A multi-task cooperative scheduling and resource optimization method and system based on myxomycete algorithm

Abstract

The present application belongs to the field of computer simulation and optimization algorithm, and relates to a multi-task cooperative scheduling and resource optimization method and system based on slime algorithm. The method comprises: constructing a multi-task and multi-resource cooperative scheduling model, establishing the allocation relationship between tasks and resources, and introducing time window constraints, resource capacity constraints and task priority constraints; encoding the scheduling scheme to represent it, and mapping it into a searchable solution space; constructing a multi-objective optimization model containing task completion time, running cost and resource energy consumption, and realizing multi-objective coordinated optimization through dynamic weight; using slime algorithm for iterative solution, optimizing the scheduling scheme through fitness evaluation, weight updating and position adjustment, and improving the solution performance by combining adaptive parameter adjustment and random disturbance; and outputting the optimal or near-optimal scheduling scheme after meeting the termination condition. The present application can improve resource utilization efficiency and scheduling performance, and is suitable for complex system scheduling optimization.

Description

Technical Field

[0001] This invention belongs to the field of computer simulation and intelligent optimization algorithms, and particularly relates to a method and system for multi-task and multi-resource collaborative scheduling problems, which achieves resource optimization by constructing a scheduling model and combining it with swarm intelligence optimization algorithms. Background Technology

[0002] With the rapid development of information technology and intelligent systems, multi-task collaborative scheduling problems are widely found in logistics and distribution, cloud computing resource management, multi-robot systems, and intelligent manufacturing. In such systems, it is typically necessary to rationally allocate and schedule multiple tasks under limited resource conditions to improve overall system efficiency and reduce resource consumption. In practical applications, multi-task scheduling is often characterized by a large number of tasks, complex resource types, and diverse constraints. For example, different tasks may have time window constraints and priority requirements, while resources have capacity limitations and differences in service capabilities, resulting in complex coupling relationships between tasks and resources. Therefore, how to achieve efficient task allocation and rational resource utilization while satisfying multiple constraints has become an important research problem in the field of optimization scheduling. Existing research mainly focuses on solving scheduling problems using rule-based methods, heuristic algorithms, and traditional optimization methods. For example, priority rules are constructed or genetic algorithms and particle swarm optimization are used to optimize scheduling schemes. However, the above methods often have the following shortcomings when dealing with large-scale and complex scheduling problems: on the one hand, some methods are prone to getting trapped in local optima and it is difficult to obtain the global optimal solution; on the other hand, in multi-objective optimization scenarios, there is a lack of effective coordination mechanisms between different optimization objectives, making it difficult to take into account multiple needs such as efficiency, cost and energy consumption.

[0003] Furthermore, existing methods are typically based on static models for optimization, failing to fully consider the dynamic changes in system operating states, resulting in insufficient adaptability of scheduling results in practical applications. When task execution states or resource availability change, the original scheduling scheme is difficult to adjust in a timely manner, thus affecting the overall system performance. Therefore, it is necessary to propose a scheduling method that combines multi-objective optimization mechanisms with adaptive search strategies. By introducing a swarm intelligence algorithm with global search capabilities, this method can efficiently solve the multi-task collaborative scheduling problem, thereby improving resource utilization efficiency and enhancing the stability and robustness of system scheduling. Summary of the Invention

