Electricity-carbon double-factor imported uncorrelated parallel machine green scheduling method

Abstract

The invention discloses an electricity-carbon double-factor imported uncorrelated parallel machine green scheduling method, which comprises the following steps: S1, collecting production condition related parameters, and constructing an uncorrelated parallel machine scheduling model by taking the maximum completion time and the minimum electricity-carbon cost as targets; s2, constructing a distribution evolution algorithm of an adaptive mechanism and a neighborhood search mechanism, inputting production condition related parameters, and solving an uncorrelated parallel machine scheduling model to obtain an optimal scheduling method; according to the algorithm, when an uncorrelated parallel machine scheduling model is solved, population is randomly initialized, a multi-target non-dominated sorting method and congestion distance calculation are adopted, the individual diversity is improved, and the learning rate and the mutation rate are dynamically adjusted through an information entropy self-adaptive mechanism. A simulation result shows that the ANEDA algorithm is remarkably superior in the aspects of maximum completion time and total electricity and carbon cost optimization, and the effectiveness and the practical value of the algorithm are verified.

Description

Technical Field

[0001] The invention belongs to the field of green manufacturing and production scheduling optimization, and specifically relates to an unrelated parallel machine green scheduling method with the introduction of electricity-carbon dual factors. Background Art

[0002] In recent years, with the gradual establishment and development of the carbon trading market, the manufacturing industry has become more concerned about energy conservation and emission reduction. In order to alleviate the severe situation of resources and optimize the energy structure, the incremental power price (IBP) policy has been gradually implemented in China. In this context, manufacturing companies are not only faced with the challenge of improving production efficiency, but also need to reduce energy consumption and carbon emissions as much as possible while ensuring contract requirements.

[0003] The unrelated parallel machine green scheduling problem (UPMGSP) came into being. It is a typical multi-objective optimization problem, which aims to minimize the total cost of electricity and carbon emissions while minimizing the maximum completion time. However, the complexity of UPMGSP makes it difficult for traditional optimization methods to solve it effectively. Faced with the huge search space, the exhaustive method is not only time-consuming but also difficult to guarantee the optimal solution. Therefore, the development of efficient optimization algorithms becomes the key. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides an uncorrelated parallel machine green scheduling method with the introduction of electricity-carbon dual factors. Applying ANEDA to UPMGSP can not only effectively improve the optimization effect of scheduling, but also provide valuable management suggestions for production plants in actual operations, which is helpful to achieve green manufacturing and sustainable development goals.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions: a green scheduling method for unrelated parallel machines with the introduction of electricity-carbon dual factors, comprising the following steps:

[0006] S1. Collect relevant parameters of production conditions and build an unrelated parallel machine scheduling model with the goal of maximizing completion time and minimizing electricity and carbon cost;

[0007] S2. Construct a distributed evolutionary algorithm with adaptive mechanism and neighborhood search mechanism, input parameters related to production conditions, solve the unrelated parallel machine scheduling model, and obtain the optimal scheduling method; when solving the unrelated parallel machine scheduling model, the algorithm randomly initializes the population, adopts a multi-objective non-dominated sorting method and crowding distance calculation to improve individual diversity, and dynamically adjusts the learning rate and mutation rate through the information entropy adaptive mechanism.

[0008] Furthermore, in the aforementioned step S1, the production condition related parameters include the number of workpieces, the number of machines, the machine processing speed v the maximum completion time C max, penalty cost P0, total energy consumption TEC, standard processing time t i，j , actual energy consumption E i，j，v .

[0009] Furthermore, the aforementioned unrelated parallel machine scheduling model is as follows:

[0010] Min f1=C max #(3)

[0011] Min f2=Cost1+Cost2=F1(TEC)+{0,P0}#(4)

[0012]

[0013] In the formula, C max is the maximum completion time, P0 is the penalty cost, TEC is the total energy consumption, t i，j is the standard processing time, t i，j，v is the actual processing time of job i on machine j with speed level v, E i，j，v is the actual energy consumption, x i，j，v is a binary variable, n is the number of workpieces, and v is the speed.

[0014] Furthermore, the aforementioned electricity price cost function Cost1=F1(TEC) is as follows:

[0015]

[0016] In the formula, P1, P2 and P3 are three-tier electricity prices, E is energy consumption, and E1 and E2 are two tier thresholds for energy consumption;

[0017] The penalty formula Cost2 is as follows:

[0018]

[0019] Where α is the portion of total energy consumption using carbon, β is the power factor of the carbon thermal power unit, and αβTEC is the carbon emission.

