CN104537425B - A kind of Optimization Scheduling of the production assembling process of vehicle air conditioning outlet - Google Patents
A kind of Optimization Scheduling of the production assembling process of vehicle air conditioning outlet Download PDFInfo
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Abstract
The present invention relates to a kind of Optimization Schedulings of the production assembling process of vehicle air conditioning outlet, belong to workshop intelligent optimization dispatching technique field.The present invention passes through the production assembling process scheduling model and optimization aim for determining vehicle air conditioning outlet, and is optimized using the Optimization Scheduling of ADAPTIVE MIXED Estimation of Distribution Algorithm to optimization aim；Wherein the process time of the part of scheduling model foundation vehicle air conditioning outlet on each machine establishes with the final assembly deadline, to minimize mean completion time as optimization aim.The invention enables the expression of the production assembling process of vehicle air conditioning outlet is clear and accurate；More careful local search is carried out to the quality area that global search is found, to reach preferable balance between global and local search.
Description
Technical Field
The invention relates to an optimized scheduling method for a production and assembly process of an air outlet of an automobile air conditioner, and belongs to the technical field of intelligent optimized scheduling of a production workshop.
Background
At present, domestic automobile interior part production companies enter the stage of micro-profit development, how to produce products with higher quality and lower cost is related to whether enterprises can continue to live, and in the face of the problem of the great importance, various strategies are considered by all companies, and one of the good methods is to try to shorten the working hours by optimizing production and assembly procedures so as to reduce the cost and improve the price competitiveness of the products.
In modern manufacturing enterprises, the assembly workload accounts for 20% -70% of the workload of the whole product, the average is 45%, and particularly, the assembly time of automobiles, locomotives and the like accounts for 40% -60% of the manufacturing time of the whole product. In recent years, as a host factory pays more attention to the cost of the whole automobile and the technology of the air outlet of the automobile is more mature, the host factory can stand alone without fail only by providing an air outlet which is more beautiful, humanized, high in quality and low in price. In the Chinese market, the price is undoubtedly the fatal weakness of enterprise competition. At present, China is in the stage of rapid development of manufacturing industry, and the automation degree is quite low, so that the assembly line is reasonably balanced, and the efficiency is improved, thereby bringing huge benefits to enterprises.
In the production and assembly process of the air outlet of the automobile air conditioner, the method mainly comprises 3 stages of processing, transporting and assembling parts of the air outlet of the automobile air conditioner. 4 parts which are respectively processed on 4 pieces of equipment in the first stage are required to be assembled in the third stage to form each automobile air-conditioning air outlet; after the 4 parts corresponding to each air outlet of the automobile air conditioner are completely processed in the first stage, the parts are immediately collected and transported from the second stage to the third stage to be assembled; parts corresponding to various automobile air-conditioning air outlets are sequentially processed through three stages according to the processing sequence of the automobile air-conditioning air outlets; any processing equipment in the first stage can only process one part at the same time, and the sequence of different parts is related to set time, wherein the set time depends on the processing sequence; the assembling equipment in the third stage can only assemble the same type of air outlet of the automobile air conditioner at the same time, and the setting time of different air outlets of the automobile air conditioner is 0.
The production and Assembly process of the air outlet of the automobile air conditioner belongs to a typical Three-Stage Assembly line production process, the academic community defines the Assembly line as a Three-Stage Assembly line (TSAF), and proves that the TSAF scheduling problem with more than two machines in the first Stage belongs to an NP difficult problem, namely, a complex problem which can be solved by an algorithm in polynomial time does not exist. Obviously, the TSAF scheduling problem (namely, the scheduling problem of the production assembly line of the air outlet of the automobile air conditioner) with 4 machines in the first stage also belongs to the NP difficult problem category. The problem is reasonably scheduled, and the production efficiency of the production assembly line system of the air outlet of the automobile air conditioner can be obviously improved.
Because the scheduling problem of the production assembly line of the air outlet of the automobile air conditioner is an NP difficult problem, the problem cannot be solved by a traditional mathematical programming method, and therefore, the invention designs an improved optimized scheduling method of an adaptive mixed Distribution Estimation Algorithm (IAEDA), and an excellent solution of the scheduling problem of the production assembly process of the air outlet of the automobile air conditioner can be obtained in a short time.
