Order delivery deadline workshop task scheduling method based on improved sled dog optimization algorithm

Abstract

The invention relates to multi-workpiece production scheduling and scheduling optimization in the field of industrial production, in particular to an order delivery time workshop task scheduling method based on an improved sled dog optimization algorithm, which comprises the following steps: constructing a multi-target scheduling model of an aluminum ingot casting workshop; based on the multi-target scheduling model, improving initialization of a sled dog algorithm to obtain an initial population; performing sled dog group iteration updating according to the initial population by using a grey wolf algorithm to obtain an optimized population; carrying out discretization coding on the optimized population, and solving a scheduling scheme to obtain a scheduling scheme candidate solution; retaining an optimal scheduling scheme candidate solution as a final scheduling scheme through multi-round iteration and screening; and performing task scheduling of the aluminum ingot casting workshop based on the final scheduling scheme. According to the method, the total production cost is reduced, the idle and switching frequency of equipment is reduced, the default rate of the order delivery time can be strictly controlled, and the overall production efficiency of a workshop is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of workshop scheduling, and in particular to an order delivery deadline workshop task scheduling method based on an improved sled dog optimization algorithm. Background Art

[0002] The traditional aluminum processing industry faces dual environmental and economic pressures stemming from high energy consumption and emissions. As a crucial component of aluminum processing, aluminum ingot casting workshops face significant challenges in production scheduling, impacting not only production efficiency and delivery timeliness but also energy management and equipment maintenance, which are crucial for reducing overall costs and environmental impact. Existing scheduling methods primarily focus on optimizing the sequence of production tasks, while insufficiently considering multi-objective constraints such as electric power consumption, penalties for breach of delivery deadlines, and equipment maintenance costs. This makes it difficult to achieve true energy savings while ensuring on-time order delivery.

[0003] Traditional scheduling optimization methods are mainly based on intelligent optimization algorithms such as genetic algorithms, particle swarm optimization (PSO), and gray wolf optimization (GWO). These methods can solve complex scheduling problems to a certain extent, but each has certain limitations. For example, the particle swarm optimization algorithm is prone to falling into local optimality, and it is often difficult to obtain the global optimal solution under high-dimensional and multi-constrained conditions; although the gray wolf optimization algorithm performs well in global search, it may have shortcomings in local development capabilities; and the traditional sled dog optimization algorithm has advantages in local search speed, but its overall global search capabilities are limited. These shortcomings limit its practical application effect in complex industrial scheduling problems, especially in multi-objective and multi-constrained scheduling scenarios such as aluminum ingot casting workshops. Its solution is difficult to take into account both delivery time window requirements and energy conservation and consumption reduction goals.

[0004] In summary, currently available technical solutions lack a comprehensive optimization method for workshop energy consumption management and equipment maintenance cost control. Therefore, there is an urgent need for a scheduling optimization method that can take into account multi-objective optimization requirements such as power consumption, breach of contract penalties, and equipment maintenance costs while considering delivery time window constraints. This method can also improve global search capabilities and local search accuracy through improved algorithms, thereby achieving efficient scheduling and energy conservation and consumption reduction in aluminum ingot casting workshops. Summary of the Invention

[0005] The present invention addresses the high costs and low efficiency issues in aluminum ingot production or other types of manufacturing workshops caused by uneven order delivery deadlines, varying equipment loads, and frequent switching. This paper proposes a method for scheduling workshop tasks based on an improved sled dog optimization algorithm to meet order delivery window constraints while effectively reducing power consumption, minimizing penalties for breach of contract, and controlling equipment maintenance costs, thereby achieving energy conservation and cost control in the production process. To this end, the present invention constructs a multi-objective scheduling mathematical model, employs a hybrid initialization strategy, and employs an improved intelligent optimization algorithm, taking into account both global and local search capabilities, ultimately obtaining an optimal scheduling solution.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A method for scheduling shop tasks with order delivery deadlines based on an improved sled dog optimization algorithm, comprising:

