Numerical control multi-objective optimization energy-saving method and system based on improved wolf pack algorithm

Abstract

The invention provides a numerical control multi-objective optimization energy-saving method and system based on an improved wolf pack algorithm, and the method comprises the steps: constructing a mixed integer linear programming model of multi-objective flexible job shop scheduling, taking machine tool distribution, a machining sequence, tool distribution and a machining speed as decision variables, and taking total weighted tardiness and total energy consumption as optimization targets; the method comprises the following steps: constructing an MOGWO-ALNS algorithm for solving a mixed integer linear programming model based on an MOGWO algorithm and an adaptive large neighborhood search mechanism, constructing a three-stage collaborative optimization architecture by the MOGWO-ALNS algorithm through a dual-threshold trigger mechanism, solving the mixed integer linear programming model based on the MOGWO-ALNS algorithm, obtaining a Pareto optimal solution set of the mixed integer linear programming model, decoding the Pareto optimal solution set, and finally obtaining the mixed integer linear programming model. And generating a multi-target balanced energy-saving scheduling scheme. According to the method, collaborative optimization of the delivery date and the energy consumption in numerical control machining is achieved, the solving efficiency and the optimization effect are improved, and the method has good engineering application value.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology, specifically to a CNC multi-objective optimization energy-saving method and system based on an improved wolf pack algorithm. Background Technology

[0002] With the rapid development of the manufacturing industry, CNC machining is increasingly widely used in industrial production. However, CNC machining suffers from problems such as high energy consumption and unreasonable scheduling, which not only increases production costs but also contradicts the development concept of green manufacturing.

[0003] In the field of CNC machining scheduling optimization, traditional single-objective optimization methods often focus only on a single dimension of production efficiency (such as manufacturing span, delay time) or energy consumption, making it difficult to achieve a coordinated balance among multiple objectives. At the same time, existing optimization algorithms generally suffer from slow convergence speed, low solution quality, and poor adaptability to multiple resource constraints when solving complex multi-objective scheduling problems, making it difficult to meet the needs of efficient and energy-saving scheduling schemes in actual production.

[0004] In recent years, research on energy-saving flexible work workshop scheduling that addresses non-human resource constraints has gradually attracted attention. Xu et al. constructed a mixed-integer programming model that simultaneously optimizes total energy consumption and manufacturing span, and designed a heuristic algorithm based on AGV coding and local search to achieve high solution quality for integrated AGV green scheduling; Du et al. used an improved DQN method to solve the scheduling problem constrained by cranes, and through state-action reinforcement learning and dual deep Q-networks, achieved coordination between multi-stage transportation and machine states, thereby optimizing manufacturing span and energy consumption; Li et al. proposed a dual-population equilibrium multi-objective evolutionary algorithm, combining a fuzzy processing time model and a multi-stage transportation coordination mechanism, to simultaneously optimize the maximum fuzzy completion time and energy efficiency index, demonstrating the advantages of resource synergy; Liu et al. studied the FJSP-AGV problem and proposed a multi-population optimization algorithm based on critical path co-evolution (MCEA), which achieved coordinated optimization of completion time and total energy consumption through four-dimensional subproblem decomposition and dynamic energy consumption optimization; Fontes et al. extended the energy-saving FJSP considering transportation resources, proposed a dual-objective mixed-integer linear programming model, and designed a multi-objective partially stochastic critical genetic algorithm to optimize the scheduling of speed-adjustable machines and vehicles, and to achieve a Pareto solution that balances makespan and total energy consumption.

[0005] However, existing research does not adequately consider the constraints of key machining resources such as cutting tools and fixtures, and the energy-saving optimization framework for the collaborative scheduling of multiple resources (especially cutting tools) is still incomplete. This makes it difficult to effectively solve the problem of co-optimizing total weighted delay and total energy consumption under the coupling of multi-dimensional decisions such as machine tool allocation, machining sequence, tool allocation, and machining speed adjustability in actual CNC workshops. Therefore, there is an urgent need for a method and system that can integrate multiple resource constraints, achieve deep collaborative optimization of multiple objectives in CNC machining, and improve solution efficiency and optimization results. Summary of the Invention

[0006] The purpose of this application is to provide a CNC multi-objective optimization energy-saving method and system based on an improved wolf pack algorithm to solve the above-mentioned technical problems.

[0007] According to one aspect of this application, a CNC multi-objective optimization energy-saving method based on an improved wolf pack algorithm is proposed, the method comprising the following steps:

[0008] S1. Construct a mixed-integer linear programming model for multi-objective flexible workshop scheduling. The model takes total weighted delay and total energy consumption as optimization objectives, and machine tool allocation, processing sequence, tool allocation and processing speed adjustability as decision variables.

[0009] S2. Based on the MOGWO algorithm and the adaptive large neighborhood search mechanism, the MOGWO-ALNS algorithm for solving mixed integer linear programming models is constructed. The MOGWO-ALNS algorithm constructs a three-stage collaborative optimization architecture through a dual threshold triggering mechanism.

[0010] S3. Solve the mixed-integer linear programming model based on the MOGWO-ALNS algorithm to obtain the Pareto optimal solution set of the mixed-integer linear programming model;

[0011] S4. Decode the Pareto optimal solution set to generate a multi-objective balanced energy-saving scheduling scheme.

[0012] In the above technical solution, by constructing a dual-objective mathematical model and a hierarchical optimization architecture, the synergistic optimization of delivery time and energy consumption is achieved, breaking through the limitations of traditional single-objective scheduling and providing a systematic energy-saving solution for CNC workshops.

[0013] Furthermore, the expression for the mixed-integer linear programming model is:

[0014] min∑ i∈N wt i (1)

[0015] min∑ m∈NC (ep m +ei m (2)

[0016] The constraints include:

[0017]

[0018] In the formula, N represents the set of workpieces, i∈N; wt i The weighted delay time for workpiece i is represented; NC represents the set of CNC machine tools; ep m Indicates the total energy consumption of machine tool m during operation; ei mW represents the total energy consumption of machine tool m in idle state. i This represents the weight of workpiece i; Let the non-negative continuous variable be workpiece i at the Kth position. i The start time of the operation; NC represents the set of CNC machine tools, m∈NC; Indicates the Kth workpiece i i The set of selectable processing speeds for each operation; Indicates the Kth workpiece i i If the operation is performed on machine tool m at speed s, the binary variable is 1; otherwise, it is 0. Indicates the Kth workpiece i i The time required for processing at speed s in this operation; W i Indicates the delivery date of workpiece i; O i K represents the fixed processing sequence of workpiece i. i Indicates the number of operations for workpiece i, O i = (1,2,...,K) i ), k∈O i S i,k Let S represent the set of selectable processing speeds for the k-th operation on workpiece i. i,k ;z m,i,k,s Let P represent the k-th operation of workpiece i being processed on machine tool m at speed s, then the binary variable is 1; i,k,s E represents the time required for the k-th operation of workpiece i to be processed at speed s; i,k,s Let represent the power required for machining workpiece i at speed s in the k-th operation; E represents the power of the machine tool in idle state; mc m Let m be the non-negative continuous variable representing the end time of machine tool m.

[0019] In the above technical solution, by accurately quantifying the mathematical relationship between delay and energy consumption, a theoretical basis is provided for multi-objective optimization, ensuring that the scheduling scheme generated by the algorithm simultaneously meets the dual objectives of production efficiency and energy conservation.

[0020] Furthermore, the three-stage collaborative optimization architecture of the MOGWO-ALNS algorithm includes:

[0021] In the first stage, heuristic rules and random strategies were used to generate the initial population, and Pareto frontier exploration was carried out based on the standard gray wolf optimization algorithm.

[0022] In the second stage of optimization, in response to the algorithm running time reaching the first perturbation threshold, a local perturbation based on an adaptive large neighborhood search mechanism is introduced for the α wolf.

[0023] In the third stage of optimization, in response to the algorithm running time reaching the second perturbation threshold, the adaptive large neighborhood search mechanism is diffused to β wolf and δ wolf for local perturbation;

[0024] The first stage includes: using heuristic rules to generate a guiding subpopulation for minimizing the total weighted delay and a subpopulation for minimizing the total energy consumption, and using a random initialization strategy to generate a wide range of individuals covering the solution space;

[0025] Heuristic rules include the earliest due date rule, the shortest processing time rule, the weighted shortest processing time rule, the shortest completion time rule, the apparent lateness cost rule, the minimum relaxation rule, the maximum processing speed priority strategy, and the lowest energy consumption priority strategy, among which:

[0026] The earliest due date rule prioritizes tasks with the earliest due date.

[0027] The shortest processing time rule prioritizes tasks with the shortest processing time.

[0028] The weighted shortest processing time rule prioritizes tasks with the longest weighted processing time.

[0029] The shortest completion time rule prioritizes tasks with the closest due date.

[0030] The apparent lateness cost rule prioritizes tasks with the highest delay costs and urgency, and its expression is: In the formula, D i P represents the delivery date of workpiece i. i W represents the total machining time for all operations on workpiece i at constant speed. i Let represent the weight of workpiece i, t′ represent the earliest start time of the current workpiece i, and F represent the scaling parameter. This indicates the average processing time for the remaining workpieces.

[0031] The minimum relaxation rule prioritizes tasks with the shortest relaxation time, and its expression is: max(0, D) i -P i -t′);

[0032] The maximum processing speed priority strategy prioritizes the fastest processing speed.

[0033] The lowest energy consumption priority strategy prioritizes the processing speed with the lowest energy consumption, and its expression is P. i,k / S i,k ×E i,k In the formula, P i,k S represents the time required for the k-th operation of workpiece i. i,k E represents the set of selectable processing speeds for workpiece i during the k-th operation. i,k This represents the power required for the k-th operation of workpiece i.

[0034] In the above technical solution, by focusing on the optimization of solutions of different quality in stages, balancing global exploration and local development, the algorithm converges to the Pareto front, and the diversity and uniformity of the solution set are improved.

[0035] Furthermore, in the second stage of optimization, in response to the algorithm's running time reaching the first perturbation threshold, a local perturbation based on an adaptive large neighborhood search mechanism is introduced for the α wolf, and a step-by-step energy consumption optimization strategy is executed; and / or in the third stage of optimization, in response to the algorithm's running time reaching the second perturbation threshold, the adaptive large neighborhood search mechanism is spread to the β wolf and δ wolf for local perturbation, and a step-by-step energy consumption optimization strategy is executed.

