CN106610655A

CN106610655A - Improved particle swarm optimization algorithm for solving job-shop scheduling problem

Info

Publication number: CN106610655A
Application number: CN201610116651.6A
Authority: CN
Inventors: 姜艾佳; 胡成华
Original assignee: Sichuan Yonglian Information Technology Co Ltd
Current assignee: Sichuan Yonglian Information Technology Co Ltd
Priority date: 2016-03-02
Filing date: 2016-03-02
Publication date: 2017-05-03

Abstract

The invention provides an improved particle optimization algorithm for solving a job-shop scheduling problem, and relates to the technical field of job-shop scheduling. Improvements are performed in order to solve a problem that the traditional particle swarm optimization algorithm is poor in processing for a discrete optimization problem and easily falls into local optimum. Firstly, an improvement is performed on a traditional PSO (Particle Swarm Optimization) method which generates an initial solution randomly, and a weighted average method is introduced to set the initial solution of particles; secondly, an improvement is performed on a mean shift algorithm, the next state of the initial solution is predicted by using the improved mean shift algorithm, a predicted solution is compared with the current optimal solution, the better solution is enabled to act as the current optimal solution, and a problem that abnormal changes in particle information are not considered in the particle swarm optimization algorithm is solved; and thirdly, a tabu search algorithm is introduced to perform further update on the particle information, and the problem that the particle swarm optimization algorithm easily falls into local optimum is just solved.

Description

Improved particle swarm algorithm for solving job shop scheduling problem

Field of the invention

The invention relates to the field of job shop scheduling, in particular to a method for solving a job shop scheduling problem by using an algorithm.

Background

The Job-Shop Scheduling Problem (JSP) is one of the core and the focus of manufacturing execution system research, and the research not only has important practical significance, but also has far-reaching theoretical significance. The JSP reasonably distributes resources according to the manufacturing requirements of the products, and further achieves the purposes of reasonably utilizing the manufacturing resources of the products and improving the economic benefits of enterprises. JSP is a problem coexisting in the product manufacturing industry, is closely related to factory management and product manufacturing hierarchy of Computer Integrated Manufacturing Systems (CIMS), and is an important subject of research in the field of CIMS. JSP is a typical NP-hard problem, and the research of JSP has a meaningful influence on the research of NP problem.

Over the past several decades, various algorithms have been applied to solve job shop scheduling problems. Traditionally, optimization methods and approximation methods are generally used to solve the problem of automatic generation of job shop scheduling schemes. Optimization methods include enumeration and mathematical planning techniques. Approximations typically use branch-and-bound methods, precedence rules, heuristic methods, iterative local search algorithms, and evolutionary algorithms.

The Particle Swarm Optimization (PSO) is an intelligent algorithm which is initially inspired by the activity rule of a bird swarm, and the movement of the whole swarm is subjected to an evolution process from disorder to order in a problem solving space by utilizing the sharing of the swarm to individual information, so that an optimal solution is obtained. However, the particle swarm optimization does not deal well with the discrete optimization problem and tends to fall into local optimization.

Disclosure of Invention

Aiming at the defects in the prior art, the invention aims to provide an improved particle swarm algorithm based on a mean shift algorithm and a tabu search algorithm.

The invention aims to overcome the defects existing in the prior art: the particle swarm algorithm is easy to fall into local optimization; the particle swarm optimization only processes the current particle swarm information, and does not process the abnormal condition of the change of some particle information; the particle swarm optimization only disturbs the current optimal solution, so that the search range is narrowed.

The technical scheme adopted by the invention for realizing the purpose is as follows: an improved particle swarm algorithm solves the job shop scheduling problem, and the algorithm comprises the following steps:

step 1: initializing algorithm parameters: including information on the number, position, and velocity of the PSO particles.

Step 2: obtaining an initial optimal solution: and setting the priority of the initial particles by adopting a weighted average method to obtain an initial optimal solution.

Step 2.1: numbering each particle;

step 2.2: counting the sum of the speeds of all the particles, and dividing the speed sum by the speed of each particle to obtain the priority value of each particle;

step 2.3: and determining the particle sequence according to the priority, wherein the workpiece with the high priority value is preferentially executed.

And step 3: obtaining a traditional current optimal solution: and updating the particle information by using a particle swarm algorithm to obtain the current optimal solution of the current traditional particle swarm algorithm.

And 4, step 4: predicting the current optimal solution: and adding an improved mean shift algorithm, and predicting the position and the overall position of each particle on the basis of the initial optimal solution by using the mean shift algorithm.