[0008] Construct a multi-objective scheduling model for an aluminum ingot casting workshop; wherein the multi-objective scheduling model includes factors such as order delivery deadline, earliest possible start time, equipment switching loss, and idling energy consumption;

[0009] Based on the multi-objective scheduling model, the initialization of the sled dog algorithm is improved to obtain the initial population;

[0010] Using the gray wolf algorithm, iteratively updating the sled dog population according to the initial population to obtain an optimized population;

[0011] Discretizing and encoding the optimized population, and solving a scheduling solution to obtain a candidate scheduling solution;

[0012] Through multiple rounds of iteration and screening, the best candidate scheduling solution is retained as the final scheduling solution;

[0013] Based on the final scheduling plan, task scheduling of the aluminum ingot casting workshop is carried out.

[0014] Optionally, the multi-objective scheduling model is:

[0015]

[0016] Among them, c is the unit cost generated when processing the order, n is the number of orders to be scheduled, m is the number of available equipment, d ij is the switching energy consumption factor of order i and order j on the same device, x ij k is a Boolean variable indicating whether order i is executed by process j on the kth equipment, y i kis a Boolean variable indicating whether order i is put into processing on equipment k, Gk is the idling loss of equipment k, P b is the idle cost constant per unit time, f(t i ) is the penalty function for measuring whether order i is started too early or delivered late, a, b are the penalty coefficients for premature or delayed delivery, E i is the earliest possible start time of order i, L i is the latest allowed completion time of order i, t i is the actual completion time of order i.

[0017] Optionally, the workshop scheduling model is provided with constraints; wherein the constraints include: order uniqueness constraint, equipment capacity constraint, time window constraint, and order sequence connection constraint.

[0018] Optionally, obtaining the initial population includes:

[0019] Latin hypercube sampling is used to uniformly sample each solution vector dimension in the workshop scheduling problem and construct the initial sample matrix.

[0020] Based on the initial sample matrix, a Cubic chaotic map is introduced into each sample to construct a bidirectional coupling mechanism to obtain a chaotically disturbed sample;

[0021] The chaotically disturbed samples are converted to the preset feasible solution domain through linear mapping, and the samples that do not meet the boundary conditions or violate the hard constraints of workshop scheduling are corrected to obtain an initial population with uniform distribution and diversity.

[0022] Optionally, using the Gray Wolf Algorithm to iteratively update the sled dog population based on the initial population to obtain an optimized population includes:

[0023] In each iteration, the sled dogs are sorted according to their fitness, and the top several sled dogs with the highest fitness are selected as leaders.

[0024] Generate a random vector for each individual and calculate the convergence factor and the bootstrap coefficient for each leader to update the bootstrap term for all individuals in the population;

[0025] Based on the guidance coefficient, the distance between the individuals in the population and the leader is used to update the individual position in a preset manner, and the updated position of the gray wolf algorithm is obtained by averaging the guidance effects of all leaders;

[0026] The individual position is adjusted according to the distance between the leader information and the current individual, and adaptive weights are used to weightedly fuse the gray wolf information guidance results with the original sled dog speed update mechanism;

[0027] According to the individual's fitness ranking, the individual's local weight is modified.

[0028] Optionally, discretizing and encoding the optimized population and solving a scheduling solution to obtain a candidate scheduling solution includes:

[0029] The orders to be scheduled and the available equipment in the workshop are discretized into integer coding form, where each individual solution vector is composed of order number and equipment number according to a fixed rule, indicating the processing sequence of each order and its assigned equipment;

[0030] Decode the individual solution vectors and calculate the earliest possible start time, equipment switching time, energy consumption cost, and delivery default cost for each order to determine the start and end time of the order during the processing;

[0031] For candidate solutions that do not meet the conditions after decoding due to order delivery constraints or equipment load constraints, the fitness is reduced by imposing penalties or performing feasibility corrections;

[0032] The individual fitness is continuously updated and evaluated in the main loop iteration until the preset number of iterations is reached or the convergence judgment conditions are met, thereby outputting the optimal production scheduling plan that meets the order delivery deadline, equipment capacity and comprehensive production cost optimization requirements.

