CN105590143B - Multi-machine assembly line chip mounter load balancing optimization method in PCB assembly process - Google Patents
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Abstract
The invention discloses a multi-machine assembly line chip mounter load balancing optimization method in a PCB assembly process, which comprises the steps of describing and analyzing optimization problems of a PCB assembly line, establishing a mathematical model with balanced load according to the description and the analysis of the optimization problems, designing an algorithm according to the solving characteristics of the mathematical model to obtain a component mounting sequence with balanced load of each chip mounter, and finally applying the algorithm to a production line control system to mount components on each chip mounter in an optimal scheduling mode, wherein the algorithm adopts an intelligent optimization algorithm combining a cuckoo search algorithm and a particle swarm algorithm. The invention adopts the improved cuckoo search algorithm to solve the optimized scheduling mathematical model with balanced load of each chip mounter on the production line, and obtains the overall optimal component mounting scheduling scheme, thereby balancing the load of each chip mounter and improving the efficiency of the production line.
Description
Technical Field
The invention relates to an intelligent scheduling optimization method for a PCB (printed circuit board) assembly production line, belonging to the technical field of intelligent optimization scheduling and control of production systems.
Background
The surface assembly production process is taken as a key process of the electronic information manufacturing industry in China, the international core research result in the aspect is rarely disclosed, the domestic exploration on the key common theory problem and the realization technology is just started, and the bottleneck for restricting the electronic information industry in China to overtake the international advanced manufacturing level is formed.
The assembly of a Printed Circuit Board (PCB) is a core process of a surface assembly production line, and electronic elements are assembled on the PCB so as to realize the interconnection of the electronic elements. Electronic manufacturing technology is becoming more and more important in the electronic information industry, and printed circuit board assembly is the fundamental industry of the electronic information industry and the industry of its support.
Printed circuit assembly lines must accommodate multi-user, multi-tasking, multi-variety production requirements to achieve maximum throughput in a minimum amount of time at a minimum cost and a minimum reject rate. An effective way to meet this problem is the overall process optimal control.
The chip mounter is the most critical equipment in the surface assembly production line, and the performance of the production capacity of the whole production line is limited by the working efficiency. Therefore, in order to better meet the requirements of multiple varieties, variable batches, short period, low cost and high quality in the manufacturing process of electronic equipment, the theory and practical application problem of the optimized operation of the surface assembly production line and the bottleneck equipment thereof, namely the chip mounter, is researched, an effective method for improving the production efficiency of the production line and the equipment is sought, the load balance optimization problem of each chip mounter on the production line is analyzed, and the method becomes one of the hot spots of research of relevant scholars at home and abroad in recent years. Meanwhile, the research and practice of the problems can not only promote the innovation and the upgrade of the domestic surface assembly technology, but also effectively improve the optimized management and control level of the surface mounting equipment in the existing surface assembly process, solve the production scheduling optimization problem existing in the traditional production line and generate great and direct economic and social benefits.
The scheduling problem of the surface assembly production line is the synthesis and popularization of the workshop scheduling problem and the parallel machine scheduling problem, is a strong NP-hard problem, is characterized in that certain difficult and multi-target properties can better reflect the actual production process, and the theory and the method have higher application value. Many scholars at home and abroad use Ant Colony Optimization (ACO), Genetic Algorithm (GA), tabu search algorithm (TS), Particle Swarm Optimization (PSO) and the like to solve the scheduling problem of the line production workshop, and a good effect is achieved. At present, the load balancing optimization algorithm of a multi-machine flow production line is relatively less researched in China, the genetic algorithm has the global search capability in a large range, but the feedback information is not fully utilized, and a large amount of useless redundant iteration is often performed when the solution reaches a certain degree; the ant colony algorithm has a feedback mechanism but has a slow convergence speed; the PSO algorithm has high convergence speed, but cannot ensure that an optimal solution is obtained, and the cuckoo search algorithm is a novel intelligent algorithm proposed in recent years and has the advantages of less parameter setting, high convergence speed, strong global optimization capability and the like; but the algorithm has the defects of weak local optimization capability and slow search speed.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a scheduling optimization method for load balancing optimization of a surface mounting production line chip mounter based on an improved cuckoo algorithm, solves the optimization problem of component mounting path planning of a PCB assembly production line, obtains a component mounting scheduling scheme with load balancing optimization, and determines an optimal production load scheme for each chip mounter; the processing time of each chip mounter is equal and minimum, so that the load of each chip mounter is balanced, and the efficiency of a production line is improved.
