WO2022000924A1

WO2022000924A1 - Double-resource die job shop scheduling optimization method based on ammas-ga nested algorithm

Info

Publication number: WO2022000924A1
Application number: PCT/CN2020/127971
Authority: WO
Inventors: 初红艳; 李�瑞; 刘志峰; 赵凯林; 黄凯峰
Original assignee: 北京工业大学
Priority date: 2020-07-01
Filing date: 2020-11-11
Publication date: 2022-01-06
Also published as: CN111966050A; CN111966050B

Abstract

A double-resource die job shop scheduling optimization method based on an AMMAS-GA nested algorithm. On the basis of comprehensive analysis of energy consumption, completion time and equipment and personnel load conditions of a workshop, a double-resource job shop multi-target scheduling problem model is established, wherein the load balance condition of equipment and personnel is measured by calculating the standard deviation of the accumulated load of the equipment and personnel, and the energy consumption of the workshop considers the energy consumption of the equipment in standby and processing states; then, an AMMAS-GA nested algorithm is designed to carry out scheduling model optimization solution, and procedure sorting is carried out by adopting a genetic algorithm by an inner layer according to the resource selection result as a constraint; and finally, the scheduling scheme result is fed back to an outer layer algorithm to influence selection of ants on resources. The method can be used for workshop scheduling and production scheduling, the workshop production efficiency is improved, energy consumption is reduced, green and energy-saving production is promoted, and meanwhile equipment and personnel load balance in production can be satisfied.

Description

Optimization method for dual-resource mold job shop scheduling based on AMMAS-GA nesting algorithm

technical field

The invention relates to job shop scheduling technology, in particular to a dual-resource job shop scheduling modeling and optimization method, in particular to a digital job shop for mold production using high-end numerical control processing equipment, and belongs to the technical field of intelligent manufacturing and scheduling.

Background technique

Job shop scheduling problem is a kind of resource allocation problem that satisfies the requirements of task configuration and sequence constraints, and is a typical NP problem. Among them, the scheduling problem when only machine tool equipment resources are constrained is called single-resource scheduling problem; but in actual production, equipment operators are often a very common type of constrained resources, and different operators can operate equipment types and The numbers are generally different; therefore, the scheduling problem in which the two resources, processing equipment and operators, are constrained, is generally referred to as a dual-resource scheduling problem. When this kind of scheduling problem is optimized and solved, it is not only necessary to select two types of resources, but also to sequence the processes. The problem is more complicated to solve. If a single algorithm is used to solve it, it is difficult to solve and it is difficult to obtain the desired solution. Therefore, it has important theoretical significance and engineering application value to study this kind of dual-resource job shop scheduling model and optimization method in combination with different actual production requirements.

The basic idea of ant colony algorithm is derived from the shortest path principle of ants foraging in nature. It has been widely used in various combinatorial optimization problems that are difficult to solve, including traveling salesman problem, scheduling problem, and path optimization problem. Ant colony algorithm has the following advantages: positive feedback, strong robustness, distributed computing, easy to combine with other algorithms, etc. At the same time, it also has its own shortcomings: it requires a long computing time, and it is easy to fall into local optimum and stagnate.

The genetic algorithm borrows the idea of biological genetics, and realizes the improvement of individual fitness by simulating natural selection, crossover, mutation and other operations, and iterates continuously to gradually find the optimal solution (or suboptimal solution). With implicit parallelism and global solution space search ability, it is widely used in the field of production scheduling, and the classical genetic algorithm has better global optimization solving ability.

Aiming at a digital mold production workshop, the invention comprehensively analyzes the equipment energy consumption, equipment and personnel load and completion time of the mold production workshop on the basis of considering the diverse needs of enterprises, and establishes a dual-resource workshop multi-objective scheduling The problem model is proposed, and an AMMAS-GA (Adaptive Max-MinAnt SystemAnd Genetic Algorithm) nested algorithm is proposed to optimize the solution.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a workshop scheduling method for mold production operations, so as to reasonably allocate workshop resources, balance the load of various resources in the workshop, minimize energy consumption, and shorten the completion time, improve the production efficiency of mold production enterprises, and shorten the production cycle. , reduce costs and facilitate enterprise production management.