[0020] Furthermore, in the aforementioned step S2, the distributed evolutionary algorithm of the adaptive mechanism and the neighborhood search mechanism includes the following steps:

[0021] S2.1. Initialize the population: including initialization based on the time efficiency of the workpiece, initialization of part of the population based on the energy efficiency of the work, and random generation of chromosomes: the correspondence between the workpieces assigned to the machines for processing and the processing speed of the jobs; and use the binary tournament rule for population selection, i.e. randomly select two individuals from the population, and select a better individual to be put into the elite group by comparing the Pareto sequence and the crowding distance, until the elite group meets the required number of individuals;

[0022] S2.2, Multi-objective non-dominated sorting: Multi-objective non-dominated sorting method and crowding distance calculation are used to improve the diversity of individuals;

[0023] S2.3, Adaptive mechanism: Calculate the probability distribution information of the solution space, design an adaptive mechanism based on information entropy, and dynamically adjust the learning rate and mutation rate;

[0024] S2.4, Neighborhood search mechanism: Set neighborhood search operators for benchmark machines and non-benchmark machines based on problem characteristics to improve local search capabilities;

[0025] S2.5. Population variation: Use population variation to maintain individual diversity and prevent premature convergence.

[0026] Furthermore, the aforementioned step S2.2 is to determine the job allocation probability matrix and the speed selection probability matrix according to the job classification and job processing speed, and then iterate, specifically:

[0027] The job allocation probability matrix at the gth generation is expressed as:

[0028]

[0029] In the formula, ρ i,j (g) represents the probability distribution of machine j in the gth generation processing job i,

[0030] The speed selection probability matrix at the gth generation is expressed as:

[0031]

[0032] At the beginning of the iteration, the probability matrix should be uniformly distributed, as follows:

[0033]

[0034] The iteration method of each generation probability matrix is ​​as follows:

[0035]

[0036] Where: α g is the learning rate when generating g generations; Ψ is the proportion of elite solutions used for iteration; and Boolean variable g.th iteration.

[0037] Furthermore, in the aforementioned step S2.3, the dynamic adjustment of the learning rate is specifically: the information entropy of the job allocation probability matrix Information entropy of speed selection probability matrix Let E0 = k0*E(0) and adjust adaptively using the following formula:

[0038]

[0039] Where: k0, k1, k2 are adjustment parameters, β∈(0,1) is the base of the exponential function, E0 is the threshold of the initial probability matrix information E(0), k0 is the threshold ratio, α0 is the upper bound of the learning rate, and the learning rate α g Take E0 as the boundary.

[0040] Furthermore, the above-mentioned step S2.3 dynamically adjusts the mutation rate as follows: based on the mutation rate m g Perturbing or mutating the probability matrix helps maintain the appropriate search width of the algorithm and guides the algorithm to search different areas. The mutation rate adaptive formula is as follows:

[0041]

[0042] Where: mr min is the lower limit of mutation rate, γ is the increase control parameter, γ>1, m g is a monotonically increasing function with E(g) as the independent variable, and its range is mr min and γ*mr min between.

[0043] Furthermore, in the aforementioned step S2.4, for the non-reference machine, the processing speed is reduced to reduce energy consumption, and the non-reference machine is traversed in turn, and each workpiece whose speed is not the lowest is slowed down by one level, and the workpieces are sorted from large to small according to the energy consumption reduction thus generated, and the sorted workpieces are selected in turn, and the processing speed of the workpiece is reduced by one level, so that the completion time of the machine does not exceed the maximum completion time, until the speed of each job on the machine is reduced or the difference between the completion time of the machine and the maximum completion time is within a preset range;

[0044] For the baseline machine, two methods are included to reduce the completion time:

[0045] Method A: Select the workpiece with the shortest processing time on one of the machines and place it on another non-reference machine to minimize the increase in energy consumption while keeping the workpiece processing speed unchanged;

[0046] Method B: On the benchmark machine j * , select The smallest workpiece i is exchanged to machine l. For the workpiece to be exchanged on machine l, traverse the workpieces on it until it can reduce the maximum completion time of the two machines and minimize the increase in energy consumption, e i,j is the ratio of the minimum processing time of workpiece i on all machines to its processing time on machine j, which represents the processing time efficiency of workpiece i on machine j, e i,j=(min 1≤l≤m t i,l ) / t i,j , 1 <i<n,1<j<m。

[0047] Furthermore, the aforementioned unrelated parallel machine green scheduling method with dual-factor electricity-carbon introduction also includes testing of the unrelated parallel machine scheduling model of step S3, specifically including the following sub-steps:

