A green scheduling method for uncorrelated parallel machines with the introduction of electricity and carbon dual factors

Abstract

This invention discloses a green scheduling method for unrelated parallel machines using dual factors of electricity and carbon. The method includes the following steps: S1, collecting parameters related to production conditions, and constructing an unrelated parallel machine scheduling model with the goal of maximizing completion time and minimizing electricity and carbon costs; S2, constructing a distributed evolutionary algorithm with adaptive and neighborhood search mechanisms, inputting the parameters related to production conditions, solving the unrelated parallel machine scheduling model, and obtaining an optimal scheduling method. When solving the unrelated parallel machine scheduling model, the algorithm randomly initializes the population, employs 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 an information entropy adaptive mechanism. Simulation results show that the ANEDA algorithm performs significantly better in optimizing maximum completion time and total electricity and carbon costs, verifying the algorithm's effectiveness and practical value.

Description

Technical Field

[0001] The present 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 increasingly concerned with energy conservation and emissions reduction. To alleviate the dire resource situation and optimize the energy structure, the Incremental Power Pricing (IBP) policy has been gradually implemented in China. In this context, manufacturing companies not only face the challenge of improving production efficiency but also need to minimize energy consumption and carbon emissions while meeting contractual requirements.

[0003] The Uncorrelated Parallel Machine Green Scheduling Problem (UPMGSP) has emerged as a classic multi-objective optimization problem. Its goal is to minimize the maximum completion time while minimizing the total cost of electricity and carbon emissions. However, the complexity of UPMGSP makes it difficult for traditional optimization methods to effectively solve it. Faced with a vast search space, exhaustive methods are not only time-consuming but also difficult to guarantee an optimal solution. Therefore, developing efficient optimization algorithms is crucial. Summary of the Invention

[0004] In response to 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 conducive to achieving green manufacturing and sustainable development goals.

[0005] To solve the above technical problems, the present invention provides the following technical solution: a green scheduling method for uncorrelated parallel machines with the introduction of electricity and 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 costs;

[0007] S2. Constructing a distributed evolutionary algorithm with an adaptive mechanism and a neighborhood search mechanism, inputting parameters related to production conditions, solving an unrelated parallel machine scheduling model, and obtaining an optimal scheduling method. When solving the unrelated parallel machine scheduling model, the algorithm randomly initializes the population, uses 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 an information entropy adaptive mechanism.

[0008] The unrelated parallel machine scheduling model is as follows:

[0009] Min f1=C max #(3)

[0010] Min f2=Cost1+Cost2=F1(TEC)+{0,P0}#(4)

[0011]

[0012] Where 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;

[0013] The electricity price cost function Cost1=F1(TEC) is as follows:

[0014]

[0015] In the formula, P1, P2, and P3 are three tiers of electricity prices, E is energy consumption, and E1 and E2 are two tier thresholds for energy consumption. The penalty formula Cost2 is as follows:

[0016]

[0017] Where α is the portion of total energy consumption that uses carbon, β is the power factor of the carbon thermal power unit, and αβTEC is carbon emission;

[0018] The distributed evolutionary algorithm of the adaptive mechanism and neighborhood search mechanism includes the following steps:

[0019] S2.1. Population initialization: This includes initialization based on the time efficiency of the workpiece, initialization of a portion of the population based on the energy efficiency of the job, and random generation of chromosomes: the correspondence between the workpieces assigned to the machines for processing and the processing speed of the job. The population is selected using the binary tournament rule, which randomly draws two individuals from the population. By comparing the Pareto sequence and crowding distance, the better individual is selected and placed in the elite group until the elite group meets the required number of individuals.

[0020] 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;

[0021] 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;

[0022] S2.4. Neighborhood search mechanism: Set neighborhood search operators for both benchmark and non-benchmark machines based on problem characteristics to improve local search capabilities.

[0023] S2.5. Population variation: Use population variation to maintain individual diversity and prevent premature convergence.