[0004] The purpose of this invention is to improve the existing multi-task collaborative scheduling methods, which are prone to getting trapped in local optima under complex constraints, and are difficult to balance multi-objective optimization and adapt to dynamic system changes. The invention proposes a multi-task collaborative scheduling and resource optimization method and system based on the slime mold algorithm. By constructing a task-resource collaborative model and combining it with an adaptive optimization mechanism, the invention achieves efficient search of scheduling schemes and optimization of resource allocation, thereby improving the overall operating efficiency of the system and reducing resource consumption.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A multi-task cooperative scheduling and resource optimization method based on slime mold algorithm includes the following steps: 1) Construct a task-resource collaboration model: Obtain the task set in the target system. and resource collection Each task Includes task requirements Execution time window Execution time and priority , can be represented as: Each resource Including resource capacity constraints Unit usage cost , ; Assign variables through tasks Indicates task With resources The matching relationship between them ,in Indicates task Allocate to resources , Indicates task Unallocated to resources ; 2) Generate scheduling decision representation: Define and encode scheduling decision vectors ,in, Assign a variable matrix to the task. For task execution order variables, Indicates task The execution order position in the scheduling sequence; For resource occupancy state variables, Representing resources The occupancy status during the scheduling process includes resource capacity occupancy status and resource time occupancy status; task Start execution time and completion time Instead of being used as an independent scheduling decision variable, it is determined based on the task allocation variable A, the task execution order variable O, and the resource occupancy status variable U; the combined values ​​of the above task allocation variable, task execution order variable, and resource occupancy status variable uniformly represent the solution space location corresponding to different candidate scheduling schemes; 3) Initialize the candidate scheduling scheme set: Based on the task set, resource set, and constraints such as time window, resource capacity, priority, and resource conflict, generate multiple candidate scheduling schemes using a combination of random and heuristic generation methods to obtain the initial candidate solution set. Where P is the total number of candidate scheduling schemes, the random generation method is used to randomly determine the task allocation relationship, task execution order and resource occupancy status, and the heuristic generation method generates candidate scheduling schemes according to preset heuristic rules, which include at least one of nearest resource priority, low-cost resource priority, or high-priority task priority; the ratio of the number of random generation schemes to the number of heuristic generation schemes is determined by a preset control ratio parameter ρ, where the value of ρ ranges from 0 < ρ < 1, and the number of randomly generated candidate scheduling schemes is... The number of candidate scheduling schemes generated heuristically is When the generated candidate scheduling scheme does not meet the constraints, it is repaired or regenerated to obtain the initial candidate solution set. 4) Establish a scheduling performance evaluation mechanism: Construct a multi-dimensional performance evaluation system around three indicators: task completion efficiency, resource usage cost, and system energy consumption, and use it to measure the merits of different scheduling schemes; 5) Perform search optimization based on slime mold algorithm: By simulating the adaptive search behavior of slime mold in the environment, the candidate scheduling scheme is iteratively updated, and the individual distribution is dynamically adjusted according to the fitness evaluation results to achieve continuous optimization of the solution space; 6) Introducing an optimization and enhancement mechanism: During the iterative update of candidate scheduling schemes, fitness-based weight updates, random perturbations, diversity preservation, and retention of the current best individual are performed. Among them, fitness-based weight updates are used to adjust the search weights according to the comprehensive fitness value of the candidate scheduling schemes, random perturbations are used to increase the diversity of the candidate solution set, diversity preservation is used to avoid premature convergence of the candidate solution set, and retention of the current best individual is used to prevent the current best scheduling scheme from being lost during the iteration process. 7) Perform individual selection and population update: After each iteration, compare the comprehensive fitness values ​​of the candidate scheduling schemes before and after the update, and use a greedy selection strategy to select; when the comprehensive fitness value of the candidate scheduling scheme after the update is less than or equal to the comprehensive fitness value of the candidate scheduling scheme before the update, replace the candidate scheduling scheme before the update with the candidate scheduling scheme after the update, otherwise retain the candidate scheduling scheme before the update. 8) Output scheduling optimization results: Stop iteration when the preset termination condition is met, and output the scheduling scheme with the best comprehensive fitness value and that meets the constraints; the preset termination condition includes at least one of the following: the number of iterations reaches the preset maximum number of iterations, the change of the best comprehensive fitness value within a consecutive preset number of generations is less than the preset convergence threshold, and the best comprehensive fitness value reaches the preset target value.

[0006] Preferably, the task-resource coordination model constructed in step 1) can be a discrete scheduling model or a continuous scheduling model. The task set and resource set are defined within a preset system scope, and their matching relationship is characterized by task requirement parameters and resource capability parameters. The relevant parameters can be dynamically updated according to the system operating status to enhance the adaptability of the model.