Disclosure of Invention
The invention aims to solve the technical problem of obtaining an excellent solution of the scheduling problem of the production and assembly process of the air outlet of the automobile air conditioner in a short time, and provides an optimal scheduling method of the production and assembly process of the air outlet of the automobile air conditioner.
The technical scheme of the invention is as follows: an optimized scheduling method for the production and assembly process of an air outlet of an automobile air conditioner is characterized in that a scheduling model and an optimized target of the production and assembly process of the air outlet of the automobile air conditioner are determined, and the optimized target is optimized by using an optimized scheduling method of a self-adaptive mixed distribution estimation algorithm; the scheduling model is established according to the processing time and the final assembly completion time of the parts of the air outlet of the automobile air conditioner on each machine, and the minimum average completion time is taken as an optimization target:
wherein,the n automobile air-conditioning outlets to be processed are arranged based on the processing sequence,for assembling air outlet of automobile air conditionerThe automobile air conditioner air outlet part which needs to be processed on the kth equipment in the first stage,as a componentAnd partsSet time in between and as a componentThe time required for the processing of (a),belongs to the air outlet of the automobile air conditioner for the second stage collection and transportationTo the third stage of assembly of the apparatus,belongs to the air outlet of an automobile air conditionerAll parts of (2) are subjected to the maximum processing time required for the first stage processing and the second stage collection, transportation and for air outlet of automobile air conditionerAt the time of assembly in the third stage,for air outlet of automobile air conditionerIs completed by The average completion time of all the air outlets of the automobile air conditioner is calculated; the optimization target is to find one pi in a set pi of all processing sequences of the air outlets of the automobile air conditionerP*So that the objective functionAnd minimum.
The optimal scheduling method of the self-adaptive mixed distribution estimation algorithm comprises the following specific steps:
step1, encoding mode: coding is carried out according to the processing and assembling sequence of each type of air outlet of the automobile air conditionerWherein n is the number of the air outlets of the automobile air conditioner to be processed,for the air outlet of the vehicle air conditioner to be assembledParts to be machined on the kth equipment in the first stage;
step2, population and probability model initialization: the population scale is M, and an initialization population is generated by adopting a random method until the number of initial solutions meets the requirement of the population scale; an n x n dimensional matrix P (gen) is adopted to represent the probability distribution model of the gen generation of the algorithm;
wherein, Pi(gen)＝[Pi1(gen),Pi2(gen),…,Pin(gen)]Is the ith row vector in P (gen), Pij(gen) is the ith row and the jth column element of P (gen) and represents the probability that the automobile air conditioner air outlet j appears at the ith position of an individual or a solution in the gen generationP (gen) numerically reflects the processing priority relationship of different air outlets of the automobile air conditioner, Pij(gen) is larger, the larger the probability that the automobile air conditioner air outlet j appears at the ith position of the individual in the gen generation is;
step3, sampling and generating new populations: sampling the probability model by adopting a roulette mode;
step4, "Insert" mutation operation based on the first improved leap-out principle: performing a local search for the best individual or solution in the population using an "Insert" mutation operation that first improves the principle of escape;
step5, updating the probability model: firstly, judging whether the obtained optimal individual is continuously updated for ten generations, and if so, initializing a probability matrix; otherwise, adopting a learning rate and variation rate self-adaptive adjustment mechanism based on the information entropy, and updating the probability matrix by using the 'optimal individual' found in the searching process by the algorithm;
step6, end conditions: setting the maximum iteration times of the termination condition as 200, and if the maximum iteration times are met, outputting an optimal individual; otherwise, go to Step3, and repeat iteration until the termination condition is satisfied.
The working principle of the invention is as follows:
step 1: and establishing a production assembly process scheduling model and an optimization target of the air outlet of the automobile air conditioner.