Step 4.1: particle position information is initialized.

Step 4.2: and determining the current particle swarm center.

Step 4.3: and calculating a particle swarm weight matrix.

Step 4.4: and calculating the weight of the particles.

Step 4.5: and predicting the position and the speed of the next particle by using a high-low point method.

Step 4.6: a similarity function is calculated.

Step 4.7: and calculating a mean shift vector, and determining the optimal prediction position and speed of the particle swarm according to the mean shift vector.

Step 4.8: step 4.2 to step 4.7 are executed in a loop until the exit condition is met.

And 5: initially selecting the current optimal solution: and comparing the predicted optimal position and speed with the previous optimal position and speed of the group by using the evaluation standard of the particle swarm algorithm, and taking the better position information as the best current position information.

Step 6: determining the current optimal solution: and executing a tabu search algorithm to find the current optimal solution.

Step 6.1: given a current solution and a domain structure, candidate solutions are then determined within the current domain structure.

Step 6.2: if the objective function corresponding to the best candidate solution is better than the reserved best solution, the taboo characteristic is ignored, the current solution and the best solution are represented by the taboo characteristic, the corresponding characteristic is added into a taboo table, and meanwhile, the taboo table is modified;

step 6.3: if the candidate solution does not exist, selecting the best non-taboo solution from the candidate solutions as a new current solution regardless of the advantages and disadvantages of the current solution, adding the response characteristic of the solution into a taboo table, and modifying the taboo table;

step 6.4: looping steps 6.1 through 6.3 until a stop criterion is met;

and 7: and (6) circularly executing the step 2 to the step 6 until the stop condition is reached.

The invention has the beneficial effects that:

1. the particle priority is set by means of a weighted value, uncertainty inference caused by random generation of an initial solution is avoided, and blind search time is reduced.

2. The mean shift algorithm is improved a little, and then the improved mean shift algorithm is used for predicting the particle position information, so that the interference of part of abnormally-changed particles on the whole algorithm is reduced.

3. A tabu search algorithm is added to avoid search trapping into local optimality;

drawings

FIG. 1 is a basic flow chart of the algorithm of the present invention.

FIG. 2 is a flow chart of an improved mean shift algorithm.

Fig. 3 is a flow chart of the tabu search algorithm.

Fig. 4 is a flow chart of a basic particle swarm algorithm.

Detailed Description

The traditional particle swarm algorithm has the advantages of high searching speed, high efficiency and simple algorithm, and is suitable for real-time processing. But the discrete optimization problem is not well processed and is easy to fall into local optimization. Therefore, in order to solve these problems, the algorithm is firstly improved on the traditional PSO method of randomly generating an initial solution: setting an initial solution of the particles by introducing a weighted average method; secondly, the mean shift algorithm is improved: the method comprises the steps of predicting the next state of an initial solution by using an improved mean shift algorithm, comparing the predicted solution with the current optimal solution, and taking a better solution as the current optimal solution, so that the condition that particle information is abnormally changed and is not considered in a particle swarm optimization is solved; and thirdly, a tabu search algorithm is introduced to further update the particle information, so that the problem that the particle swarm algorithm is easy to fall into local optimum is solved.

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to fig. 1 to 4.

Job shop scheduling

One JSP can be described as follows: assume that there are n jobs that need to be scheduled on m machines. First the specific operation of each workpiece is determined and data for each sequence is given. The present invention establishes in advance some assumptions: (1) the processing sequence of each job has been determined; (2) each machine processes at most one job at the same time and once the work is started cannot be terminated (3) the jobs are independent of each other, i.e. each job can be processed in any order; (4) all jobs are started at time 0 waiting to be processed. In order to illustrate the algorithm for solving the JSP problem proposed by the present invention, the following mathematical model is designed to show the specific implementation process (table 1 is defined by JSP model symbols):

n	number of jobs
		m	Number of machines
j	Job indexing
		p	Job operation index
k	Machine index
		l	Machine operation index
M_k	Kth machine
		N_j	J (th) job
O_jpkl	J-th job operation p/k-th machine operation l
		S_jpkl	O_jpklStarting time
C_jpkl	O_jpklCompletion time
		P_jpkl	O_jpklTime of treatment
B_operation	Adjacent operation buffer time

TABLE 1

(1) Establishing a 0-1 planning model:

(2) constraint function:

S_j(p+1)k(l+1)＝Max(C_jpk'l',C_j'p'kl) (3)

P_jpkl＝C_jpkl-S_jpkl(4)