[0048] S3.1, Test instance setting: Design 45 instances, including different combinations of machine number, job number, and speed settings. Each team combination has 10 instances, the workpiece processing time is randomly set between 1h and 20h, and the machine speed is {1.0, 1.1, 1.2, 1.3}. Set 5 key parameters: population size Set 5 key parameters: population size, elite solution ratio, information entropy threshold ratio, learning rate upper limit, mutation rate lower limit, and use Taguchi orthogonal experimental design method to explore the impact of parameters on performance;

[0049] S3.2, the simulation process is to implement the algorithm in the Python environment and run it using a specific computer configuration; use non-dominated sorting and crowding calculation to evaluate and select the population; dynamically adjust the learning rate and mutation rate, perform crossover and mutation operations, generate and optimize new populations; merge parent and child populations, retain excellent individuals, and repeat iterations until the set termination condition is reached;

[0050] S3.3. Use the overall non-dominated vector generation (ONVG) and C Metric to evaluate the algorithm performance and compare the effects of the adaptive EDA algorithm with other variants and traditional algorithms.

[0051] S3.4. Based on the simulation results, put forward suggestions for optimizing electricity price strategy and carbon quota management to achieve energy conservation and emission reduction goals.

[0052] Compared with the prior art, the beneficial technical effects of the present invention using the above technical solution are as follows:

[0053] 1. The adaptive mechanism and neighborhood search mechanism have significantly improved the performance of the algorithm, and the performance of ANEDA is also better than the traditional NSGA2 algorithm.

[0054] 2. The adaptive mechanism based on information entropy can properly regulate the learning rate and mutation rate, ensure the algorithm's search depth and convergence speed, and improve the diversity and quality of Pareto solutions. The neighborhood search mechanism can promote the algorithm's exploration of a single area, get rid of suboptimal solutions, and further improve the algorithm's search efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Figure 1 is a flow chart of the ANEDA algorithm.

[0056] Figure 2 This is a comparison chart of the number of steps.

[0057] Figure 3 This is a comparison chart of step lengths.

[0058] Figure 4 This is a tiered price comparison chart. DETAILED DESCRIPTION

[0059] In order to better understand the technical content of the present invention, specific embodiments are given and described as follows in conjunction with the accompanying drawings.

[0060] Various aspects of the invention are described herein with reference to the accompanying drawings, in which many illustrative embodiments are shown. The embodiments of the invention are not limited to those described in the accompanying drawings. It should be understood that the invention is implemented by any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed in the invention are not limited to any implementation. In addition, some aspects disclosed in the invention may be used alone or in any appropriate combination with other aspects disclosed in the invention.

[0061] refer to Figure 1 , the method flow chart of the present invention comprises the following steps:

[0062] S1. Collect relevant parameters of production conditions and build an unrelated parallel machine scheduling model with the goal of maximizing completion time and minimizing electricity and carbon cost.

[0063] For the unrelated parallel machine green scheduling problem, there are n independent jobs J = {1, 2, ..., i, ..., n} processed on m unrelated parallel machines M = {1, 2, ..., j, ..., m}. Each machine can only process one job at any time, and each job can only be processed on one machine. Preemption is prohibited. For each machine, there are S groups of different processing speeds V = {1, 2, ..., v, ..., S}, where we set V1 < V2 < ... < V s , let V v Represents the processing speed of the machine. In the present invention, all unrelated parallel machines share the same processing speed at level v. The standard processing time of job i on machine j is t i，j Represents a dependency on the job itself and the machine that processes it.

[0064] The actual processing time of job i on machine j with speed level v is t i，j，v , by t i，j，v =t i，j / V vAt the same time, the power consumption per unit time of machine j running at speed level v when processing a job is p j，v The actual energy consumption required by machine j with processing speed v when processing task i is recorded as E i，j，v , multiply the actual processing time by the corresponding energy consumption rate to get E i，j，v =p j，v ×t i，j / V v Therefore, the total energy consumption is expressed as TEC. In addition, the faster the speed, the less time the machine has to process the job, and the more energy the machine consumes. That is, if V v <V s , then t i，j，v >t i，j,s , while E i，j，v <E i，j，s .

[0065] For the green scheduling problem of uncorrelated parallel machines with variable speeds, two decision objectives are set. One is the maximum completion time C max , and the other is the electric carbon cost, including electricity cost and penalty cost, that is, Cost1+Cost2=F1(TEC)+{0,P0}.