The dispatching model is established according to the processing time and the final assembly completion time of the parts of the air outlet of the automobile air conditioner on each machine, and the aim of minimizing the average completion time is taken as the optimization
Wherein,the n automobile air-conditioning outlets to be processed are arranged based on the processing sequence,for assembling air outlet of automobile air conditionerThe automobile air conditioner air outlet part which needs to be processed on the kth equipment in the first stage, as a componentAnd partsThe set time in between is set to be,as a componentThe time required for the processing of (a),belongs to the air outlet of the automobile air conditioner for the second stage collection and transportationTo the third stage of assembly of the apparatus,belongs to the air outlet of an automobile air conditionerThe maximum processing time required for all parts to be processed in the first stage and collected and transported in the second stage,for air outlet of automobile air conditionerAt the time of assembly in the third stage,for air outlet of automobile air conditionerThe time of completion of the process of (c),the average completion time of all the air outlets of the automobile air conditioner is calculated; the optimization target is to find one pi in a set pi of all processing sequences of the air outlets of the automobile air conditionerP*So that the objective functionAnd minimum.
Step 2: and (5) representing the solution.
The invention provides a coding mode based on the processing sequence of an air outlet of an automobile air conditioner. For example, for the scheduling problem of the production and assembly processes of the automobile air conditioner air outlet with n-6 and m-3,is a solution or permutation of the problem. The arrangement shows that the automobile air-conditioning outlet with the number of 6 is firstly processed, namely a part [6 ] corresponding to the automobile air-conditioning outlet with the number of 6]1、[6]2、[6]3Respectively at the first stageThe first processing of the 1 st, 2 nd and 3 rd equipment, and then the first processing of the second stage and the third stage; secondly, the 2 nd part of the automobile air-conditioning air outlet with the number of 3 is processed, namely, the part [3 ] corresponding to the automobile air-conditioning air outlet with the number of 3]1、[3]2、[3]3Tightening of parts [6 ] on 1 st, 2 nd, 3 rd apparatus in a first stage, respectively]1、[6]2、[6]3Processing, and then processing the 2 nd through a second stage and a third stage; the air outlets of the automobile air conditioners with the numbers 5, 1, 4 and 2 are processed in sequence. For other problems of different scale, the values of n and m may differ, expressed in the same manner as above.
And step 3: and (4) carrying out a population initialization strategy.
When the population is initialized, a part of individuals or solutions are generated by adopting an expanded SPT rule, so that the initial population can be ensured to comprise certain high-quality individuals, and high-quality solution information can be accumulated when the probability distribution matrix is updated for the first time by utilizing dominant sub-populations in the population; the rest of the individuals are generated in a random mode, which is beneficial to maintaining the diversity and the dispersity of the population. The extended SPT rule generation mode is as follows: 1) sequencing the parts processed on each device in the first stage in an ascending order according to the processing time, so that m sequences exist, and then replacing the parts in each sequence with the air outlets of the automobile air conditioners to which the parts belong to obtain m individuals; 2) replacing the 'ascending sorting according to the processing time' in the step 1) with 'ascending sorting according to the sum of the processing time and the setting time', and then performing the same operation as the step 1) to obtain other m individuals; 3) arranging the air outlets of the automobile air conditioner assembled on the equipment in the third stage in an ascending order according to the assembling time to obtain 1 individual; 4) and (2) calculating the average processing time of all parts of each automobile air-conditioning outlet on m machines in the first stage, calculating the sum of the average processing time of the first stage of each automobile air-conditioning outlet and the processing time of the first stage and the processing time of the second stage of each automobile air-conditioning outlet, and sequencing the automobile air-conditioning outlets according to the sum to obtain 1 individual. This resulted in 2m +2 individuals.
And 4, step 4: and initializing a strategy by using the probability distribution model.