[0033] Optionally, after multiple rounds of iteration and screening, the best candidate scheduling solution is retained as the final scheduling solution, including:

[0034] The execution is repeated continuously in multiple rounds of iterations, and the individual position, speed and fitness are updated in each round of iteration until the termination condition is met and the optimal individual is selected as the final scheduling solution.

[0035] The beneficial effects of the present invention are:

[0036] This invention significantly improves the scheduling performance of flexible job shops in complex manufacturing environments, particularly those with multiple varieties, multiple batches, and strict time window constraints, by constructing a comprehensive scheduling model that integrates multiple practical constraints and cost factors, such as order delivery deadlines, earliest start times, equipment switching losses, and idling energy consumption, and by making key improvements to the sled dog optimization algorithm. The key innovation at the algorithmic level lies in: in the initialization phase, the ergodicity of the Cubic chaos map and the uniformity of Latin hypercube sampling are synergistically utilized to generate a high-quality initial population, effectively broadening the search space coverage and preventing premature convergence; in the iterative phase, the information-guided strategy of the Gray Wolf Optimization Algorithm is introduced to dynamically balance global exploration and local development capabilities, thereby enhancing the algorithm's ability to escape local optimality and accelerating convergence to the global optimal solution. The collaborative optimization of this model and algorithm enables the present invention to obtain a scheduling solution with significantly reduced total production costs, including processing, switching, idling, and early / late delivery penalty costs, effective control of order delivery deadline default risks, and significantly improved equipment utilization and energy efficiency, compared to traditional methods and unimproved optimization algorithms. It demonstrates stronger global optimization capabilities, faster convergence efficiency, and better adaptability and practical value to complex actual production scenarios.

[0037] This paper constructs a specialized mathematical model for a specific industrial problem (multi-objective scheduling in an aluminum ingot casting plant). It also proposes a specific improvement to the sled dog optimization algorithm, organically integrating key concepts from other optimization strategies (such as the guidance mechanism and specific initialization methods of the Gray Wolf Algorithm) to form a complete, collaborative algorithmic process. This specific combination and improvement can more effectively solve the comprehensive optimization problem in this specific scenario than existing technologies, particularly in terms of balancing order delivery, energy conservation, and cost control. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0039] Figure 1 This is a flow chart of a method for scheduling order delivery deadlines in a workshop based on an improved sled dog optimization algorithm according to an embodiment of the present invention;

[0040] Figure 2 Schematic diagram of a workshop scheduling model according to an embodiment of the present invention;

[0041] Figure 3 This is a schematic diagram of the initialization process of the improved sled dog algorithm according to an embodiment of the present invention;

[0042] Figure 4 This is a flow chart of information guidance steps for introducing the Grey Wolf Algorithm according to an embodiment of the present invention;

[0043] Figure 5 is a detailed block diagram of a scheduling method according to an embodiment of the present invention;

[0044] Figure 6 Schematic diagram showing cost comparison between the method according to an embodiment of the present invention and other methods. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0046] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] like Figure 1 As shown, this embodiment proposes a method for scheduling order delivery deadline workshop tasks based on an improved sled dog optimization algorithm, which mainly includes:

[0048] Construct a multi-objective scheduling model for an aluminum ingot casting workshop; the multi-objective scheduling model includes factors such as order delivery deadline, earliest possible start time, equipment switching loss, and idling energy consumption;

[0049] Based on the multi-objective scheduling model, the initialization of the sled dog algorithm is improved to obtain the initial population;

[0050] Using the gray wolf algorithm, the sled dog population is iteratively updated based on the initial population to obtain the optimized population;

[0051] Discretize and encode the optimized population, solve the scheduling scheme, and obtain candidate scheduling solutions;

[0052] Through multiple rounds of iteration and screening, the best candidate scheduling solution is retained as the final scheduling solution;

[0053] Based on the final scheduling plan, the tasks of the aluminum ingot casting workshop are scheduled.

