CN105022852A - Method for solving product assembly sequence planning problem on the basis of immune particle swarm algorithm - Google Patents

Abstract

The invention discloses a method for solving a product assembly sequence planning problem on the basis of an immune particle swarm algorithm. The method comprises the setting of the naming rules and algorithms of parts and specifically comprises the following steps: firstly, setting the naming rule of each part, and then, combining an immune algorithm with particle swarm optimization through two self-defining functions to solve a product assembly sequence problem. The method carries out serial mixing on two algorithms including the artificial immune algorithm and the particle swarm optimization, establishes a novel mixed algorithm which can combine the advantages of the two algorithms and overcome the respective defects of the two algorithms and can be used for solving the product assembly sequence planning problem. For example, the method can be used for solving the assembly sequence planning problem of lithium ion batteries.

Description

The method of Product Assembly Sequence Planning problem is solved based on immunity particle cluster algorithm

Technical field

The invention belongs to the fields such as digital product, concurrent engineering, Visual Manufacturing, relate to the method for the assembly sequence-planning problem solving product, especially solve the method for lithium ion battery assembly sequence-planning problem.

Background technology

The Assembly sequences of engineering goods directly has influence on product quality and cost, and assembly sequence-planning is the important content of product design.In order to solve the assembly sequence-planning problem of a considerable number of part of the same race in product, the combination of monomers assembly problem of such as lithium ion battery.

Lithium battery appears at 1958 the earliest, and 20 century 70s enter practical.Recently, lithium ion battery starts to develop to electrokinetic cell.Because developing rapidly of fuel-engined vehicle brings two large problems: the oil consumption day by day increased, the natural resources day by day reduced and automobile pollution on the environment have had influence on the health of the mankind.Oil is replaced to become the road that must walk with other energy.Lithium-ion-power cell is one of current main selection.

Every portion electric automobile needs hundreds if not thousands of battery unit to be assembled into battery module to be assembled into large-scale Vehicular battery group again.Obviously, very complicated is compared in the assembling of automobile-used Li-ion batteries piles, and it assembles cost used is also considerable.In order to solve this many Assembly of the parts problem, improve the efficiency of assembling of lithium-ion-power cell group and reduce its assembly cost, good assembly sequence-planning is a good breach.

Relevant research shows that assemble planning good in product design can reduce manufacturing expense 20% ~ 40%, and throughput rate improves 100% ~ 200% ^[1-2].Assembly sequence-planning (Assembly sequence planning, ASP) is the core component of DFA, plays a part very important in product design process and management and running activity ^[3].Assembly sequence-planning is a combinatorial optimization problem with strong constraint, and its target solves to meet various assembly constraint condition and the feasible Assembly sequences with optimal cost.A feasible Assembly sequences, must have geometric feasibility and mechanical feasibility etc.Geometric feasibility depends on the geometrical-restriction relation of assembly; Machinery feasibility is relevant with the mechanical connection of specific component.Assembling geometrical-restriction relation refers to the existence of a part, to the geometrical interference that the assembling of another part causes.In Product Assembly process, once violate the assembling geometrical-restriction relation between part, the interference of assembling will inevitably be caused, the assembly manipulation task of product can not be completed ^[4].

The Assembly sequences of engineering goods directly has influence on product quality and cost, and assembly sequence-planning is the important content of product design.And assembly sequence-planning question essence is NP (uncertainty) difficult problem, be difficult to obtain the Assembly sequences that meets matching requirements.Conventional assembly sequence-planning method is the cut-set power space based on graph theory, its maximum drawback is when the number of components in assembly increases, sequence number exponentially increases, internal calculation process is consuming time, even likely produce shot array problem because there is too much useless result, therefore this algorithm is only applicable to the less assembly parts of number of parts.

Assembly sequence-planning (Assembly sequence planning, ASP) with disassembly sequence planning (Disassembly sequenceplanning, DSP) be area of computer aided assemble planning (Computer-aided assembly planning, CAAP) with green manufacturing in two oppose and unified core component, be also the combinatorial optimization problem typically in engineering reality with strong constraint feature.In order to avoid increase with component number and cause combined sequence blast impact, researchist's sequential use genetic algorithm (Geneticalgorithm, GA), the heuristic value such as simulated annealing, particle cluster algorithm (Particle swarm optimization, PSO) and ant group algorithm solve this NP-hard problem ^[5].

Nineteen ninety-five, F.Benneville ^[6]first official proposes genetic algorithm to be used for assembly sequence-planning research.When carrying out Sequence Planning with genetic algorithm, each sequence is taken as a chromosome in initial population, and this chromosome is made up of the gene code of binary representation.But the quality of Assembly sequences is not determined by fitness function, but differentiated by the knowledge base of similar expert system.Chromosome is through a series of genetic manipulations such as intersection, variations, and the optimum results finally obtained is exactly an optimum or suboptimal chromosome.This chromosome correspond to the Assembly sequences after optimization; S.Chen ^[7]still use binary coding representation chromosome, extend the kind of genetic manipulation, and using fitness function value as the chromosomal standard of evaluation; G.Din [8] adopts metric coded representation method, for better simply three-dimensional assembling, and proposes the method for segmented genes coding.

In recent years, the soft computing technique such as simulated annealing, genetic algorithm, ant group algorithm are constantly attached in assembly sequence-planning research, and achieve good result.At present, soft computing technique has become the new effective technology of the class that solves assembly sequence-planning problem.The cooling of simulated annealing simulation substance material and crystallization process, by annealing temperature command deployment process, but when problem scale is larger, the time that system enters thermal equilibrium state (corresponding optimum solution) is longer; Genetic algorithm has drawn the achievement in research of biological evolution and hereditary variation, is a kind of global optimization search, and have strong robustness, feature that adaptability is good, but there is precocious phenomenon, search efficiency is low, can not keep the limitations such as individual diversity very well; Ant group algorithm has the features such as positive feedback, " greediness " be heuristic, can one group of feasible solution of Generating Problems fast, but due to initial stage pheromones deficient, cause solving speed slow, and easily converge on local optimum ^[4].