IAEDA adopts an n multiplied by n dimensional matrix P (gen) to represent the probability distribution model of the gen generation of the algorithm, namely:
wherein, Pi(gen)＝[Pi1(gen),Pi2(gen),…,Pin(gen)]Is the ith row vector in P (gen), Pij(gen) is the ith row and the jth column element of P (gen) and represents the probability that the automobile air conditioner air outlet j appears at the ith position of an individual or a solution in the gen generationP (gen) numerically reflects the processing priority relationship of different air outlets of the automobile air conditioner, Pij(gen) is larger, the larger the probability that the automobile air conditioner air outlet j appears at the ith position of the individual in the gen generation is;
at algorithm initialization (gen ═ 0), P is setij(0) 1/(n × n), i, j 1, …, n. Setting P relative to conventional mannerij(0) Setting P as 1/nij(0) After the initial update (from P (0) to P (1)) and the "line" normalization are performed, P (gen) can accumulate more information of good-quality individuals in the initial population, namely, the product bj (bje e {1, …, n }) corresponding to the ith (i ═ 1, …, n) in the good-quality individuals can be increased in P (n × n), and the number of the product bj is increased in PiThe value of the bj column in (gen) ensures that the automobile air conditioner air outlet bj is in the pair Pi(gen) the probability of being selected when the roulette sample generates the ith digit of a new individual increases. This is advantageous for guiding the algorithm to search near high-quality individuals, and can suitably improve the initial searching ability of the algorithm.
And 5: and (3) a probability distribution model self-adaptive updating mechanism.
For an algorithm based on EDA, a probability distribution model determines the searching direction of the algorithm, and the updating mechanism of the probability distribution model has great influence on the performance of the algorithm. For IAEDA, the update of the probability distribution model or matrix P (gen) depends mainly on the learning rate and the variation rate. Firstly, a smaller learning rate or a larger variation rate is beneficial to maintaining the population diversity level, so that the algorithm can obtain a better search width, but the convergence rate becomes slower or even does not converge, so that the search depth of the algorithm is difficult to ensure; secondly, the convergence rate of the algorithm can be increased by a larger learning rate or a smaller variation rate, the algorithm has a better search depth, but the algorithm is easy to fall into local optimum, thereby causing premature convergence, and enabling the search width of the algorithm to be incapable of being maintained. How to reasonably set the learning rate and the variation rate in the algorithm evolution process so as to ensure that the algorithm finds reasonable balance between the search width and the search depth is the key for effectively improving the performance of the algorithm. Therefore, an adaptive regulation mechanism based on learning rate and variance ratio of information entropy is proposed for updating p (gen). Let E (gen) be the information entropy of the gen generation P (gen), namely:
starting from the 1 st generation of the algorithm, P increases with the number of running or evolution generations genij(gen) will gradually approach 0or 1 (the optimal solution or optimal individual corresponding element approaches 1, other elements approach 0) so that E (gen) decreases continuously and eventually tends towards 0. Therefore, the evolution process of IAEDA is also a gradual decline process of e (gen), which can reflect the degree of evolution of the algorithm to some extent. Therefore, the learning rate r (gen) of the gen generation of the algorithm is calculated by the following formula:
wherein E is0For information entropy threshold, set to E0＝0.6EM(EMUpper limit of E (gen) for nlnn), rfTo the final learning rate (rf ═ 0.08), rminTo a minimumLearning rate (r)min0.02 and rmin< rf < 1), α is a control parameter (generally the value is between 2 and 6). in the early stage of algorithm evolution, r (gen) has relatively large value, and with the increase of gen, E (gen) gradually approaches E0And r (gen) decreases gradually and approaches rf。
In order to better ensure the directionality of the algorithm search, IAEDA adopts the optimal individuals found by the algorithm till the gen generationP (gen) is updated as a dominant sub-population. Let B (gen) be the gen generation n × n dimensional update matrix. Elements in B (gen) other than when the subscripts (i, j) thereof belong toThe value is not more than 1, and the other values are all 0. P (gen) is updated using the formula:
P(gen+1)＝(1-r(gen))×P(gen)+(r(gen)/n)×B(gen)
in the early stage of algorithm evolution, r (gen) has larger value, so that after P (gen) is updated to P (gen +1) and P (gen +1) is further normalized in a row way, P can be obviously increasedi(gen +1) thThe values listed (i ═ 1, …, n) result in productsIn pair Pi(gen +1) the probability of being selected increases when the roulette sample generates the ith digit of a new individual. This helps to group at πPbest(gen) nearby searches, the strength and depth of the search may be increased. With the increase of gen, the value of r (gen) is gradually reduced, and at the moment, the air outlet of the automobile air conditioner is not onlyThe probability of being selected when generating the i-th bit of a new individual is relatively small, and the convergence rate of P (gen +1) (i.e., P (g))The speed at which the elements in en +1) gradually go to 0or 1) is properly slowed down. This is beneficial to keeping the diversity of the population in the later stage of the algorithm, and can improve the width and the precision of the search.