[0007] The scheduling decision vector is represented by a parameterized encoding method. Each scheduling scheme includes at least task allocation variables, task execution order variables, and resource occupancy status variables. Through unified encoding, the scheduling problem is transformed into an optimization problem in a searchable solution space.

[0008] Preferably, the scheduling scheme must meet the following constraints: tasks are completed within a specified time window, resource allocation does not exceed its capacity limit, task execution order meets priority requirements, and there are no resource conflicts or illegal occupation between different tasks, so as to ensure the feasibility and rationality of the scheduling results.

[0009] Preferably, during the optimization process, when a candidate scheduling scheme violates the constraints, it is screened through a feasibility judgment, or its fitness value is reduced by introducing a penalty function, and the influence of infeasible solutions is reduced in subsequent iterations, thereby ensuring the stability of the optimization process.

[0010] Preferably, the fitness function takes task completion time as the core indicator and combines resource usage cost and system energy consumption for comprehensive evaluation. A comprehensive fitness function is constructed through multi-indicator normalization and dynamic weight allocation to achieve coordinated optimization among multiple objectives.

[0011] A multi-task cooperative scheduling and resource optimization system based on slime mold algorithm, comprising: The data input module is used to acquire task information, resource information, and related constraint parameters; The scheduling modeling module is used to build a task-resource coordination model and establish a matching relationship between tasks and resources; The decision encoding module is used to generate scheduling decision vectors and construct candidate solution sets; The performance evaluation module is used to evaluate the performance of scheduling schemes based on a multi-objective evaluation mechanism. The optimization solution module is used to iteratively optimize the candidate solution set based on the slime mold algorithm and to achieve solution space search through fitness-driven approach. The constraint management module is used to detect whether the scheduling scheme meets the constraints and to handle them through repair or penalty strategies. The results output module is used to output the optimized scheduling scheme and corresponding performance indicators.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: 1) This invention transforms the complex scheduling problem into a unified optimization problem by constructing a task-resource collaborative scheduling model, thereby achieving collaborative optimization of task allocation and resource configuration and improving the overall operating efficiency of the system; 2) This invention introduces a swarm intelligence optimization method based on slime mold algorithm, which utilizes its self-organization and global search capabilities to efficiently search for the optimal scheduling scheme in a complex solution space, and has stronger optimization capabilities compared with traditional heuristic methods. 3) By constructing a multi-objective evaluation function and introducing a dynamic weight adjustment mechanism, a balanced optimization between task completion efficiency, cost, and energy consumption can be achieved, avoiding performance deviations caused by single-objective optimization; 4) This invention introduces constraint handling and penalty mechanisms during the optimization process, which effectively reduces the impact of infeasible solutions on the optimization process and improves the feasibility of the scheduling scheme; 5) This invention is applicable to a variety of complex application scenarios such as logistics scheduling, cloud computing resource allocation, and multi-robot collaboration, and has good versatility and scalability. Attached Figure Description