P_jpkl≥0 (5)

C_jpkl≥S_jpkl(6)

S_j(p+1)kl-C_jpk'l'＝B_jB_j∈(0,∞) (7)

S_jpk(l+1)-C_j'p'kl＝B_kB_k∈(0,∞) (8)

an objective function:

MakeSpan＝Min(Max(C_jpkl)) (9)

constraints (1) and (2) summarize the limits that are satisfied by the number of machines and the processing job at the same time in all cases. Constraint (3) means that there is a possibility of a waiting time before the job starts to operate. In this case, the machine M_kUpper N_jDoes not exceed the start time of job N_jThe completion time of (c). Constraints (4), (5) and (6) ensure the accuracy of the processing time. Constraints (7) and (8) indicate that the latency between two operations on the same machine can be of any length.

Second, description of key steps of algorithm

Suppose that a spatially optimal solution is found in a D-dimensional search space and a particle swarm of N particles. Each particle has its own unique velocity and position information. In the t-th iteration, the velocity of the particle is recordedThe position of the particles is notedLocal optimum positionAnd global optimum positionAre respectively marked asAndthe specific flow of the algorithm is shown in fig. 1, and with reference to fig. 1, the following is a specific implementation process of the algorithm and a corresponding algorithm model.

1. The step 2 obtains an initial optimal solution: setting the initial particle excellence by weighted averaging

And (3) obtaining an initial optimal solution in an advanced stage, wherein a weighted average method model is as follows:

(1) each particle is randomly numbered.

(2) Calculating the priority of the particle initial solution:

(3) obtaining an initial optimal solution: sorting according to priority size, and then sorting according to the sorted sequence

The jobs are executed in a post-order.

2. The step 3 obtains a conventional current optimal solution, which is described below with reference to fig. 4:

in each step the particles are updated according to the following formula:

t represents the number of iterations, ω, c₁，c₂Is a constant and affects the quality and speed of the optimal solution. r is₁，r₂Are random numbers uniformly distributed between (0, 1). Criteria for terminating an iteration are whether the maximum number of iterations or the designed P is reached_gAnd (4) determining the fitness value.

3. The mean shift algorithm improved in step 4 is combined with fig. 2, and the specific calculation mode of each step is as follows:

(1) the velocity of the particles is recordedThe position of the particles is noted Predicting a local optimum positionAnd predicting a global optimum positionAre respectively marked asAnd

(2) determining the current center particle: specifying the most dense point of velocity as the velocity center particle, the most dense point of position as the position center particle, and the velocity center and the position center are respectively recorded asAnd

(3) calculating a weight matrix: calculating the distance of each particle from the central point in an iterative manner

Then the weight function w_ij＝1-d_ijH, where h is t_max,t_maxIs a time limit.

Normalized coefficient

(4) Firstly abstracting a workshop production scheduling space into an RGB color space, quantizing the RGB color space into interval bins of 16 × 16 × 16, then calculating the proportion of red, green and blue components of each particle by the formula T of 256 × r +16 × g + b, and then calculating the proportion of red, green and blue components of each particle by the formulaThe total weight of the particles in the histogram statistics is calculated. And finally, normalizing the weight value to obtain the target weight value.

(5) And (3) predicting the trend of the speed and the position of the particle by using a high-low point method: the calculation formula is as follows:

wherein, b represents the part of the position information parameter obtained from the last iteration which changes according to a certain ratio, namely:

(6) determining a predicted particle swarm center point by the method of (2) above

(7) Calculating a similarity function value: the invention uses the hattachyarya coefficient as a similarity function, which is defined as:

its value is between 0 and 1. Similarity between two modelsIs proportional to the value of (i.e. 1)The larger the value of (a) is, the more similar the two models are, and the closer the predicted value and the actual value are in the JSP.

(8) Calculation of mean shift vector: target location is to find the point that maximizes the similarity function value. From the center position y of this previous frame₀The target for the best match is initially found.

The similarity function is:

wherein,order to

Thereby, it is possible to obtain:

M_h,G(v) is the center of the target from the starting point v₀Vector moving towards v.

(9) And comparing values predicted by a high-low point method and the mean shift vector, and taking the better group of values as the optimal predicted value.

4. And 5, comparing the predicted optimal position and speed with the former optimal position and speed of the group, and taking the better position information as the current best position information, which is specifically expressed as follows: if the predicted optimal solution is better than the original optimal solution, taking the predicted optimal solution as the optimal solution; otherwise, the optimal solution is unchanged.