[0066] For the total electricity cost, the mainstream electricity purchase policy is used as the ladder electricity price, and the electricity price cost function is Cost1 = F1 (TEC). The initial electricity price function of the algorithm is:

[0067]

[0068] In the formula, P1, P2 and P3 are three levels of electricity prices, E is energy consumption, and E1 and E2 are two grading thresholds of energy consumption.

[0069] At the same time, let α be the part of the total energy consumption using carbon, and β be the power factor of the carbon thermal power unit. In the carbon trading market, when the carbon emissions (αβTEC) exceed the given carbon quota Q0, a penalty mechanism is introduced. Therefore, the penalty calculation formula is as follows.

[0070]

[0071] Also set x i,j，v As a decision variable, when workpiece i is processed on machine j at speed level v, it is 1, otherwise it is 0.

[0072] Constraints include non-preemption constraints, a workpiece can only be processed by one machine, and a machine can only process one workpiece at any one time.

[0073] The scheduling model of unrelated parallel machines is as follows:

[0074] Min f1=C max #(3)

[0075] Min f2=Cost1+Cost2=F1(TEC)+{0,P0}#(4)

[0076]

[0077]

[0078] Where n is the total number of workpieces, m is the total number of machines, S is the number of speed gears, i is the workpiece index, j is the machine index, v is the speed index, and C max is the maximum completion time, V v is the machine processing speed, t i，j is the standard processing time, t i，j，v is the actual processing time, p j，v is the unit energy consumption, E i，j，v is the actual energy consumption, α is the proportion of total electricity consumption using carbon, β is the power factor of the carbon thermal power unit, P0 is the penalty cost, Q0 is the carbon quota, x i，j，v Binary variable.

[0079] Formula (3) and Formula (4) indicate that the object to be optimized is to minimize the maximum completion time and the total electricity carbon cost. Formula (5) constrains that for each workpiece, there can only be one processing machine and one processing speed. Formula (6) and Formula (7) define makespan and total energy consumption respectively.

[0080] S2. Construct a distributed evolutionary algorithm ANEDA with adaptive mechanism and neighborhood search mechanism, input parameters related to production conditions, solve the unrelated parallel machine scheduling model, and obtain the optimal scheduling method; when solving the unrelated parallel machine scheduling model, the algorithm randomly initializes the population, adopts a multi-objective non-dominated sorting method and crowding distance calculation to improve individual diversity, and dynamically adjusts the learning rate and mutation rate through the information entropy adaptive mechanism.

[0081] The distributed evolutionary algorithm of the adaptive mechanism and the neighborhood search mechanism includes the following steps:

[0082] S2.1. Initialize the population: including initialization based on the time efficiency of the workpiece, initialization of part of the population based on the energy efficiency of the work, and random generation of chromosomes: the correspondence between the workpieces assigned to the machines for processing and the processing speed of the jobs; and use the binary tournament rule for population selection, i.e. randomly select two individuals from the population, and select a better individual to be put into the elite group by comparing the Pareto sequence and the crowding distance, until the elite group meets the required number of individuals;

[0083] S2.2, Multi-objective non-dominated sorting: Multi-objective non-dominated sorting method and crowding distance calculation are used to improve the diversity of individuals;

[0084] S2.3, Adaptive mechanism: Calculate the probability distribution information of the solution space, design an adaptive mechanism based on information entropy, and dynamically adjust the learning rate and mutation rate;

[0085] S2.4, Neighborhood search mechanism: Set neighborhood search operators for benchmark machines and non-benchmark machines based on problem characteristics to improve local search capabilities;

[0086] S2.5. Population variation: Use population variation to maintain individual diversity and prevent premature convergence.

[0087] For the problem, a solution consists of two parts, namely, assigning each job to the appropriate machine and selecting the appropriate processing speed. Therefore, the encoding is composed of two parts. The first part is the machine chromosome, which determines which machine to process according to the machine number assigned to the workpiece, and decomposes the sub-problem into machine allocation; the latter is the speed chromosome, which determines the processing speed of the job, corresponding to the speed selection sub-problem. Combining the two encoding methods to form a complete chromosome is a feasible way to solve this problem. The length of the first part of the gene string is n, expressed as J1, J2, J3, ..., J n , where the i-th gene J i is an integer in [1,m], representing the number of the processing machine for the i-th process. In the following part, the length of the gene string is also n, corresponding to a series of speed level positions arranged on the corresponding jobs. For example, there are 5 jobs to be processed on 3 machines at 2 speed levels. We can get the chromosome [3,2,3,1,1][2,1,1,1]. This means that J1 is processed at speed 2 on machine 3, J2 is processed at speed 1 on machine 2, and so on.