[0054] Specifically, the core process of this embodiment is as follows: First, a comprehensive scheduling model is constructed that includes factors such as order delivery deadlines, earliest possible start time, equipment switching, and idling losses, providing a clear and computable basis for subsequent algorithm optimization; second, based on the original sled dog algorithm, the initial solution is collaboratively generated by combining Cubic chaos mapping and Latin Hypercube Sampling (LHS) to improve the diversity and distribution uniformity of the solution space; at the same time, a Grey Wolf Optimization Algorithm (Grey Wolf Optimization Algorithm) is introduced. The information-guided strategy of the sled dog group is based on the GWO (Ground Wolf Optimizer) algorithm. Through the GWO's ability to balance global exploration and local development, it helps the sled dog group escape the local optimal trap and accelerate convergence. Then, the workshop scheduling problem is discretized in the form of integer coding, and the individual solution vector is constructed using the order number and the equipment number. During the decoding process, factors such as the processing sequence, equipment switching time, and energy consumption cost are comprehensively calculated. By iteratively updating the sled dog positions, the candidate solutions with high fitness are dynamically evaluated and screened, and finally the optimal scheduling solution that takes into account the order delivery deadline, equipment capacity, and comprehensive cost is obtained. Finally, through comparative experiments with common particle swarm optimization, gray wolf algorithm, and original sled dog algorithm, the results show that the present invention can reduce the total production cost, reduce equipment idleness and switching frequency, strictly control the order delivery default rate, and significantly improve the overall production efficiency of the workshop. The present invention has wide applicability to manufacturing scenarios with multiple varieties, multiple batches, and strict time window constraints.

[0055] Specifically, if Figure 5 As shown, the present embodiment proposes a method for scheduling order delivery deadline workshop tasks based on the improved sled dog optimization algorithm, including the following detailed steps:

[0056] S1: Build a workshop scheduling model: Based on the actual manufacturing environment and order requirements, establish a comprehensive scheduling model that includes factors such as order delivery deadlines, earliest possible start time, equipment switching losses, and idling energy consumption. This will clarify various constraints and provide a calculable basis for subsequent optimization.

[0057] S2: Improved initialization of the sled dog algorithm: Based on the original sled dog algorithm, Cubic chaotic mapping and Latin Hypercube Sampling (LHS) are used to collaboratively generate the initial solution to expand the diversity of the solution space and ensure uniform distribution of solutions across the entire domain.

[0058] S3: Introducing information guidance from the Grey Wolf Optimizer (GWO): During the iteration process of the sled dog group, the Grey Wolf Optimizer (GWO) dynamically adjusts the direction and speed of the sled dog group, preventing the algorithm from falling into local optimality too early and accelerating convergence.

[0059] S4: Discrete Coding and Scheduling Solution: Convert the shop scheduling problem into integer coding form, construct individual solution vectors based on order numbers and equipment numbers, calculate the processing sequence, equipment switching time, and energy consumption cost through the decoding process, and continuously evaluate individual fitness during iterative updates;

[0060] S5: Obtain the optimal production scheduling result: After multiple rounds of iteration and screening, the best sled dog individuals are retained as the final production scheduling plan to ensure that order delivery deadlines are met, equipment idleness and switching frequency are reduced, and overall production costs and efficiency are taken into account.

[0061] This embodiment proposes a scheduling optimization method. By constructing a multi-objective scheduling mathematical model, key factors such as order delivery time window, power consumption, breach of contract penalty and equipment maintenance costs are comprehensively optimized to ensure on-time delivery of orders while reducing energy consumption and operating costs. This embodiment uses Cubic chaotic mapping and Latin hypercube sampling to achieve uniform initialization, and introduces gray wolf optimization information to guide the improved sled dog algorithm to enhance global search and local development capabilities. At the same time, it ensures stable convergence through adaptive parameter adjustment and local anti-trapping mechanism. Simulation experiments and actual working condition tests have demonstrated its excellent performance in processing planning, cost control and energy saving and consumption reduction, providing strong technical support for the green transformation under the "dual carbon" strategy.