In order to achieve the above objects, the present invention establishes a multi-objective scheduling problem model for a dual-resource workshop with the optimization objectives of completion time, energy consumption and equipment and personnel load balance for a digital mold production workshop. And based on this model, an AMMAS-GA nesting algorithm is proposed, which is composed of an improved adaptive max-min ant colony system and a genetic algorithm nested, which can effectively solve the optimal solution or sub-optimal solution of multi-objective scheduling problems. optimal solution. Finally, an example is carried out to verify the feasibility and effectiveness of the algorithm in solving the multi-objective scheduling problem of dual-resource job shop.

A dual-resource mold production job shop scheduling method, the steps are as follows:

Step 1: Establish a dual-resource job shop multi-objective scheduling model with the optimization goals of completion time, energy consumption and equipment and personnel load balance. The dual-resource mold workshop includes several workpieces to be processed, several processing equipment with different functional types, and several workers who can operate different types of equipment. It is necessary to determine the completion time, energy consumption and Loads of equipment personnel and to minimize completion time, energy consumption and load balancing.

Step 1.1 Establish a dual-resource job shop equipment and personnel load model

Load balance refers to the load balance degree of each processing equipment and personnel in the processing process. The present invention uses the standard deviation of the cumulative load of each equipment and personnel to measure the load balance degree. The smaller the standard deviation, the more reasonable the processing equipment and personnel used in the task will be, and the load will be balanced. The calculation formulas for the degree of load balance between equipment and personnel are as follows:

Among them, L ^e is the load balance degree of all equipment, L ^p is the load balance degree of all personnel, M is the total number of processing equipment, K is the total number of workers, m is the equipment number, k is the personnel number,

is the total time that the mth equipment is in the processing state,

is the total time that the kth worker is in the state of operating the equipment;

Step 1.2 Establish workshop energy consumption model

In the actual production process, the energy consumption of the workshop includes two parts: equipment standby energy consumption and equipment processing energy consumption. The energy consumption of each part is equal to the product of power and time. The formula for calculating the total energy consumption of the workshop is as follows:

Among them, E is the total energy consumption,

M is the total time of the device is in the processing state, T _m is the idle time waiting processing on the m devices,

is the standby power of the mth device,

is the processing power of the mth device;

Step 1.3 Build the shop make-time model

The completion time of a single workpiece is the total time taken from the moment the workpiece starts to be processed to the completion of the last operation. Therefore, the total completion time of shop completion is equal to the maximum completion time of all workpieces, which can be expressed as follows:

C=max{c ₁ ,c ₂ ,...,c _n } (4)

Among them, c _i is the total processing completion time of the ith workpiece, and C is the maximum completion time of all workpieces;

Step 2: For the dual-resource job shop multi-objective scheduling model established in step 1, the resource selection problem in the model can be regarded as a path optimization problem. At the same time, the ant colony algorithm has a strong search ability in path optimization. The basic ant colony algorithm is prone to the shortcomings of stagnation and long search time. The invention designs an improved self-adaptive maximum and minimum ant colony system to select equipment and personnel resources, which effectively overcomes the long search time and easy trapping of the basic ant colony algorithm. When the optimal stagnation phenomenon occurs, the resource allocation is optimized; then, according to the resource constraints selected by the ants, the genetic algorithm is used to sort the process.

The outer layer of the AMMAS-GA nesting algorithm uses the adaptive maximum and minimum ant colony system to complete the allocation of two types of resources, and the inner layer uses the genetic algorithm to sort the processes according to the resource selection result as a constraint, and finally feeds back the results of the scheduling scheme to the outer layer algorithm. Influence ants' choice of resources. The main flow of the algorithm is as follows:

a. The maximum and minimum ant colony system parameters are initialized, and the pheromone is initialized as τ _max ;

b. Select resource paths for each ant;

c. Substitute the resources selected by the ants into the genetic algorithm as constraints, and initialize the parameters of the genetic algorithm to generate an initial population;

d. Determine the optimal scheduling scheme under the resource constraints of each ant through genetic operations;

e. Feed back the scheduling results to the maximum and minimum ant colony system, and update the pheromone for the ants with the optimal solution in the current iteration (the optimal solution in this iteration) or the ants with the optimal solution since the beginning of the experiment (the global optimal solution);

f. Limit the range of the pheromone trajectory amount on each solution element (each edge of the path) to the _{interval [τ min} ,τ _max ];

g. Return to b until the iteration termination condition is met.