[0088] For the initialization population, three methods for generating the initial population are defined. The first one is based on the time efficiency of the workpiece. For each job, the machine with the smallest processing time is assigned to process it, and the corresponding processing speed is set to the fastest level. The second is to initialize part of the population according to the energy efficiency of the job. Because the faster the speed, the higher the energy consumption. For each job, the processing speed is set to the slowest level, and the machine is set to make E i,j,v The smallest machine. The last one is the random generation of chromosomes.

[0089] Since the processing order of the workpieces on each machine does not affect the objective function, based on these two sub-problems, two relative probability matrices of job allocation and speed selection are designed. For the job allocation probability matrix, ρ i,j(g) represents the probability distribution of machine j in the gth generation processing job i. The speed selection probability matrix ρ i,v (g) represents the probability distribution of job i with speed level v in the gth generation. The task allocation probability matrix in the gth generation is expressed as:

[0090]

[0091] The i-th row represents the probability that job i is processed on each machine, and the sum of them is 1.

[0092] At the same time, the speed selection probability matrix at the gth generation is expressed as:

[0093]

[0094] The i-th row represents the probability of job i being processed at each speed level, and the sum is also 1.

[0095] At the beginning of the iteration, the probability matrix should be uniformly distributed, as follows:

[0096]

[0097] The iterative method for each generation of the probability matrix is ​​defined as follows:

[0098]

[0099] Where: α g is the learning rate when generating g generations; Ψ is the proportion of elite solutions used for iteration; and Boolean variable g.th iteration.

[0100]

[0101] The present invention adopts a binary competition selection method to obtain an elite group, that is, two individuals are randomly selected from a group, and a better individual is selected and put into the elite group by comparing the Pareto sequence and the crowding distance, until the elite group meets the required number of individuals.

[0102] Although a larger learning rate or a smaller mutation rate can promote rapid convergence, it is easy to fall into the local optimal solution, resulting in premature algorithm maturity. The adaptive mechanism based on information entropy dynamically adjusts the learning rate and mutation rate, balances the search depth and width, improves algorithm performance, and avoids the above shortcomings.

[0103] Step S2.3, the dynamic adjustment of the learning rate is as follows: the information entropy of the job assignment probability matrix

[0104] Information entropy of speed selection probability matrix Let E0 = k0*E(0). When the probability matrix is ​​uniformly distributed, it is the most disordered, that is, E(g) is the largest; and when there is only one workpiece or speed corresponding to any machine, that is, ρ i,j (g) = 1, and the rest may all be 0. At this time, the probability matrix is ​​ranked the highest and E(g) is the smallest.

[0105] Adaptively adjust through the following formula:

[0106]

[0107] Where: k0, k1, k2 are adjustment parameters, β∈(0,1) is the base of the exponential function, k1=0.3, k1=0.7, β=0.25, E0 is the threshold of the initial probability matrix information E(0), k0 is the threshold ratio, α0 is the upper bound of the learning rate, and the learning rate α g Take E0 as the boundary.

[0108] Step S2.3 dynamically adjusts the mutation rate as follows: based on the mutation rate m g Perturbing or mutating the probability matrix helps maintain the appropriate search width of the algorithm and guides the algorithm to search different areas. The mutation rate adaptive formula is as follows:

[0109]

[0110] Where: mr min is the lower limit of mutation rate, γ is the increase control parameter, γ>1, m g is a monotonically increasing function with E(g) as the independent variable, and its range is mr min and γ*mr min Between, take γ=3.

[0111] In order to maintain the diversity of the population, the probability matrix needs to be mutated appropriately to prevent premature convergence during the iteration process.

[0112] Randomly select a value between [0,1] less than m g , then the probability matrix is ​​mutated by the following formula.

[0113]

[0114] Among them, m g is the mutation rate. When the population just starts to iterate and E(g) is large, m g Set it to a smaller value, that is, reducing the mutation probability is beneficial to increasing the search depth of the algorithm and increasing the convergence speed. When E(g) is small, m g Setting it to a larger value, that is, increasing the mutation probability, is beneficial to increasing the search width of the algorithm and preventing the algorithm from converging prematurely.

[0115] The newly generated population is combined with the elite population after polynomial mutation according to the probability matrix. After non-dominated sorting calculation and crowding distance allocation, the next generation population is generated through the elite retention strategy.

[0116] The present invention proposes three neighborhood search methods to obtain more efficient and richer offspring. The newly generated offspring is surrounded by a large number of suboptimal solutions. In order to get rid of these suboptimal solutions and speed up efficiency, three neighborhood search methods are defined as follows.