[0036] Furthermore, the tiered energy consumption optimization strategy includes:

[0037] Step a': Decode the scheduling schemes corresponding to α wolf, β wolf and / or δ wolf, and generate the corresponding production plan table;

[0038] Step b': Calculate the subsequent backlash time and available tool backlash time for the current process that is not the final process and is not the minimum processing speed in the production schedule. If the subsequent backlash time and available tool backlash time are greater than the deceleration delay time of the current process, adjust the processing speed corresponding to the current process. The subsequent backlash time is the time interval between the end of the current process and the start of the next process on the machine tool of the current process.

[0039] Step c': After traversing all current processes that are not the final process and do not have the minimum processing speed, update the production plan table, encode the scheduling scheme corresponding to the updated production plan table, and restart the search.

[0040] In the above technical solution, by dynamically adjusting the processing speed to fill the machine tool idle time, energy consumption is reduced without increasing the delay, thus achieving a deep synergistic optimization of production efficiency and energy saving.

[0041] Furthermore, the adaptive large neighborhood search mechanism includes differentiated destruction and repair strategies based on processing sequence and machine tool allocation, wherein:

[0042] The destruction strategies include:

[0043] Destruction operators based on processing order include random destruction operators, scarce tool-oriented destruction operators, tool gap-based destruction operators, and tool load-based destruction operators;

[0044] Destruction operators based on machine tool allocation include dynamic idle ratio destruction operators, destruction operators based on release time intervals, destruction operators based on tool intervals, and destruction operators based on TWT.

[0045] The remediation strategies include:

[0046] Repair operators based on processing order include random insertion repair operators, forward insertion repair operators, and backward insertion repair operators;

[0047] Repair operators based on machine tool allocation include load balancing repair operators and energy efficiency optimization repair operators.

[0048] Furthermore, based on the multi-armed gambling machine model, the operator selection in the destruction and / or repair strategies is implemented, with the specific formula as follows:

[0049]

[0050] In the formula, scores g The cumulative score for operator g, attempts g is the number of times operator g is called, otal_attempts represents the total number of operator calls, and c is a hyperparameter for adjusting the exploration intensity.

[0051] In the above technical solution, the adaptive operator selection mechanism improves the efficiency of local search, avoids getting trapped in local optima, and enhances the algorithm's adaptability and robustness to complex scheduling problems.

[0052] Furthermore, the MOGWO-ALNS algorithm includes the following sub-steps:

[0053] Step a, initialize the wolf pack population, with each individual corresponding to a set of real-number codes for potential scheduling schemes;

[0054] Step b: Calculate the objective function value and construct an external archive. The objective function value includes the total weighted delay and total energy consumption.

[0055] Step c: Determine if the algorithm has reached the set maximum running time. If "no", continue iteratively to step d; if "yes", output the approximate Pareto optimal solution set saved in the external file and end the operation.

[0056] Step d: Calculate the attenuation factor and select α wolf, β wolf, and δ wolf from the external archive;

[0057] Step e: Determine the first perturbation threshold that the current running time is greater than or equal to the total time. If "yes", apply ALNS local perturbation to the α wolf and execute the stepped energy consumption optimization strategy, then proceed to step f; if "no", proceed directly to step g.

[0058] Step f: Determine if the current running time is greater than or equal to the second perturbation threshold of the total time. If yes, apply ALNS local perturbation to β wolves and δ wolves, and execute a stepped energy consumption optimization strategy, then proceed to step g; if no, proceed to step g.

[0059] Step g: Update the individual wolf pack positions. Based on the standard MOGWO mechanism and guided by α, β, and δ wolves, update the position of the entire wolf pack.

[0060] Step h: Recalculate the objective function value, update the external file, and return to execute step c.

[0061] In the above technical solution, a complete iterative process and archive maintenance mechanism ensure that the algorithm converges efficiently to the Pareto front, and the generated solution set has good distribution and convergence, providing decision-makers with a rich selection of optimization schemes.

[0062] Furthermore, the calculation formula for the destruction operator based on tool gaps is as follows:

[0063]

[0064] In the formula, K i Let jst be the number of operations performed on the i-th workpiece on machine tool m. m,i,k and JCT m,i,k-1 Let represent the start time of the k-th operation on the i-th workpiece on machine tool m and the completion time of the previous operation, respectively.

[0065] The release time interval of the destruction operator based on the release time interval is expressed as:

[0066]

[0067] In the formula, gst′ m,i , gct′ m,i-1 and R′ m,i These are the start time, completion time, and release time of the i-th workpiece on machine tool m, respectively.

[0068] In the above technical solution, by quantizing the gaps between tools and the release time, inefficient scheduling segments are specifically disrupted, guiding the algorithm to explore better solutions and improving the quality of the solution set and optimization efficiency.

[0069] Secondly, this application proposes a numerical control multi-objective optimization energy-saving system based on an improved wolf pack algorithm, the system comprising:

[0070] The model building module is configured to build a mixed-integer linear programming model for multi-objective flexible job shop scheduling. The model takes total weighted delay and total energy consumption as optimization objectives, and machine tool allocation, processing sequence, tool allocation and processing speed adjustability as decision variables.

[0071] The algorithm construction module is configured to build the MOGWO-ALNS algorithm for solving mixed integer linear programming models based on the MOGWO algorithm and the adaptive large neighborhood search mechanism. The MOGWO-ALNS algorithm constructs a three-stage collaborative optimization architecture through a dual threshold triggering mechanism.

[0072] The solution module is configured to solve mixed-integer linear programming models based on the MOGWO-ALNS algorithm, and obtain the Pareto optimal solution set of the mixed-integer linear programming model;

[0073] The decoding module is configured to decode the Pareto optimal solution set and generate a multi-objective balanced energy-saving scheduling scheme.

[0074] Compared with the prior art, the beneficial results of the present invention are as follows:

[0075] (1) This application constructs a “mixed integer linear programming model + MOGWO-ALNS hierarchical optimization architecture” to achieve coordinated optimization of total weighted delay and total energy consumption. Its core lies in the dual threshold triggering mechanism and external file maintenance strategy: initially, it relies on the MOGWO algorithm and combines a multi-rule collaborative initialization strategy based on problem characteristics (effectively improving the quality and diversity of the initial population, enhancing the distribution and convergence speed of the solution) to conduct global exploration; when the AT1 threshold is reached, the ALNS module based on reinforcement learning is introduced for the α wolf, and a step-by-step energy consumption optimization strategy is executed simultaneously to achieve rapid convergence of the solution and energy consumption balance; when the search process reaches the AT2 threshold, a three-level collaborative perturbation mechanism is enabled to extend the mixed perturbation strategy to the β and δ leader wolves, to achieve a dynamic balance between global exploration and local development, further improving the quality and distribution balance of the solution set, and ultimately making the convergence and distribution of the Pareto front better than traditional algorithms, solving the problem of “at the expense of one’s own interests” under multi-objective conflict.

[0076] (2) This application addresses the multi-dimensional constraints of machine tool allocation, tool sharing, and speed scaling in flexible workshops. The invention innovatively designs a differentiated ALNS destruction / repair strategy and a tiered energy consumption optimization logic: It accurately captures scheduling bottlenecks through tool gap destruction operators and release time gap operators, and dynamically selects the optimal operator combination using a multi-arm gambling machine model, thereby improving the algorithm's solution efficiency in small-batch customized production scenarios. Simultaneously, the tiered speed reduction strategy reduces machine tool energy consumption without increasing delays, breaking through the traditional perception that "high efficiency inevitably leads to high energy consumption."

[0077] (3) This application directly transforms the optimal solution of the algorithm into an executable production scheduling scheme through a closed-loop "encoding-decoding" design. Furthermore, the modular system architecture (model building, algorithm solving, and scheme generation) can be quickly deployed in the MES system of a CNC workshop. Experimental verification shows that this method can stably output high-quality solution sets in test instances of different scales, and is particularly suitable for high-end manufacturing scenarios with multiple product types and high energy consumption, such as aerospace and precision electronics, providing enterprises with a feasible technical solution to reduce production costs and achieve green manufacturing. Attached Figure Description

[0078] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments and, together with the description, serve to explain the principles of the invention. Many anticipated advantages of the embodiments and other embodiments of the invention will be readily recognized as they become better understood through reference to the following detailed description. Elements in the drawings are not necessarily to scale. The same reference numerals refer to corresponding similar parts.

[0079] Figure 1 This is a flowchart of a CNC multi-objective optimization energy-saving method based on an improved wolf pack algorithm according to an embodiment of this application;

[0080] Figure 2 This is a flowchart of a multi-objective optimization algorithm for a CNC multi-objective optimization energy-saving method based on an improved wolf pack algorithm, according to an embodiment of this application.

[0081] Figure 3 This is a schematic diagram of a stepped energy consumption optimization strategy for a multi-objective optimization energy-saving method for numerical control based on an improved wolf pack algorithm, according to an embodiment of this application.

[0082] Figure 4 This is a schematic diagram of the decoding mechanism of a CNC multi-objective optimization energy-saving method based on an improved wolf pack algorithm according to an embodiment of this application;

[0083] Figure 5 This is an example of encoding and decoding based on the processing sequence, processing speed, and machine tool allocation according to the embodiments of this application;

[0084] Figure 6 This is a trend analysis chart of the IGD index of each parameter in a CNC multi-objective optimization energy-saving method based on an improved wolf pack algorithm according to an embodiment of this application;

[0085] Figure 7 The box plots are obtained according to MOGWO-ALNS, A1, A2 and A3 of the embodiments of this application;

[0086] Figure 8 This is a framework diagram of a CNC multi-objective optimization energy-saving system based on an improved wolf pack algorithm according to an embodiment of this application; Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0088] refer to Figure 1 , Figure 1 The flowchart of the CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm of this application is shown in the figure. The method includes the following steps:

[0089] S101. Construct a mixed-integer linear programming model for multi-objective flexible workshop scheduling. The model takes total weighted delay and total energy consumption as optimization objectives, and machine tool allocation, processing sequence, tool allocation and processing speed adjustability as decision variables.