[0024] 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 .

[0025] Furthermore, the aforementioned step S2.2 is to determine the job allocation probability matrix and the speed selection probability matrix based on the job classification and job processing speed, and then iterate, specifically:

[0026] The job assignment probability matrix at the gth generation is expressed as:

[0027]

[0028] Where, ρ i,j (g) represents the probability distribution of machine j in the gth generation processing job i,

[0029] The speed selection probability matrix at the gth generation is expressed as:

[0030]

[0031] At the beginning of the iteration, the probability matrix should be uniformly distributed as follows:

[0032]

[0033] The iterative method of each generation probability matrix is ​​as follows:

[0034]

[0035] Where: α g is the learning rate when generating g generations; Ψ is the proportion of elite solutions used for iteration; and is a Boolean variable.

[0036] Furthermore, in the aforementioned step S2.3, the dynamic adjustment of the learning rate is specifically: 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:

[0037]

[0038] 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 With E0 as the boundary.

[0039] Furthermore, the above-mentioned step S2.3 dynamically adjusts the mutation rate specifically 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:

[0040]

[0041] Where: mr min is the lower limit of mutation rate, γ is the control parameter, γ>1, m g It is a monotonically increasing function with E(g) as the independent variable, and its range of variation is mr min and γ*mr min between.

[0042] Furthermore, in step S2.4, the processing speed of non-reference machines is reduced to reduce energy consumption. The non-reference machines are traversed in sequence, and each workpiece whose speed is not the lowest is slowed down by one level. The workpieces are sorted from largest to smallest according to the resulting energy consumption reduction. The sorted workpieces are selected in sequence, 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. This continues until the speed of each job on the machine is reduced or the difference between the machine's completion time and the maximum completion time is within a preset range.

[0043] For the baseline machine, two methods are included to reduce the completion time:

[0044] Method A: Select the workpiece with the shortest processing time on one machine and place it on another non-reference machine to minimize the increase in energy consumption while keeping the workpiece processing speed unchanged;

[0045] Method B, on the benchmark machine j * On the The smallest workpiece i is exchanged to machine l; for the workpiece to be exchanged on machine l, traverse the workpieces on it until the maximum completion time of the two machines can be reduced and the energy consumption increase can be minimized, 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。

[0046] Furthermore, the aforementioned green scheduling method for unrelated parallel machines with dual-factor electricity and carbon introduction further includes testing the unrelated parallel machine scheduling model of step S3, specifically including the following sub-steps:

[0047] S3.1. Test case setup: Design 45 cases with different combinations of machine number, job number, and speed settings. Each team has 10 cases. The workpiece processing time is randomly set between 1 hour and 20 hours, and the machine speed is {1.0, 1.1, 1.2, 1.3}. Set five key parameters: population size, elite solution ratio, information entropy threshold ratio, learning rate upper limit, and mutation rate lower limit. Use the Taguchi orthogonal experimental design method to explore the impact of these parameters on performance.

[0048] S3.2. The simulation process involves implementing the algorithm in a Python environment and running it on a specific computer configuration. The algorithm uses non-dominated sorting and crowding calculations to evaluate and select populations. The learning rate and mutation rate are dynamically adjusted, crossover and mutation operations are performed, and new populations are generated and optimized. Parent and child populations are merged, and the best individuals are retained. The iterations are repeated until the set termination condition is reached.

[0049] S3.3. Use the overall non-dominated vector generation (ONVG) and C Metric to evaluate the performance of the algorithm and compare the effects of the adaptive EDA algorithm with other variants and traditional algorithms.

[0050] S3.4. Based on the simulation results, propose management recommendations for optimizing electricity pricing strategies and carbon quotas to achieve energy conservation and emission reduction goals.

[0051] Compared with the prior art, the beneficial technical effects of the present invention using the above technical solution are as follows:

[0052] 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.