In a word, ant group algorithm is better than other 2 kinds of algorithms in optimizing mechanism, population scale, sequence initialization and usable range; And the robustness of genetic algorithm is relative with the scope of application best; But simulated annealing is most effective ^[9].

Based on simulation immune system antibody and antigen recognizing, antibody generation process and abstract immune algorithm out, fully reflect these features immune.When immune algorithm is dealt with problems, the data input that antigen correspondence will be dealt with problems, as objective function, constraint etc.; The solution of antibody correspondence problem.Compared with other hydropower unit, immune algorithm has following characteristics [10]: the 1. diversity of candidate individual, can produce various candidate individual solution, be convenient to the global solution obtaining problem; 2. self-control, by promoting or suppress the generation of antibody, the antibody tormation of self-control necessity, efficiently solves the local convergence problem of iterative search; 3. learning and memory, the antigen that fast processing occurred in the past and antibody, can ensure that learning and memory obtains global solution with higher speed.At present, immune algorithm shows excellent performance and efficiency in the field questions such as machine learning, production scheduling, Optimal Structure Designing solve.

Immune algorithm has fully demonstrated the features such as immune diversity, immune self-control, immunological memory and distributed parallel.Immune algorithm compares to genetic algorithm and has stronger ability of searching optimum and speed of convergence faster, can effectively to overcome in genetic algorithm the immature oils that easily occurs and search time long situation, achieve effective improvement of global convergence performance and speed of convergence ^[4].

According to the Liquified gas tanker of complex product assemble planning problem, propose one and solve assembly sequence-planning (assemblysequenceplanning, ASP) particle swarm optimization algorithm of problem, the particle cluster algorithm being generally used for continuous space optimization is successfully expanded to ASP field. algorithm is according to the feature of ASP problem decision-making solution, the position of particulate and speed and relevant various operations are defined at Sorting space. the shortcoming of local optimum is easily absorbed in for basic particle group algorithm, adopt new study mechanism, enhance the optimizing ability of algorithm. based on interference matrix, connection matrix and proppant matrix establish with assembly feasibility, assembly stability and assembly direction change into the objective function of evaluation index.

But in the face of the singularity of ASP problem and complicacy, each algorithm all shows self advantage and defect, is all faced with the double challenge of time performance and Optimal performance.The mutual mixing of different hydropower unit, having complementary advantages, is a new trend of Current software computing application.

For the feature of assembly sequence-planning problem, ant group algorithm and genetic algorithm mix by document 4, set up a kind of can in conjunction with two kinds of algorithm advantages, the assembly sequence-planning hybrid algorithm overcoming respective defect.In this hybrid algorithm, the feasible sequence generated by ant group algorithm injects genetic algorithm as heuristic information, guides GA search, makes GA Fast Convergent; Solution after genetic algorithm optimization is converted to the pheromones distribution on ant path, accelerate the accumulation of pheromones on ant optimizing path, improve the search efficiency of ant.By the cross-call of two kinds of algorithms, to realizing the doulbe-sides' victory of Optimal performance and time performance.Experimental result shows, hybrid algorithm has better performance solving in assembly sequence-planning problem ^[4].

Leading reference

1.MOLLOY E,YANG H,BROWNE J.Feature-based modeling in design for assembly[J].International Journal of Computer Integrated Manufacturing,1993,6(12):119-125.

2. Wang Junfeng, Li Shiqi, Liu Jihong. area of computer aided assemble planning Review Study [J]. Journal of Engineering Graphics, 2005,26 (2): 1-6.

3. in good roc, Wang Chengen, Zhang Wenlei. based on the explosive view automatic generation method [J] of assembly sequence-planning. mechanical engineering journal, 2010,46 (21): 1-5.

4. Ning Lihua, Gu Tianlong. based on the assembly sequence-planning problem solving [J] of immune algorithm. computer integrated manufacturing system, 2007,13 (1): 1-4.

5. in good roc, Wang Chengen, Wang Jianxi. based on the assembly sequence-planning [J] of maximum-minimum Ant ColonySystem. mechanical engineering journal, 2012,48 (23): 1-4.

6.BONNEVILLE F，PERRARD C，HENRIOUD J M.A genetic algorithmto generate andevaluate assembly plansA.IEEE Symposium on EmergingTechnology and Factory Automation[C].New Jersey：IEEEPress，1995.231-239.

7.CHENShiangfong.Assembly planning a genetic approach[A].IEEEConference on Roboticsand Automation[C].New Jersey：IEEE Press，1998.307-313.

8.DINI G,FAILI F,LAZZERINI B,et al.Generation of optimized assemblysequences usinggenetic algorithms[A].Annals of the CIRP[C].Berne：CIRP Publishers，1999.17-20.

9. respect stone to open, Li Liansheng, Zeng Sen, Liu Jihong. intelligent optimization algorithm storehouse [J] .2010 of used for products assembly sequence-planning, 22 (9): 5-7.

10.MORI K，TSUKIYAMA M，FUKUDA T.Application of animmune algorithm to multi—optimization problems[J].Electrical Engineering in Japan，1998，122(2)：30-37.

Summary of the invention

The object of the present invention is to provide a kind of method solving lithium ion battery assembly sequence-planning problem based on immunity particle cluster algorithm.

For achieving the above object, solution of the present invention is:

A kind of method solving Product Assembly sequence problem based on immunity particle cluster algorithm (ISPO), it is characterized in that: the naming rule first formulating each part, then the combination of immune algorithm (Immune Algorithm) and particle swarm optimization algorithm (PSO algorithm) is achieved by two self-defining function, mainly comprise eight large important steps: setup parameter, initialization, renewal population, immune operation, renewal data base, end condition checking, check and correction, output.

The naming rule of described part is: the form adopting ' AB ', and A represents the kind code of part, and B represents the spatial position code of part, and wherein A, B are natural number;

According to the priority of locus, arranged in sequence; Its spatial location priority is: first left and then right, previously again after, first up and then down; Symbolically is: left < is right, after front <, under upper <.