Because the scheduling problem of the production assembly process of the air outlet of the automobile air conditioner is a strong NP-hard problem, the problem solution space is very complex, and in order to avoid the algorithm from falling into local optimum early, after the gen 1 is started, P (gen) is updated to P (gen +1), and then the self-adaptive variation rate P is adoptedM(gen) certain perturbations or variations are made on P (gen +1) to further increase the diversity of the population. PM(gen) calculated using the formula:
PM(gen)＝Pmin×exp[lnβ×((EM-E(gen))/EM)]
wherein, PminThe lower limit of the variation rate (P)min＝0.4)，PM(gen) is the variation rate of the gen-th generation, β is the amplification control parameter (β ═ 2). with the increase of gen, E (gen) gradually approaches to 0, and P (gen) gradually approaches to 0M(gen) will gradually increase to β Pmin.
Let random (0,1) be generated as [0,1 ]]Random (0or 1) is randomly generated to be 0or 1, and C (gen) is a gen generation n × n dimensional variation matrix. Each element in C (gen) is assigned a value by random (0or 1) at each generation. After performing r (gen) to update P (gen +1) to P (gen), if random (0,1) < PM(gen) if true, P (gen +1) is mutated using the following formula:
P(gen+1)＝(1-rM(gen))P(gen+1)+rM(gen)×C(gen)
wherein r isM(gen) is the rate of variation. In order to properly enhance the effect of mutation, r is addedMThe value of (gen) is r (gen)/2. With the increase of gen, PM(gen) is gradually increased, the probability of executing mutation on P (gen +1) is increased, which can effectively slow down the convergence speed of P (gen +1), thereby preventing premature convergence to some extent.
To further avoid the algorithm falling into local optima, start with gen ═ 1, atAfter the information entropy E (gen) of the gen generation P (gen) is calculated, if the optimal individual pi in the populationPbest(gen) is not changed in 10 continuous generations or E (gen) is less than 1, the initialization operation executed by the P (gen) is forced to be reset, the algorithm is ensured to be guided to search more different areas, and then the reset P (gen) is updated by using the learning rate and the variation rate. In addition, after the learning rate and the variation rate are executed to update the learning rate and the variation rate, the row normalization processing needs to be carried out on P (gen +1), namely, P is ensurediThe sum of the elements in (gen +1) is 1, so that a new population is generated by using roulette in the next step.
Step 6: a new population sampling generation method.
Sampling to generate a new population, namely updating the ith position P of each individual in the gen +1 generation populationi(gen +1) roulette sample generation (i ═ 1, …, n) is performed. To further ensure good quality individualsIs maintained, first from pi, as each new individual is generatedPbest(gen) L (L ═ 0.2n) positions are randomly selected, their corresponding elements or products are retained in the same positions of the new individual, and then the remaining n-L positions of elements are determined from the roulette sample. In roulette sampling, if the element selected at a certain position is the same as any of the previously determined elements, the sampling is repeated until a different element is selected.
And 7: based on findfirstSkipnInsertLocal search of the neighborhood.
To enhance the local search capabilities of the IAEDA, a "Insert" neighborhood based search can be performed on the individuals or solutions with the best history in the new population generated. Let NInsert(π, u, v) is the insertion of the element or product at the u-th position in the permutation π into the v-th position. Arranging pi on the basis of NInsertThe neighborhood of (pi, u, v) can be expressed as:
Ninsert(π)＝{πtemp＝Insert(π,u,v)|v≠u,u-1；u,v＝1,2,…,n}
first-improved leap-out principle of Insert neighborhood search to NInsert(pi, u, v) the first better neighborhood solution then jumps out of the current loop and takes the neighborhood solution as the current best solution. Based on the above definition, FindFirstSkipnInsertThe procedure for (π, u, v) is as follows:
step 7.1: let u be 1, v be 2,
step 7.2:
step 7.3: if it isThen
Step 7.3.1: u + 1;
step 7.3.2: if u is less than or equal to n, go to step 7.2, otherwise, go to step 7.5;
step 7.4: if it isThen v ═ v + 1;
step 7.4.1, if v is less than or equal to n and v is not equal to u, turning to step 7.2, otherwise, turning to step 7.3.1;
step 7.5: output of
And 8: and judging whether an optimization result is output or not.