The purpose of the invention is realized by the following technical scheme:
a multi-machine assembly line chip mounter load balancing optimization method in a PCB assembly process comprises the steps of describing and analyzing optimization problems of a PCB assembly line, establishing a mathematical model with balanced load according to the description and the analysis of the optimization problems, designing an algorithm according to solving characteristics of the mathematical model to obtain a component mounting sequence with balanced load of each chip mounter, and finally applying the algorithm to a production line control system to mount components on each chip mounter in a production line according to an optimal scheduling mode, wherein the algorithm adopts an intelligent optimization algorithm combining a cuckoo search algorithm and a particle swarm algorithm.
As a preferred scheme, the method for optimizing the load balance of the chip mounters of the multi-machine assembly line in the PCB assembly process is characterized by comprising the following steps: the method comprises the following steps:
1) establishment of mathematical model
Describing the load balancing problem of the multi-machine flow production line of the PCB from the actual start of the multi-machine flow production line for assembling the PCB, and establishing an optimized scheduling mathematical model with constraint conditions for load balancing of all chip mounters of the production line according to the description of the problem;
2) solving for
Solving the mathematical model of the component mounting scheduling of the multi-machine flow production line of the PCB, which is established in the step 1), by adopting an optimization method combining a cuckoo search algorithm and a particle swarm algorithm so as to obtain an optimal solution which enables the processing time of each chip mounter to be equal and to reach the minimum;
3) control mounting
And (3) respectively providing the optimal solution of component mounting scheduling obtained in the step 2) to a mounting control subsystem and an intelligent feeding distribution subsystem of the production line, so that each chip mounter of the whole production line carries out component mounting according to an optimal scheduling mode.
Preferably, in step 1), the mathematical model is established as follows:
a. firstly, aiming at the actual characteristics of the flow line production, the load balancing problem of the multi-machine flow line production line of the PCB is described, and the description method comprises the following steps:
if c elements are arranged on the PCB, the elements are processed on m chip mounters, and for convenience of description and problem analysis, the element types of all the chip mounters and the PCB are respectively expressed by mathematical numbers as follows:
the chip mounter is integrated as follows: m ═ {1,2, …, M }; the types of the PCB board are collected as follows: c ═{1,2, …, c }; the processing requirement set is as follows: w ═ W1,w2,…,wk,…,wcGet wkIs of type k (k)<C) The number of PCB boards of (a). Setting the processing or assembling time of the PCB with the type k to t on a chip mounter with the serial number of i E Mik，TiThe time required for the chip mounter numbered i e M to complete its assigned task. The following decision variables 0-1 were introduced:
b. aiming at the problem description in the step a, a mathematical model for load balancing optimization scheduling problem is established, and the mathematical model is expressed as follows:
an objective function:
wherein,
constraint conditions are as follows:
xike (0, 1), i is 1, a, m; k 1.., C, indicating that the variable is a 0-1 variable constraint.
Preferably, in the step 2), the optimization method using the combination of the cuckoo search algorithm and the particle swarm algorithm is as follows: the positions in the cuckoo algorithm are continuously updated by the particle swarm algorithm, specifically, the cuckoo randomly walks according to a LevyFlight mechanism, and updates the path according to the particle swarm algorithm at a later stage, so that the local optimization capability of the cuckoo search algorithm is improved.