[0090] In some specific embodiments, specifically within the Multi-Objective Flexible Job Shop Scheduling Problem with Tool Resource Constraint (MOFJSP-TRC) implementation, the research object is a production workshop consisting of m identical parallel Computer Numerical Control (CNC) machines. The CNCs within the workshop share t different types of cutting tools, and each operation can be performed on any machine tool. The workshop needs to process n independent workpieces, each with a known release time and due date. The machining process for each workpiece is pre-designed, comprising multiple sequential operations. Each operation has specific tool requirements and selectable machining speeds. Selectable tools are given in sets, and machining time and power requirements vary depending on the selected machining speed. Idle energy consumption still occurs when the machine tools are idle, i.e., when there are no machining tasks. This energy consumption is calculated from the minimum idle power and idle time of the machine tools. Workpieces can be loaded into slots for machining when the machine tools are idle. To ensure successful workpiece machining, the order of operations must be strictly followed. Simultaneously, the workpiece will wait on the machine tool until at least one tool meeting the requirements of the current operation is available. Specific assumptions include: (1) Since the CNC machining center is fully automatic and the production process is precise, uncertainty is not considered; (2) The importance of each task is different; (3) At a given machining speed, the processing time of each operation is consistent across all machine tools; (4) Regardless of which tool of the same type is selected, the processing time of each operation remains unchanged at a given machining speed; (5) Only one workpiece can be processed on one machine tool at a time; (6) Each tool can only be used for one operation at a time during the machining process; (7) Once an operation on a workpiece begins in the CNC machining center, it cannot be interrupted; (8) Once a workpiece begins machining on a machine tool, it cannot be unloaded until all operations are completed; (9) Since the transition time between different machine tools is short and negligible relative to the machining time, the transport time and setup time are also negligible; (10) Waiting time is allowed between operations; (11) All machine tools start at time 0. If there is no ongoing task on a machine tool, it will enter standby mode and shut down immediately after completing the last task. In this production environment, the goal is to develop a production plan that determines the processing sequence of each workpiece, machine tool allocation, cutting tools used for each operation, and processing speed, thereby achieving a synergistic minimization of total weighted tardiness (TWT) and total energy consumption (TEC).

[0091] First, commonly used notation in Mixed Integer Linear Programming (MILP) is given. The decision variables used in MILP include:

[0092] (1)x i,i′,m The binary variable is equal to 1 only when workpiece i is processed on machine tool m and then workpiece i′ is processed; otherwise, it is 0.

[0093] (2)y i,m If workpiece i is assigned to machine tool m, the binary variable is 1; otherwise, it is 0.

[0094] (3)y i′,m If workpiece i′ is assigned to machine tool m, then the binary variable is 1; otherwise, it is 0.

[0095] (4)st i,k The non-negative continuous variable is the start time of the k-th operation of workpiece i;

[0096] (5) The non-negative continuous variable is the workpiece i at the Kth position. i The start time of the last operation;

[0097] (6)st i,k-1 The non-negative continuous variable is the start time of the (k-1)th operation of workpiece i;

[0098] (7)z m,i,k,s If workpiece i is processed on machine tool m at speed s during the kth operation, then the binary variable is 1; otherwise, it is 0.

[0099] (8) Workpiece i, Kth i If the last operation is performed on machine tool m at speed s, then the binary variable is 1; otherwise, it is 0.

[0100] (9)β 0,e,t The binary variable β is only considered when tool t is used to process virtual operation 0 followed by operation e. 0,e,t Only if it equals 1, otherwise it equals 0;

[0101] (10)β e,e′,t The binary variable β is only considered when the tool t is used to process operation e followed by operation e′. e,e′,t Only if it equals 1, otherwise it equals 0;

[0102] (11)γ e,t If the operation e is performed using tool t, the binary variable is equal to 1; otherwise, it is 0.

[0103] (12)γ e′,t If the operation e′ is processed using the tool t, the binary variable is equal to 1; otherwise, it is 0.

[0104] (13)st′ e The non-negative continuous variable is the start time of operation e, where e∈KN;

[0105] (14)st′ e′ The non-negative continuous variable is the start time of operation e′, where e∈KN;

[0106] (15)mc m The non-negative continuous variable is the end time of machine tool m;

[0107] (16)wt i Weighted delay of workpiece i;

[0108] (17)ep m Total energy consumption of machine tool m during operation;

[0109] (18)ei m Total energy consumption of machine tool m in idle state;

[0110] The parameters involved in MILP include:

[0111] (19) N: Set of workpieces;

[0112] (20) N′: a set of workpiece indicators containing a virtual job 0, i.e., N′=N∪{0};

[0113] (21)NC: Numerical control machine tool set;

[0114] (22)K i The number of operations required for workpiece i, i.e., the number of times workpiece i needs to go through K. i Step, i∈N;

[0115] (23)O i The fixed operation sequence for workpiece i means that the operations must be performed in this order, i∈N, O i = (1,2,...,K) i );

[0116] (24)R i : Release time of workpiece i, i.e. the earliest time when processing can begin, where i∈N;

[0117] (25)D i : The delivery date of workpiece i, i.e. the deadline for completing processing, where i∈N;

[0118] (26)W i The weight (importance) of workpiece i, i∈N;

[0119] (27)S i,k: The set of selectable processing speeds for workpiece i in the k-th operation, i∈N, k∈O i ;

[0120] (28) Workpiece i, Kth i The set of selectable processing speeds for the last operation, i∈N;

[0121] (29)P i,k,s : The time required for workpiece i to be processed in the k-th operation at speed s, where i∈N, k∈O i ;

[0122] (30) Workpiece i, Kth i The time required for the last operation to be processed at speed s, where i∈N; (31)KN: the set of all operations for all workpieces;

[0123] (32) KN′: The set of all operations of all artifacts containing virtual operation 0, i.e., KN′=KN∪{0};

[0124] (33)TL: Toolkit;

[0125] (34)TS e The set of tools that can be used to complete operation e according to process requirements, where e∈KN;

[0126] (35)P′ m,e,s : The time required for operation e to perform machining at speed s on machine tool m, where e∈KN, m∈NC;

[0127] (36)E i,k,s : Power required (energy consumption per unit time) for processing workpiece i in the k-th operation at speed s, where i∈N, k∈O i s∈ i,k ;

[0128] (37)E: Power of the machine tool in idle state;

[0129] (38)JK i,k The index of the k-th operation on workpiece i, i.e. Where i∈N, k∈O i ;

[0130] (39)B: a binary set, B = {0, 1};

[0131] (40)M: A large positive number in the form of big-M.

[0132] Based on these symbols, the mixed-integer programming model of MOFJSP-TRC can be expressed as follows:

[0133] min∑ i∈N wt i (1)

[0134] min∑ m∈NC (ep m +hey m ) (2)

[0135]

[0136] ∑ i′∈N′ x i,i′,m =y i,m ,i∈N′,m∈NC (8)

[0137] ∑ i∈N′,i≠i′ x i,i′,m =y i′,m ,i′∈N′,m∈NC (9)

[0138] ∑ m∈NC yes i,m =1,i∈N (10)

[0139] ∑ m∈NC yes i,m =|NC|,i=0 (11)

[0140]

[0141] st i,k-1 +P i,k-1,s ≤st i,k ,k∈2,3,...,K i ,i∈N (13)

[0142] st i,1 +P i,1,s ≤st i′,1 +M×(2-y i,m -x 0,i,m ),m∈NC,i,i′∈N,i≠i′ (14)

[0143] ∑ e∈KN′,e≠e′ β e,e′,t =γ e′,t ,e′∈KN′,t∈TL (15)

[0144] ∑ e′∈KN′,e≠e′ β e,e′,t =γ e,t ,e∈KN′,t∈TL (16)

[0145]

[0146] ∑ t∈TL γe,t =1,e∈KN (18)

[0147] ∑ t∈TL γ e,t =|TL|,e=0 (19)

[0148] st′ e +P′ m,e,s ≤st′ e′ + M × (1 − β e,e′,t ),e,e′∈KN,e≠e′,t∈TL (20)

[0149] st′ e +P′ m,e,s ≤st′ e′ +M ×(2−γ e′,t -β 0,e,t ),e,e′∈KN,e≠e′,t∈TL (21)

[0150] st′ j =st i,k ,j=JK i,k ,i∈N,k∈O i (22)

[0151] P′ m,j,s =P i,k,s ,j=JK i,k ,i∈N,k∈O i ,s∈S i,k (23)

[0152]

[0153]

[0154] x i,i′,m ∈B,i∈N′,i′∈N′,m∈NC (26)

[0155] y i,m ∈B,i∈N′,m∈NC (27)

[0156] z m,i,k,s ∈B,m∈NC,i∈N,k∈O i ,s∈S i,k (28)

[0157] st i,k ≥R i ,i∈N,k∈O i (29)

[0158] β e,e′,t ∈B,e,e′∈KN′,t∈TL (30)

[0159] γ e,t ∈B,e∈KN′,t∈TL (31)

[0160] st′ e ≥0, e∈KN (32)

[0161] wt i ≥0, i∈N (33)

[0162] ep m ≥0, m∈NC (34)

[0163] ei m ≥0, m∈NC (35)

