisfy the precedence relationship constraint.
2) the All Jobs element time sum of a workstation will satisfy the beat constraint.
3) distribution of operation element has uniqueness, promptly can only be assigned to a workstation.
According to mentioned above principle,, just obtained a feasible solution when all operations all assign.
(3) relevance grade function
Employing formula (12) is as the relevance grade function, and objective function of the present invention is to minimize, for satisfy the fitness function value on the occasion of, it is transformed, the computing formula that obtains is:
Figure 464953DEST_PATH_IMAGE049
（12）
Where
Figure 2011102668413100002DEST_PATH_IMAGE050
is the same generation groups in the objective function value is the maximum of the objective function value of chromosomes.
(4) genetic manipulation
Genetic operators, including selection, crossover and mutation operators, which in turn acts on the population
Figure 724902DEST_PATH_IMAGE051
, resulting in new species
Figure 2011102668413100002DEST_PATH_IMAGE052
.
Select two chromosomes as parents from population at random, and select a mating zone thereon arbitrarily, obtain two new child chromosome.Because parent is feasible solution, the filial generation after therefore intersecting also is a feasible solution, and simultaneously, this method still can produce variation effect to a certain degree under the identical situation of two father's chromosomes, and this has certain effect to keeping variation certain in the colony.In assembly line balancing, because the constraint of assemble sequence, in order to increase the legal quantity of separating in variation back, this paper adopts the displacement variation and exchanges the mode that variation combines.In order not violate precedence constraint relation, the position that element can insert can only be the element or the back back of element tightly before it is tight.
The process flow diagram of genetic algorithm as shown in Figure 1.
Concrete algorithm steps is following:
Step1: determine the population size
Figure 268359DEST_PATH_IMAGE053
, and the control algorithm coefficients, ever-temperature coefficient , retreat temperature coefficient
Figure 2011102668413100002DEST_PATH_IMAGE054
, crossover and mutation operations coefficient,
Figure 705123DEST_PATH_IMAGE042
, ,
Figure 286332DEST_PATH_IMAGE044
,
Figure 918695DEST_PATH_IMAGE045
, to generate the initial population , and to make an initial optimal solution
Figure 2011102668413100002DEST_PATH_IMAGE056
, the number of iterations .
Step2: on population
Figure 844867DEST_PATH_IMAGE055
Calculate the fitness function value
Figure 2011102668413100002DEST_PATH_IMAGE058
, determine whether the termination condition is reached, and if so, over, the output optimal solution.Otherwise change Step3.
Step3: adopt tournament method to carry out colony and select, implement elite's retention strategy simultaneously.
Step4: recomputate the chromosome target function value, intersect respectively and mutation operation, carry out elite's retention strategy simultaneously by crossover probability and variation probability.
Step5: After crossover and mutation on the group, in the neighborhood of chromosomes randomly generated new individuals
Figure 839892DEST_PATH_IMAGE059
and
Figure 17933DEST_PATH_IMAGE004
, using the Metropolis criterion, ie if
Figure 2011102668413100002DEST_PATH_IMAGE060
, when
Figure 296861DEST_PATH_IMAGE061
or
Figure 2011102668413100002DEST_PATH_IMAGE062
when individuals
Figure 26788DEST_PATH_IMAGE059
Copy to the next generation, otherwise, will
Figure 709442DEST_PATH_IMAGE004
Copy to next-generation groups.
Step6: Update the rules by cooling down the temperature,
Figure 440243DEST_PATH_IMAGE063
.
Step7: whether reach the iterations of regulation, if then export optimum solution, otherwise change Step2.
The result that is optimized at last is as shown in table 1.Identical being provided with under the parameters conditions; Algorithm of the present invention and GA, SA algorithm are contrasted, and as shown in table 2, the result shows; The minimum workstation quantity that algorithm of the present invention is asked, the evolutionary generation the when standard deviation of workstation load, convergence and all be better than GA and SA algorithm working time.
Table 1 Optimization result
Figure 2011102668413100002DEST_PATH_IMAGE064
Table 2 algorithm of the present invention and the contrast of other arithmetic result
Figure 649376DEST_PATH_IMAGE065
The above is a simple embodiment of the present invention, does not constitute the restriction to flesh and blood of the present invention, and protection scope of the present invention is as the criterion with claims.