[0013] Figure 1 This is an overall flowchart of the multi-task collaborative scheduling and resource optimization method of the present invention; Figure 2 This is a schematic diagram of a task-resource collaborative scheduling model; Figure 3 This is a schematic diagram of the scheduling decision vector encoding structure; Figure 4 To illustrate the comparison of scheduling performance indicators before and after optimization, Figure 4(a) shows the comparison of total completion time. Figure 4 Figure 4(b) is a comparison chart of total scheduling costs; Figure 4(c) is a comparison chart of total energy consumption. Figure 5 This is a block diagram of the multi-task collaborative scheduling and resource optimization system of the present invention; Figure 6 The graph shows the convergence curve of the optimization process based on the slime mold algorithm. Figure 7 Optimize the delivery scheduling flowchart. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] This invention provides a technical solution: A multi-task cooperative scheduling and resource optimization method based on slime mold algorithm includes the following steps: Constructing a task-resource collaboration model: Obtaining the task set in the target system. and resource collection Each task Includes task requirements Execution time window Execution time and priority , can be represented as: Each resource Including resource capacity constraints Unit usage cost , ; Assign variables through tasks Indicates task With resources The matching relationship between them ,in Indicates task Allocate to resources , Indicates task Unallocated to resources ; 2) Generate scheduling decision representation: Define and encode scheduling decision vectors ,in, Assign a variable matrix to the task. For task execution order variables, Indicates task The execution order position in the scheduling sequence; For resource occupancy state variables, Representing resources The occupancy status during the scheduling process includes resource capacity occupancy status and resource time occupancy status; task Start execution time and completion time Instead of being used as an independent scheduling decision variable, it is determined based on the task allocation variable A, the task execution order variable O, and the resource occupancy status variable U; the combined values ​​of the above task allocation variable, task execution order variable, and resource occupancy status variable uniformly represent the solution space location corresponding to different candidate scheduling schemes; 3) Initialize the candidate scheduling scheme set: Based on the task set, resource set, and constraints such as time window, resource capacity, priority, and resource conflict, generate multiple candidate scheduling schemes using a combination of random and heuristic generation methods to obtain the initial candidate solution set. Where P is the total number of candidate scheduling schemes, the random generation method is used to randomly determine the task allocation relationship, task execution order and resource occupancy status, and the heuristic generation method generates candidate scheduling schemes according to preset heuristic rules, which include at least one of nearest resource priority, low-cost resource priority, or high-priority task priority; the ratio of the number of random generation schemes to the number of heuristic generation schemes is determined by a preset control ratio parameter ρ, where the value of ρ ranges from 0 < ρ < 1, and the number of randomly generated candidate scheduling schemes is... The number of candidate scheduling schemes generated heuristically is When the generated candidate scheduling scheme does not meet the constraints, it is repaired or regenerated to obtain the initial candidate solution set. 4) Establish a scheduling performance evaluation mechanism: Construct a multi-dimensional performance evaluation system around three indicators: task completion efficiency, resource usage cost, and system energy consumption, and use it to measure the merits of different scheduling schemes; 5) Perform search optimization based on slime mold algorithm: By simulating the adaptive search behavior of slime mold in the environment, the candidate scheduling scheme is iteratively updated, and the individual distribution is dynamically adjusted according to the fitness evaluation results to achieve continuous optimization of the solution space; 6) Introducing an optimization and enhancement mechanism: During the iterative update of candidate scheduling schemes, fitness-based weight updates, random perturbations, diversity preservation, and retention of the current best individual are performed. Among them, fitness-based weight updates are used to adjust the search weights according to the comprehensive fitness value of the candidate scheduling schemes, random perturbations are used to increase the diversity of the candidate solution set, diversity preservation is used to avoid premature convergence of the candidate solution set, and retention of the current best individual is used to prevent the current best scheduling scheme from being lost during the iteration process. 7) Perform individual selection and population update: After each iteration, compare the comprehensive fitness values ​​of the candidate scheduling schemes before and after the update, and use a greedy selection strategy to select; when the comprehensive fitness value of the candidate scheduling scheme after the update is less than or equal to the comprehensive fitness value of the candidate scheduling scheme before the update, replace the candidate scheduling scheme before the update with the candidate scheduling scheme after the update, otherwise retain the candidate scheduling scheme before the update. 8) Output scheduling optimization results: Stop iteration when the preset termination condition is met, and output the scheduling scheme with the best comprehensive fitness value and that meets the constraints; the preset termination condition includes at least one of the following: the number of iterations reaches the preset maximum number of iterations, the change of the best comprehensive fitness value within a consecutive preset number of generations is less than the preset convergence threshold, and the best comprehensive fitness value reaches the preset target value.