[0164] In the formula: (1) represents the objective function of minimizing the total weighted delay. (2) represents the objective function of minimizing the total energy consumption; constraint (3) describes wt i The relationship between the weighted delay times of each workpiece and the workpiece; constraints (4) and (5) describe ep m and ei m The relationship between the machine tool in the running state and the idle state; constraints (6) and (7) represent the machine tool shutdown time; M represents a large positive number in the big-M form; y i,m This indicates that if workpiece i is assigned to machine tool m, the binary variable is 1; otherwise, it is 0. i,i′,m The binary variable is equal to 1 only when workpiece i is processed on machine tool m and then workpiece i′ is processed; otherwise, it is 0, i′∈N, i′≠i; constraints (8) and (9) represent the relationship between variables; N′ represents the set of workpiece indices containing a virtual job 0, i.e., N′=N∪{0}, i∈N′; y i′,m If workpiece i′ is assigned to machine tool m, the binary variable is 1; otherwise, it is 0. Constraint (10) ensures that each job is assigned to only one machine tool. Constraint (11) assigns virtual job 0 to each machine tool. In constraint (12), the completion time of the last operation of a workpiece must be less than or equal to the start time of the first operation of the next workpiece. i′,1 The non-negative continuous variable represents the start time of the first operation of workpiece i′; constraint (13) indicates that the processing sequence of each workpiece is fixed, st i,k-1 P represents the start time of the (k-1)th operation of workpiece i, which is a non-negative continuous variable. i,k-1,sLet represent the time required for the (k-1)th operation of workpiece i to be processed at speed s; constraint (14) indicates that the first operation of the workpiece processed after the virtual workpiece has the earliest completion time; constraints (15) and (16) indicate the relationship between variables; KN′ represents the set of all operations of all workpieces containing virtual operation 0, i.e., KN′=KN∪{0}, KN represents the set of all operations of all workpieces, e′ represents the operation contained in KN′, e∈KN′, e≠e′, e′∈KN′; β e,e′,t This indicates that the binary variable β only occurs when the tool t is used to process operation e, followed by operation e′. e,e′,t It equals 1 only if it is γ, otherwise it is 0; e′,t This means that if the operation e′ is processed using tool t, the binary variable is equal to 1; otherwise, it is 0. e,t This means that if tool t is used to process operation e, the binary variable is equal to 1, otherwise it is 0; constraint (17) means that each operation is processed using only one of the same tools; TS e This represents the set of tools that can be used to complete operation e according to the process requirements; constraint (18) indicates that only one tool is selected for each operation; constraint (19) indicates that each tool processes one virtual operation 0; constraint (20) indicates that for each tool, the completion time of the previous operation is less than or equal to the start time of the next operation; st′ e P′ represents the start time of operation e, which is a non-negative continuous variable. m,e,s This represents the time required for operation e to perform machining at speed s on machine tool m; st′ e′ Let β represent the start time of operation e′, which is a non-negative continuous variable; constraint (21) ensures that the operation following the virtual operation has the minimum completion time; 0,4,t This indicates that the binary variable β only occurs when tool t processes virtual operation 0 followed by operation e. 0,e,t Only equals 1, otherwise equals 0; constraints (22) to (25) represent the relationship between two variables; st′ j This indicates the start time of the operation at index j, where j = JK. i,k i∈N, k∈O i ;st i,k Let j represent the start time of the k-th operation of workpiece i, which is a non-negative continuous variable; j represents the index of the k-th operation of workpiece i in KN, where j = JK. i,k i∈N, k∈O i JK i,k P′ represents the index of the k-th operation on workpiece i; m,j,s Let represent the time required for the operation at index j to be processed at speed s on machine tool m; constraints (26) to (35) define the range of values ​​for each variable; B represents a binary set, B = {0, 1}; R i This indicates the release time of workpiece i.

[0165] S102. Based on the MOGWO algorithm and the adaptive large neighborhood search mechanism, the MOGWO-ALNS algorithm for solving mixed integer linear programming models is constructed. The MOGWO-ALNS algorithm constructs a three-stage collaborative optimization architecture through a dual threshold triggering mechanism.

[0166] In some specific embodiments, the three-stage collaborative optimization architecture of the MOGWO-ALNS algorithm includes:

[0167] In the first stage, heuristic rules and random strategies are used to generate an initial population that covers a wide range of the solution space, and the standard gray wolf optimization algorithm is used to explore the Pareto frontier.

[0168] In the second stage of optimization, in response to the algorithm running time reaching the first perturbation threshold, a local perturbation based on an adaptive large neighborhood search mechanism is introduced for the α wolf.

[0169] In the third stage of optimization, in response to the algorithm's running time reaching the second perturbation threshold, the adaptive large neighborhood search mechanism is diffused to β wolves and δ wolves for local perturbation.

[0170] Among them, the Multi-Objective Gray Wolf Optimization Algorithm (MOGWO) is an intelligent optimization method inspired by the hierarchical structure and cooperative hunting behavior of gray wolves, capable of effectively solving multi-objective optimization problems. Its core mechanisms include: Social Hierarchy: MOGWO constructs a hierarchical framework using four types of gray wolves: α, β, δ, and ω. α wolves represent the optimal solution for the current population, guiding the search direction; β and δ wolves represent the second-best and third-best individuals, respectively, assisting in guiding and improving the diversity and robustness of the population; the remaining ω wolves complete the global exploration of the search space under the guidance of the other three. Cooperative Hunting Mechanism: The algorithm dynamically updates individual positions by simulating the encirclement, tracking, and hunting behaviors of gray wolves. Vector coefficients are introduced during the update process. and To adjust the search intensity and direction, The value decreases as the iteration progresses, achieving a smooth transition from global exploration to local development. Individual positions are updated comprehensively based on the guiding information from α, β, and δ, driving the population to gradually converge to the Pareto front. External archive mechanism: An external archive is introduced to preserve historical non-dominated solutions, preventing the loss of high-quality solutions. The archive uses non-dominated sorting to select advantageous solutions; if the capacity limit is exceeded, individuals in dense regions are deleted according to the crowding distance criterion to maintain the diversity of the solution set and its boundary expansion capability. Leader selection strategy: α, β, and δ leaders are preferentially selected from the sparsest non-dominated solutions in the external archive, guiding the search to expand towards sparse regions of the solution space, improving the coverage and balance of the solution set. The multi-objective gray wolf optimization algorithm uses a one-dimensional real-number encoded sequence as the position vector of individual wolves. It achieves optimization by simulating the social hierarchy and hunting behavior of the gray wolf pack, specifically including:

[0171] Step 1: Initialize the wolf pack population, with each individual corresponding to a set of real-number codes for a potential scheduling scheme;

[0172] Step two: Calculate the fitness value of individuals based on the dual objectives of total weighted delay and total energy consumption. Then, determine the α, β, and δ wolves in the wolf pack (corresponding to the current optimal, suboptimal, and near-optimal solutions, respectively) through fast non-dominated sorting and crowding calculation. The remaining individuals (ω wolves) update their own codes by tracking the positions of the α, β, and δ wolves. This updated code represents a one-dimensional real-number sequence of scheduling schemes, containing decision information on machine tool allocation, processing sequence, and processing speed. The update formula is: in, This represents the positional difference vector between wolf ω and wolves α, β, or δ. The calculation result is a set of non-negative real numbers, which corresponds to the encoding level. Each component reflects the degree of difference between a certain decision dimension (such as the processing sequence, processing speed, and machine tool allocation of a certain process) in the ω-wolf encoding and the better solution encoding, providing a quantitative basis for subsequent adjustments; The position vectors representing α, β, or δ wolves, i.e., the one-dimensional real-valued encoded sequence corresponding to the known better solution in the current iteration, have an encoding structure similar to... Consistent, including scheduling decision information that has passed the fitness assessment (better total weighted delay and total energy consumption); Let ω represent the position vector of the wolf at the current iteration time t, corresponding to a one-dimensional real-number encoded sequence of potential scheduling schemes. The integer part, first decimal place, and second decimal place of each real number in the sequence carry decision information regarding processing order, processing speed, and machine tool allocation, respectively. This represents the updated position vector of ω wolf, i.e., the new one-dimensional real number encoding sequence. It adjusts each real number in the original encoding sequence (such as correcting the decimal part corresponding to the processing speed and the second decimal part corresponding to the machine tool allocation), so that the new encoding moves closer to the decision information of the better solution, thereby iteratively optimizing the scheduling scheme. and This represents a coefficient vector with dimensions matching the length of the real-number encoded sequence, where... The component values ​​decrease linearly from 2 to 0, used to control the direction of ω wolf. By getting closer, global exploration can be achieved. When the absolute value is large) and partial development ( Equilibrium when the absolute value is small The value decreases as the iteration progresses, achieving a smooth transition from global exploration to local development; The components are randomly generated in the interval [0,2] to introduce randomness and prevent the algorithm from getting stuck in local optima. Its randomness promotes the exploration of the solution space by adjusting the weights of each decision dimension in the real number encoding.

[0173] Step 3: After a preset number of iterations, select the Pareto optimal solution set from the non-dominated solution set of the final population.

[0174] The first stage includes: using heuristic rules to generate a guiding subpopulation for minimizing the total weighted delay and a subpopulation for minimizing the total energy consumption, and using a random initialization strategy to generate a wide range of individuals covering the solution space;

[0175] Heuristic rules include the earliest due date rule, the shortest processing time rule, the weighted shortest processing time rule, the shortest completion time rule, the apparent lateness cost rule, the minimum relaxation rule, the maximum processing speed priority strategy, and the lowest energy consumption priority strategy, among which:

[0176] The earliest due date rule prioritizes tasks with the earliest due date.

[0177] The shortest processing time rule prioritizes tasks with the shortest processing time.

[0178] The weighted shortest processing time rule prioritizes tasks with the longest weighted processing time.

[0179] The shortest completion time rule prioritizes tasks with the closest due date.

[0180] The apparent lateness cost rule prioritizes tasks with the highest delay costs and urgency, and its expression is: In the formula, D i P represents the delivery date of workpiece i. i W represents the total machining time for all operations on workpiece i at constant speed. i Let represent the weight of workpiece i, t′ represent the earliest start time of the current workpiece i, and F represent the scaling parameter. This indicates the average processing time for the remaining workpieces.

[0181] The minimum relaxation rule prioritizes tasks with the shortest relaxation time, and its expression is: max(0, D) i -P i -t′);

[0182] The maximum processing speed priority strategy prioritizes the fastest processing speed.

[0183] The lowest energy consumption priority strategy prioritizes the processing speed with the lowest energy consumption, and its expression is P. i,k / S i,k ×E i,k In the formula, P i,k S represents the time required for the k-th operation of workpiece i. i,k E represents the set of selectable processing speeds for workpiece i during the k-th operation. i,k This represents the power required for the k-th operation of workpiece i.

[0184] Specifically, the diversity of the initial population and the quality of the solutions have a significant impact on the algorithm. This application designs a multi-rule collaborative initialization strategy, aiming to generate structurally reasonable and representative initial solutions by combining problem characteristics, thereby improving the convergence speed of the algorithm and reducing computational resource consumption. This strategy introduces a heuristic rule-based initialization method to construct a subpopulation in the region close to the lower bound of the optimization objective, thus effectively compressing the search space and improving solution efficiency. The specific initialization rules used are shown in Table 1. Simultaneously, a random initialization strategy is employed to generate a wide range of individuals covering the solution space, providing diversity support for subsequent evolution and enhancing the algorithm's ability to explore non-dominated frontiers.