The setting of described algorithm comprises: 3.1 constraint conditions; 3.2 objective function; 3.3 immunity particle cluster algorithm.

(do new definition according in the standard that described method can reach for geometric feasibility standard and continuity standard

Make P={p ₁, p ₂..., p _nrepresent the set of part in assembly, π={ π ₁, π ₂..., π _mrepresent Assembly sequences, wherein, π _i=[q ₁, q ₂... q _n], (1) i=1,2 ..., m; (2) q _j∈ P, j=1,2 ..., N; (3) q _j≠ q _k,

P is represented with mobile limit (MW) _iand p _jbetween geometrical constraint in assembling process.MW (p _i, p _j)={+X ,-X ,+Y ,-Y ,+Z ,-Z} represent at Assembly part p _iin process, p _iwith Assembly part p _jthe set of the assembly direction do not interfered.

Ω is made to be part q _ithe set of the part before assembling, then

Define 1 geometric feasibility standard

If Assembly sequences π _i=[q ₁, q ₂... q _n], so, Assembly sequences π _imeeting geometric feasibility, i.e. π _irepresent an Assembly sequences not having geometrical interference; If π _ido not meet geometric feasibility, then π _irepresent an Assembly sequences having geometrical interference.

Define 2 continuity standards

For Assembly sequences π _i=[q ₁, q ₂..., q _n], if so Assembly sequences π _imeet continuity, wherein, symbol V represents Boolean logic ' OR ' operational symbol, and symbol ∑ represents that arithmetical logic summation operation accords with.

The combination of immune algorithm (Immune Algorithm) and particle swarm optimization algorithm (PSOalgorithm) is realized according to described design two self-defining function, name two function ξ () and τ () herein, be defined as follows:

Definition 3 by be mapped to π ' _iformula meet following condition:

(1) if x _ij< x _ik, so q ' _j< q ' _k;

(2) if x _ij=x _ikand j < k, so q ' _j< q ' _k;

Wherein, X _i=(x _i1, x _i2..., x _iN) ^t, π ' _i=[q ' ₁, q ' ₁..., q ' _n],

X _ij∈ R, q ' _j∈ R, 1≤i≤M, 1≤j≤N, M ∈ R, N ∈ R, R represents nature number field.

Definition 4 is by π ' _ibe mapped to π _iformula be τ (π ' _i)=π _i, meet: q _jinherit q ' _jcontent of text, difference is that field of definition is different.Wherein, π ' _i=[q ' ₁, q ' ₁..., q ' _n], π _i=[q ₁, q ₁..., q _n], q ' _j∈ R, q _j∈ W, 1≤i≤M, 1≤j≤N.

M ∈ R, N ∈ R, R represents nature number field, and W represents textview field.)

Single algorithm application, when solving assembly sequence-planning problem, is all have respective relative merits.In order to make up defect when single algorithm is applied in assembly sequence-planning, and make full use of its advantage, Artificial Immune Algorithm and particle swarm optimization algorithm two kinds of algorithm serials mix by the present invention, set up a kind of can in conjunction with two kinds of algorithm advantages, overcome respective defect and adapt to the novel hybrid algorithm of the assembly sequence-planning of the efficient assembly problem of lithium ion battery.

Wherein, particle swarm optimization algorithm PSO (Particie Swarm Optimization) is a kind of new global optimization evolution algorithm invented by doctor Eberhart and doctor Kennedy, and it comes from the simulation to birds predation.As a kind of important optimization tool, it has convergence advantage that is fast, that easily realize, but has the Premature convergence similar with genetic algorithm.Immune algorithm has fully demonstrated the features such as immune diversity, immune self-control, immunological memory and distributed parallel.There is stronger ability of searching optimum and speed of convergence faster, can effectively overcome the immature oils that easily occurs in genetic algorithm and search time long situation, achieve effective improvement of global convergence performance and speed of convergence.

Content of the present invention mainly comprises two parts: the naming rule of part, the design of specific algorithm.Finally carry out assembly sequence-planning optimization for the typical lithium ion battery of one.

1, the naming rule of lithium battery part

Generally speaking, assembled product is all made up of the part of numerous species, and the number of often kind of part generally only has one, therefore often adopts natural number to each part name.

But lithium-ion-power cell is made up of the part of numerous species, and the number of often kind of part is many.If still give the name of each part with natural number, be then difficult to find out which part belongs to same classification from the name of part.

The present invention adopts following rule to name part: ' AB ', and A represents the kind code of part, and B represents the spatial position code of part, and wherein A, B are natural number.

The naming rule of A and B is as follows:

According to the priority of locus, arranged in sequence.Its spatial location priority as shown in Figure 1, first left and then right, previously again after, first up and then down.This naming rule can symbolically be: left (in Fig. 1 summit 1,2,3,4 regions surrounded) (summit 5, the < right side, 6,7,8 regions surrounded), front (summit 1,2,5,6 regions surrounded) (summit 3,4 after <, 7,8 regions surrounded), upper (summit 1,3,5,7 regions surrounded) (summit 2 under <, 4,6,8 regions surrounded).Wherein ' < ' represents priority, and such as ' A<B ' represents that the priority of A is higher than B, and instantiation as shown in Figure 3.

2, algorithm design

2.1 constraint condition

2.1.1 geometric feasibility

Make P={p ₁, p ₂..., p _nrepresent the set of part in assembly, π={ π ₁, π ₂..., π _mrepresent Assembly sequences, wherein, π _i=[q ₁, q ₂... q _n], (1) i=1,2 ..., m; (2) q _j∈ P, j=1,2 ..., N; (3) q _j≠ q _k,

P is represented with mobile limit (MW) _iand p _jbetween geometrical constraint in assembling process.MW (p _i, p _j)={+X ,-X ,+Y ,-Y ,+Z ,-Z} represent at Assembly part p _iin process, p _iwith Assembly part p _jthe set of the assembly direction do not interfered.

Ω is made to be part q _ithe set of the part before assembling, then

Definition 1: geometric feasibility standard

If Assembly sequences so, Assembly sequences π _imeeting geometric feasibility, i.e. π _irepresent an Assembly sequences not having geometrical interference; If π _ido not meet geometric feasibility, then π _irepresent an Assembly sequences having geometrical interference.