Further preferably, in the step 2), the optimization method using a combination of the cuckoo search algorithm and the particle swarm algorithm specifically includes the following steps:
step a: initializing basic parameters
The number N of nests selected by cuckoo and the discovery probability PaMaximum population number h, learning factor c1、c2Maximum iteration number maxgeneration;
step b: randomly selecting the position of the nest by cuckoo
Randomly generating and preferentially selecting n sequences, and combining Xi(i ═ 1,2, …, N), as initial bird nest, replacing the bird nest positions with the arrangement of the PCB board component mounting process based on the random key coding of the minimum position value rule, calculating and evaluating the scheduling target value of each bird nest according to the positions of the bird nests, and initially selecting to obtain the current optimal bird nest XbestRecording the sequencing and scheduling target value of the current optimal post device, wherein the iteration number is 1;
step c: analyzing the advantages and disadvantages of various position solutions, and respectively establishing a poor solution cluster and a good solution species cluster;
step d: turning to step f for the optimal solution population; for the poor solution population, sequentially executing;
step e: according to a first updating mode in the standard cuckoo search algorithm, specifically as formula I, searching the position of a bird nest and comparing the position with the original position, preferentially selecting the position to update the bird nest, updating the corresponding posting sequencing and scheduling target value, turning to step g,
formula I:
wherein,
represents t +Candidate positions for the ith nest in generation 1;
representing the position of the ith nest in the t generation, α is the control step length;
is point-to-point multiplication; l (lambda) is a random search path obeying Levy distribution, and turning to step g;
step f: according to the particle swarm algorithm, specifically formula II, searching other bird nest positions and comparing with the original position, preferentially selecting the positions to update bird nests, updating corresponding mounting sequencing and scheduling target values,
formula II:
wherein,
indicating a location;
represents a speed; random () is [0,1 ]]A random number in between; c. C1、c2Is a learning factor, is a non-negative constant; w is the coefficient of inertia; piRepresenting individual optimal particles; g represents a global optimum particle;
step g: generating random number random () for each updated bird nest and probability P of finding out foreign bird eggsaComparing, if random () < Pa, the host gives up updating the bird nest and creates a new bird nest randomly, so as to obtain a group of new bird nests, then the positions of the new bird nests are compared with the updated bird nests, if better, the new bird nests are used as the existing bird nests, and meanwhile, the corresponding posting sequencing and scheduling target values are updated;
step h: evaluating the target modulation values of all the nests, laying eggs in the updated nests if the target modulation values of the nests are more optimal after updating, finding out the corresponding optimal nest positions, reserving the optimal nests, updating the corresponding mounting sequencing and scheduling target values,
step i: keeping the optimal arrangement of the attaching process and a scheduling target value, increasing the iteration times by 1, turning to the step j if the maximum iteration times is reached, and turning to the step c if the maximum iteration times is not reached, and performing the next round of optimization;
step j: and outputting the optimal value and the final production scheduling scheme.
The principle of the invention is as follows:
step 1) of the invention, aiming at the characteristic that the assembly production line of the PCB is a parallel flow production line (specifically, the detailed description is shown in the figure 1 and the figure 2) with a plurality of chip mounters working simultaneously, the invention assumes that the processing time of various PCBs on different chip mounters is known, takes the minimization of the whole assembly time as an optimization target and aims to construct an intelligent optimization method for determining the assembly sequence and the processing task allocation scheme of the PCBs. From the characteristics of flow production and continuous batch production, the chip mounter with the longest processing time determines the completion time of the whole processing procedure. If the processing time of each chip mounter on the production line can be equal and minimum, the whole production line can finish load balancing, and the highest production efficiency can be obtained. Therefore, an optimized scheduling mathematical model with constraint conditions for load balancing of all chip mounters of a production line is established so as to obtain an optimal solution which enables the processing time of all the chip mounters to be equal and to reach the minimum.
In the step 2), an improved cuckoo search algorithm is adopted, and mutual conversion between continuous position vectors of host bird nests selected by cuckoos and component mounting sequences of various PCB boards is realized in a random key coding mode based on a minimum position value rule; and then improving the cuckoo search algorithm by using a Particle Swarm Optimization (PSO), so that the cuckoo updates the path according to the PSO algorithm at the later stage on the basis of random walk of the cuckoo according to a Levy Flight mechanism, thereby not only maintaining the global optimizing capability of the cuckoo search algorithm, but also greatly improving the local optimizing capability of the cuckoo search algorithm, further achieving the global optimal solution of the optimized scheduling mathematical model for load balancing of a production line and obtaining the mounting sequence of all components of various PCBs corresponding to the scheduling scheme with the optimal load balancing.
The invention has the beneficial effects that:
on the basis of the advantages and the disadvantages of each algorithm in the prior art, in order to make the various algorithms draw the strong points and make up the weak points and improve the optimization efficiency of the algorithm, the invention combines the reality of chip mounter production, proposes to fuse the cuckoo search algorithm and the particle swarm algorithm, and applies the fusion to the solution of the load balance optimization problem of the multi-machine flow production line assembled by PCB boards. According to the working process and characteristics of the surface assembly line, the optimal scheduling mathematical model of the component mounting sequence of various PCBs on the production line is established, the mounting time of various chip mounters on the production line is equal and minimum through the optimal scheduling of various chip mounters, the optimal scheduling mathematical model with balanced load of various chip mounters on the production line is solved by adopting an improved cuckoo search algorithm, and a globally optimal component mounting scheduling scheme is obtained, so that the load of various chip mounters is balanced, and the efficiency of the production line is improved.