Step 2.1 The adaptive maximum and minimum ant colony system is designed as follows:

In this scheduling problem, we first solve the problem of selecting equipment and personnel for each process of each workpiece; when using the ant colony algorithm, we first regard the available equipment of each process of the workpiece as the first layer (equipment layer) that ants first travel. Nodes, and then according to the processing equipment of each process selected by the ants, the optional operators of the processing equipment in each process are regarded as the second layer (personnel layer) nodes that the ants need to travel, and the ants travel through the equipment layer and personnel in the order of the workpiece process Each node of the layer is selected, and the processing equipment and operator of each process of each workpiece are selected.

Step 2.1.1 Resource selection strategy design of maximum and minimum ant colony system

Equipment selection strategy design: According to the cumulative load of the equipment and the energy consumption of the equipment processing, the processing equipment is determined, and the equipment with the small cumulative load of the equipment and the low energy consumption of the equipment processing is preferentially selected.

Personnel selection strategy design: According to the cumulative load of optional operators, determine the personnel, and give preference to workers with small cumulative load.

Step 2.1.2 Inspire Information Design

Design heuristic information, so that ants preferentially select equipment with low cumulative load of equipment and low energy consumption for equipment processing when selecting nodes at the equipment layer, and preferentially select workers with low cumulative load when selecting nodes at the personnel layer.

Step 2.1.3 Adaptive adjustment of pheromone retention coefficient

When the pheromone retention coefficient ρ is too large and the number of pheromone in the solution increases, the possibility of the previously searched solution being selected is too large, which will affect the global search ability of the algorithm; although the global search ability of the algorithm can be improved by reducing ρ Search ability, but it will slow down the convergence speed of the algorithm. Therefore, we can adjust the pheromone retention coefficient to ensure the global search ability of the algorithm in the early stage and not make the algorithm converge too slowly.

Step 2.1.4 Adaptive pheromone update design

a. Adaptive pheromone increment design: In general pheromone increment allocation, pheromone increments of the same size are allocated to different sections of the same path, but obviously different sections on the same path have a significant effect on ants searching for the best path different. Therefore, it is necessary to allocate a larger pheromone increment to a better road section and a smaller pheromone increment to a poor road section according to the road section conditions.

b. Pheromone update operator design

The pheromone update operator is designed so that the optimal path pheromone is continuously accumulated, and it will not converge too quickly or even stagnate.

Step 2.2 Genetic Algorithm Design:

As the inner loop of the nested algorithm, it is necessary to take the resource allocation scheme selected by each ant in the outer loop as a constraint, and sequence the processes to solve the optimal scheduling scheme under each ant's resource selection scheme.

Step 2.2.1 Coding: The chromosome coding method adopts the integer coding based on the process, and each chromosome can represent the processing sequence of all workpieces.

Step 2.2.2 Generation of initial solution: generate most of the initial population individuals by random generation, and generate a small number of initial population individuals by heuristic rules.

Step 2.2.3 Calculation of fitness function value: take the weighted sum of the unified dimension of target completion time C and energy consumption E of the scheduling scheme corresponding to each individual as the fitness value of the individual population.

Step 2.2.4 Genetic manipulation

a. Selection: According to the fitness value of each individual, the selection method of the championship is used to select individual genes from the parent group and inherit them to the next generation;

b. Crossover: carry out single-point crossover with a certain crossover probability.

c. Mutation: randomly carry out two-point exchange gene mutation and insertion mutation with a certain mutation probability.

The beneficial effects of the invention are as follows: for the digital mold production workshop, a multi-objective scheduling model of the dual-resource workshop is established with the optimization goals of completion time, energy consumption and equipment and personnel load balance. And based on this model, an AMMAS-GA nested algorithm is proposed, which can effectively solve the optimal or sub-optimal solution of multi-objective scheduling problems, which can be used for workshop scheduling, improve workshop production efficiency, reduce energy consumption, and satisfy Equipment and personnel load balance production.