[0062] Furthermore, if Figure 2 As shown, S1 specifically includes:

[0063] S1.1: Discretize the orders to be scheduled and the available equipment in the workshop into integer solution vectors, so that each individual solution corresponds to a set of "order-equipment" processing sequences;

[0064] S1.2: When decoding the coded solution, factors such as the earliest possible start time of the order, switching time, energy consumption cost, and delivery date are comprehensively calculated, and individuals that do not meet the hard constraints are corrected to ensure the feasibility of the solution.

[0065] Therefore, considering the actual manufacturing environment and order requirements, a comprehensive scheduling model is constructed. The description of each parameter variable in the scheduling model is shown in Table 1. The specific expression of the scheduling model is:

[0066]

[0067] Table 1 Parameter variable description

[0068]

[0069]

[0070] In addition, when establishing the above-mentioned comprehensive scheduling model, in order to ensure the feasibility of the solution, it is necessary to impose constraints on the use of orders and equipment, processing sequence, and time windows. Generally, the following aspects may be included:

[0071] 1. Order uniqueness constraint:

[0072]

[0073] This constraint ensures that each order is only scheduled for complete processing once on a certain device during the entire scheduling process, avoiding duplicate scheduling or missed processing.

[0074] 2. Equipment capacity constraints:

[0075]

[0076] where p ij represents the processing time required for order i in processing step j, T k represents the available processing time of equipment k during the scheduling period. This constraint ensures that within the given available working hours, the equipment is not assigned to process orders that exceed its capacity.

[0077] 3. Time window constraints:

[0078]

[0079] where s i represents the actual start time of order i, t i Indicates the actual completion time. If the work starts too early or is completed late, there will be a premature penalty or a late penalty, which is specifically determined by f(t i ) to reflect.

[0080] 4. Order sequence connection constraints:

[0081] If order i and order j are processed successively on the same device k, the switching energy consumption needs to be considered:

[0082]

[0083] It is used to ensure that the connection processing time between orders does not overlap and the switching energy consumption is correctly accounted for.

[0084] Through the combined effect of the above constraints, the objective function described by model (1) can flexibly incorporate actual production factors such as order delivery deadlines, equipment switching losses, and idling energy consumption while meeting the rigid feasibility requirements, providing an accurate evaluation basis for the optimization and solution of subsequent algorithms.

[0085] Furthermore, if Figure 3 As shown, S2 is specifically:

[0086] S2.1: Use LHS to perform global uniform sampling on each solution vector dimension in the workshop scheduling problem to construct an initial sample matrix. This strategy first constructs the initial sample matrix X of LHS in the D-dimensional solution space. LHS ∈R N×D , where N is the population size and D is the number of dimensions of the optimization problem. Specifically, each dimensional solution space is divided into N equally probable subspaces through a hierarchical mechanism, and the initial sampling points are constructed using a random permutation function πj and a uniform offset ui,j. Its mathematical expression is:

[0087]

[0088] Among them, i is the index of the individual in the population, i∈[1,N]; j is the dimension index of the solution space, that is, j∈[1,D]; u i,j is uniformly distributed in the interval [0,1), which represents the random offset of the i-th individual in the j-th dimension subinterval during the LHS process; π j (i) represents the subinterval number to which the i-th individual is assigned in the j-th dimension.