If the set maximum iteration number is 200, outputting an optimal individual; otherwise, let gen be gen +1 and return to step 5.
The invention has the beneficial effects that:
1. the scheduling model and the optimization target of the production and assembly process of the air outlet of the automobile air conditioner are provided, so that the expression of the production and assembly process of the air outlet of the automobile air conditioner is clear and accurate;
2. a probability distribution model initialization strategy is provided, so that more effective information can be accumulated by P (0), and a better initial search area is improved for the subsequent search of the algorithm;
3. providing a distribution model self-adaptive updating mechanism, measuring the evolution degree of the algorithm by using the information entropy, updating P (gen +1) in real time according to the evolution degree, generating a new population with a good mode according to P (gen +1) and realizing global search;
4. performing more detailed local search on the high-quality area found by the global search, thereby achieving better balance between the global search and the local search; the IAEDA is expected to become an effective algorithm for solving a scheduling model of the production and assembly process of the air outlet of the automobile air conditioner.
Drawings
FIG. 1 is a schematic view of the production and assembly process of an air outlet of an automobile air conditioner in the present invention;
FIG. 2 is a Gantt diagram of two production and assembly processes of an air outlet of an automobile air conditioner;
FIG. 3 is a flow chart of the algorithm of the present invention;
FIG. 4 is a diagram illustrating the problem scale of the present invention as n-6 solution;
FIG. 5 is a schematic diagram of an "Insert" based variation of the present invention.
Detailed Description
Example 1: as shown in fig. 1-5, an optimized scheduling method for a production assembly process of an air outlet of an automotive air conditioner is implemented by determining a scheduling model and an optimized target for the production assembly process of the air outlet of the automotive air conditioner, and optimizing the optimized target by using an optimized scheduling method of an adaptive hybrid distribution estimation algorithm; the scheduling model is established according to the processing time and the final assembly completion time of the parts of the air outlet of the automobile air conditioner on each machine, and the minimum average completion time is taken as an optimization target:
wherein,the n automobile air-conditioning outlets to be processed are arranged based on the processing sequence,for assembling air outlet of automobile air conditionerThe automobile air conditioner air outlet part which needs to be processed on the kth equipment in the first stage,as a componentAnd partsSet time in between and as a componentThe time required for the processing of (a),belongs to the air outlet of the automobile air conditioner for the second stage collection and transportationTo the third stage of assembly of the apparatus,belongs to the air outlet of an automobile air conditionerAll parts of (2) are subjected to the maximum processing time required for the first stage processing and the second stage collection, transportation and for air outlet of automobile air conditionerAt the time of assembly of the third stageIn the middle of the furnace, the gas-liquid separation chamber,for air outlet of automobile air conditionerIs completed byThe average completion time of all the air outlets of the automobile air conditioner is calculated; the optimization target is to find one pi in a set pi of all processing sequences of the air outlets of the automobile air conditionerP*So that the objective functionAnd minimum.