Description of drawings

Figure 1 is the flow chart of the AMMAS-GA nesting algorithm

Figure 2 is the iterative process diagram of the unified dimension sum of the optimization objective

Figure 3 is a Gantt chart for device-based scheduling

Figure 4 is a Gantt chart for personnel-based scheduling

detailed description

The technical solutions of the present invention are described in detail below in conjunction with the accompanying drawings:

The general mold production process includes: roughing, finishing, drilling, complex surface processing, heat treatment, etc. The mold production workshop includes a number of workers with different operating capabilities, a number of rough machining equipment with different specifications and models, a number of finishing CNC milling machines with different specifications and models, a number of five-axis deep hole drills with different specifications and models, and a number of different specifications and models. Five-axis high-speed milling and several laser quenching equipment for surface machining or finishing. The workshop equipment adopts numerical control processing equipment. The numerical control processing program is sent to the workshop along with the production process. The dependence of the processing process on people is reduced. The proficiency and level of workers no longer affect the processing process, and there will be no processing time due to different proficiency of workers. different phenomena. Therefore, once the processing technology is determined, the processing time of the process will not change with the selected equipment and personnel. What is more important for workers is whether they can operate different CNC equipment.

The job shop scheduling problem for dual-resource mold production can be described as: there are N workpieces to be processed, M processing equipment with different functions, and P workers with different operating capabilities, where the number of workers P is less than the number of equipment M, so at least one worker needs to Ability to operate more than one piece of equipment, and the type and quantity of equipment each worker can operate may vary. It is known that each workpiece consists of multiple processes, the processing time of each process is determined, and the sequence of each process of each workpiece is pre-determined; it is necessary to select a selection for each process of each workpiece according to the requirements of the process type and the function model of the equipment. Corresponding available equipment, at the same time, it is necessary to determine the corresponding optional operators according to the equipment type of each equipment, and form the available equipment table of each workpiece and each process and the optional operator table of each equipment. By optimizing resource allocation and process sequencing, the best performance indicators can be obtained under the condition that equipment capacity and worker capacity constraints are met at the same time.

Step 1: Establish a dual-resource job shop multi-objective scheduling model with the optimization goals of completion time, energy consumption and equipment and personnel load balance.

Now make the following assumptions:

1) The processing time of each process is determined and will not be different due to different equipment or personnel;

2) At a certain time, a certain equipment or personnel can only process a certain process;

3) Once the workpiece starts to be processed, it cannot be interrupted;

4) The priority of each workpiece is the same, and there is no front-to-back constraint relationship between the processes of different workpieces;

5) There are priority constraints between the processes of the same workpiece;

6) The installation and unloading time of the workpiece is included in the given processing time;

7) There is at least one available equipment for each workpiece and each process;

8) At least one worker can operate a certain equipment, and at least one worker needs to have the ability to operate more than one equipment.

The relevant symbol definitions are shown in Table 1:

Table 1 Symbol Definition

The model constraints and calculation formulas are as follows:

Must satisfy l _i ≤l _m and d _i ≤d _m (5)

0≤b _i,j ≤e _i,j (6)

e _i,j-1 ≤b _i,j (7)

t _i,j = e _i,j -b _i,j (9)

Among them, formula (5) is that the available equipment must meet the workpiece processing space constraints, formula (6) is that the start processing time of the jth process of the workpiece must be less than the completion time of its corresponding process, and the start processing time of all workpiece processes is greater than Equal to 0, the formula (7) is that the workpiece can only be processed in the next process after the previous process is completed. The formula (8) is that each workpiece can only be processed on one equipment in each process, and the formula (9) is the calculation formula of the processing time of the jth operation of the ith workpiece, formula (10) is the calculation formula of the total time of the mth equipment in the processing state, and formula (11) is the completion time of the workpiece equal to the last operation of the workpiece completion time.