[0089] S2.2 Based on the LHS initial solution, a Cubic chaotic map is introduced for each sample to construct a bidirectional coupling mechanism: on the one hand, the deterministic distribution of the LHS is used to constrain the initial value sensitivity of the chaotic sequence; on the other hand, the nonlinear perturbation of the chaotic system breaks the rigid orthogonal structure of the LHS. Its dynamic process can be expressed as:

[0090] x Cubic =λ·x LHS (1-(x LHS ) 2 ) (6)

[0091] Where: x LHS is the initial value obtained after LHS sampling; x Cubic represents the intermediate value of the nonlinear perturbation after Cubic mapping; λ is the parameter that controls the chaotic behavior;

[0092] S2.3 Transform the chaotically disturbed samples into the feasible solution domain of “order-equipment” through linear mapping [L b ,U b ], the specific expression is:

[0093]

[0094] The samples that do not meet the boundary conditions or violate the hard constraints of workshop scheduling are corrected to obtain an initial population that is evenly distributed and diverse.

[0095] The initial population refers to the initial set of solutions used to start the sled dog optimization algorithm. It refers to a set of potential solutions or plans (possibly encoded forms of scheduling plans) that will be refined during the subsequent optimization process. Each solution represents a possible scheduling arrangement.

[0096] An individual refers to each specific solution in the population. For scheduling problems, each individual may represent a specific scheduling solution, which includes the specific allocation and arrangement of factors such as order delivery deadlines, earliest possible start time, equipment switching losses, and idling energy consumption. Through improvement and evolution, each individual ultimately aims to achieve an optimized scheduling solution.

[0097] Furthermore, if Figure 4 As shown, the information guidance of the S3 Gray Wolf algorithm has the following characteristics:

[0098] S3.1: In each iteration, sort the individual sled dogs according to their fitness and select the top three individuals with the highest fitness as leaders, denoted as α, β, and δ respectively;

[0099] S3.2: Generate random vectors r1 and r2 for each individual and calculate the convergence factor and the convergence factor for each leader L∈{X α ,X β ,X δ}, for all individuals X in the population i Update the guidance coefficient of the guidance item:

[0100]

[0101] Among them, t is the current iteration number and T is the maximum iteration number.

[0102] S3.3: Then use the population individual X i The distance D from the leader L is used to update the individual position according to the method shown in expression (12). Finally, the updated position of GWO is obtained by averaging the guidance effects of all leaders according to expression (13);

[0103] D=|C·LX i | i=1,2,3 (10)

[0104]

[0105] Among them, D α 、D β and D δ are the current positions of the leaders α, β, and δ, respectively. X1, X2, and X3 are the forward length and direction of the wolf ω toward the wolf α, β, and δ, respectively. GWO is the final position of ω wolf;

[0106] S3.4: Adjust the individual position based on the distance D between the leader information and the current individual, and use adaptive weights to weightedly fuse the gray wolf information guidance results with the original sled dog speed update mechanism. The adaptive weights are determined by the following formula:

[0107]

[0108] S3.5: Since different individuals in the population perform differently, to avoid a one-size-fits-all update approach, the algorithm weights each individual based on its fitness ranking. Therefore, the local weight of the individual is calculated according to equation (16), and then the dynamic adaptive weight is used according to equation (17) to organically integrate the updates of GWO and SDO.

[0109]

[0110] v j =ξ SDO,L ·v i +ξ GWO,L ·(X GWO -x i ) (16)

[0111] Among them, N is the population size, R is the individual ranking after sorting according to fitness, v i Update speed of the i-th sled dog in the current iteration, x i is the position of the i-th individual in the population in the search space, that is, the position vector of the current solution, v j The hybrid velocity is finally used to update the individual position, which is obtained by weighting the velocity calculated by SDO and the displacement calculated by GWO according to their respective weights.