[0016] Step 1) specifically includes the following steps:

[0017] 1.1 Definition of Task and Resource Sets: First, determine the composition of tasks and resources in the system based on the actual application scenario. Let the task set be:

[0018] The resource set is as follows:

[0019] Each task Includes task requirements Execution time window Execution time and priority , can be represented as: Each resource With resource capacity constraints and unit usage cost , can be represented as: .

[0020] In this invention, task requirement parameters refer to the task requirements, execution time window, and priority included in the task; resource capacity parameters refer to the resource capacity constraints and unit usage cost of the resource. Task requirements characterize the task's requirements for resource processing capacity or occupancy, the execution time window characterizes the allowed execution time range of the task, and the priority characterizes the scheduling requirements between tasks; resource capacity constraints characterize the upper limit of task requirements that the resource can bear, and unit usage cost characterizes the scheduling cost incurred when the resource is occupied.

[0021] 1.2 Task-Resource Allocation Modeling: To describe how tasks are allocated to different resources, the following 0-1 decision variables are introduced:

[0022] in, Indicates task With resources The matching relationship between them is a core component of the scheduling scheme, and all task allocation variables constitute the task allocation variable matrix:

[0023] Specifically, the 0-1 decision variable is used to indicate whether there is an allocation relationship between tasks and resources; when the decision variable takes a value of 1, it means that the corresponding task is allocated to the corresponding resource; when the decision variable takes a value of 0, it means that the corresponding task is not allocated to the corresponding resource. The matching relationship between tasks and resources is determined based on task requirement parameters and resource capability parameters, including: based on task requirements... Resource capacity constraints Determine if the capacity matches; based on the task execution time window. Check if the timing matches the resource scheduling availability status; determine based on task priority. Order of task execution Determine whether priority constraints are met. This transforms the relationship between task resource requirements and resource service capabilities into a unified task-resource allocation and matching relationship.

[0024] 1.3 Construction of scheduling constraints: After completing the definition of basic variables, it is necessary to further construct scheduling constraints to ensure that the generated scheduling scheme is feasible in practice.

[0025] (1) Unique task allocation constraint:

[0026] This constraint is used to ensure that each task is assigned to only one resource.

[0027] (2) Resource capacity constraints:

[0028] This constraint is used to ensure that resources are allocated. The total requirements of the tasks shall not exceed the capacity limit of the resource.

[0029] (3) Time window constraint:

[0030] in, Indicates task The start time of execution. Indicates task The completion time, and satisfying:

[0031] (4) Priority constraints:

[0032] in, and Representing tasks and tasks priority, and Representing tasks and tasks The execution order position in the scheduling sequence. This constraint indicates that if the task... Priority is higher than task Then the task Should be in the task Previously executed.

[0033] (5) Resource conflict constraints:

[0034] This constraint is used to ensure that the same resource is not occupied by multiple conflicting tasks within the same time period.

[0035] 1.4 Formal Representation of the Scheduling Model: Based on the above definitions, the scheduling problem is uniformly represented as:

[0036] in, Represents the set of decision variables. Represents a set of constraints. This represents the set of system parameters. Specifically, it represents the set of decision variables. Including task allocation variable matrix Task execution order variables and resource usage state variables Constraint Set This includes constraints such as unique task allocation, resource capacity, time window, priority, and resource conflict; and a set of system parameters. Parameters including task requirements, resource capacity, unit usage cost, scheduling cycle, and processing rules provide a unified input structure for subsequent coding and optimization.

[0037] Step 2) specifically includes the following steps:

[0038] 2.1 Scheduling Scheme Coding After constructing the scheduling model, the scheduling decisions need to be transformed into a computable, structured representation for subsequent optimization algorithms to search. This invention encodes a complete scheduling scheme as a scheduling decision vector. , is represented as:

[0039] Among them, the task allocation variable matrix Represented as:

[0040] Task execution order variable Represented as:

[0041] Resource usage state variables Represented as:

[0042] in, Used to describe the allocation relationship between tasks and resources; Used to describe the sequential execution relationship between tasks; Used to describe resources The occupancy status during the scheduling process includes resource capacity occupancy status and resource time occupancy status.