Drawings
FIG. 1 is a schematic view showing the flow line characteristics of a PCB assembly line according to the present invention;
FIG. 2 is a schematic diagram of a parallel feature of the PCB assembly line of the present invention;
fig. 3 is a block diagram of an improved cuckoo search algorithm in the present invention.
Detailed Description
Example 1:
referring to fig. 1, where 1 is a PCB, 21 is a component 1, 22 is a component 2, 23 is a component 3, 24 is a component 4, 25 is a component 5, 26 is a component 6, 27 is a component 7, 28 is a component 8, 29 is a component 9, in the scheduling optimization method for load balancing optimization of a chip mounter in a surface assembly line based on an improved cuckoo algorithm according to the present invention, the flow line is characterized in that: the distribution of the PCB is carried out according to types, and the PCB of the same type is usually processed on a chip mounter; the assembly task of each part is completed by all chip mounters on the production line together, and the processing task of each chip mounter is completely different;
as shown in fig. 2 and 3, the conveyor belt is a conveyor belt, in the scheduling optimization method for load balancing optimization of a chip mounter in a surface assembly production line based on an improved cuckoo algorithm, the flow production line is characterized in that: the chip mounter is characterized in that a plurality of chip mounters are arranged in parallel, various PCBs are distributed to different chip mounters to complete machining and assembling, one chip mounter performs machining on a certain PCB (composed of a plurality of elements), and other chip mounters also perform machining operation on other components;
the dispatching optimization method for the load balance optimization of the chip mounter in the surface assembly production line based on the improved cuckoo algorithm comprises the following specific processes:
the method comprises the following steps: aiming at the practical characteristics of the flow line production, the load balancing problem of the multi-machine flow line production line of the PCB is described as follows: if c elements are arranged on the PCB, the elements are processed on m chip mounters, and for convenience of description and problem analysis, the element types of all the chip mounters and the PCB are respectively expressed by mathematical numbers as follows:
the chip mounter is integrated as follows: m ═ {1,2, …, M }; the types of the PCB board are collected as follows: c ═ 1,2, …, C }; the processing requirement set is as follows: w ═ W1,w2,…,wk,…,wcGet wkIs of type k (k)<C) The number of PCB boards of (a). Setting the processing or assembling time of the PCB with the type k to t on a chip mounter with the serial number of i E Mik，TiThe time required for the chip mounter numbered i e M to complete its assigned task. The following decision variables 0-1 were introduced:
step two: aiming at the problem description in the step pair, the idea of the chip mounter optimization scheduling is to determine an optimal production load scheme for each chip mounter; the processing time of each chip mounter is equal and minimum, so that the efficiency of a production line is optimal, and the load balancing optimization scheduling problem is expressed by a mathematical model as follows:
an objective function:
wherein,
constraint conditions are as follows:
xike (0, 1), i is 1, a, m; k 1.., C, indicating that the variable is a 0-1 variable constraint;
step three: as shown in fig. 3, according to the mathematical model of the mounting and dispatching of the components in the production line established in the second step, the cuckoo search algorithm and the Particle Swarm Optimization (PSO) are combined to solve the mathematical model, the cuckoo search algorithm is improved, and the PSO algorithm is integrated into the optimization, so that the cuckoo randomly walks according to a Levy Flight mechanism and updates a path according to the PSO algorithm at a later stage, thereby maintaining the global optimization capability of the cuckoo search algorithm and greatly improving the local optimization capability of the cuckoo search algorithm; therefore, the optimization and adjustment of the position updating mode in the cuckoo algorithm by utilizing the PSO algorithm is a key innovation point of the optimization method; the method comprises the following concrete steps:
step a: initializing basic parameters
The number N of nests selected by cuckoo and the discovery probability PaMaximum population number h, learning factor c1、c2Maximum iteration number maxgeneration;
step b: randomly selecting the position of the nest by cuckoo
Random productGenerating and preferentially selecting n sequences, and combining Xi(i ═ 1,2, …, N), as initial bird nest, replacing the bird nest positions with the arrangement of the PCB board component mounting process based on the random key coding of the minimum position value rule, calculating and evaluating the scheduling target value of each bird nest according to the positions of the bird nests, and initially selecting to obtain the current optimal bird nest XbestRecording the sequencing and scheduling target value of the current optimal post device, wherein the iteration number is 1;
step c: analyzing the advantages and disadvantages of various position solutions, and respectively establishing a poor solution cluster and a good solution species cluster;