2.1.2 continuity

In order to keep the stability of assembling, whole assembling process must meet continuity requirement.Namely must there is contact relation with one or more part assembled in a part being about to be assembled, otherwise need auxiliary component to complete assembly manipulation, this will directly cause higher assembly cost and more installation time.Although it is feasible Assembly sequences (namely meeting geometric feasibility), consider from cost angle, it is most economical scarcely.Therefore, best Assembly sequences must meet continuity.

Contact matrix CM is made to represent relation between part.If CM is (p _i, p _j)=1, then represent p _iand p _jbetween there is contact relation; Otherwise, if CM is (p _i, p _j)=0, then represent p _iwith p _jbetween there is not contact relation.

Define 2 continuity standards

For Assembly sequences π _i=[q ₁, q ₂..., q _n], if so Assembly sequences π _imeet continuity, wherein, symbol V represents Boolean logic ' OR ' operational symbol, and symbol ∑ represents that arithmetical logic summation operation accords with.

2.2 objective function

Target function value is larger, then feasible solution is more close to optimum solution.In this article, objective function is as follows:

$\left.\begin{array}{c}f=f_1\&times;f_2\&times;f_3\\ f_1={\mathrm{\&omega;}}_b\&times;B+{\mathrm{\&omega;}}_t\&times;(N-1-n_t)+{\mathrm{\&omega;}}_d\&times;(N-1-N_d)\\ f_2=\mathrm{FG}\\ F_3=\mathrm{FC}\end{array}\right\}---\left(1\right)$

Wherein, f ₁represent the manufacturability of objective function, f ₂represent the geometric feasibility of objective function, f ₃represent the continuity of objective function, N is the total number of part in assembly.

2.2.1 the manufacturability of objective function

If the basic part of assembly is positioned at first of Assembly sequences, then B=kk; Otherwise B=0.

In order to emphasize that basic part is positioned at the primary importance of Assembly sequences, kk=N-1=50. herein

N _tand n _drepresent the number of transitions of assembly tool and the number of transitions of assembly direction respectively.

ω _b, ω _tand ω _drepresent weight, wherein 0≤ω _b≤ 1,0≤ω _t≤ 1,0≤ω _d≤ 1, and ω _b+ ω _t+ ω _d=1,

Computing formula is as follows:

$W_k=\frac{n+1-k}{{\mathrm{\&Sigma;}}_{l=1}^{n}1}=\frac{2(n+1-k)}{n(n+1)}---\left(2\right)$

Wherein, n represents the element total number in engineering information, and k represents the importance information of element in engineering information.Suppose that the sequence of importance of the project data in equation 1 is: basic part > assembly tool > assembly direction.Weights omega from equation 2 _b(k=1)=1/2, ω _t(k=2)=1/3, and ω _d(k=3)=1/6.

2.2.2 the geometric feasibility of objective function

FG is used for detecting the geometric feasibility of Assembly sequences, and its computing formula is as follows:

$\mathrm{FG}=\frac{N-\mathrm{NG}}{N-1}---\left(3\right)$

Wherein, NG represents the part sum that geometrical interference occurs in assembling process.For an Assembly sequences, if any one part i (except basic part) interferes with any one part assembled before it, then this Assembly sequences meeting geometric feasibility requirement.FG=1 in this case; Otherwise this Assembly sequences does not meet geometric feasibility, now 0≤FG≤1.

2.2.3 the continuity of objective function

FC is used to detect p in Assembly sequences _iand p _jbetween continuity, its computing formula is as follows:

$\mathrm{FC}=\frac{N-\mathrm{NG}}{N-2}---\left(4\right)$

Wherein NC represents the total number do not come in contact between part in assembling process.For an Assembly sequences, if each part (first part and last part except) with arbitrarily Assembly part there is contact relation, then this Assembly sequences meets continuity requirement, in this case, FC=1; Otherwise this Assembly sequences does not meet continuity requirement, 0≤FC < 1 in this case.

According to formula 1 ~ formula 4, being calculated as follows of objective function:

$f=[\frac{1}{2}\&times;B+\frac{1}{3}\&times;(N-1-n_t)+\frac{1}{6}\&times;(N-1-n_d)]\&times;\frac{N-\mathrm{NG}}{N-1}\&times;\frac{N-\mathrm{NC}}{N-2}---\left(5\right)$

2.3 immunity particle cluster algorithm

This algorithm comprises eight important steps: setup parameter, initialization, renewal population, immune operation, renewal data base, end condition checking, check and correction, output.

2.3.1 step one: setup parameter

(1) M: Population Size;

(2) W: inertia weight, $W=0.9-0.5*\frac{t}{T_{\max }};$

(3) C ₂: accelerator coefficient;

(4) λ: similarity threshold;

(5) L: immunological regulation numbers of particles;

(6) Pc: crossover probability;

(7) T _max: iterations.Make initial value be 100, if iterations is not restrained in iterative refinement procedure, so, just increase T _max.

2.3.2 step 2: initialization

A stochastic generation M particle, as iterations t=1, position and the speed of each particle are respectively: $X_i^1={(X_{i1}^1,X_{i2}^1,...,X_{\mathrm{iN}}^1)}^T$ With $V_i^1={(v_{i1}^1,v_{i2}^1,...,v_{\mathrm{iN}}^1)}^T,$ Thus generate initialization population pop1, namely $\mathrm{pop}1=(X_1^1,V_1^1;X_2^1,V_2^1;...;X_M^1,V_M^1).$

In order to calculate the fitness of particle with formula 5, name two function ξ () and τ () herein, be defined as follows:

Definition 3 by be mapped to π ' _iformula meet following condition:

(1) if x _ij< x _ik, so q ' _j< q ' _k;

(2) if x _ij=x _ikand j < k, so q ' _j< q ' _k;

Wherein, X _i=(x _i1, x _i2..., x _iN) ^t, π ' _i=[q ' ₁, q ' ₁..., q ' _n],

X _ij∈ R, q ' _j∈ R, 1≤j≤M, 1≤j≤N, M ∈ R, N ∈ R, R represents nature number field.