Step 1.1 Establish a dual-resource job shop equipment and personnel load model

Step 1.2 Establish workshop energy consumption model

Step 1.3 Build the shop make-time model

C=max{c ₁ ,c ₂ ,...,c _n } (15)

Step 2: For the above scheduling problem model, the scheduling problem can be attributed to two parts: resource selection and process sequencing; in this way, when optimizing and solving, it is not only necessary to select resources for workpieces, but also to sequence processes. When an algorithm is used, it is difficult to solve and it is difficult to obtain the desired solution. The resource selection problem in this model can be regarded as a path optimization problem. At the same time, the ant colony algorithm has strong search ability in path optimization, but the basic ant colony algorithm has the shortcomings of easy stagnation and long search time. Therefore, the present invention designs The improved adaptive maximum and minimum ant colony system is used to select equipment and personnel resources. While effectively overcoming the shortcomings of the basic ant colony algorithm that pheromone accumulation is prone to stagnation and long search time, it optimizes resource allocation; Resource constraints enter the genetic algorithm for process sequencing, and the resulting scheduling results are fed back to the ant colony algorithm, which affects the update of pheromone and promotes ant path selection.

The outer layer of the AMMAS-GA nesting algorithm uses the adaptive maximum and minimum ant colony system to complete the allocation of two types of resources, and the inner layer uses the genetic algorithm to sort the processes according to the resource selection result as a constraint, and finally feeds back the results of the scheduling scheme to the outer layer algorithm. Influence ants' choice of resources. The algorithm flow is shown in Figure 1, and the main contents are as follows:

The initialization parameters include the number of iterations N _c , the number of ants k, the pheromone importance factor α, the heuristic information importance factor β, and the pheromone retention coefficient ρ; the pheromone on each path is initialized as τ _max .

b. Select resource paths for each ant;

Each ant selects equipment and personnel for the process based on the number of pheromones on each path and heuristic rule information.

In step b each ant selected equipment, personnel resources into a genetic algorithm for solving the schedule constraints; genetic algorithm parameter initialization, including population size P _size, number of iterations N _G, crossover and mutation probability P _c, P _m; And generate the initial scheduling solution population.

The population determines the optimal scheduling scheme under the resource constraints selected by each ant through a series of genetic operations such as selection, crossover, and mutation.

At the end of each iteration of the genetic algorithm, the optimal scheduling scheme under the resource constraints selected by each ant will be saved; then the ant with the optimal solution in the current iteration (the optimal solution in this iteration) or the optimal solution since the beginning of the experiment is selected. Ants (global optimal solution) perform pheromone update, and only this ant in the maximum and minimum ant colony system can perform pheromone update.

In order to avoid the phenomenon of "premature" stagnation, after each pheromone update, the value range of the pheromone trajectory on each solution element (each edge of the path) must be limited to the interval _{[τ min} ,τ _{max ]} .

g. Return to b until the iteration termination condition is met.

Whether the maximum number of iterations or the termination criterion is satisfied (when the optimal solution does not change significantly after multiple iterations, the iteration termination condition is satisfied).

In this scheduling problem, we first solve the problem of selecting equipment and personnel for each process of each workpiece; when using the ant colony algorithm, we first regard the available equipment of each process of the workpiece as the first layer (equipment layer) that ants first travel. Nodes, and then according to the processing equipment of each process selected by the ants, the optional operators of the processing equipment in each process are regarded as the second layer (personnel layer) nodes that the ants need to travel, and the ants travel through the equipment layer and For each node of the personnel layer, select the processing equipment and operators for each process of each workpiece.

Equipment selection strategy design: For the selection of available equipment for each process of the workpiece, calculate the cumulative processing time of each equipment as the cumulative load of the equipment, determine the processing equipment according to the cumulative load of the equipment and the energy consumption of the equipment processing, and give priority to the equipment with small cumulative load and equipment. Processing equipment with low energy consumption.

Personnel selection strategy design: Calculate the cumulative processing time of each person as the cumulative load of the personnel. Since the ants have determined the processing equipment for each process of the workpiece at the first layer node, now according to the optional operator of the equipment and the cumulative load of each operator , determine the personnel, and give preference to workers with a small cumulative load.