[0043] In this invention, the task Start execution time and completion time Not used as a scheduling decision vector Instead of independent variables, variables are assigned based on the task. Task execution order variables and resource usage state variables Determined jointly. Specifically, when the task... Assigned to resources Then, based on resources Existing time occupancy status, tasks Execution order position in the scheduling sequence And tasks The execution time window is used to determine the task. Start execution time ;Task Completion time Based on start time and execution time Determined, that is:

[0044] By combining the values ​​of the above-mentioned task allocation variables, task execution order variables, and resource occupancy status variables, different scheduling decision vectors can be formed. Each scheduling decision vector corresponds to a candidate scheduling scheme, thereby transforming the multi-task collaborative scheduling problem into an optimization problem in a searchable solution space.

[0045] 2.2 Definition of Solution Space In this invention, the solution space is determined by task allocation variables. Task execution order variables and resource usage state variables It consists of all possible combinations. The feasible solution space is defined as:

[0046] Wherein, if the scheduling decision vector If the corresponding candidate scheduling scheme satisfies the time window constraint, resource capacity constraint, priority constraint, and resource conflict constraint, then the scheduling decision vector belongs to the feasible solution space. If any of the above constraints are violated, the scheduling decision vector is considered an infeasible solution. The optimization algorithm searches within the feasible solution space and its neighborhood, and evaluates the merits of different candidate scheduling schemes using a comprehensive fitness function.

[0047] Step 3) specifically includes the following steps:

[0048] 3.1 Initial Population Generation: To initiate the optimization process, an initial set of candidate scheduling schemes needs to be generated.

[0049] in, This represents the initial set of candidate scheduling schemes. Indicates the first One initial candidate scheduling scheme This indicates the population size, i.e., the total number of candidate scheduling schemes.

[0050] Each candidate scheduling scheme is obtained through random generation or heuristic generation. Random generation is used to randomly determine the task allocation relationship, task execution order, and resource occupancy status within the scope of the task set, resource set, and scheduling constraints. Heuristic generation is used to generate candidate scheduling schemes according to preset heuristic rules, which include at least one of the following: nearest resource priority, low-cost resource priority, or high-priority task priority.

[0052] 3.2 Initialization Strategy: To clarify the proportion of random generation and heuristic generation in the initial candidate solution set, a control ratio parameter is introduced. ,in:

[0053] Let the total number of candidate scheduling schemes be The number of randomly generated candidate scheduling schemes is:

[0054] The number of candidate scheduling schemes generated heuristically is:

[0055] in, This represents the floor function. It controls the scaling parameter. The parameters can be preset according to the scheduling scale, constraint complexity, or feasibility rate of candidate solutions of the target system; when the feasibility rate of randomly generated candidate solutions is low, the proportion of heuristic generation should be increased; when the diversity of candidate solutions is insufficient, the proportion of random generation should be increased.

[0056] The initial set of candidate scheduling schemes can be represented as:

[0057] in, Indicates based on task set Resource collection Constraints and the number of random generation Generate random candidate scheduling schemes; Indicates based on task set Resource collection Constraints Heuristic rules and the number of heuristically generated Generate heuristic candidate scheduling schemes; This represents time window constraints, resource capacity constraints, priority constraints, and resource conflict constraints. This indicates a pre-defined heuristic rule.

[0058] 3.3 Feasibility handling mechanism: After the initial candidate scheduling schemes are generated, the feasibility of the candidate scheduling schemes is determined. If the candidate scheduling scheme meets the time window constraint, resource capacity constraint, priority constraint, and resource conflict constraint, it is taken as a feasible candidate scheduling scheme in the initial candidate solution set; if the candidate scheduling scheme does not meet any of the above constraints, it is repaired or regenerated.