[0112] Furthermore, S4 optimization and cost reduction include the following features:

[0113] S4.1 discretizes the orders and available equipment to be scheduled in the aluminum ingot factory workshop into integer encoding form, where each individual solution vector is composed of "order number" and "equipment number" according to a fixed rule, clearly indicating the processing sequence of each order and its assigned equipment;

[0114] S4.2 decodes the encoded solution and calculates each order's earliest possible start time, equipment switching time, energy consumption cost, and delivery default cost, determining the start and end times of the order during processing. Encoding, in this case, translates the shop's scheduling problem (e.g., which orders are processed on which equipment and in what order) into a computer-processable sequence of integers or a data structure in a specific format. Each such encoding (called an "individual solution vector") represents a possible scheduling solution. Subsequent "decoding" translates this integer encoding back into the actual scheduling arrangement to evaluate its pros and cons.

[0115] S4.3 For candidate solutions that do not meet the conditions after decoding due to order delivery constraints, equipment load constraints, etc., reduce their fitness by imposing penalties or performing feasibility corrections to ensure that the final candidate solutions meet all hard constraints;

[0116] S4.4 continuously updates and evaluates individual fitness during the main loop iterations until it reaches a preset number of iterations or meets convergence criteria, thereby outputting an optimal production schedule that meets order delivery deadlines, equipment capacity, and overall production cost optimization requirements. The optimal production schedule is a high-quality scheduling solution candidate, the interim optimal result obtained after iteration and evaluation in this stage, and will be included in subsequent screening to determine the final scheduling solution.

[0117] This embodiment proposes a method for scheduling workshop tasks based on an improved sled dog optimization algorithm for order delivery deadlines. The method first constructs a multi-objective scheduling model that includes key factors such as order delivery deadlines, earliest start time, equipment switching losses, and idling energy consumption. Then, Latin hypercube sampling and Cubic chaotic mapping are combined to collaboratively generate the initial population, and the leader information guidance mechanism of the gray wolf optimization algorithm is introduced to achieve a dynamic balance between global exploration and local development. In the scheduling solution stage, the production scheduling problem is discretized into an integer-coded "order-equipment" solution vector, and the key costs and constraints are calculated through decoding. The individual fitness is dynamically evaluated and updated in multiple rounds of iterations, and finally the sled dog individual with the highest fitness is selected as the optimal production scheduling solution. Figure 6 As shown in the figure, simulation experiments and actual working condition verification show that this embodiment has significant improvements in total production cost, equipment switching frequency, energy consumption control and order punctuality rate compared with PSO, GWO and original sled dog algorithms, and has fast convergence and good robustness, providing reliable technical support for manufacturing enterprises to achieve green and low-carbon transformation.

[0118] This example constructs a specialized mathematical model for a specific industrial problem (multi-objective scheduling in an aluminum ingot casting plant). It also proposes a specific improvement to the sled dog optimization algorithm, organically integrating key concepts from other optimization strategies (such as the guidance mechanism and specific initialization methods of the Gray Wolf Algorithm) to form a complete, collaborative algorithmic process. This specific combination and improvement can more effectively solve the comprehensive optimization problem in this specific scenario than existing technologies, particularly in terms of balancing order delivery, energy conservation, and cost control.

[0119] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for scheduling order delivery deadlines in a workshop based on an improved sled dog optimization algorithm, characterized in that: include: Construct a multi-objective scheduling model for an aluminum ingot casting workshop; wherein the multi-objective scheduling model includes factors such as order delivery deadline, earliest possible start time, equipment switching loss, and idling energy consumption; Based on the multi-objective scheduling model, the initialization of the sled dog algorithm is improved to obtain the initial population; Using the gray wolf algorithm, iteratively updating the sled dog population according to the initial population to obtain an optimized population; Discretizing and encoding the optimized population, and solving a scheduling solution to obtain a candidate scheduling solution; Through multiple rounds of iteration and screening, the best candidate scheduling solution is retained as the final scheduling solution; Based on the final scheduling plan, task scheduling of the aluminum ingot casting workshop is carried out.