[0117] First, define j * =j for max{C j |j=1,2,…,m} is the benchmark machine in the scheduling scheme, j * The processing time is the longest among all the machines.

[0118] In step S2.4, for non-reference machines, the processing speed is reduced to reduce energy consumption, and the non-reference machines are traversed in turn, and each workpiece whose speed is not the lowest is slowed down by one level, and the workpieces are sorted from large to small according to the energy consumption reduction thus generated, and the sorted workpieces are selected in turn, and the processing speed of the workpieces is reduced by one level, so that the completion time of the machine does not exceed the maximum completion time, until the speed of each job on the machine is reduced or the difference between the completion time of the machine and the maximum completion time is within a preset range;

[0119] For the baseline machine, two methods are included to reduce the completion time:

[0120] Method A: Select the workpiece with the shortest processing time on one of the machines and place it on another non-reference machine to minimize the increase in energy consumption while keeping the workpiece processing speed unchanged;

[0121] Method B: On the benchmark machine j * , select The smallest workpiece i is exchanged to machine l. For the workpiece to be exchanged on machine l, traverse the workpieces on it until it can reduce the maximum completion time of the two machines and minimize the increase in energy consumption, e i,j is the ratio of the minimum processing time of workpiece i on all machines to its processing time on machine j, which represents the processing time efficiency of workpiece i on machine j, e i,j =(min 1≤l≤m t i,l ) / t i,j , 1 <i<n,1<j<m。

[0122] Finally, the distributed evolutionary algorithm of the adaptive mechanism and neighborhood search mechanism of the present invention is verified, including the following steps: the optimal parameter combination of ANEDA is explored and determined by Taguchi orthogonal experimental design method. These parameters include population size NP, elite solution ratio Ψ, information entropy threshold ratio k0, learning rate upper limit α0 and mutation rate lower limit mr min The performance parameters of the algorithm were optimized through orthogonal test tables and response value analysis.

[0123] The process of comparing the ANEDA algorithm with the EDA algorithm without adaptive mechanism (E1) and the EDA algorithm without neighborhood search mechanism (E2) was designed to verify the significant improvement of algorithm performance by adaptive mechanism and neighborhood search mechanism. Through the CMetric measurement method, it is shown that ANEDA obtains a better Pareto solution set in most instances. Based on the simulation test results, specific suggestions on tiered electricity price and carbon quota management are proposed.

[0124] Specifically, in order to verify the effectiveness of the algorithm, the following experiments were conducted. Considering that this model introduces the dual factors of electricity and carbon into the green scheduling problem of unrelated parallel machines, compared with the penalty mechanism under the carbon quota, the incremental step price mechanism (IBP) has a more significant impact on the target. Therefore, the example scale is m, n, S = {2, 50, 3}, and each case is run 10 times to obtain the composite Pareto frontier, so as to mainly discuss and analyze the relevant parameters of the step price policy.

[0125] The parameters of the step pricing mechanism design include the number of steps, the length of steps, and the price of steps. Initially, the number of steps is three, and the values ​​of each parameter are E1=260, E2=400, P1=0.617, P2=0.667, and P3=0.917.

[0126] First, the number of steps is discussed and compared. When the number of steps is 1, the uniform electricity prices are P = 0.617 and P = 0.917 respectively; when the number of steps is 4, E3 = 600, P4 = 1.4. The Pareto frontier surface is compared between these three cases and the initial electricity price, as shown in Figure 2. Figure 2 shown.

[0127] In addition, from Figure 2It can be seen that when the unified electricity price is P = 0.617, it is equivalent to the reduction of the second and third tier electricity prices. Compared with the initial electricity price mechanism, the total cost is relatively reduced and the makespan is relatively increased. When the unified electricity price is P = 0.917, its makespan and total cost are significantly increased compared with the initial electricity price mechanism. When one more level is added, C(initial, P4 = 1.4) = 0.467, C(P4 = 1.4, initial) = 0.222. Since the total energy consumption accounts for a small proportion in the fourth level, the total cost has only a slight increase compared with the initial level.

[0128] Next, the effect of step length on the target was explored. When the step length is shortened, the energy consumption threshold is E1 = 150, E2 = 300; when the step length is extended, the energy consumption threshold is E1 = 400, E2 = 500. The Pareto frontier of these two cases is compared with the initial electricity price, as shown in the figure below: Figure 3 shown.