[0053] 2. An adaptive mechanism based on information entropy can appropriately regulate the learning rate and mutation rate, ensuring the algorithm's search depth and convergence speed, and improving the diversity and quality of Pareto solutions. The neighborhood search mechanism promotes the algorithm's exploration of a single region, avoiding suboptimal solutions and further improving the algorithm's search efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is the flow chart of the ANEDA algorithm.

[0055] Figure 2 This is a comparison chart of the number of steps.

[0056] Figure 3 This is a comparison chart of step lengths.

[0057] Figure 4 This is a tiered price comparison chart. DETAILED DESCRIPTION

[0058] In order to better understand the technical content of the present invention, specific embodiments are given and described below with reference to the accompanying drawings.

[0059] Various aspects of the present invention are described herein with reference to the accompanying drawings, which show a number of illustrative embodiments. The embodiments of the present invention are not limited to those described in the accompanying drawings. It should be understood that the present invention can be implemented by any of the various concepts and embodiments described above, as well as the concepts and implementations described in detail below, because the concepts and embodiments disclosed herein are not limited to any particular implementation. In addition, some aspects disclosed herein may be used alone or in any appropriate combination with other aspects disclosed herein.

[0060] refer to Figure 1 , the method flow chart of the present invention comprises the following steps:

[0061] S1. Collect parameters related to production conditions and build an unrelated parallel machine scheduling model with the goal of maximizing completion time and minimizing electricity and carbon costs.

[0062] For the unrelated parallel machine green scheduling problem, we have n independent jobs J = {1, 2, ..., i, ..., n} being 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.

[0063] 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 v Calculate. At 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 a processing speed of v when processing operation 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 .

[0064] 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 , the other is the electric carbon cost, including electricity cost and penalty cost, that is, Cost1+Cost2=F1(TEC)+{0,P0}.

[0065] For the total cost of electricity, 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:

[0066]

[0067] In the formula, P1, P2 and P3 are three levels of electricity prices, E is energy consumption, and E1 and E2 are two tier thresholds of energy consumption.

[0068] Let α be the fraction of total energy consumption using carbon, and β be the power factor of the carbon-fired power unit. In a carbon trading market, a penalty mechanism is introduced when carbon emissions (αβTEC) exceed a given carbon quota, Q0. Therefore, the penalty calculation formula is as follows.

[0069]

[0070] Also set x i,j,v As a decision variable, it is 1 when workpiece i is processed on machine j at speed level v, and 0 otherwise.

[0071] 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.

[0072] The unrelated parallel machine scheduling model is as follows:

[0073] Min f1=C max #(3)

[0074] Min f2=Cost1+Cost2=F1(TEC)+{0,P0}#(4)

[0075]

[0076] 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 price, Q0 is the carbon quota, and x i,j,v Binary variable.

[0077] Equations (3) and (4) indicate that the optimization objective is to minimize the maximum completion time and total electricity-carbon cost. Equation (5) constrains that for each workpiece, there can only be one processing machine and one processing speed. Equations (6) and (7) define makespan and total energy consumption, respectively.

[0078] S2. Construct a distributed evolutionary algorithm (ANEDA) with adaptive and neighborhood search mechanisms. 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, uses 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 an information entropy adaptive mechanism. The distributed evolutionary algorithm with adaptive and neighborhood search mechanisms includes the following steps:

[0079] S2.1. Population initialization: This includes initialization based on the time efficiency of the workpiece, initialization of a portion of the population based on the energy efficiency of the job, and random generation of chromosomes: the correspondence between the workpieces assigned to the machines for processing and the processing speed of the job. The population is selected using the binary tournament rule, which randomly draws two individuals from the population. By comparing the Pareto sequence and crowding distance, the better individual is selected and placed in the elite group until the elite group meets the required number of individuals.

[0080] 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;

[0081] 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;

[0082] S2.4. Neighborhood search mechanism: Set neighborhood search operators for both benchmark and non-benchmark machines based on problem characteristics to improve local search capabilities.