Definition 4 is by π ' _ibe mapped to π _iformula be τ (π ' _i)=π _i, meet: q _jinherit q ' _jcontent of text, difference is that field of definition is different.Wherein, π ' _i=[q ' ₁, q ' ₁..., q ' _n], π _i=[q ₁, q ₁..., q _n], q ' _j∈ R, q _j∈ W, 1≤i≤M, 1≤j≤N.

M ∈ R, N ∈ R, R represents nature number field, and W represents textview field.

The function ξ () defined based on engineering experience and two and τ (), the particle that a meeting geometric feasibility and continuity require just has designed.Then this particle is named to be finally will be stored into data base.

The initial position of particle i is made to be its fitness function value is calculated as follows:

(1) ${\mathrm{\&pi;}}_i=\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(X_i^1\right)}^T\right)\right);$

(2) according to formula 5 and Fig. 3, f (π _i) and can derive from.Wherein,

$P_g^1={(P_{g1}^1,P_{g2}^1,...,P_{\mathrm{gN}}^1)}^T=\left\{P_i^1\right|{\max }_{i=1}^{M}f\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(p_i^1\right)}^T\right)\right)\right)\}.$

2.3.3 step 3: upgrade population

4th step of whole algorithm has used immunological regulation, and in process of immune regulation, L new particle adds in addition, namely needs on the basis based on concentration choosing principles, from high to low, selects M particle in M+L particle.If very low for the concentration of particle i at t, so t+1 for time, this particle can not be selected, namely particle i there will not be t+1 generation in.Speed and the position of the particle before therefore making each renewal are herein respectively: with be respectively after renewal with formula 6 and formula 7 is utilized to upgrade position and the speed of each particle in whole immunity particle cluster algorithm.

$V_i^{t+1}=w\&CenterDot;v_i^t+c_2\&CenterDot;r_2\&CenterDot;(P_g^t-X_i^t)---\left(6\right)$

$X_i^{t+1}=X_i^t+V_i^{t+1}---\left(7\right)$

If $\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(X_i^{t+1}\right)}^T\right)\right)\right)\&GreaterEqual;\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(X_i^t\right)}^T\right)\right)\right),$ So, $X_i^{t+1}=X_i^t+V_i^{t+1};$

If $\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(X_i^{t+1}\right)}^T\right)\right)\right)<\&GreaterEqual;\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(X_i^t\right)}^T\right)\right)\right),$ So, $X_i^{t+1}=X_i^t;$

2.3.4 step 4: immune operation

(1) immunological regulation

The diversity of antibody is an immune important feature.In immunoregulatory process, have the antibody of larger affinity and lower concentration to be promoted, and the antibody of those low affinity, high concentration can be suppressed, thus, the diversity of antibody population just can be inherited.Immunoregulatory settlement steps to deal is as follows:

1) random generation L particle;

2) basis individual to (M+L) particle is converted to the Assembly sequences { π of (M+L) bar _i=[q ₁, q ₂..., q _n] | 1≤i≤M+L};

3) according to formula 14 ~ formula 17, the survival expectation value e of calculating antibody _i; From (M+L) individual particle, M particle is selected to form new population pop by the order of successively decreasing ^t+1,

Clearly,

${\mathrm{pop}}^{(t+1)*}=(X_1^{(t+1)*},V_1^{(t+1)*};X_2^{(t+1)*},V_2^{(t+1)*};...;X_M^{(t+1)*},V_M^{(t+1)*}).$

(2) immunity inoculation

Immunity inoculation probably comprises two stages: extract vaccine, vaccine inoculation.

1) vaccine is extracted: because colony optimal location P _gvery close with the group optimal solution in the process of particle swarm optimization algorithm, so select P _gfor vaccine.

2) vaccine inoculation:

Order

${\mathrm{pop}}_A^{(t+1)*}=(x_{A1}^{(t+1)*},v_{A1}^{(t+1)*};x_{A2}^{(t+1)*},v_{A2}^{(t+1)*};...;x_{\mathrm{AZ}}^{(t+1)*},v_{\mathrm{AZ}}^{(t+1)*}),$

${\mathrm{pop}}_B^{(t+1)*}=(x_{B1}^{(t+1)*},v_{B1}^{(t+1)*};x_{B2}^{(t+1)*},v_{B2}^{(t+1)*};...;x_{B(M-Z)}^{(t+1)*},v_{B(M-Z)}^{(t+1)*}),$

First, from population pop ^{(t+1) *}middle selection Z particle is as population wherein Z=MP.

Then, population with colony optimal location P _gin carry out interlace operation.Handle afterwards be designated as

$\stackrel{\&OverBar;}{{\mathrm{pop}}_A^{(t+1)*}}=(\stackrel{\&OverBar;}{x_{A1}^{(t+1)*}},\stackrel{\&OverBar;}{v_{A1}^{(t+1)*}};\stackrel{\&OverBar;}{x_{A2}^{(t+1)*}},\stackrel{\&OverBar;}{v_{A2}^{(t+1)*}};...;\stackrel{\&OverBar;}{x_{\mathrm{AZ}}^{(t+1)*}},\stackrel{\&OverBar;}{v_{\mathrm{AZ}}^{(t+1)*}})$

Wherein, $\stackrel{\&OverBar;}{X_{\mathrm{Ai}}^{(t+1)*}}=X_{\mathrm{Ai}}^{(t+1)*}+\mathrm{\&alpha;}\&CenterDot;(P_g-X_{\mathrm{Ai}}^{(t+1)*}),1\&le;i\&le;Z,\mathrm{\&alpha;}=0.5.$

(3) Immune Selection

The principle of Immune Selection is as follows:

If $\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(\stackrel{\&OverBar;}{X_{\mathrm{Ai}}^{(t+1)*}}\right)}^T\right)\right)\right)\&GreaterEqual;\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(\stackrel{\&OverBar;}{X_{\mathrm{Ai}}^{(t+1)}}\right)}^T\right)\right)\right),$ So, just select instead of select

If $\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(\stackrel{\&OverBar;}{X_{\mathrm{Ai}}^{(t+1)*}}\right)}^T\right)\right)\right)<\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(\stackrel{\&OverBar;}{X_{\mathrm{Ai}}^{(t+1)}}\right)}^T\right)\right)\right),$ So, just select instead of select

Based on above rule, from population and population middle selection Z particle, and this Z particle is designated as so, a brand-new population pop ^{(t+1) * *}just create.