Step 2.1.2 Inspire Information Design

The heuristic information used by ants for selection is designed according to the rules for ants to select resources for each process. Since ants need to traverse the equipment layer and the personnel layer in turn, and then select equipment and personnel, the ants travel path (i, j) in the equipment layer. The heuristic information on or the heuristic information of ants on the travel path (i, j) of the personnel layer is calculated as follows:

Among them, P _j represents the energy consumption factor of the optional equipment j that travels to the next process,

is the cumulative load of optional equipment j that travels to the next process;

Represents the cumulative load of the optional operator j who travels to the next process; the ants are inspired to choose the resource route with smaller cumulative load of equipment, lower energy consumption and lower cumulative load of personnel.

Step 2.1.3 State transition operator

Ants determine the state transition probability of ants through heuristic information and pheromone on each path during their travels, using

It represents the probability that ant k selects equipment or personnel i at time t, and the next process selects equipment or personnel j, namely

Among them, options{} represents the set of optional processing equipment or the set of optional personnel corresponding to the equipment when ant k travels to the next process, α and β are the pheromone importance factor and the heuristic information importance factor, respectively, τ _{i, j} (t) represents the pheromone concentration of the path (i, j) at time t.

Step 2.1.4 Adaptive adjustment of pheromone retention coefficient

When the pheromone retention coefficient ρ is too large and the number of pheromone in the solution increases, the possibility of the previously searched solution being selected is too large, which will affect the global search ability of the algorithm; although the global search ability of the algorithm can be improved by reducing ρ Search ability, but it will slow down the convergence speed of the algorithm. Therefore, the value of ρ is adaptively changed by the following method. The initial value of ρ is set to ρ(t ₀ )=0.9. When the optimal value obtained by the algorithm does not change significantly within N cycles, the value of ρ adopts the following formula:

Step 2.1.5 Adaptive pheromone update design

The pheromone of the path (i,j) at time _{t is represented by τ i,j} (t). When all ants in each iteration obtain a complete solution of equipment and personnel resource allocation, the resource allocation solution is passed to the genetic algorithm , the genetic algorithm finds the optimal scheduling scheme according to resource constraints, and then according to the completion time of each optimal scheduling scheme, equipment, personnel load and energy consumption, the pheromone is updated according to the following scheme.

a. Adaptive pheromone increment design: In general pheromone increment allocation, pheromone increments of the same size are allocated to different sections of the same path, but different sections on the same path have an obvious effect on the ant colony searching for the best path different. Therefore, the strategy adopted by the present invention is: assigning a larger increment of pheromone to a better road section; assigning a smaller increment of pheromone to a poor road section. The specific implementation method is: set the total number of times that the path (i, j) appears on each search path in the nth iteration cycle to be q, and 0≤q≤k (k is the total number of ants), then the pheromone increment Calculation formula:

Among them, f represents the path length of the optimal path ant in the current iteration.

b. Pheromone update operator design

In order to make the optimal path pheromone accumulate continuously and not converge too quickly or even stagnate, the pheromone update operator is designed as follows:

Among them, τ _min and τ _max are the lower and upper bounds of pheromone, respectively, τ _max =1/ρf, τ _min =ξτ _max 0≤ξ≤1. If the optimal path ant chooses path (i, j) at time t, then

Otherwise Δτ _i,j =0. f is the path length of the optimal path ant in the current iteration, that is, the equipment load balance degree ^Le , the personnel load balance degree L ^p , the completion time C and the energy consumption E under the selected path (i,j) on the optimal path Unified dimensional sum. avg(L ^e ) and avg(L ^p ^{) are the average values of the target equipment load balance degree L e} and the personnel load balance degree L ^p of all ants in the current iteration, respectively, avg(C) and avg(E) are the current iteration The average value of target completion time C and energy consumption E of all ants in the optimal scheduling scheme.

Step 2.2 Genetic Algorithm Design:

As the inner loop of the nested algorithm, it is necessary to take the resource allocation scheme selected by each ant in the outer loop as a constraint, and sequence the processes to solve the optimal scheduling scheme under each ant's resource selection scheme. Genetic algorithm is a commonly used algorithm for shop-floor scheduling optimization problem, and has good global optimization solving ability. Genetic algorithm is designed to solve the scheduling problem under dual resource constraints.