The algorithm is described above with reference to the accompanying drawings, and the invention is not limited thereby, and the scope of protection of the invention is determined by the contents of the claims.

Claims

1. The invention relates to the field of job shop scheduling, in particular to an improved particle swarm algorithm for solving a job shop scheduling problem, which is characterized in that: the specific steps of the algorithm are as follows:

step 1: initializing algorithm parameters: information including the number, position and velocity of PSO particles;

step 2: obtaining an initial optimal solution: setting the priority of the initial particles by adopting a weighted average method to obtain an initial optimal solution:

step 2.1: numbering each particle;

step 2.3: determining the order of the particles according to the priority, wherein workpieces with high priority are preferentially executed;

and step 3: obtaining a traditional current optimal solution: updating particle information by using a particle swarm algorithm to obtain the current optimal solution of the current traditional particle swarm algorithm;

and 4, step 4: predicting the current optimal solution: adding an improved mean shift algorithm, and predicting the position and the overall position of each particle on the basis of an initial optimal solution by using the mean shift algorithm:

step 4.1: initializing particle position information;

step 4.2: determining the current particle swarm center;

step 4.3: calculating a weight matrix of the particle swarm;

step 4.4: calculating a particle weight;

step 4.5: predicting the position and speed of the next step of particles by using a high-low point method;

step 4.6: calculating a similarity function;

step 4.7: calculating a mean shift vector, and determining the optimal predicted position and speed of the particle swarm according to the mean shift vector;

step 4.8: step 4.2 to step 4.7 are executed circularly until the exit condition is met;

and 5: initially selecting the current optimal solution: comparing the predicted optimal position and speed with the former optimal position and speed of the group by using the evaluation standard of the particle swarm algorithm, and taking better position information as the current best position information;

step 6: determining the current optimal solution: executing a tabu search algorithm to find a current optimal solution:

step 6.1: giving a current solution and a domain structure, and then determining a plurality of candidate solutions in the current domain structure;

step 6.4: looping steps 6.1 through 6.3 until a stop criterion is met;

2. The improved particle swarm algorithm for solving the job shop scheduling problem of claim 1, wherein: in the step 2, the priority of the initial particles is set by adopting a weighted average method to obtain an initial optimal solution, wherein the weighted average method model is as follows:

(1) randomly numbering each particle;

(2) calculating the priority of the particle initial solution:；

(3) obtaining an initial optimal solution: and sorting according to the priority level, and then executing the operation according to the sequence of the sorted order.

3. The improved particle swarm algorithm for solving the job shop scheduling problem of claim 1, wherein: and 5, comparing the predicted optimal position and speed with the former optimal position and speed of the group, and taking the better position information as the current best position information, which is specifically expressed as follows: if the predicted optimal solution is better than the original optimal solution, taking the predicted optimal solution as the optimal solution; otherwise, the optimal solution is unchanged.

4. The improved particle swarm algorithm for solving the job shop scheduling problem of claim 1, wherein: the specific calculation mode of each step of the mean shift algorithm improved in the step 4 is as follows:

(1) the velocity of the particles is recorded=（) The position of the particles is noted=（) The predicted local optimum position and the predicted global optimum position are respectively expressed as) And (a)）；

(2) Determining the current center particle: specifying the most dense point of velocity as the velocity center particle, the most dense point of position as the position center particle, and the velocity center and the position center are respectively recorded as；

Then weight functionWherein,in order to be the time limit,

normalized coefficient；

(4) Calculating the weight of the particles: the particle weight histogram is to count the weight occupied by each particle point, and the specific calculation process is as follows: firstly, abstracting a workshop production scheduling space into an RGB color space, and quantizing the RGB color space intoBins, then by the formulaCalculating the proportion of red, green and blue components of each particle, and calculating the proportion by the formulaCalculating the total weight of the particles in the histogram statistics, and finally normalizing the weight value to obtain a target weight;

(6) determining a predicted particle swarm center point by the method in the step (2);

its value is between 0-1, and the similarity of two models isIs proportional to the value of (i.e. 1)The larger the value of (A) is, the more similar the two models are, and the more similar the predicted value and the actual value are in JSP;

(8) calculation of mean shift vector: target location, i.e. finding the point that maximizes the similarity function value, from the center of the previous frameStart to find the best matching target:

the similarity function is:

whereinLet us order；

Thereby, it is possible to obtain:

is the center of the target from the starting pointA vector moving towards v;

(9) comparing the values predicted by the high-low point method and the mean shift vector, and making the better group of values

And the optimal predicted value is obtained.