[0185] Table 1 Initialization Rules

[0186]

[0187] Among them, D i For the delivery date of workpiece i, P i W represents the total machining time for workpiece i under constant speed operation. i Let be the weight of workpiece i, t′ be the earliest start time of current workpiece i, and F be the scaling parameter. S is the average processing time for the remaining workpieces. i,k P is the set of selectable processing speeds for the k-th operation of workpiece i. i,k E is the time required for the k-th operation of workpiece i. i,kLet be the power required for the k-th operation of workpiece i. First, based on the Earliest Due Date (EDD), Shortest Processing Time (SPT), Weighted Shortest Processing Time (WSPT), Least Flow Time (LFT), Apparent Tardiness Cost (ATC), and Minimum Slack (MS) rules, a guided subpopulation is generated, targeting the minimization of Total Weighted Tardiness (TWT), in conjunction with the Fastest Speed ​​Priority (FSP) strategy. Subsequently, using the same sorting rule combination and introducing the Lowest Energy Consumption (LEC) strategy, a subpopulation is constructed targeting the minimization of Total Energy Consumption (TEC), thus ensuring the quality of initial solution coverage under different objective orientations. Finally, by randomly initializing and supplementing the remaining individuals, we ensure that the population has sufficient structural diversity in the initial stage, thereby improving the algorithm's ability to explore non-dominated frontiers and its global search stability.

[0188] Preferably, in the second stage of optimization, in response to the algorithm running time reaching the first perturbation threshold, a local perturbation based on an adaptive large neighborhood search mechanism is introduced for the α wolf, and a step-by-step energy consumption optimization strategy is executed; and / or in the third stage of optimization, in response to the algorithm running time reaching the second perturbation threshold, the adaptive large neighborhood search mechanism is spread to the β wolf and δ wolf for local perturbation, and a step-by-step energy consumption optimization strategy is executed.

[0189] Specifically, the tiered energy consumption optimization strategy includes:

[0190] Step a': Decode the scheduling schemes corresponding to α wolf, β wolf and / or δ wolf, and generate the corresponding production plan table;

[0191] Step b': Calculate the subsequent backlash time and available tool backlash time for the current process that is not the final process and is not the minimum processing speed in the production schedule. If the subsequent backlash time and available tool backlash time are greater than the deceleration delay time of the current process, adjust the processing speed corresponding to the current process. The subsequent backlash time is the time interval between the end of the current process and the start of the next process on the machine tool of the current process.

[0192] Step c': After traversing all current processes that are not the final process and do not have the minimum processing speed, update the production plan table, encode the scheduling scheme corresponding to the updated production plan table, and restart the search.

[0193] S103. Solve the mixed-integer linear programming model based on the MOGWO-ALNS algorithm to obtain the Pareto optimal solution set of the mixed-integer linear programming model.

[0194] In some specific embodiments, a three-stage collaborative optimization architecture algorithm is constructed by using MOGWO as the basic framework and integrating an adaptive large-scale neighborhood search mechanism. (Reference) Figure 2 , Figure 2 This paper illustrates a flowchart of a multi-objective optimization algorithm for CNC multi-objective optimization energy-saving methods based on an improved wolf pack algorithm, according to an embodiment of this application. As shown, the algorithm first employs a multi-rule collaborative initialization strategy to generate an initial population and constructs an external archive based on the Pareto front. It then selects three types of leader wolves (α, β, and δ) from the archive using a roulette wheel mechanism. In the initial stage, the algorithm performs global exploration according to the MOGWO standard position update rule. When the iteration progress reaches the primary perturbation threshold (AT1), a local perturbation mechanism based on an adaptive large neighborhood search (ALNS) algorithm is introduced for the α leader wolf. A multi-armed slot machine model based on upper confidence bounds (UCB) is used to dynamically adjust the selection probability of destruction and repair operators. Simultaneously, combined with an energy-saving strategy, energy consumption is optimized in a stepwise manner by reducing processing speed. When the iteration progress reaches the deep perturbation threshold (AT2), the hybrid perturbation mechanism is further extended to the β and δ leader wolves, forming a three-level collaborative perturbation architecture to achieve a dynamic balance between global exploration and local development. After reaching the preset maximum iteration time, the algorithm outputs an approximate Pareto optimal solution set. The above algorithm specifically includes the following steps:

[0195] Step 201: Generate the initial population. Randomly create a group of wolves (solutions). Each wolf is represented by a one-dimensional real number encoding of a complete scheduling scheme, including decision variables such as process sequence, machine tool allocation, and processing speed.

[0196] Step 202: Calculate the objective function value and construct the external archive. Initialize the external archive by creating an empty set to store non-dominated solutions (Pareto optimal solutions) found during the search process. Calculate the objective values: for each wolf (scheduling scheme), calculate its total weighted delay time (TWT) and total energy consumption (TEC) as two objective function values.

[0197] Step 203, Update the archive. Add non-dominated solutions from the current population to the archive and remove old solutions dominated by the new solutions, maintaining the non-dominance of all solutions in the archive.

[0198] Step 204: Determine if the algorithm has reached the set maximum running time. If "No", continue iteratively to step 205; if "Yes", output the approximate Pareto optimal solution set saved in the external file and end the operation.

[0199] Step 205: Calculate the attenuation factor. Dynamically adjust control parameters (such as those in MOGWO). The coefficients (indicate that the algorithm is biased towards global exploration in the early stages and towards local development in the later stages) make the algorithm more inclined towards global exploration in the early stages and local development in the later stages.

[0200] Step 206: Select α wolf, β wolf, and δ wolf. Three leader wolves (α, β, δ) are selected from the external archives using a roulette wheel mechanism, representing the currently found optimal, suboptimal, and third-best solutions.

[0201] Step 207: Determine the first perturbation threshold (AT1) where the current running time is greater than or equal to the total time. If "yes", proceed to step 208; if "no", proceed to step 209. Check if the primary perturbation threshold has been reached: when the iteration time exceeds the proportion of AT1 of the total time, trigger enhanced optimization for the α wolf.

[0202] Step 208: After applying ALNS local perturbation (fine optimization of the current optimal solution) to the α wolf, proceed to step 211. Apply adaptive large neighborhood search to the α wolf: use a destruction-repair mechanism (such as random process exchange, machine tool reallocation) to locally perturb the current optimal solution and explore its neighborhood. At the same time, implement a stepped energy consumption optimization strategy for the α wolf: without increasing TWT, try to reduce the processing speed to reduce energy consumption and fill the machine tool idle time.

[0203] Step 209: If the current running time is greater than or equal to the second perturbation threshold (AT2) of the total time, proceed to step 210 if “yes”; otherwise, proceed to step 211.

[0204] Step 210: After applying ALNS local perturbation to β and δ wolves, proceed to step k. Apply adaptive large neighborhood search to β and δ wolves: expand the range of local perturbation and enhance the algorithm's ability to escape local optima. At the same time, implement a stepped energy consumption optimization strategy for β and δ wolves: further optimize the energy consumption performance of suboptimal solutions.

[0205] Specifically, a set of local search operators was designed around the two sub-problems of processing sequence and machine tool allocation, and a dual-threshold triggering mechanism was introduced: when the search iterates to the first perturbation threshold AT1, for the α wolf individual, the ALNS algorithm combined with the multi-armed gambling machine model is called and a step-by-step energy consumption optimization strategy is executed simultaneously to achieve adaptive reinforcement search of the local neighborhood; when the search reaches a higher second perturbation threshold AT2, a three-level cooperative perturbation mechanism is further triggered to extend ALNS to β and δ wolf individuals, and the global search depth and solution space exploration breadth are improved by leveraging the multi-dimensional cooperative evolution of elite solutions.

[0206] The destruction operator achieves deconstruction and recombination by removing parts of the current solution. Its core objective is to overcome the structural constraints of local optima and expand the large-scale neighborhood search capability. This application addresses the two-dimensional characteristics of the flexible job shop scheduling problem by constructing differentiated destruction strategies from two levels: processing sequence and machine tool allocation.

[0207] Destruction operators based on processing order include random destruction operators, scarce tool-oriented destruction operators, tool gap-based destruction operators, and tool load-based destruction operators:

[0208] By randomly destroying operators and randomly selecting q operations to add to the deletion set, the diversity of the search is enhanced by introducing random perturbations, which effectively avoids premature convergence of the algorithm.

[0209] The scarce tool-oriented destruction operator prioritizes the deletion of operations that use the scarcest tools, alleviating critical resource bottlenecks and reducing waiting issues caused by tool conflicts during the refactoring phase.

[0210] Based on the tool gap destruction operator, the q workpieces with the largest machining gaps due to tool occupancy are selected. The gap is defined as the cumulative time a workpiece waits for the tool to complete. Operations with severe gap occupancy are prioritized for removal to improve the overall scheduling efficiency. The formula for calculating the gap of the i-th workpiece on machine tool m due to tool waiting is:

[0211]

[0212] In the formula, K i Let jst be the number of operations performed on the i-th workpiece on machine tool m. m,i,k and JCT m,i,k-1 Let represent the start time of the k-th operation on the i-th workpiece on machine tool m and the completion time of the previous operation, respectively.

[0213] Tool load-based destruction operators selectively delete certain artifacts based on the tool's load, reducing resource concentration and improving the balance of tool usage. First, we determine the number of artifacts to be deleted from each tool using a formula. The result is obtained, where q is the number of workpieces to be deleted, and N is the set of workpieces. t It is the set of workpieces processed by tool t. Then, it is randomly selected from the workpieces processed by tool t. One workpiece.

[0214] Destruction operators based on machine tool allocation include dynamic idle ratio destruction operators, destruction operators based on release time intervals, destruction operators based on tool intervals, and destruction operators based on TWT:

[0215] The dynamic idle ratio destruction operator prioritizes removing workpieces from machine tools with high idle rates based on the machine tool idle time ratio (idle time / total running time), thereby improving equipment resource utilization.

[0216] The destruction operator based on the release time interval deletes q jobs whose machine tool waiting time is too long due to differences in workpiece release time, thereby reducing resource idle time and improving scheduling efficiency. The release time interval can be represented as:

[0217]

[0218] In the formula, gst′ m,i , gct′ m,i-1 and R′ m,i These are the start time, completion time, and release time of the i-th workpiece on machine tool m, respectively.

[0219] The tool gap-based destruction operator is similar to the tool gap destruction operator in the processing sequence dimension. It deletes operations that have a significant impact on resource scheduling based on the waiting time caused by tool conflicts.

[0220] The destruction operator based on TWT prioritizes the deletion of the q jobs that contribute the most to the total weighted delay (TWT) in order to reduce the objective function value and improve the quality of the solution.