step d: turning to step f for the optimal solution population; for the poor solution population, sequentially executing;
step e: according to a first updating mode in the standard cuckoo search algorithm, specifically as formula I, searching the position of a bird nest and comparing the position with the original position, preferentially selecting the position to update the bird nest, updating the corresponding posting sequencing and scheduling target value, turning to step g,
formula I:
wherein,
representing candidate positions of the ith nest in the t +1 th generation;
representing the position of the ith nest in the t generation, α is the control step length;
is point-to-point multiplication; l (lambda) is a random search path obeying Levy distribution, and turning to step g;
step f: according to the particle swarm algorithm, specifically formula II, searching other bird nest positions and comparing with the original position, preferentially selecting the positions to update bird nests, updating corresponding mounting sequencing and scheduling target values,
formula II:
wherein,
indicating a location;
represents a speed; random () is [0,1 ]]A random number in between; c. C1、c2Is a learning factor, is a non-negative constant; w is the coefficient of inertia; piRepresenting individual optimal particles; g represents a global optimum particle;
step g: generating random number random () for each updated bird nest and probability P of finding out foreign bird eggsaComparing, if random () < Pa, the host gives up updating the bird nest and creates a new bird nest randomly, so as to obtain a group of new bird nests, then the positions of the new bird nests are compared with the updated bird nests, if better, the new bird nests are used as the existing bird nests, and meanwhile, the corresponding posting sequencing and scheduling target values are updated;
step h: evaluating the target modulation values of all the nests, laying eggs in the updated nests if the target modulation values of the nests are more optimal after updating, finding out the corresponding optimal nest positions, reserving the optimal nests, updating the corresponding mounting sequencing and scheduling target values,
step i: keeping the optimal arrangement of the attaching process and a scheduling target value, increasing the iteration times by 1, turning to the step j if the maximum iteration times is reached, and turning to the step c if the maximum iteration times is not reached, and performing the next round of optimization;
step j: and outputting the optimal value and the final production scheduling scheme.
Step four: and C, providing the optimal mounting scheduling solution of each chip mounter in the group of production lines obtained in the step three to a PCB surface assembly production line control system, realizing optimal control of mounting components of the chip mounters, ensuring that each chip mounter in the whole production line carries out component mounting according to the optimal scheduling mode, achieving load balancing optimization of each chip mounter, and improving production efficiency.
Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. A multi-machine assembly line chip mounter load balancing optimization method in a PCB assembly process comprises the steps of describing and analyzing optimization problems of a PCB assembly line, establishing a load balancing mathematical model according to the description and the analysis of the optimization problems, designing an algorithm according to solving characteristics of the mathematical model to obtain a component mounting sequence of each chip mounter with balanced load, and finally applying the component mounting sequence to a production line control system to mount components of each chip mounter in an optimal scheduling mode on a production line, wherein the method is characterized in that: the algorithm adopts an intelligent optimization algorithm combining a cuckoo search algorithm and a particle swarm algorithm; the method comprises the following steps:
1) establishment of mathematical model
Describing the load balancing problem of the multi-machine flow production line of the PCB from the actual start of the multi-machine flow production line for assembling the PCB, and establishing an optimized scheduling mathematical model with constraint conditions for load balancing of all chip mounters of the production line according to the description of the problem;
2) solving for
Solving the mathematical model of the component mounting scheduling of the multi-machine flow production line of the PCB, which is established in the step 1), by adopting an optimization method combining a cuckoo search algorithm and a particle swarm algorithm so as to obtain an optimal solution which enables the processing time of each chip mounter to be equal and to reach the minimum;
3) control mounting
Respectively providing the optimal solution of component mounting scheduling obtained in the step 2) to a production line mounting control subsystem and an intelligent feeding distribution subsystem, so that each chip mounter of the whole production line carries out component mounting according to an optimal scheduling mode;
in the step 2), the optimization method by combining the cuckoo search algorithm and the particle swarm algorithm is as follows: the positions in the cuckoo search algorithm are continuously updated by utilizing the particle swarm algorithm, specifically, the cuckoo randomly walks according to a Levy Flight mechanism, and updates the paths according to the particle swarm algorithm at the later stage, so that the local optimizing capability of the cuckoo search algorithm is improved;