The optimal scheduling method of the self-adaptive mixed distribution estimation algorithm comprises the following specific steps:
step1, encoding mode: coding is carried out according to the processing and assembling sequence of each type of air outlet of the automobile air conditionerWherein n is the number of the air outlets of the automobile air conditioner to be processed,for the air outlet of the vehicle air conditioner to be assembledParts to be machined on the kth equipment in the first stage;
step2, population and probability model initialization: the population scale is M, and an initialization population is generated by adopting a random method until the number of initial solutions meets the requirement of the population scale; an n x n dimensional matrix P (gen) is adopted to represent the probability distribution model of the gen generation of the algorithm;
wherein, Pi(gen)＝[Pi1(gen),Pi2(gen),…,Pin(gen)]Is the ith row vector in P (gen), Pij(gen) is the ith row and the jth column element of P (gen) and represents the probability that the automobile air conditioner air outlet j appears at the ith position of an individual or a solution in the gen generationP (gen) numerically reflects the processing priority relationship of different air outlets of the automobile air conditioner, Pij(gen) is larger, the larger the probability that the automobile air conditioner air outlet j appears at the ith position of the individual in the gen generation is;
step3, sampling and generating new populations: sampling the probability model by adopting a roulette mode;
step4, "Insert" mutation operation based on the first improved leap-out principle: performing a local search for the best individual or solution in the population using an "Insert" mutation operation that first improves the principle of escape;
step5, updating the probability model: firstly, judging whether the obtained optimal individual is continuously updated for ten generations, and if so, initializing a probability matrix; otherwise, adopting a learning rate and variation rate self-adaptive adjustment mechanism based on the information entropy, and updating the probability matrix by using the 'optimal individual' found in the searching process by the algorithm;
step6, end conditions: setting the maximum iteration times of the termination condition as 200, and if the maximum iteration times are met, outputting an optimal individual; otherwise, go to Step3, and repeat iteration until the termination condition is satisfied.
The population size was set to 70.
Specific comparative experiments are as follows:
the IAEDA designed by the invention is compared with a DPSO (see the literature Tian Y, Liu DY, Yuan D H, Wang K H.A discrete PSO for two-stage assembly scheduling technical, 2013,66:481 and 499) which is a currently existing main flow algorithm, so as to verify the effectiveness of the IAEDA. The IAEDA runs for 200 generations, the DPSO algorithm runs for the same time as the IAEDA, and the test results are shown in Table 1. Table 1 gives the objective function values obtained for different problem scales:
TABLE 1 values of objective function obtained for different problem scales
| n×m | 30×2 | 40×2 | 50×3 | 60×3 |
| IAEDA | 890.56 | 1068.31 | 1380.49 | 1679.68 |
| DPSO | 896.58 | 1080.58 | 1389.07 | 1690.05 |
As can be seen from Table 1, what is considered for the present inventionIndexes are obviously superior to DPSO algorithms for the considered problems, which shows that the IAEDA is an effective algorithm for solving the optimization of the production and assembly processes of the air outlet of the automobile air conditioner.
Claims (1)
1. An optimized scheduling method for the production and assembly process of an air outlet of an automobile air conditioner is characterized by comprising the following steps: the method comprises the steps of determining a production assembly process scheduling model and an optimization target of an air outlet of the automobile air conditioner, and optimizing the optimization target by using an optimization scheduling method of a self-adaptive mixed distribution estimation algorithm; the scheduling model is established according to the processing time and the final assembly completion time of the parts of the air outlet of the automobile air conditioner on each machine, and the minimum average completion time is taken as an optimization target:
wherein,the n automobile air-conditioning outlets to be processed are arranged based on the processing sequence,for assembling air outlet of automobile air conditionerThe automobile air conditioner air outlet part which needs to be processed on the kth equipment in the first stage,as a componentAnd partsSet time in between and as a componentThe time required for the processing of (a),belongs to the air outlet of the automobile air conditioner for the second stage collection and transportationTo the third stage of assembly of the apparatus,belongs to the air outlet of an automobile air conditionerAll parts of (2) are subjected to the maximum processing time required for the first stage processing and the second stage collection, transportation and for air outlet of automobile air conditionerAt the time of assembly in the third stage,for air outlet of automobile air conditionerIs completed by The average completion time of all the air outlets of the automobile air conditioner is calculated; the optimization target is to find one pi in a set pi of all processing sequences of the air outlets of the automobile air conditionerP*So that the objective functionMinimum;