[0083] S2.5. Population variation: Use population variation to maintain individual diversity and prevent premature convergence.

[0084] 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 based on the machine number assigned to the workpiece, and decomposes the sub-problem into machine allocation; the second part 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 machine number for the i-th process. Later in the series, the length of the gene string is also n, corresponding to a series of speed level positions assigned to the corresponding job. For example, if there are five jobs to be processed on three machines at two speed levels, we can obtain the chromosomes [3, 2, 3, 1, 1][2, 1, 1, 1]. This means that J1 is processed on machine 3 at speed 2, J2 on machine 2 at speed 1, and so on.

[0085] For the initialization of the population, three methods are defined. The first is to initialize 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 based on the energy efficiency of the work. 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.

[0086] Since the processing order of the workpiece 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:

[0087]

[0088] The i-th row represents the probability that job i is processed on each machine, and the sum is 1.

[0089] At the same time, the speed selection probability matrix at the gth generation is expressed as:

[0090]

[0091] The i-th row represents the probability of job i being processed at each speed level, and the sum is also 1.

[0092] At the beginning of the iteration, the probability matrix should be uniformly distributed as follows:

[0093]

[0094] The iterative method for each generation of the probability matrix is ​​defined as follows:

[0095]

[0096] Where: α g is the learning rate when generating g generations; Ψ is the proportion of elite solutions used for iteration; and is a Boolean variable.

[0097]

[0098] The present invention adopts a binary competition selection method to obtain an elite group, that is, two individuals are randomly selected from the group, and by comparing the Pareto sequence and the crowding distance, a better individual is selected and placed in the elite group until the elite group meets the required number of individuals.

[0099] While a larger learning rate or smaller mutation rate can promote rapid convergence, it can easily lead to falling into local optimal solutions, causing the algorithm to mature prematurely. An adaptive mechanism based on information entropy dynamically adjusts the learning rate and mutation rate, balancing the depth and breadth of the search, improving algorithm performance and avoiding these drawbacks.

[0100] Step S2.3, the dynamic adjustment of the learning rate is specifically: the information entropy of the job assignment probability matrix

[0101] 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 highest and E(g) is the smallest.

[0102] Adaptively adjust using the following formula:

[0103]

[0104] 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 With E0 as the boundary.

[0105] Step S2.3 is to dynamically adjust the mutation rate: 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:

[0106]

[0107] Where: mr min is the lower limit of mutation rate, γ is the control parameter, γ>1, m g It is a monotonically increasing function with E(g) as the independent variable, and its range of variation is mr min and γ*mr min Between, take γ=3.

[0108] 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.

[0109] Randomly select a value between [0,1] less than m g , then the probability matrix is ​​mutated by the following formula.

[0110]

[0111] Among them, m g is the mutation rate. When the population just starts to iterate and E(g) is large, m g Setting 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.

[0112] 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.

[0113] This paper proposes three neighborhood search methods to obtain more efficient and richer offspring. Newly generated offspring are often surrounded by a large number of suboptimal solutions. To eliminate these suboptimal solutions and improve efficiency, three neighborhood search methods are defined as follows.

[0114] 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 machines.

[0115] In step S2.4, for non-reference machines, the processing speed is reduced to reduce energy consumption. The non-reference machines are traversed in sequence, and each workpiece whose speed is not the lowest is slowed down by one level. The workpieces are sorted from large to small according to the resulting energy consumption reduction. 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. This continues 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.

[0116] For the baseline machine, two methods are included to reduce the completion time:

[0117] Method A: Select the workpiece with the shortest processing time on one machine and place it on another non-reference machine to minimize the increase in energy consumption while keeping the workpiece processing speed unchanged;

[0118] Method B, on the benchmark machine j * On the 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。

[0119] Finally, the distributed evolutionary algorithm of the adaptive mechanism and neighborhood search mechanism of the present invention is verified, including the following steps: exploring and determining the optimal parameter combination of ANEDA through the Taguchi orthogonal experimental design method. These parameters include the population size NP, the elite solution ratio ψ, the information entropy threshold ratio k0, the upper limit of the learning rate α0 and the lower limit of the mutation rate mr min The performance parameters of the algorithm were optimized through orthogonal test tables and response value analysis.