[0059] Define constraint violation degree as:

[0060] When the following conditions are met: When, it indicates a candidate scheduling scheme. If a constraint violation occurs, it can be corrected by adjusting variables to satisfy the constraint, or the solution can be retained and a penalty term introduced into the subsequent fitness function. The correction process includes at least one of the following methods: adjusting task allocation relationships, adjusting task execution order, adjusting resource occupancy status, and recalculating task start and finish times. Through these processes, the initial candidate solution set satisfies the basic scheduling constraints and provides an initial solution space for subsequent optimization searches.

[0061] Step 4) specifically includes the following steps:

[0062] 4.1 Construction of multi-objective function: In order to comprehensively evaluate the performance of the scheduling scheme, a multi-objective function is constructed from three aspects: system operating efficiency, resource usage cost and energy consumption level.

[0063] (1) Total completion time, i.e., efficiency index:

[0064] in, Indicates task The completion time. This indicator reflects the maximum time required for all tasks to complete and is a core metric for measuring overall scheduling efficiency; the smaller the value, the higher the scheduling efficiency.

[0065] (2) Resource usage cost, i.e., economic indicators:

[0066] in, Representing resources Unit usage cost Representing resources The actual amount or status of resource usage. This metric is used to measure the economic cost of resource usage during the scheduling process.

[0067] (3) System energy consumption, i.e., energy efficiency indicators:

[0068] in, For the task In resources The energy consumption of the system is the energy consumption level during system operation.

[0069] 4.2 Index Normalization: Due to differences in the dimensions and value ranges of different objective functions, in order to avoid any single index having a dominant influence on the optimization results, it is necessary to normalize each objective.

[0070] in, Indicates the first The normalized values ​​of the objective function; Indicates the first The original values ​​of the objective function; and They represent the first The minimum and maximum values ​​of each objective function in the current candidate solution set; This represents the smallest positive number that prevents the denominator from being zero. Through normalization, all objective functions can be uniformly mapped to... This interval facilitates the subsequent construction of the comprehensive fitness function.

[0071] 4.3 Penalty Function Construction: During the scheduling process, some candidate scheduling schemes may violate time window constraints, resource capacity constraints, priority constraints, or resource conflict constraints. To ensure the feasibility of the optimization results, a penalty function is introduced to assess the degree of constraint violation. This is then added as a penalty term to the overall fitness function.

[0072] For candidate scheduling schemes Define the degree of constraint violation The sum of resource capacity violation degree, time window violation degree, priority conflict degree, and resource conflict degree:

[0073] The degree of resource capacity violation is:

[0074] The degree of violation of the time window is:

[0075] The priority conflict level is:

[0076] The degree of resource conflict is:

[0077] in, This indicates an indicator function that takes the value 1 when the condition within the parentheses is true, and 0 otherwise.

[0078] The penalty item is defined as:

[0079] The penalty coefficient is dynamically adjusted during the iteration process, and is expressed as follows:

[0080] in, The initial penalty coefficient, This represents the current iteration number. This represents the maximum number of iterations. In the early stages of optimization, the penalty coefficient is small to enhance the search and exploration capabilities; in the later stages of optimization, the penalty coefficient gradually increases to improve the feasibility of candidate scheduling schemes.

[0081] 4.4 Dynamic weighting mechanism: To achieve dynamic balance among multiple objectives, weight coefficients that change with iteration are introduced.

[0082] in, These are the initial weights; It is the adjustment coefficient; This is the current iteration number.

[0083] The dynamic weighting mechanism can adjust the importance of each objective according to the optimization stage, so that the algorithm focuses on exploration in the early stage of the search and gradually enhances the convergence ability in the later stage.

[0084] 4.5 Construct the comprehensive fitness function, which is defined as follows:

[0085] in, It is the normalized objective function. It is a dynamic weight. It is the degree of violation of the constraint. It is the penalty coefficient. By constructing a comprehensive fitness function that integrates multi-objective evaluation, dynamic weight adjustment, and constraint penalty mechanisms, the optimization process can achieve coordinated optimization of system efficiency, cost, and energy consumption while ensuring the feasibility of the scheduling scheme, thereby improving the overall performance and stability of the scheduling results.