the optimal scheduling method of the self-adaptive mixed distribution estimation algorithm comprises the following specific steps:
step1, encoding mode: coding is carried out according to the processing and assembling sequence of each type of air outlet of the automobile air conditionerWherein n is the number of the air outlets of the automobile air conditioner to be processed,for the air outlet of the vehicle air conditioner to be assembledParts to be machined on the kth equipment in the first stage;
step2, population and probability model initialization: the population scale is M, and an initialization population is generated by adopting a random method until the number of initial solutions meets the requirement of the population scale; an n x n dimensional matrix P (gen) is adopted to represent the probability distribution model of the gen generation of the algorithm;
wherein, Pi(gen)＝[Pi1(gen),Pi2(gen),…,Pin(gen)]Is the ith row vector in P (gen), Pij(gen) is the ith row and the jth column element of P (gen) and represents the probability that the air outlet j of the automobile air conditioner appears on the ith position of an individual in the gen generationP (gen) numerically reflects the processing priority relationship of different air outlets of the automobile air conditioner, Pij(gen) is larger, the larger the probability that the automobile air conditioner air outlet j appears at the ith position of the individual in the gen generation is;
when the population is initialized, a part of individuals are generated by adopting an expanded SPT rule; the extended SPT rule generation mode is as follows: 1) sequencing the parts processed on each device in the first stage in an ascending order according to the processing time, so that m sequences exist, and then replacing the parts in each sequence with the air outlets of the automobile air conditioners to which the parts belong to obtain m individuals; 2) replacing the 'ascending sorting according to the processing time' in the step 1) with 'ascending sorting according to the sum of the processing time and the setting time', and then performing the same operation as the step 1) to obtain other m individuals; 3) arranging the air outlets of the automobile air conditioner assembled on the equipment in the third stage in an ascending order according to the assembling time to obtain 1 individual; 4) calculating the average processing time of all parts of each automobile air-conditioning outlet on m machines in the first stage, calculating the sum of the average processing time of the first stage of each automobile air-conditioning outlet and the processing time of the first stage of each automobile air-conditioning outlet in the last two stages, and sequencing the automobile air-conditioning outlets according to the sum to obtain 1 individual, wherein 2m +2 individuals can be generated;
step3, sampling and generating new populations: sampling the probability model by adopting a roulette mode;
step4, "Insert" mutation operation based on the first improved leap-out principle: performing a local search on the best individuals in the population using an "Insert" mutation operation that first improves the principle of jumping out;
let NInsert(π, u, v) is the insertion of the element or product at the u-th position in the permutation π into the v-th position; arranging pi on the basis of NInsertThe neighborhood of (pi, u, v) can be expressed as:
Ninsert(π)＝{πtemp＝Insert(π,u,v)|v≠u,u-1；u,v＝1,2,…,n}
first-improved leap-out principle of Insert neighborhood search to NInsert(π,u,v) The first better neighborhood solution jumps out of the current cycle and takes the neighborhood solution as the current optimal solution; based on the above definition, FindFirstSkipnInsertThe procedure for (π, u, v) is as follows:
step 7.1: let u be 1, v be 2,
step 7.2:
step 7.3: if it isThen
Step 7.3.1: u + 1;
step 7.3.2: if u is less than or equal to n, go to step 7.2, otherwise, go to step 7.5;
step 7.4: if it isThen v ═ v + 1;
step 7.4.1, if v is less than or equal to n and v is not equal to u, turning to step 7.2, otherwise, turning to step 7.3.1;
step 7.5: output of
And 8: judging whether an optimization result is output or not;
wherein, pitempRepresents a new permutation, f (π, u, v), generated by the Insert (π, u, v) methodtemp) Is pitempThe objective function value of (1); FindFirstSkipNInsert(pi, u, v) is an Insert neighborhood search based on a first-improvement jump-out strategy;is the best individual for the gen generation,is composed ofThe objective function value of (1);
step5, updating the probability model: firstly, judging whether the obtained optimal individual is continuously updated for ten generations, and if so, initializing a probability matrix; otherwise, adopting a learning rate and variation rate self-adaptive adjustment mechanism based on the information entropy, and updating the probability matrix by using the 'optimal individual' found in the searching process by the algorithm;
step6, end conditions: setting the maximum iteration times of the termination condition as 200, and if the maximum iteration times are met, outputting an optimal individual; otherwise, go to Step3, and repeat iteration until the termination condition is satisfied.
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