[0129] from Figure 3 It can be seen that after shortening the step length, that is, starting with a higher electricity price at a smaller energy consumption threshold, its makespan and total cost are increasing relative to the initial electricity price mechanism. After extending the step length, its total cost is relatively reduced and the makespan is increasing relative to the initial electricity price mechanism.

[0130] Finally, the impact of the change in tiered electricity prices on the target was explored. In the first case, in order to reduce energy consumption and limit high emissions, the price of the first tier is reduced, and the price of the second and third tiers is increased, that is, P1 = 0.5, P2 = 0.8, P3 = 1.1; in the second case, in order to stimulate the expansion of makespan and total cost production, the price of the first and second tiers is increased, and the price of the third tier is reduced, that is, P1 = 0.65, P2 = 0.7, P3 = 0.75. The Pareto frontier surface is compared between these two cases and the initial electricity price, as shown in the figure below: Figure 4 shown.

[0131] from Figure 4 It can be seen that in the first emission reduction case, the first-tier price is reduced, and the second and third-tier electricity prices are increased. C(initial, emission reduction) = 0.143, C(emission reduction, initial) = 0.556. Compared with the initial electricity price mechanism, under the same makespan, the total cost is decreasing, which meets the requirements for emission reduction. In the second case of expanding production, compared with the initial electricity price mechanism, under the same makespan, the total cost does not increase significantly, which promotes large-scale production.

[0132] Although the present invention has been described above with preferred embodiments, it is not intended to limit the present invention. A person skilled in the art of the present invention may make various modifications and improvements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the definition of the claims.

Claims

1. A green scheduling method for unrelated parallel machines with dual-factor introduction of electricity and carbon, characterized in that: The following steps are involved: S1. Collect relevant parameters of production conditions and build an unrelated parallel machine scheduling model with the goal of maximizing completion time and minimizing electricity and carbon cost; S2. Construct a distributed evolutionary algorithm with adaptive mechanism and neighborhood search mechanism, input parameters related to production conditions, solve the unrelated parallel machine scheduling model, and obtain the optimal scheduling method; when solving the unrelated parallel machine scheduling model, the algorithm randomly initializes the population, adopts a multi-objective non-dominated sorting method and crowding distance calculation to improve individual diversity, and dynamically adjusts the learning rate and mutation rate through the information entropy adaptive mechanism.

2. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as described in claim 1 is characterized in that: In step S1, the production condition related parameters include the number of workpieces, the number of machines, the machine processing speed v the maximum completion time C max , penalty cost P0, total energy consumption TEC, standard processing time t i，j , actual energy consumption E i，j，v .

3. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as described in claim 1 is characterized in that: The scheduling model of unrelated parallel machines is as follows: Min f1=C max #(3) Min f2=Cost1+Cost2=F1(TEC)+{0,P0}#(4) In the formula, C max is the maximum completion time, P0 is the penalty cost, TEC is the total energy consumption, t i，j is the standard processing time, t i,j,v is the actual processing time of job i on machine j with speed level v, E i，j，v is the actual energy consumption, x i,j,v is a binary variable, n is the number of workpieces, and v is the speed.

4. The green scheduling method for unrelated parallel machines with dual-factor electricity-carbon introduction according to claim 3 is characterized in that: The electricity price cost function Cost1=F1(TEC) is as follows: In the formula, P1, P2 and P3 are three-tier electricity prices, E is energy consumption, and E1 and E2 are two tier thresholds for energy consumption; The penalty formula Cost2 is as follows: Where α is the portion of total energy consumption using carbon, β is the power factor of the carbon thermal power unit, and αβTEC is the carbon emission.

5. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as described in claim 1 is characterized in that: In step S2, the distributed evolutionary algorithm of the adaptive mechanism and the neighborhood search mechanism includes the following steps: S2.

1. Initialize the population: including initialization based on the time efficiency of the workpiece, initialization of part of the population based on the energy efficiency of the work, and random generation of chromosomes: the correspondence between the workpieces assigned to the machines for processing and the processing speed of the jobs; and use the binary tournament rule for population selection, i.e. randomly select two individuals from the population, and select a better individual to be put into the elite group by comparing the Pareto sequence and the crowding distance, until the elite group meets the required number of individuals; S2.2, Multi-objective non-dominated sorting: Multi-objective non-dominated sorting method and crowding distance calculation are used to improve the diversity of individuals; S2.3, Adaptive mechanism: Calculate the probability distribution information of the solution space, design an adaptive mechanism based on information entropy, and dynamically adjust the learning rate and mutation rate; S2.4, Neighborhood search mechanism: Set neighborhood search operators for benchmark machines and non-benchmark machines based on problem characteristics to improve local search capabilities; S2.