Step 2.2.1 Encoding

The chromosome coding method adopts the integer coding based on the process, each chromosome can represent the processing sequence of all the workpieces, and the length of the chromosome is the sum of the number of processes of all the workpieces. A workpiece number is stored in each locus of the chromosome, indicating the processing sequence of the workpiece, and the number of occurrences of the workpiece number is equal to the number of processes of the workpiece. For example, the individual [2,1,1,3,2,1,3,2], the individual expresses that there are 3 workpieces, and the 3 workpieces have 3, 3, and 2 processing steps respectively, and the workpiece processing sequence is (O ₂₁ O ₁₁ O ₁₂ O ₃₁ O ₂₂ O ₁₃ O ₃₂ O ₂₃ ).

Step 2.2.2 Initial solution generation

Most of the initial population individuals are generated by random generation, and a small number of initial population individuals are generated by heuristic rules. The heuristic rule prioritizes the process of selecting equipment or personnel with a large remaining load, and prioritizes the processing of the workpiece with the shortest processing time and the most remaining processing time.

Step 2.2.3 Fitness function value calculation

Under the resource constraints, when solving the scheduling scheme, the weighted sum of the unified dimension of the target completion time C and energy consumption E of the scheduling scheme corresponding to each individual is taken as the fitness value of the individual population. Calculated as follows:

where ω is the weight coefficient of the schedule completion time.

Step 2.2.4 Genetic manipulation

b. Crossover: perform single-point crossover with a certain crossover probability. First, two individuals are randomly selected from the population, and one point is randomly selected as the crossover position. The two chromosomes are crossed at a single point. After the crossover, some artifacts will appear in the chromosomes. Superfluous, the process of some workpieces is missing, so the redundant process of the workpiece becomes the process of the missing workpiece.

c. Variation: Variation adopts random two-point exchange gene mutation and insertion mutation. Two-point swap gene mutation is to randomly select two different gene positions in the parent chromosome and swap their gene values. Insertional mutation is to randomly generate two different gene positions, the latter gene is inserted into the position of the former gene, and the rest of the genes are moved backward in turn.

Example 1:

Taking a mold manufacturing enterprise as the background, there are 12 mold processing equipment and 8 equipment operators in the workshop. There are 8 production tasks in a certain scheduling cycle. Each production task includes several processing procedures. Completed on candidate equipment resources, each equipment has at least one candidate operator. First, group the equipment according to the equipment function type, and determine the optional operators for each equipment group, as shown in Table 2; The available equipment table is shown in Table 3; the processing time of each process is shown in Table 4 (time unit: min). The power table of each equipment is shown in Table 5 (power unit: kW).

Table 2 Optional operator list for each equipment group

Table 3 Available equipment for each process

Table 4 Processing timetable of each process

Table 5 Power table of each equipment

The script file and function file of the algorithm are used to simulate and optimize the scheduling model. The parameters of the algorithm are set as follows: (1) The maximum and minimum ant colony system parameters are set: the number of iterations is 200, the number of ants is 50, and the pheromone importance factor is 1 , the heuristic information importance factor is 5. (2) Genetic algorithm parameter settings: the population size is 100, the number of iterations is 100, the crossover probability is 0.5, and the mutation probability is 0.3. The weight coefficient ω of the schedule completion time can be determined by the decision maker's preference. When the decision maker only wants to minimize the maximum makepan, set the makepan weight factor to 1. Here, the weight coefficient ω takes a value of 0.7.

By running the algorithm script, ^{the changes of the unified dimension sum of the equipment load balance degree Le} , the personnel load balance degree ^Lp , the completion time C and the energy consumption E in the iterative process are obtained as shown in Figure 2, and the optimal scheduling is obtained respectively. The scheduling Gantt chart based on equipment and personnel of the scheme is shown in Figures 3 and 4 (301 in the figure represents the first process of the third workpiece). The completion time of the optimal scheduling scheme is 170min, the energy consumption is 67.7kW·h, the standard deviation of the cumulative load of equipment is 20.7min, and the standard deviation of the cumulative load of personnel is 8.8min.