the optimization method combining the cuckoo search algorithm and the particle swarm algorithm specifically comprises the following steps:
step a: initializing basic parameters
The number N of nests selected by cuckoo and the discovery probability PaMaximum population number h, learning factor c1、c2Maximum iteration number maxgeneration;
step b: randomly selecting the position of the nest by cuckoo
Randomly generating and preferentially selecting n sequences, and combining Xi(i ═ 1,2, …, N), as initial nests, replacing the nest positions with the arrangement of the PCB board component mounting process based on the random key code of the minimum position value rule, calculating and evaluating the scheduling target value of each nest according to the position of the nest, and initially selecting to obtain the current optimal nest XbestRecording the current optimal mounting sequence and a scheduling target value, and setting the iteration number as 1;
step c: analyzing the advantages and disadvantages of various position solutions, and respectively establishing a poor solution cluster and a good solution species cluster;
step d: turning to step f for the optimal solution population; for the poor solution population, sequentially executing;
step e: according to a first updating mode in the standard cuckoo search algorithm, specifically as formula I, searching the position of the nest and comparing the position with the original position, preferentially selecting the position to update the nest, updating the corresponding mounting sequencing and scheduling target values, turning to step g,
formula I:
wherein, Xi (t+1)Representing candidate positions of the ith nest in the t +1 th generation; xi (t)Representing the position of the ith nest in the t generation, α is the control step length;
is point-to-point multiplication; l (lambda) is a random search path obeying Levy distribution with the parameter of lambda, and turning to step g;
step f: according to the particle swarm algorithm, specifically formula II, searching the positions of other nests and comparing with the original positions, preferentially selecting the positions to update the nests, updating the corresponding mounting sequencing and scheduling target values,
formula II:
wherein x isi (t)Representing the position of the ith nest in the t generation; v. ofi (t)Represents a speed; random () is [0,1 ]]A random number in between; c. C1、c2Is a learning factor, is a non-negative constant; w is the coefficient of inertia; p is a radical ofiRepresenting individual optimal particles; g represents a global optimum particle;
step g: generating a random number for each updated nest, and the probability P of finding a foreign eggaA comparison is made if random () < PaIf the position of the new nest is better than the updated nest, the new nest is used as the existing nest, and the corresponding mounting sequencing and scheduling target values are updated at the same time;
step h: evaluating the target modulation values of all the nests, laying eggs in the updated nests if the target modulation values of the nests are more optimal after updating, finding out the corresponding optimal nest positions, reserving the optimal nests, updating the corresponding mounting sequencing and scheduling target values,
step i: keeping the arrangement of the optimal mounting procedure and a scheduling target value, increasing the iteration times by 1, turning to the step k if the maximum iteration times is reached, and turning to the step c if the maximum iteration times is not reached, and performing the next round of optimization;
step k: and outputting the optimal value and the final production scheduling scheme.
2. The method for optimizing load balancing of chip mounters in multiple assembly lines in a PCB assembly process according to claim 1, wherein the method comprises the following steps: in the step 1), the mathematical model is established as follows:
firstly, aiming at the practical characteristics of the flow line production, the load balancing problem of the multi-machine flow line production line of the PCB is described, and the description method comprises the following steps:
if c elements are arranged on the PCB, the elements are processed on m chip mounters, and for convenience of description and problem analysis, the element types of all the chip mounters and the PCB are respectively expressed by mathematical numbers as follows:
the chip mounter is integrated as follows: m ═ {1,2, …, M }; the types of the PCB board are collected as follows: c ═ 1,2, …, C }; the processing requirement set is as follows: w ═ W1,w2,…,wk,…,wcGet wkIs of type k (k)<C) The number of the PCB boards of (1); setting the processing or assembling time of the PCB with the type k to t on a chip mounter with the serial number of i E Mik，TiThe time required for the chip mounter with the serial number of i belonging to M to complete the distributed task is obtained; the following decision variables 0-1 were introduced:
aiming at the problem description in the step pair, a mathematical model for load balancing optimization scheduling problem is established, and the mathematical model is expressed as follows:
an objective function:
wherein,
constraint conditions are as follows:
xike (0, 1), i is 1, a, m; k 1.., C, indicating that the variable is a 0-1 variable constraint.
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