5. Population variation: Use population variation to maintain individual diversity and prevent premature convergence.

6. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as described in claim 5 is characterized in that: Step S2.2 is to determine the job allocation probability matrix and the speed selection probability matrix according to the job classification and job processing speed, and then iterate, specifically: The job allocation probability matrix at the gth generation is expressed as: In the formula, ρ i,j (g) represents the probability distribution of machine j in the gth generation processing job i, The speed selection probability matrix at the gth generation is expressed as: At the beginning of the iteration, the probability matrix should be uniformly distributed, as follows: The iteration method of each generation probability matrix is ​​as follows: Where: α g is the learning rate when generating g generations; Ψ is the proportion of elite solutions used for iteration; and Boolean variable g.th iteration.

7. The green scheduling method for unrelated parallel machines with dual-factor electricity-carbon introduction according to claim 5 is characterized in that: Step S2.3, the dynamic adjustment of the learning rate is as follows: the information entropy of the job assignment probability matrix Information entropy of speed selection probability matrix Let E0 = k0*E(0) and adjust adaptively using the following formula: Where: k0, k1, k2 are adjustment parameters, β∈(0,1) is the base of the exponential function, E0 is the threshold of the initial probability matrix information E(0), k0 is the threshold ratio, α0 is the upper bound of the learning rate, and the learning rate α g Take E0 as the boundary.

8. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as described in claim 5 is characterized in that: Step S2.3 dynamically adjusts the mutation rate as follows: based on the mutation rate m g Perturbing or mutating the probability matrix helps maintain the appropriate search width of the algorithm and guides the algorithm to search different areas. The mutation rate adaptive formula is as follows: Where: mr min is the lower limit of mutation rate, γ is the increase control parameter, γ>1, m g is a monotonically increasing function with E(g) as the independent variable, and its range is mr min and γ*mr min between.

9. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as described in claim 5 is characterized in that: In step S2.4, for non-reference machines, the processing speed is reduced to reduce energy consumption, and the non-reference machines are traversed in turn, and each workpiece whose speed is not the lowest is slowed down by one level, and the workpieces are sorted from large to small according to the energy consumption reduction thus generated, and the sorted workpieces are selected in turn, and the processing speed of the workpieces is reduced by one level, so that the completion time of the machine does not exceed the maximum completion time, until the speed of each job on the machine is reduced or the difference between the completion time of the machine and the maximum completion time is within a preset range; For the baseline machine, two methods are included to reduce the completion time: Method A: Select the workpiece with the shortest processing time on one of the machines and place it on another non-reference machine to minimize the increase in energy consumption while keeping the workpiece processing speed unchanged; Method B: On the benchmark machine j * , select Enable i,j* The smallest workpiece i is exchanged to machine l. For the workpiece to be exchanged on machine l, traverse the workpieces on it until it can reduce the maximum completion time of the two machines and minimize the increase in energy consumption, e i,j is the ratio of the minimum processing time of workpiece i on all machines to its processing time on machine j, which represents the processing time efficiency of workpiece i on machine j, e i,j =(min 1≤l≤m t i,l ) / t i,j , 1 <i<n,1<j<m。 10. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as described in claim 1, characterized in that: The method also includes testing the unrelated parallel machine scheduling model of step S3, which specifically includes the following sub-steps: S3.1, Test instance setting: Design 45 instances, including different combinations of machine number, job number, and speed settings. Each team combination has 10 instances, the workpiece processing time is randomly set between 1h and 20h, and the machine speed is {1.0, 1.1, 1.2, 1.3}. Set 5 key parameters: population size Set 5 key parameters: population size, elite solution ratio, information entropy threshold ratio, learning rate upper limit, mutation rate lower limit, and use Taguchi orthogonal experimental design method to explore the impact of parameters on performance; S3.2, the simulation process is to implement the algorithm in the Python environment and run it using a specific computer configuration; use non-dominated sorting and crowding calculation to evaluate and select the population; dynamically adjust the learning rate and mutation rate, perform crossover and mutation operations, generate and optimize new populations; merge parent and child populations, retain excellent individuals, and repeat iterations until the set termination condition is reached; S3.

3. Use the overall non-dominated vector generation (ONVG) and C Metric to evaluate the algorithm performance and compare the effects of the adaptive EDA algorithm with other variants and traditional algorithms. S3.

4. Based on the simulation results, put forward suggestions for optimizing electricity price strategy and carbon quota management to achieve energy conservation and emission reduction goals.

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