[0120] A comparison process was designed to test the ANEDA algorithm with an EDA algorithm lacking an adaptive mechanism (E1) and an EDA algorithm lacking a neighborhood search mechanism (E2). The results verified that the adaptive and neighborhood search mechanisms significantly improved algorithm performance. Using the CMetric metric, ANEDA demonstrated that it achieved a superior Pareto solution set in most instances. Based on the simulation test results, specific recommendations were proposed regarding tiered electricity pricing and carbon quota management.

[0121] Specifically, to verify the effectiveness of the algorithm, the following experiments were conducted. Considering that this model introduces both electricity and carbon factors into the green scheduling problem for uncorrelated parallel machines, the impact of the incremental pricing mechanism (IBP) on the target is more significant than the penalty mechanism under carbon quotas. Therefore, a case scale of m, n, S = {2, 50, 3} was used, and each case was run 10 times to obtain a composite Pareto frontier, thereby focusing on the relevant parameters of the tiered pricing policy.

[0122] The parameters for designing the tiered pricing mechanism include the number of tiers, the length of the tiers, and the price of the tiers. Initially, there are three tiers, and the values ​​of these parameters are E1 = 260, E2 = 400, P1 = 0.617, P2 = 0.667, and P3 = 0.917.

[0123] 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 and P4 = 1.4. The Pareto frontier of these three cases is compared with the initial electricity price, as shown in the following example: Figure 2 shown.

[0124] In addition, from Figure 2 It can be seen that when the unified electricity price is P = 0.617, which is equivalent to a reduction in the second and third tier electricity prices, the total cost is relatively reduced and the makespan is relatively increased compared to the initial electricity price mechanism. When the unified electricity price is P = 0.917, its makespan and total cost are significantly increased compared to the initial electricity price mechanism. When one tier is added, C(initial, P4 = 1.4) = 0.467 and C(P4 = 1.4, initial) = 0.222. Since the total energy consumption in the fourth tier accounts for a small proportion, the total cost only increases slightly compared to the initial tier.

[0125] Next, we explored the impact of step length on the target. When the step length is shortened, the energy consumption thresholds E1 = 150 and E2 = 300; when the step length is extended, the energy consumption thresholds E1 = 400 and E2 = 500. The Pareto frontiers of these two cases are compared with the initial electricity price. Figure 3 shown.

[0126] from Figure 3 It can be seen that when the step length is shortened, that is, a higher electricity price is started at a lower energy consumption threshold, both the makespan and total cost increase compared to the initial electricity price mechanism. However, when the step length is extended, the total cost decreases relatively, while the makespan increases.

[0127] 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 lowered and the prices of the second and third tiers are raised, 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 prices of the first and second tiers are raised and the price of the third tier is lowered, that is, P1 = 0.65, P2 = 0.7, P3 = 0.75. The two cases are compared with the initial electricity price on the Pareto frontier, as shown in the figure below. Figure 4 shown.

[0128] from Figure 4 As can be seen, in the first emission reduction scenario, the first tier price is reduced, while the second and third tier prices are increased. C(initial, emission reduction) = 0.143, and C(emission reduction, initial) = 0.556. Compared to the initial electricity price mechanism, under the same makespan, total costs are reduced, meeting the emission reduction requirements. In the second production expansion scenario, compared to the initial electricity price mechanism, under the same makespan, total costs do not increase significantly, indicating that large-scale production is promoted.

[0129] While the present invention has been described above with reference to preferred embodiments, this is not intended to limit the present invention. Persons skilled in the art will readily appreciate that various modifications and variations can be made 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 appended claims.