[0221] The repair operator is used to re-insert deleted operations into the scheduling sequence to reconstruct the solution. This application designs the following repair strategy from the perspectives of processing sequence and machine tool allocation:

[0222] Repair operators based on processing order include random insertion repair operators, forward insertion repair operators, and backward insertion repair operators:

[0223] A random insertion repair operator randomly inserts q jobs from the deletion set into arbitrary positions in the scheduling sequence. This process is executed independently multiple times, ultimately retaining the optimal solution to enhance solution diversity.

[0224] The forward insertion repair operator prioritizes inserting the job to be repaired at the beginning of the sequence, reducing the waiting time of critical jobs and machine idle time, thereby reducing the total weighted delay and standby power consumption.

[0225] The backward insertion repair operator prioritizes inserting jobs at the end of the scheduling sequence, effectively alleviating resource congestion at the front end and improving the slackness and robustness of the scheduling scheme.

[0226] Repair operators based on machine tool allocation include load balancing repair operators and energy efficiency optimization repair operators:

[0227] The load balancing repair operator allocates workpieces to the feasible machine tool with the lowest current load, thereby achieving resource load balancing and optimizing scheduling performance and total weighted delay index.

[0228] The energy efficiency optimization and repair operator allocates workpieces to the feasible machine tool with the highest current load, centralizes resource scheduling to reduce idle periods, and improves energy efficiency.

[0229] Furthermore, to enable adaptive adjustment of the operator selection process, this application introduces a dynamic selection strategy based on the Multi-Armed Bandit (MAB) model, modeling the operator selection problem as a profit maximization problem. This strategy employs an Upper Confidence Bound (UCB) mechanism, which, while balancing exploration and development, tends to select operators with better historical performance, thereby improving global optimization capability and search efficiency. Specifically, the MAB model first guides the selection of operators related to processing sequence and machine tool allocation, and then selects corresponding destruction and repair operators. The performance of each operator is scored through a reward mechanism. Initially, all operators have a score of 0; in each iteration, if a selected operator can generate a candidate solution not dominated by an archived solution, its score will increase by 1. The UCB value of an operator is calculated based on the cumulative score and the number of calls, as follows:

[0230]

[0231] Among them, scores g The cumulative score for operator g, attempts g Let be the number of times operator g is called, otal_attempts represent the total number of operator calls, and c is a hyperparameter that adjusts the exploration intensity. For operators that have not yet been called, the algorithm will prioritize allocating selection opportunities to ensure sufficient exploration of the search space. Ultimately, operators with higher UCB values ​​will be selected to participate in subsequent searches, thereby effectively guiding the search process towards a better solution domain.

[0232] Specifically, the ALNS algorithm process is as follows:

[0233] Step A': Initialize the call count and score of each selection operator, destruction operator, and repair operator to 0, and initialize the total call count to 0.

[0234] Step B': If the stopping condition is not met, repeat the following steps in a loop:

[0235] Based on the UCB (Upper Confidence Bound) multi-armed gambling machine strategy, a selection operator is selected, and the number of calls to the selection operator and the total number of calls are updated;

[0236] Similarly, based on the UCB multi-armed gambling machine strategy, a destruction operator D is selected.- and a repair operator R + Update the call counts of these two operators;

[0237] Apply the selected destruction operator D to the current solution - and repair operator R + This leads to a new solution;

[0238] If the new solution is not dominated by a solution in the external file, the current solution is replaced with the new solution, the external file is updated, and the scores of the selection operator, destruction operator, and repair operator are increased.

[0239] Regardless of whether the new solution is better, the score of the selection operator is increased.

[0240] Step C': When the stopping condition is met, return the optimized solution.

[0241] Specifically, to further reduce Total Energy Consumption (TEC), this application proposes a rate-adjustment-based energy-saving strategy, namely a stepped energy consumption optimization strategy, which aims to optimize energy consumption by combining the resource constraint characteristics of the TRC-MOFJSP problem. In this problem, machining operations are not only limited by machine tool availability but also by the synchronous constraint of tool resources. If the tool is temporarily unavailable, even if the preceding operation is completed at extremely high speed, the subsequent operation cannot be connected in time, resulting in the machine tool being in standby mode and generating double energy consumption losses: on the one hand, high-speed machining itself brings high operating energy consumption; on the other hand, the subsequent idle waiting also generates significant standby energy consumption. To alleviate the above-mentioned energy consumption superposition problem, this application proposes to moderately reduce the machining rate while keeping the total weighted delay time (TWT) unchanged, so as to extend the machining time of the current operation, thereby shortening the machine tool idle time between it and its subsequent operations, and ultimately reducing operating and standby energy consumption in a coordinated manner. This strategy only involves adjusting the machining rate, while the operation sequence and machine tool allocation remain unchanged, so TEC can be effectively optimized without sacrificing timeliness. Implementing this strategy requires meeting the following three constraints: (1) The current process speed is not at its lowest level (i.e., S). i,k >1); (2) The time gap between the current process and its subsequent processes is greater than the processing time delay caused by the speed adjustment; (3) The available gap of the tool currently used also meets the above time delay requirements.

[0242] refer to Figure 3 , Figure 3 This diagram illustrates a stepped energy consumption optimization strategy for a multi-objective optimization energy-saving method for CNC machining based on an improved wolf pack algorithm, according to an embodiment of this application. Figure 3As shown, the complexity of this strategy lies in the collaborative optimization of tool resources. In practice, three key time parameters need to be calculated simultaneously: the subsequent operation backhaul time (the time interval between the end of the current operation and the start of the next operation) and the available tool backhaul time (the time interval between the release of the tool in the current operation and its next invocation). Rate downgrading is only performed when both meet threshold conditions. By traversing all non-terminal operations (i.e., the last operation that is not the final job), this mechanism can systematically eliminate potential machine tool idle time. Figure 3 By comparing upper and lower Gantt charts, the implementation process of the energy-saving strategy is visually demonstrated. Before optimization, the 2.1 process of Job2 was completed early due to high-speed machining, causing machine tool M2 and associated tools (such as T4) to have idle periods (shown in red boxes), resulting in a double waste of energy consumption from high-speed machining and idle standby. Under the triple constraints of "the current process machining rate is not at the lowest level, the process gap and the available tool gap are greater than the machining time delay caused by the rate adjustment", a speed reduction operation is performed on this process to extend its machining time (the orange block becomes longer), filling the original idle period. After optimization, the idle of machine tool M2 and tool T4 is eliminated, the standby energy consumption is reduced, and since subsequent processes are not delayed, the total weighted delay time (TWT) remains unchanged, achieving a reduction in total energy consumption (TEC). This verifies that the energy-saving strategy based on rate adjustment can effectively optimize operating and standby energy consumption while ensuring timeliness.

[0243] Step 211: Update the individual wolf pack positions. Based on the standard MOGWO mechanism and guided by α, β, and δ wolves, update the overall wolf pack position (solution encoding).

[0244] Step 212: Recalculate the objective function value, update the external archive, and return to step 204. Evaluate the TWT and TEC of the updated solution, add the new non-dominated solution to the archive, and remove the dominated old solution.

[0245] S104 decodes the Pareto optimal solution set and generates a multi-objective balanced energy-saving scheduling scheme.

[0246] In some specific embodiments, for the MOFJSP-TRC problem, the scheduling scheme involves four key decision dimensions: machining sequence, machining speed, machine tool allocation, and tool selection. The machining sequence, machining speed level, and machine tool allocation are uniformly encoded as a one-dimensional real number sequence and then restored to a feasible scheduling solution through a specific decoding mechanism. Specifically, the machining sequence is determined using the Smallest Position Value (SPV) rule, and both the machining speed level and machine tool allocation are decoded based on a uniform partitioning strategy. Tool allocation adopts the earliest available priority principle to improve resource utilization and scheduling flexibility.

[0247] refer to Figure 4 and Figure 5, Figure 4 This diagram illustrates the decoding mechanism of a CNC multi-objective optimization energy-saving method based on an improved wolf pack algorithm according to an embodiment of this application. Figure 5 An example of encoding and decoding for processing sequence, processing speed, and machine tool allocation according to embodiments of this application is shown. For example... Figure 4 As shown, the decoding process includes:

[0248] Step 401: Obtain the real-number encoded sequence. Map the solution space of the scheduling problem (covering decision dimensions such as processing sequence, machine tool allocation, and processing speed) into real-number encoded individuals, which serve as the basic input for subsequent scheduling decisions. For example... Figure 5 (a) Taking the real number encoding sequence [4.72, 2.23, 1.93, 3.87, 1.35] as an example, each real number in the real number encoding [4.72, 2.23, 1.93, 3.87, 1.35] corresponds to a different scheduling decision dimension. The integer part is only used as a sorting basis in the SPV rule and has no actual semantics. The first decimal place of the fractional part is used to map the processing speed level, and the second decimal place of the fractional part is used to map the machine tool allocation (only valid for the first operation).

[0249] Step 402 involves decoding the real-number encoded sequence using both the SPV rule and the uniform segmentation method, specifically including:

[0250] The processing sequence is generated from the real-number encoded sequence using the SPV rule. This rule first sorts the real-number codes in ascending order, and then determines the processing order based on the original indices of the sorted elements. For example, the real-number encoded sequence [4.72, 2.23, 1.93, 3.87, 1.35], after sorting, becomes [1.35, 1.93, 2.23, 3.87, 4.72], with the corresponding original indices (5, 3, 1, 4, 2). Therefore, the initial processing order is (5, 3, 1, 4, 2), which is: Process 5 → Process 3 → Process 1 → Process 4 → Process 2. Although the SPV rule effectively simplifies the sequence conversion process, the operation sequence generated by this method may not conform to specific job constraints (such as the requirement that job operations must be executed in a predetermined order). To ensure the feasibility of the operation sequence, a repair mechanism is used to adjust the initial operation sequence to satisfy the job order constraints. Specifically, suppose the operation order of task 1 is (1,2,3), and the operation order of task 2 is (4,5), while the initial operation sequence is S0 = (5,3,1,4,2), which does not meet the constraints. The repair step first adjusts the sequence according to the operation order of task 1, replacing the indices of the second, third, and fifth positions in S0, resulting in the corrected sequence S1 = (5,1,2,4,3). Subsequently, the first and fourth positions are adjusted according to the order of task 2, finally yielding a feasible solution S2 = (4,1,2,5,3) that satisfies all constraints.