Claims

The dual-resource mold job shop scheduling optimization method based on the AMMAS-GA nesting algorithm is characterized in that it includes the following steps:

Step 1: Comprehensively consider the energy consumption, equipment and personnel load balance and completion time in the mold production workshop scheduling cycle, and establish a dual-resource job shop multi-objective scheduling model with the completion time, energy consumption and equipment and personnel load balance as the optimization goals;

Step 2: For the multi-objective scheduling model established in the first step, an AMMAS-GA nested algorithm is proposed to optimize and solve the multi-objective scheduling model.
The dual-resource mold job shop scheduling optimization method based on AMMAS-GA nesting algorithm according to claim 1, is characterized in that, the implementation process of step 1 is as follows,

Step 1.1 Establish a dual-resource job shop equipment and personnel load model

The standard deviation of the cumulative load of each equipment and personnel is used to measure the balance of the load; the smaller the standard deviation, the more reasonable the processing equipment and personnel used in the task will be, and the load will be balanced;

Step 1.2 Establish workshop energy consumption model

In the actual production process, the energy consumption of the workshop includes two parts: equipment standby energy consumption and equipment processing energy consumption, and the energy consumption of each part is equal to the product of power and time;

Step 1.3 Build the shop make-time model

The completion time of a single workpiece is all the time taken from the time the workpiece starts to be processed to the completion of the last process; the total completion time of the workshop is equal to the maximum completion time of all workpieces.
The dual-resource mold job shop scheduling optimization method based on AMMAS-GA nesting algorithm according to claim 1, is characterized in that, the implementation process of step 2 is as follows,

The outer layer of the AMMAS-GA nesting algorithm adopts the adaptive maximum and minimum ant colony system to complete the selection of two types of resources for each process in the scheduling task. The results of the scheme are fed back to the outer algorithm, which affects the selection of resources by the ants in the next iteration. The key steps of the algorithm are as follows:

a. The parameters of the maximum and minimum ant colony system are initialized, and the pheromone is initialized;

b. According to the designed equipment and personnel selection heuristic strategy and the number of pheromone on each resource path, select each process resource for each ant;

c. Substitute the resources selected by the ants for each process as process constraints into the genetic algorithm, initialize the parameters of the genetic algorithm, and generate the initial population by random and process sorting heuristic rules;

d. Determine the optimal scheduling scheme under the constraints of process resources selected by each ant after multiple iterations of the population and genetic operations;

e. Feed back the optimal scheduling scheme of each ant to the maximum and minimum ant colony system, and calculate the unified dimension of the multi-objective of the ant scheduling scheme and the length of the path selected by the ants; only the ants with the optimal solution in the current iteration or since the beginning of the experiment The ant with the optimal solution performs pheromone update;

f. Determine τ max according to the path length of the global optimal solution, and limit the value range of the pheromone trajectory amount on each path within the interval [τ min ,τ max ];

g. Return to b until the iteration termination condition is met.
The dual-resource mold job shop scheduling optimization method based on the AMMAS-GA nesting algorithm according to claim 3, wherein the resource selection heuristic strategy in step b is designed as follows:

Equipment selection strategy design: According to the cumulative load of the equipment and the energy consumption of the equipment processing, the processing equipment is determined, and the equipment with the small cumulative load of the equipment and the low energy consumption of the equipment processing is preferentially selected;

Personnel selection strategy design: According to the cumulative load of optional operators, determine personnel, and give priority to workers with small cumulative load.
The dual-resource mold job shop scheduling optimization method based on the AMMAS-GA nesting algorithm according to claim 3, wherein the adaptive pheromone update design in step e is as follows,

1) Adaptive adjustment of pheromone retention coefficient;

The pheromone retention coefficient is designed to be adaptively adjusted. When the optimal value does not change significantly within N iterations, the influence of pheromone on the path is reduced by adjusting the pheromone retention coefficient to ensure the globality of the resource selection solution for each process. And not less than ρ min , it will not make the algorithm converge too slowly;

2) Adaptive pheromone incremental design;

Different road sections on the same path are allocated different pheromone increments; when designing pheromone increments, the pheromone increments are allocated according to the total number of occurrences of each resource selection road section on each path in the current iteration cycle.