That is: ${\mathrm{pop}}_A^{(t+1)**}=\underset{\&OverBar;}{{\mathrm{pop}}_A^{(t+1)*}}\&cup;{\mathrm{pop}}_B^{(t+1)*}$

$=(x_1^{(t+1)**},v_1^{(t+1)*};x_2^{(t+1)**},v_2^{(t+1)*};...;x_M^{(t+1)**},v_M^{(t+1)*})$

2.3.5 step 5: upgrade data base

According to formula calculate population pop ^{(t+1) *}in the value of objective function of each particle, then according to formula $P_g^{t+!}=\left\{X_i^{(t+1)**}\right|\max f\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(X_i^{(t+1)**}\right)}^T\right)\right)\right)\}$ Calculate value.

If $\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(P_g^{t+1}\right)}^T\right)\right)\right)\&GreaterEqual;\&Integral;\left(\mathrm{\&tau;}\left(\mathrm{\&xi;}\left({\left(P_g\right)}^T\right)\right)\right),$ So otherwise, P _g=P _g.

2.3.6 step 6: end condition

Generally speaking, when algorithm meets any one in following three situations, it just stops:

(1) optimized individual target fitness reaches predefined threshold value;

(2) mean value of the target fitness of optimized individual target fitness and population is all restrained along with the increase of iterations;

(3) iterations reaches the value preset.

In this article, the end condition that the second situation is immunity particle cluster algorithm is chosen.Once the second situation meets, namely this immunity particle cluster algorithm jumps to the 7th step, otherwise jumps to the 3rd step.

2.3.7 step 7: check and correction

First, according to formula τ (ξ ((P _g) ^t)), the P in data base _gbe converted into the Assembly sequences π consistent with it; Then, check Assembly sequences π according to Fig. 3 whether to conform to actual conditions.If π does not conform to the fact, just adjust π, and jump to step 8; Otherwise leap to step 8.

2.3.8 step 8: export

Export best Assembly sequences π, process flow diagram as shown in Figure 2.

Owing to have employed technique scheme, the invention has the beneficial effects as follows: Artificial Immune Algorithm and particle swarm optimization algorithm two kinds of algorithm serials are mixed, set up a kind of can in conjunction with two kinds of algorithm advantages, the novel hybrid algorithm overcoming respective defect, can be used for the problem solving Product Assembly Sequence Planning, such as, adapt to the assembly sequence-planning of the efficient assembly problem of lithium ion battery.

Accompanying drawing explanation

Fig. 1 be the present invention by part kind, locus naming rule legend, intersection point represents a part.

Fig. 2 is that the present invention utilizes immunity particle cluster algorithm to obtain the process flow diagram of best Assembly sequences.

Fig. 3 is a kind of Li-ion batteries piles example schematic that application the inventive method obtains best Assembly sequences.

Fig. 4 is the immunity particle cluster algorithm parameter C2=2 in the best, when M=100, L=50, PC=0.6, and the trend of target function value.

Embodiment

Below in conjunction with accompanying drawing illustrated embodiment, the present invention is further illustrated.

Below in conjunction with a kind of lithium-ion-power cell group shown in Fig. 3, application verification is done to this algorithm

By means of MATLAB software, 5 computers in workstation are tested product A (Fig. 3).

1, the name of part:

Product A is a lithium ion battery (Fig. 3) comprising 71 elements, and these elements are listed in table 1.

The parts list of table 1 product A

Part No.	Part name	Part No.	Component name
				1.1～1.2	Pressing plate	8.1～8.4	Web joint
2.1～2.2	Nut	9.1～9.6	Insulating lid
				3.1～3.2	Screw	10.1～10.6	Battery unit
4.1～4.4	Web joint	11.1～11.7	Coldplate
				5.1～5.16	Bolt	12.1～12.6	Insulating base
6.1～6.5	Insulator cap	13.1～13.2	Side shield
				7.1～7.5	Current carrying lug	14.1～14.4	Chain tape splicing

2, immunity particle cluster algorithm solves the Assembly sequences of Li-ion batteries piles

(1) orthogonal test method of Taguchi Design is utilized to find the best of breed of immunity particle swarm parameter.Four parameter C in immunity particle cluster algorithm ₂(accelerator coefficient), M (Population Size), L (immunological regulation granule number), Pc (crossover probability) uses A respectively, and B, C, D represent, three level values listing parameters are selective, as shown in table 2.

Table 2:IPSO tetra-factor three horizontal parameters table

Wherein, S/N represents the signal to noise ratio (S/N ratio) (in test the ratio of signal and noise, in this experiment, this ratio is the bigger the better) of Taguchi Design, and the computing formula of S/N is as follows herein

$\begin{array}{c}S/N=-10\&times;{\log }_{10}\left(\frac{1}{n}{\mathrm{\&Sigma;}}_{i=1}^n\frac{1}{{\mathrm{yi}}^2}\right)\\ \&ap;-10\&times;{\log }_{10}(\frac{1}{{\stackrel{\&OverBar;}{y}}^2}+\frac{3{\stackrel{\&OverBar;}{s}}^2}{{\stackrel{\&OverBar;}{y}}^4})\end{array}---\left(6\right)$

Wherein, n represents the sum of experiment, and yi represents the target function value of experiment i.Take signal to noise ratio (S/N ratio) as judgment criteria, the test result result after three horizontal parameters value permutation and combination of IPSO tetra-factor being carried out passing judgment on to S/N is as shown in table 3.