[0251] The processing speed decoding employs a uniform segmentation strategy, mapping the first decimal part of the real number encoding to a preset speed level range, thereby determining the processing speed of the process. Figure 5 As shown in (b). For example, suppose the speed level is [1.5, 1.2, 1.0, 0.8], and its corresponding intervals are [0, 0.25), [0.25, 0.5), [0.5, 0.75), and [0.75, 1.0]. If the real number code of a certain process is 1.35, then its first decimal is 0.3, which falls into the interval [0.25, 0.5), and the corresponding processing speed is 1.2.

[0252] Machine tool allocation is also based on a uniform partitioning strategy, such as Figure 5 As shown in (c). For the first operation of each job, the second decimal place of the real number code is extracted, scaled to the interval [0,1), and mapped to the machine tool set accordingly. For example, if there are two candidate machine tools, corresponding to the intervals [0,0.5) and [0.5,1) respectively, if the first operation code of job 1 is 2.23, the second decimal place is 3, which is 0.3 after scaling, falling into the interval [0,0.5), so it is assigned to machine tool 1; if the first operation code of job 2 is 3.87, the second decimal place is 7, which is 0.7 after scaling, falling into the interval [0.5,1), so it is assigned to machine tool 2.

[0253] Step 403, Tool Allocation. Following the earliest available strategy, and under the premise of satisfying tool resource constraints (i.e., the same tool is not simultaneously occupied by multiple operations), allocate the required tools to each operation within a feasible machining sequence to ensure a smooth machining flow. Specifically, provided that the operation's executable conditions are met, prioritize the available tool with the earliest current idle time to maximize the utilization of tool resources.

[0254] Step 404: Generate a production plan: Integrate information such as processing sequence, machine tool allocation, processing speed, and tool allocation to form a complete production execution plan, output the production plan, and guide the scheduling and execution of the actual CNC machining process.

[0255] Through the above decoding process, the abstract code obtained by the algorithm search is gradually transformed into an executable scheduling scheme that fits the actual production constraints, so as to realize the practical application of multi-objective energy-saving optimization in CNC machining.

[0256] Example

[0257] To facilitate understanding, a simple example of MOFJSP-TRC is given. Assume five workpieces need to be scheduled on three parallel machine tools (M1, M2, M3), sharing a toolkit consisting of two turning tools, one drill tool, and two milling cutters. The tools are denoted as T1 to T5: {T1, T2} is the set of turning tools labeled "tt"; {T3} is the set of drill tools labeled "dt"; and {T4, T5} is the set of milling tools labeled "mt". Each workpiece has an operation sequence, and each operation requires a specific type of tool and consumes a certain amount of machining time.

[0258] Table 2 lists the specific data for the workpieces. Taking workpiece 1 as an example, after being loaded onto the CNC machine tool, it requires 3 hours of turning at normal speed, followed by 1 hour of drilling, and finally 2 hours of milling. When a turning tool is available, workpiece 1 will use it for the first operation; after turning, workpiece 1 will wait for the drill to be ready before the milling operation. The workpiece will not be unloaded from the machine tool until all operations of workpiece 1 are completed, i.e., after the two-hour milling operation is completed.

[0259] Table 2. Job data for small-scale instances

[0260]

[0261] Table 3 lists the selectable processing speeds and corresponding power consumption for each operation. Taking the first operation of workpiece 1 as an example, the selectable processing speeds are high speed, normal speed, and low speed, with corresponding processing times of 1.5 hours, 2 hours, and 3 hours, and power consumption of 11 kW / h, 8 kW / h, and 5 kW / h, respectively.

[0262] Table 3 shows the selectable processing speeds and corresponding power data for small-scale examples.

[0263]

[0264] This paper employs the Taguchi Design of Experiments (DOE) method to determine the optimal parameter configuration for the MOGWO-ALNS algorithm. The MOGWO-ALNS algorithm comprises five key parameters: population size (Pop), exploration factor α, movement factor C, AT1, and AT2. The ranges of parameters α and C are crucial for the exploration phase of the MOGWO algorithm. Their values ​​directly affect the distance each wolf moves, specifically depending on α, β, and δ wolves. Each parameter is set to four levels, with specific values ​​shown in Table 4. To evaluate the performance of different parameter combinations, this paper selects L16(4... 5 An orthogonal array was used for the experimental design, as shown in Table 5, with instance L16 as the test case. For each parameter combination, the algorithm was run 10 times, and performance was measured by the IGD value. The IGD evaluation results are shown in Table 6.

[0265] Table 4 Parameter Levels of MOGWO-ALNS

[0266]

[0267] Table 5 Orthogonal arrays and average IGD values

[0268]

[0269]

[0270] Table 6 Parameter Response Values

[0271]

[0272] Figure 6 The figure shows the trend analysis of the IGD (Inverse Generational Distance) index of each parameter of the CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to the embodiments of this application. Figure 6 The IGD trend for each parameter level is shown. The IGD index measures how closely the Pareto front obtained by the algorithm approximates the true Pareto front; a smaller value indicates a higher quality solution set. Analysis reveals that the IGD value is minimized when the population size (Pop) is set to level 3, parameter a is set to level 1, parameter c is set to level 1, the first perturbation threshold AT1 is set to level 2, and the second perturbation threshold AT2 is set to level 2. The corresponding parameter configuration is: Pop = 40, a = 2, c = 2, AT1 = 0.2, AT2 = 0.6. This parameter combination enables the algorithm to generate a Pareto solution set that is closer to the true optimal front when solving CNC multi-objective optimization energy-saving problems, ensuring the quality of the scheduling scheme.

[0273] To demonstrate the effectiveness of the MOGWO-ALNS design in solving the MOFJSP-TRC problem, a series of comparative experiments were conducted on the various components of MOGWO-ALNS, including initialization strategies, the ALNS mechanism, and energy-saving strategies. Details of these experiments are described below.

[0274] To demonstrate the effectiveness of the hybrid initialization strategy, we conducted a comparative experiment between MOGWO-ALNS and a hybrid initialization strategy (denoted as A1) that MOGWO-ALNS did not propose.

[0275] To demonstrate the effectiveness of the ALNS strategy, a comparative experiment was conducted between MOGWO-ALNS and MOGWO-ALNS without the ALNS mechanism (denoted as A2).

[0276] To confirm the effectiveness of the energy-saving strategy, we conducted a comparative experiment between MOGWO-ALNS and MOGWO-ALNS without an energy-saving strategy (denoted as A3).

[0277] Table 7 lists the statistical means of hypervolume (HV) and inverse generational distance (IGD) for MOGWO-ALNS and its variants (A1, A2, A3) across multiple test instances. HV (Hypervolume): a core indicator for measuring solution set quality in multi-objective optimization, reflects the coverage of the Pareto front generated by the algorithm within the "total weighted delay-total energy consumption" bi-objective space. A higher value indicates more comprehensive coverage of the true optimal front and stronger multi-objective balancing ability. IGD (Inverse Generational Distance): quantifies the approximation of the Pareto front generated by the algorithm to the true optimal front. A lower value indicates better convergence of the solution set and closer proximity to the theoretical optimal solution. For each instance, MOGWO-ALNS and its variants were run independently 20 times to eliminate the influence of random fluctuations, and the average value was recorded. To analyze whether the differences between the results of MOGWO-ALNS and its variants were significant, a Wilcoxon test was performed on each indicator, and the results are listed in Table 8. To better represent the results, the optimal values ​​in each group are bolded. In addition, to display the results more intuitively, Figure 7 The results of the Tukey test for IGD and HV at a 95% confidence level are presented, and the significant differences in algorithm performance are visualized.

[0278] Table 7 HV and IGD values ​​for MOGWO-ALNS, A1, A2, and A3

[0279]

[0280]

[0281] Table 8. Results of the Wilcoxon test for MOGWO-ALNS and its variants.

[0282]

[0283] Based on the above experimental results, the following conclusions can be drawn. First, as shown in Table 7, MOGWO-ALNS achieved optimal or near-optimal HV and IGD values ​​in most instances, indicating that its designed components played a crucial role in improving overall performance. Second, as shown in Table 8, the p-values ​​of all Wilcoxon tests were less than 0.05, further validating the statistical significance and effectiveness of the designed strategy. Finally, as... Figure 7As shown, MOGWO-ALNS exhibits better central tendency and lower volatility in both HV and IGD metrics. Notably, the performance degradation of variant A2 is the most significant, indicating that the ALNS mechanism plays a crucial role in improving MOGWO-ALNS performance. In contrast, the volatility trends of A1 and A3 on the mean are relatively similar, suggesting that the hybrid initialization strategy and energy-saving strategy contribute similarly to performance improvement, although not as significantly as the ALNS mechanism. Based on the above experimental results and analysis, it can be concluded that all components of MOGWO-ALNS are effective for solving MOFJSP-TRC, and different components have varying degrees of influence on the effectiveness of MOGWO-ALNS in solving MOFJSP-TRC.

[0284] Continue to refer to Figure 8 As an implementation of the above method, in a second aspect, this application provides an embodiment of the framework diagram 800 of a numerical control multi-objective optimization energy-saving system based on an improved wolf pack algorithm. This system embodiment is similar to... Figure 1 Corresponding to the illustrated method embodiment, this system can be specifically applied to various electronic devices. The system 800 includes a model building module 801, an algorithm building module 802, a solution module 803, and a decoding module 804 that are interconnected, wherein:

[0285] Model building module 801 is configured to build a mixed integer linear programming model for multi-objective flexible job shop scheduling. The model takes total weighted delay and total energy consumption as optimization objectives, and machine tool allocation, processing sequence, tool allocation and processing speed adjustability as decision variables.

[0286] Algorithm building module 802 is configured to build the MOGWO-ALNS algorithm for solving mixed integer linear programming models based on the MOGWO algorithm and adaptive large neighborhood search mechanism. The MOGWO-ALNS algorithm constructs a three-stage collaborative optimization architecture through a dual threshold triggering mechanism.

[0287] Solver module 803 is configured to solve mixed-integer linear programming models based on the MOGWO-ALNS algorithm to obtain the Pareto optimal solution set of the mixed-integer linear programming model;

[0288] The decoding module 804 is configured to decode the Pareto optimal solution set and generate a multi-objective balanced energy-saving scheduling scheme.