Claims

1. A green scheduling method for unrelated parallel machines with the introduction of electricity and carbon dual factors, characterized by: 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 costs; S2. Constructing a distributed evolutionary algorithm with an adaptive mechanism and a neighborhood search mechanism, inputting parameters related to production conditions, solving an unrelated parallel machine scheduling model, and obtaining an optimal scheduling method. When solving the unrelated parallel machine scheduling model, the algorithm randomly initializes the population, uses 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 an information entropy adaptive mechanism. The unrelated parallel machine scheduling model is as follows: Min f1=C max (3) Min f2=Cost1+Cost2=F1(TEC)+{0,P0} (4) Where 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; The electricity price cost function Cost1=F1(TEC) is as follows: In the formula, P1, P2, and P3 are three tiers of 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 that uses carbon, β is the power factor of the carbon thermal power unit, and αβTEC is carbon emission; The distributed evolutionary algorithm of the adaptive mechanism and neighborhood search mechanism includes the following steps: S2.

1. Initialize the population: This includes initializing the population based on the time efficiency of the workpiece, initializing the population based on the energy efficiency of the job, and randomly generating chromosomes: the correspondence between the workpieces assigned to the machines for processing and the processing speed of the jobs; The binary tournament rule is used for population selection, i.e., two individuals are randomly selected from the population, and by comparing the Pareto sequence and crowding distance, a better individual is selected and placed in the elite group 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 both benchmark 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.

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 υ, and 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: Step S2.2 is to determine the job allocation probability matrix and the speed selection probability matrix based on the job classification and job processing speed, and then iterate. Specifically, The job assignment probability matrix at the gth generation is expressed as: Where, 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 iterative 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 is a Boolean variable.

4. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as described in claim 1 is characterized in that: Step S2.3, the dynamic adjustment of the learning rate is specifically: 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 With E0 as the boundary.

5. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as claimed in claim 1, characterized in that: Step S2.3 is to dynamically adjust the mutation rate: 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 It is a monotonically increasing function with E(g) as the independent variable, and its range of variation is mr min and γ*mr min between.

6. The green scheduling method for unrelated parallel machines with dual-factor electricity and carbon as claimed in claim 1, characterized in that: In step S2.4, for non-reference machines, the processing speed is reduced to reduce energy consumption. The non-reference machines are traversed in sequence, and each workpiece whose speed is not the lowest is slowed down by one level. The workpieces are sorted from large to small according to the resulting energy consumption reduction. 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. This continues 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 machine 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 * On the left, 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 the maximum completion time of the two machines can be reduced and the energy consumption increase can be minimized, 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。 7. The green scheduling method for unrelated parallel machines with the introduction of electricity and carbon dual factors according to claim 1 is characterized in that: The test of the unrelated parallel machine scheduling model in step S3 is also included, which specifically includes the following sub-steps: S3.

1. Test case setup: Design 45 cases with different combinations of machine number, job number, and speed settings. Each team has 10 cases. The workpiece processing time is randomly set between 1 hour and 20 hours, and the machine speed is {1.0, 1.1, 1.2, 1.3}. Set five key parameters: population size, elite solution ratio, information entropy threshold ratio, learning rate upper limit, and mutation rate lower limit. Use the Taguchi orthogonal experimental design method to explore the impact of these parameters on performance. S3.

2. The simulation process involves implementing the algorithm in a Python environment and running it on a specific computer configuration. The algorithm uses non-dominated sorting and crowding calculations to evaluate and select populations. The learning rate and mutation rate are dynamically adjusted, crossover and mutation operations are performed, and new populations are generated and optimized. Parent and child populations are merged, and the best individuals are retained. The iterations are repeated until the set termination condition is reached. S3.3, use the overall non-dominated vector generation ONVG and C Metric measurement method to evaluate the algorithm performance, S3.

4. Based on the simulation results, propose management recommendations for optimizing electricity pricing strategies and carbon quotas to achieve energy conservation and emission reduction goals.

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