2. The method for scheduling order delivery deadlines in a workshop based on the improved sled dog optimization algorithm according to claim 1, characterized in that: The multi-objective scheduling model is: Among them, c is the unit cost generated when processing the order, n is the number of orders to be scheduled, m is the number of available equipment, d ij is the switching energy consumption factor of order i and order j on the same device, x ij k is a Boolean variable indicating whether order i is executed by process j on the kth equipment, y i k is a Boolean variable indicating whether order i is put into processing on equipment k, Gk is the idling loss of equipment k, P b is the idle cost constant per unit time, f(t i ) is the penalty function for measuring whether order i is started too early or delivered late, a, b are the penalty coefficients for premature or delayed delivery, E i is the earliest possible start time of order i, L i is the latest allowed completion time of order i, t i is the actual completion time of order i.

3. The method for scheduling order delivery deadlines in a workshop based on the improved sled dog optimization algorithm according to claim 1, characterized in that: The multi-objective scheduling model is provided with constraints; wherein, the constraints include: order uniqueness constraint, equipment capacity constraint, time window constraint, and order sequence connection constraint.

4. The method for scheduling order delivery deadlines in a workshop based on an improved sled dog optimization algorithm according to claim 1, characterized in that: Obtaining the initial population includes: Latin hypercube sampling is used to uniformly sample each solution vector dimension in the workshop scheduling problem and construct the initial sample matrix. Based on the initial sample matrix, a Cubic chaotic map is introduced into each sample to construct a bidirectional coupling mechanism to obtain a chaotically disturbed sample; The chaotically disturbed samples are converted to the preset feasible solution domain through linear mapping, and the samples that do not meet the boundary conditions or violate the hard constraints of workshop scheduling are corrected to obtain an initial population with uniform distribution and diversity.

5. The method for scheduling order delivery deadlines in a workshop based on an improved sled dog optimization algorithm according to claim 1, characterized in that: The gray wolf algorithm is used to iteratively update the sled dog population based on the initial population to obtain the optimized population including: In each iteration, the sled dogs are sorted according to their fitness, and the top several sled dogs with the highest fitness are selected as leaders. Generate a random vector for each individual and calculate the convergence factor and the bootstrap coefficient for each leader to update the bootstrap term for all individuals in the population; Based on the guidance coefficient, the distance between the individuals in the population and the leader is used to update the individual position in a preset manner, and the updated position of the gray wolf algorithm is obtained by averaging the guidance effects of all leaders; The individual position is adjusted according to the distance between the leader information and the current individual, and adaptive weights are used to weightedly fuse the gray wolf information guidance results with the original sled dog speed update mechanism; According to the individual's fitness ranking, the individual's local weight is modified.

6. The method for scheduling order delivery deadlines in a workshop based on an improved sled dog optimization algorithm according to claim 1, characterized in that: Discretizing and encoding the optimized population and solving the scheduling solution to obtain candidate scheduling solutions include: The orders to be scheduled and the available equipment in the workshop are discretized into integer coding form, where each individual solution vector is composed of order number and equipment number according to a fixed rule, indicating the processing sequence of each order and its assigned equipment; Decode the individual solution vectors and calculate the earliest possible start time, equipment switching time, energy consumption cost, and delivery default cost for each order to determine the start and end time of the order during the processing; For candidate solutions that do not meet the conditions after decoding due to order delivery constraints or equipment load constraints, the fitness is reduced by imposing penalties or performing feasibility corrections; The individual fitness is continuously updated and evaluated in the main loop iteration until the preset number of iterations is reached or the convergence judgment conditions are met, thereby outputting the optimal production scheduling plan that meets the order delivery deadline, equipment capacity and comprehensive production cost optimization requirements.

7. The method for scheduling order delivery deadlines in a workshop based on an improved sled dog optimization algorithm according to claim 1, characterized in that: After multiple rounds of iteration and screening, the best candidate scheduling solutions are retained as the final scheduling solutions, including: The execution is repeated continuously in multiple rounds of iterations, and the individual position, speed and fitness are updated in each round of iteration until the termination condition is met and the optimal individual is selected as the final scheduling solution.

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