[0289] Although the principles of the present invention have been described in detail above with reference to preferred embodiments, those skilled in the art should understand that the above embodiments are merely illustrative explanations of the implementation of the present invention and are not intended to limit the scope of the present invention. The details in the embodiments do not constitute a limitation on the scope of the present invention. Any obvious changes, such as equivalent transformations or simple substitutions, based on the technical solutions of the present invention without departing from the spirit and scope of the present invention fall within the protection scope of the present invention.

Claims

1. A CNC multi-objective optimization energy-saving method based on an improved wolf pack algorithm, characterized in that, The method includes: S1. Construct a mixed-integer linear programming model for multi-objective flexible workshop scheduling. The model takes total weighted delay and total energy consumption as optimization objectives, and machine tool allocation, processing sequence, tool allocation and processing speed adjustability as decision variables. S2. Based on the MOGWO algorithm and the adaptive large neighborhood search mechanism, construct the MOGWO-ALNS algorithm to solve the mixed integer linear programming model. The MOGWO-ALNS algorithm constructs a three-stage collaborative optimization architecture through a dual threshold triggering mechanism. S3. Solve the mixed-integer linear programming model based on the MOGWO-ALNS algorithm to obtain the Pareto optimal solution set of the mixed-integer linear programming model; S4. Decode the Pareto optimal solution set to generate a multi-objective balanced energy-saving scheduling scheme.

2. The CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to claim 1, characterized in that, The mixed-integer linear programming model uses machine tool allocation, machining sequence, tool allocation, and machining speed adjustability as decision variables, and its expression is: min∑ i∈N wt i (1) min∑ m∈NC (ep m +no m ) (2) The constraints include: In the formula, N represents the set of workpieces, i∈N; wt i The weighted delay time for workpiece i is represented; NC represents the set of CNC machine tools; ep m Indicates the total energy consumption of machine tool m during operation; ei m W represents the total energy consumption of machine tool m in idle state. i This represents the weight of workpiece i; Let the non-negative continuous variable be workpiece i at the Kth position. i The start time of the operation; NC represents the set of CNC machine tools, m∈NC; Indicates the Kth workpiece i i The set of selectable processing speeds for each operation; Indicates the Kth workpiece i i If the operation is performed on machine tool m at speed s, the binary variable is 1; otherwise, it is 0. Indicates the Kth workpiece i i The time required for processing at speed s in this operation; W i Indicates the delivery date of workpiece i; O i K represents the fixed processing sequence of workpiece i. i Indicates the number of operations for workpiece i, O i = (1,2,...,K) i ), k∈O i S i,k Let S represent the set of selectable processing speeds for the k-th operation on workpiece i. i,k ;z m,i,k,s Let P represent the k-th operation of workpiece i being processed on machine tool m at speed s, then the binary variable is 1; i,k,s E represents the time required for the k-th operation of workpiece i to be processed at speed s; i,k,s Let represent the power required for machining workpiece i at speed s in the k-th operation; E represents the power of the machine tool in idle state; mc m Let m be the non-negative continuous variable representing the end time of machine tool m.

3. The CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to claim 1, characterized in that, The three-stage collaborative optimization architecture of the MOGWO-ALNS algorithm includes: In the first stage, heuristic rules and random strategies were used to generate the initial population, and Pareto frontier exploration was carried out based on the standard gray wolf optimization algorithm. In the second stage of optimization, in response to the algorithm running time reaching the first perturbation threshold, a local perturbation based on the adaptive large neighborhood search mechanism is introduced for the α wolf. In the third stage of optimization, in response to the algorithm running time reaching the second perturbation threshold, the adaptive large neighborhood search mechanism is diffused to β wolf and δ wolf for local perturbation; The first stage includes: using heuristic rules to generate a guiding subpopulation for the goal of minimizing the total weighted delay and a subpopulation for the direction of minimizing the total energy consumption, and using a random initialization strategy to generate a wide range of individuals covering the solution space; The heuristic rules include the earliest due date rule, the shortest processing time rule, the weighted shortest processing time rule, the shortest completion time rule, the apparent lateness cost rule, the minimum relaxation rule, the maximum processing speed priority strategy, and the lowest energy consumption priority strategy, wherein: The earliest due date rule prioritizes tasks with the earliest due date. The shortest processing time rule prioritizes tasks with the shortest processing time. The weighted shortest processing time rule prioritizes tasks with the longest weighted processing time. The shortest completion time rule prioritizes tasks with the closest due date. The apparent lateness cost rule prioritizes tasks with the highest delay costs and urgency, and its expression is: In the formula, D i P represents the delivery date of workpiece i. i W represents the total machining time for all operations on workpiece i at constant speed. i Let represent the weight of workpiece i, t′ represent the earliest start time of the current workpiece i, and F represent the scaling parameter. This indicates the average processing time for the remaining workpieces. The minimum relaxation rule prioritizes tasks with the shortest relaxation time, and its expression is: max(0,D) i -P i -t′); The maximum processing speed priority strategy prioritizes the fastest processing speed. The lowest energy consumption priority strategy prioritizes the processing speed with the lowest energy consumption, and its expression is P. i,k / S i,k ×E i,k In the formula, P i,k S represents the time required for the k-th operation of workpiece i. i,k E represents the set of selectable processing speeds for workpiece i during the k-th operation. i,k This represents the power required for the k-th operation of workpiece i.

4. The CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to claim 3, characterized in that, In the second stage of optimization, in response to the algorithm running time reaching the first perturbation threshold, a local perturbation based on the adaptive large neighborhood search mechanism is introduced for the α wolf, and a step-by-step energy consumption optimization strategy is executed. And / or the third stage optimization, in response to the algorithm running time reaching the second perturbation threshold, the adaptive large neighborhood search mechanism is diffused to β wolf and δ wolf for local perturbation, and a step-by-step energy consumption optimization strategy is executed.

5. The CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to claim 4, characterized in that, The tiered energy consumption optimization strategy includes: Step a': Decode the scheduling schemes corresponding to α wolf, β wolf and / or δ wolf, and generate the corresponding production plan table; Step b': Calculate the subsequent backlash time and available tool backlash time for the current process that is not the final process and is not the minimum processing speed in the production plan table in sequence; in response to the subsequent backlash time and available tool backlash time being greater than the deceleration delay time of the current process, adjust the processing speed corresponding to the current process, wherein the subsequent backlash time is the time interval from the end of the current process of the machine tool to the start of the next process; Step c': After traversing all current processes that are not the final process and do not have the minimum processing speed, update the production plan table, encode the scheduling scheme corresponding to the updated production plan table, and restart the search.

6. The CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to claim 3, characterized in that, The adaptive large neighborhood search mechanism includes differentiated destruction and repair strategies based on processing sequence and machine tool allocation, wherein: The destruction strategies include: Destruction operators based on processing order include random destruction operators, scarce tool-oriented destruction operators, tool gap-based destruction operators, and tool load-based destruction operators; Destruction operators based on machine tool allocation include dynamic idle ratio destruction operators, destruction operators based on release time intervals, destruction operators based on tool intervals, and destruction operators based on TWT. The remediation strategies include: Repair operators based on processing order include random insertion repair operators, forward insertion repair operators, and backward insertion repair operators; Repair operators based on machine tool allocation include load balancing repair operators and energy efficiency optimization repair operators.

7. The CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to claim 4, characterized in that, The MOGWO-ALNS algorithm includes the following sub-steps: Step a, initialize the wolf pack population, with each individual corresponding to a set of real-number codes for potential scheduling schemes; Step b: Calculate the objective function value and construct an external file, wherein the objective function value includes the total weighted delay and the total energy consumption; Step c: Determine if the algorithm has reached the set maximum running time. If "no", continue iterating to step d. If "yes", output the approximate Pareto optimal solution set saved in the external file and end the operation; Step d: Calculate the attenuation factor and select α wolf, β wolf, and δ wolf from the external archive; Step e: Determine the first perturbation threshold that the current running time is greater than or equal to the total time. If "yes", apply ALNS local perturbation to the α wolf and execute the stepped energy consumption optimization strategy, then proceed to step f; if "no", proceed directly to step g. Step f: Determine if the current running time is greater than or equal to the second perturbation threshold of the total time. If "yes", apply ALNS local perturbation to β wolves and δ wolves, and execute a stepped energy consumption optimization strategy, then proceed to step g; if "no", proceed to step g. Step g: Update the individual wolf pack positions. Based on the standard MOGWO mechanism and guided by α, β, and δ wolves, update the position of the entire wolf pack. Step h: Recalculate the objective function value, update the external file, and return to execute step c.

8. The CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to claim 6, characterized in that, The operator selection in the destruction strategy and / or the repair strategy is implemented based on a multi-armed gambling machine model, and the specific formula is as follows: In the formula, scores g The cumulative score for operator g, attempts g is the number of times operator g is called, otal_attempts represents the total number of operator calls, and c is a hyperparameter for adjusting the exploration intensity.

9. The CNC multi-objective optimization energy-saving method based on the improved wolf pack algorithm according to claim 6, characterized in that, The calculation formula for the destruction operator based on tool gaps is: In the formula, K i Let jst be the number of operations performed on the i-th workpiece on machine tool m. m,i,k and JCT m,i,k-1 Let represent the start time of the k-th operation on the i-th workpiece on machine tool m and the completion time of the previous operation, respectively. The release time interval of the destruction operator based on the release time interval is expressed as: In the formula, gst′ m,i , gct′ m,i-1 and R′ m,i These are the start time, completion time, and release time of the i-th workpiece on machine tool m, respectively.

10. A numerical control multi-objective optimization energy-saving system based on an improved wolf pack algorithm, characterized in that, The system includes: The model building module is configured to build a mixed-integer linear programming model for multi-objective flexible job shop scheduling. The model takes total weighted delay and total energy consumption as optimization objectives, and machine tool allocation, processing sequence, tool allocation and processing speed adjustability as decision variables. The algorithm construction module is configured to build the MOGWO-ALNS algorithm for solving the mixed integer linear programming model based on the MOGWO algorithm and the adaptive large neighborhood search mechanism. The MOGWO-ALNS algorithm constructs a three-stage collaborative optimization architecture through a dual threshold triggering mechanism. The solution module is configured to solve the mixed-integer linear programming model based on the MOGWO-ALNS algorithm to obtain the Pareto optimal solution set of the mixed-integer linear programming model; The decoding module is configured to decode the Pareto optimal solution set and generate a multi-objective balanced energy-saving scheduling scheme.

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