Claims (1)

1. restructural assembly line balancing method towards mass customization is characterized in that described restructural assembly line balancing method carries out according to following steps:
(1) foundation is towards the restructural assembly line balancing model of mass customization
1) set up the idle status evaluation index of assembly line:
The idle situation of whole production line can be measured with following index:
Figure 2011102668413100001DEST_PATH_IMAGE002
（1）
Formula (1) for a given assembly line maximum working time,
Figure 2011102668413100001DEST_PATH_IMAGE004
are
Figure 2011102668413100001DEST_PATH_IMAGE006
workstations working hours,
Figure 2011102668413100001DEST_PATH_IMAGE008
is the number of workstations;
2) set up the balancing the load evaluation index of assembly line:
Assembly line can utilize the evaluation index of the standard deviation of each workstation load as balancing the load;
Figure 2011102668413100001DEST_PATH_IMAGE010
（2）
Formula (2) in the
Figure 2011102668413100001DEST_PATH_IMAGE012
for a given assembly line beats,
Figure 811961DEST_PATH_IMAGE004
are
Figure 257243DEST_PATH_IMAGE006
workstations working hours,
Figure 707684DEST_PATH_IMAGE008
is the number of workstations;
3) set up the production efficiency evaluation index of assembly line:
As far as the restructural assembly line, the demand of production is that the order by the client spurs, and can consider the production efficiency of assembly line with the production cycle of order requirements;
Figure 2011102668413100001DEST_PATH_IMAGE014
（3）
Wherein: T is the production cycle of order requirements;
is the number of workstations;
Figure 2011102668413100001DEST_PATH_IMAGE016
is the boolean decision variable, when the first
Figure 56942DEST_PATH_IMAGE006
jobs element is used = 1, otherwise = 0;
Figure 2011102668413100001DEST_PATH_IMAGE018
is the first
Figure 2011102668413100001DEST_PATH_IMAGE020
The number of kinds of products;
Figure 2011102668413100001DEST_PATH_IMAGE022
is the first
Figure 603789DEST_PATH_IMAGE006
jobs element of working time;
Figure 2011102668413100001DEST_PATH_IMAGE024
is the number of types of products;
Figure 2011102668413100001DEST_PATH_IMAGE026
is the total number of elements in the job;
4) set up the mathematical model of restructural assembly line balancing:
Comprehensive step 1), 2), 3) promptly obtain the mathematical model of restructural assembly line balancing, be shown below:
Figure 2011102668413100001DEST_PATH_IMAGE028
（4）
Formula (4) in the weight values
Figure 2011102668413100001DEST_PATH_IMAGE030
can according to the actual situation in the assembly line or expert judgment method to get; formula (4) in the
Figure 2011102668413100001DEST_PATH_IMAGE032
reaction assembly line idle state,
Figure 2011102668413100001DEST_PATH_IMAGE034
reaction assembly line load balance,
Figure 2011102668413100001DEST_PATH_IMAGE036
reaction assembly line production efficiency; due
Figure 2011102668413100001DEST_PATH_IMAGE038
the dimension of the same, with different weight values
Figure 612457DEST_PATH_IMAGE030
, by a linear combination of the three parts, you can also consider the assembly line idle least time, load balancing and assembly lines maximum productivity three goals, in order to evaluate the entire balance of reconfigurable assembly line, the fitness function value is smaller, the better the balance of the assembly line;
Satisfy constraint condition simultaneously:
Figure 2011102668413100001DEST_PATH_IMAGE040
（5）
Figure 2011102668413100001DEST_PATH_IMAGE042
（6）
Figure 2011102668413100001DEST_PATH_IMAGE044
（7）
If
Figure 2011102668413100001DEST_PATH_IMAGE046
, (8)
Formula (5) for the occurrence of constraint to ensure that any job elements can only be assigned to a workstation that can not repeat the same job elements assigned to multiple workstations; formula (6) to ensure that all job elements are assigned; formula (5) and Formula (6) Guarantee element set into mutually exclusive and completeness; formula (7) for the beat constraint, which means that all assigned to either a workstation operating time of job elements and must be no larger than the beat
Figure 704434DEST_PATH_IMAGE012
; formula (8) for the job element takes precedence relation constraints, ensure job elements assigned to meet assembly precedence relations, there is no element is assigned to a job than their previous job yuan;
(2) gene code
Encoded using genetic algorithms in the form of real numbers, each bit represents a job elements gene, chromosome length is equal to the number of job elements, store them in the order of priority to meet the assembly sequence constraint relationships, and in subsequent operations to meet each job elements The serial number can not be repeated; assembly first sequence diagram with priority matrix said that in order to accelerate the convergence speed, in order to meet the first assembly diagram based on the use of heuristic rules and random search sorting method to generate the initial population ;
(3) genetic manipulation
Select two chromosomes as parents from population at random, and select a mating zone thereon arbitrarily, obtain two new child chromosome; Because parent is feasible solution, the filial generation after therefore intersecting also is a feasible solution, and simultaneously, this method still can produce variation effect to a certain degree under the identical situation of two father's chromosomes, and this has certain effect to keeping variation certain in the colony;
In line balancing, since the assembly sequence constraint legal solutions in order to increase the number of mutation, using the displacement variation and combination of swap mutation, crossover probability and mutation probability
Figure 2011102668413100001DEST_PATH_IMAGE052
choice affect the behavior and performance of genetic algorithm key directly affects convergence of the algorithm; in the standard genetic algorithm, and
Figure 281796DEST_PATH_IMAGE052
general rule of thumb is taken as a fixed value, establishes a crossover probability and mutation probability adaptive reconstruction strategy;
Figure 2011102668413100001DEST_PATH_IMAGE054
(10)
Figure 2011102668413100001DEST_PATH_IMAGE056
(11)
Formula (10), (11) in,
Figure 2011102668413100001DEST_PATH_IMAGE058
is a constant, whose value is (0,1);
Figure 2011102668413100001DEST_PATH_IMAGE060
is the largest population fitness value, as each generation population average fitness value;
Figure 14259DEST_PATH_IMAGE032
as to intersect the larger of the two individual fitness value; for the population variance of the individual to the fitness value;
(4) the temperature operation is selected and moved back to initial temperature
The initial temperature selection
Figure 2011102668413100001DEST_PATH_IMAGE066
form, optionally
Figure 2011102668413100001DEST_PATH_IMAGE068
= 10,20,100 ... other test values; wherein
Figure 286976DEST_PATH_IMAGE060
as the initial population of the largest objective function value,
Figure 2011102668413100001DEST_PATH_IMAGE070
is the initial population of the smallest objective function value; retreat temperature function used commonly
Figure 2011102668413100001DEST_PATH_IMAGE072
form, where ;
(5) iterate
If, then repeating the operating process of (2) ~ (5) less than the predefined algebraically that falls, can accomplish subalgebra.
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Application publication date: 20120215