The test result of table 3:S/N

As can be seen from Figure 4, when adopting the 9th group of parameter value, signal to noise ratio (S/N ratio) S/N is maximum, so A Selecting parameter the 3rd level value, and B Selecting parameter the 3rd horizontal parameters value, C Selecting parameter the 2nd horizontal parameters value, D Selecting parameter the 1st horizontal parameters value.So with reference to table 2, completing steps two (setup parameter), the optimal parameter combination of parameter immunity particle cluster algorithm is: C ₂=2, M=1000, L=50, P _c=0.6, carry out the renewal rewards theory of step 3 to step 6 subsequently, obtain optimum, its target function value is 44.5, and whole convergence of algorithm process as shown in Figure 4.

Proofread result according to step 7, the assemble sequence after check and correction exports and is:

π＝[(1.1,2.1,3.1,4.1,4.2),8.4,5.4,8.2,5.2,14.4,5.8,14.3,5.7,14.1,5.5,14.2,5.6,11.1,(9.1,10.1,12.1),11.2,(9.2,10.2,12.2),11.3,(9.3,10.3,12.3),13.2,13.1,11.4,(9.4,10.4,12.4),11.5,(9.5,10.5,12.5),11.6,(9.6,10.6,12.6),11.7,(1.2,2.2,3.2,4.3,4.4),5.14,5.16,5.9,5.10,5.11，5.12,7.1,6.1,7.2,6.2,7.3,6.3,7.4,6.4,7.5,6.5,8.3,5.3,8.1,5.1,5.15,5.13]。

Above-mentioned is can understand and apply the invention for ease of those skilled in the art to the description of embodiment.Person skilled in the art obviously easily can make various amendment to these embodiments, and General Principle described herein is applied in other embodiments and need not through performing creative labour.Therefore, the invention is not restricted to embodiment here, those skilled in the art, according to announcement of the present invention, do not depart from improvement that scope makes and amendment all should within protection scope of the present invention.

Claims (7)

1. solve a method for Product Assembly sequence problem based on immunity particle cluster algorithm, it is characterized in that: comprise the naming rule of part, the setting of algorithm; First formulate the naming rule of each part, then realized the combination of immune algorithm and particle swarm optimization algorithm by two self-defining function to solve Product Assembly sequence problem.

2. the method solving Product Assembly sequence problem based on immunity particle cluster algorithm according to claim 1, it is characterized in that: the naming rule of described part is: the form adopting ' AB ', A represents the kind code of part, and B represents the spatial position code of part, and wherein A, B are natural number;

According to the priority of locus, arranged in sequence; Its spatial location priority is: first left and then right, previously again after, first up and then down; Symbolically is: left < is right, after front <, under upper <.

3. the method solving Product Assembly sequence problem based on immunity particle cluster algorithm according to claim 1, is characterized in that: the setting of described algorithm comprises: 3.1 constraint conditions; 3.2 objective function; 3.3 immunity particle cluster algorithm.

4. the method solving Product Assembly sequence problem based on immunity particle cluster algorithm according to claim 3, is characterized in that: described constraint condition comprises:

3.1.1 geometric feasibility

Make P={p ₁, p ₂..., p _nrepresent the set of part in assembly, π={ π ₁, π ₂..., π _mrepresent Assembly sequences, wherein, π _i=[q ₁, q ₂... q _n], (1) i=1,2 ..., m; (2) q _j∈ P, j=1,2 ..., N; (3) q _j≠ q _k,

P is represented with mobile limit (MW) _iand p _jbetween geometrical constraint in assembling process; MW (p _i, p _j)={+X ,-X ,+Y ,-Y ,+Z ,-Z} represent at Assembly part p _iin process, p _iwith Assembly part p _jthe set of the assembly direction do not interfered;

Ω is made to be part q _ithe set of the part before assembling, then

Definition 1: geometric feasibility standard

If Assembly sequences π _i=[q ₁, q ₂... q _n], so, Assembly sequences π _imeeting geometric feasibility, i.e. π _irepresent an Assembly sequences not having geometrical interference; If π _ido not meet geometric feasibility, then π _irepresent an Assembly sequences having geometrical interference;

3.1.2 continuity

In order to keep the stability of assembling, whole assembling process must meet continuity requirement;

Contact matrix CM is made to represent relation between part.If CM is (p _i, p _j)=1, then represent p _iand p _jbetween there is contact relation; Otherwise, if CM is (p _i, p _j)=0, then represent p _iwith p _jbetween there is not contact relation;

Define 2 continuity standards

For Assembly sequences π _i=[q ₁, q ₂... q _n], if so Assembly sequences π _imeet continuity, wherein, symbol V represents Boolean logic ' OR ' operational symbol, and symbol ∑ represents that arithmetical logic summation operation accords with.

5. the method solving Product Assembly sequence problem based on immunity particle cluster algorithm according to claim 3, is characterized in that: described objective function is as follows:

Wherein, f ₁represent the manufacturability of objective function, f ₂represent the geometric feasibility of objective function, f ₃represent the continuity of objective function, N is the total number of part in assembly;

3.2.1 the manufacturability of objective function

If the basic part of assembly is positioned at first of Assembly sequences, then B=kk; Otherwise B=0;

In order to emphasize that basic part is positioned at the primary importance of Assembly sequences, kk=N-1=50. herein

N _tand n _drepresent the number of transitions of assembly tool and the number of transitions of assembly direction respectively;

ω _b, ω _tand ω _drepresent weight, wherein 0≤ω _b≤ 1,0≤ω _t≤ 1,0≤ω _d≤ 1, and ω _b+ ω _t+ ω _d=1,

Computing formula is as follows:

Wherein, n represents the element total number in engineering information, and k represents the importance information of element in engineering information; Suppose that the sequence of importance of the project data in equation 1 is: basic part > assembly tool > assembly direction.Weights omega from equation 2 _b(k=1)=1/2, ω _t(k=2)=1/3, and ω _d(k=3)=1/6;

3.2.2 the geometric feasibility of objective function

FG is used for detecting the geometric feasibility of Assembly sequences, and its computing formula is as follows:

Wherein, NG represents the part sum that geometrical interference occurs in assembling process; For an Assembly sequences, if any one part i (except basic part) interferes with any one part assembled before it, then this Assembly sequences meeting geometric feasibility requirement; FG=1 in this case; Otherwise this Assembly sequences does not meet geometric feasibility, now 0≤FG < 1;

3.2.3 the continuity of objective function

FC is used to detect p in Assembly sequences _iand p _jbetween continuity, its computing formula is as follows:

Wherein NC represents the total number do not come in contact between part in assembling process; For an Assembly sequences, if first part exists contact relation with each part outside last part with any Assembly part, then this Assembly sequences meets continuity requirement, in this case, and FC=1; Otherwise this Assembly sequences does not meet continuity requirement, 0≤FC < 1 in this case;

According to formula 1 ~ formula 4, being calculated as follows of objective function:

6. the method solving Product Assembly sequence problem based on immunity particle cluster algorithm according to claim 3, it is characterized in that: described immunity particle cluster algorithm comprises the following steps: setup parameter, initialization, renewal population, immune operation, renewal data base, end condition checking, check and correction, output;

3.3.1 step one: setup parameter

(1) M: Population Size;

(2) W: inertia weight,

(3) C ₂: accelerator coefficient;

(4) λ: similarity threshold;

(5) L: immunological regulation numbers of particles;

(6) Pc: crossover probability;

(7) T _max: iterations.Make initial value be 100, if iterations is not restrained in iterative refinement procedure, so, just increase T _max;

3.3.2 step 2: initialization

A stochastic generation M particle, as iterations t=1, position and the speed of each particle are respectively: with thus generate initialization population pop1, namely

In order to calculate the fitness of particle with formula 5, name two function ξ () and τ () herein, be defined as follows:

Definition 3 by be mapped to π ' _iformula meet following condition:

(1) if x _ij< x _ik, so q ' _j< q ' _k;

(2) if x _ij=x _ikand j < k, so q ' _j< q ' _k;

Wherein, X _i=(x _i1, x _i2..., x _iN) ^t, π ' _i=[q ' ₁, q ' ₁..., q ' _n],

X _ij∈ R, q ' _j∈ R, 1≤i≤M, 1≤j≤N, M ∈ R, N ∈ R, R represents nature number field;

Definition 4 is by π ' _ibe mapped to π _iformula be τ (π ' _i)=π _i, meet: q _jinherit q ' _jcontent of text, difference is that field of definition is different.Wherein, π ' _i=[q ' ₁, q ' ₁..., q ' _n], π _i=[q ₁, q ₁..., q _n], q ' _j∈ R, q _j∈ W, 1≤i≤M, 1≤j≤N;

M ∈ R, N ∈ R, R represents nature number field, and W represents textview field;

The function ξ () defined based on engineering experience and two and τ (), the particle that a meeting geometric feasibility and continuity require just has designed; Then this particle is named to be finally will be stored into data base;

The initial position of particle i is made to be its fitness function value is calculated as follows:

(1)

(2) f (π _i) and can derive from; Wherein,

3.3.3 step 3: upgrade population

4th step of whole algorithm has used immunological regulation, and in process of immune regulation, L new particle adds in addition, namely needs on the basis based on concentration choosing principles, from high to low, selects M particle in M+L particle; If very low for the concentration of particle i at t, so t+1 for time, this particle can not be selected, namely particle i there will not be t+1 generation in; Therefore the speed of the particle before each renewal and position is made to be respectively: with be respectively after renewal with formula 6 and formula 7 is utilized to upgrade position and the speed of each particle in whole immunity particle cluster algorithm;

If so,

If so,

3.3.4 step 4: immune operation

(1) immunological regulation

Immunoregulatory settlement steps to deal is as follows:

1) random generation L particle;

2) basis individual to (M+L) particle is converted to the Assembly sequences { π of (M+L) bar _i=[q ₁, q ₂..., q _n] | 1≤i≤M+L};

3) according to formula 14 ~ formula 17, the survival expectation value e of calculating antibody _i; From (M+L) individual particle, M particle is selected to form new population pop by the order of successively decreasing ^t+1,

Clearly,

(2) immunity inoculation

Immunity inoculation probably comprises two stages: extract vaccine, vaccine inoculation;

1) vaccine is extracted: because colony optimal location P _gvery close with the group optimal solution in the process of particle swarm optimization algorithm, so select P _gfor vaccine;

2) vaccine inoculation:

Order

First, from population pop ^{(t+1) *}middle selection Z particle is as population wherein Z=MP.

Then, population with colony optimal location P _gin carry out interlace operation.Handle afterwards be designated as

Wherein,

(3) Immune Selection

The principle of Immune Selection is as follows:

If so, just select instead of select

If so, just select instead of select

Based on above rule, from population and population middle selection Z particle, and this Z particle is designated as so, a brand-new population pop ^{(t+1) * *}just create;

That is:

3.3.5 step 5: upgrade data base

According to formula calculate population pop ^{(t+1) *}in the value of objective function of each particle, then according to formula calculate value;

If so otherwise, P _g=P _g;

3.3.6 step 6: end condition

When algorithm meets any one in following three situations, it just stops:

(1) optimized individual target fitness reaches predefined threshold value;

(2) mean value of the target fitness of optimized individual target fitness and population is all restrained along with the increase of iterations;

(3) iterations reaches the value preset.

3.3.7 step 7: check and correction

First, according to formula τ (ξ ((P _g) ^t)), the P in data base _gbe converted into the Assembly sequences π consistent with it; Then, check Assembly sequences π whether to conform to actual conditions; If π does not conform to the fact, just adjust π, and jump to step 8; Otherwise leap to step 8;

3.3.8 step 8: export

Export best Assembly sequences π.

7. the method solving Product Assembly sequence problem based on immunity particle cluster algorithm according to claim 6, it is characterized in that: in step 6, choosing described (2) situation is the end condition of immunity particle cluster algorithm, meet once meet the second situation, namely this immunity particle cluster algorithm jumps to the 7th step, otherwise jumps to the 3rd step.