[0086] Step 5) specifically includes the following steps: 5.1 Individual Update Mechanism: After obtaining the comprehensive fitness function, iterative updates of individuals in the population are needed to achieve solution space search and optimization. This invention updates candidate scheduling schemes based on the shrinking-expanding behavior of the slime mold algorithm. To avoid conflicts with task priorities... Obfuscation, the exploration and exploitation control threshold in the slime mold algorithm is denoted as The individual update rules are as follows:

[0087] in, For the first The individual in the first The position of the generation, i.e., the candidate scheduling scheme; It is the currently globally optimal individual; and These are randomly selected candidate scheduling schemes; and This is the search step size coefficient; For search weight; This indicates element-wise multiplication; A random number between 0 and 1; To control the threshold for exploration and development.

[0088] when When an individual moves closer to the current optimal solution, it performs local development; when At that time, random difference updates are performed, and global exploration is executed to achieve a dynamic balance between global search and local development.

[0089] 5.2 Weight Update Mechanism: To reflect differences in individual fitness, a fitness-based search weight update mechanism is introduced.

[0090] in, Individual In the The overall fitness value at the next iteration; and These are the best and worst combined fitness values ​​for the current population, respectively. This is the weight scaling factor; To prevent extremely small positive numbers with a denominator of zero, high-quality individuals are given larger weights to guide the search direction, while low-quality individuals are given smaller weights to reduce their influence, thereby enhancing the guiding ability of excellent solutions and improving convergence efficiency.

[0091] 5.3 Adaptive Search Coefficients: To achieve a smooth transition from global exploration to local development in the search process, adaptive search coefficients are introduced.

[0092] Where t is the current iteration number, This represents the maximum number of iterations. (Initial optimization phase) Larger size, wider search range; later optimization stages By gradually decreasing the size, the search becomes more refined, thereby improving the algorithm's convergence stability.

[0093] Step 6) specifically includes the following steps:

[0094] 6.1 Random perturbation mechanism: To avoid the algorithm getting trapped in local optima, random perturbation is introduced after each individual update.

[0095] in, The disturbance intensity coefficient is... It follows a standard normal distribution. By introducing random perturbations into the solution space, the diversity of the candidate solution set can be increased.

[0096] The candidate scheduling scheme after the perturbation is represented as follows:

[0097] 6.2 Diversity Maintenance Mechanisms: To prevent premature convergence of populations during evolution, population diversity indices are defined as follows:

[0098] in, For the first Average position of the population at the next iteration Population size.

[0099] When the population diversity is below a preset threshold, perform perturbation enhancement:

[0100] in, For diversity threshold, To enhance the perturbation coefficient, when the population distribution is too concentrated, the search space is expanded again through perturbation enhancement.

[0101] 6.3 Elite Preservation Strategy: To prevent the optimal solution from being lost during the iteration process, an elite preservation mechanism is adopted:

[0102] This formula indicates that the current best individual directly enters the next generation of candidate solutions, thus ensuring the stability of the optimization process.

[0103] Step 7) specifically includes the following steps:

[0104] 7.1 Individual selection mechanism: After each generation of candidate scheduling schemes is updated, the candidate scheduling schemes before and after the update are compared, and greedy selection is performed according to the comprehensive fitness value.

[0105] set up Indicates the first The th iteration in the One candidate scheduling scheme, This represents the candidate scheduling scheme obtained after updating with the slime mold algorithm, random perturbation, and constraint repair. This represents the overall fitness value of the candidate scheduling schemes before the update. This represents the overall fitness value of the updated candidate scheduling scheme. The individual selection rule is as follows:

[0106] Since the comprehensive fitness function in this invention is optimized by minimization, a smaller comprehensive fitness value indicates a better candidate scheduling scheme. Through the above greedy selection strategy, it can be ensured that the overall quality of the candidate solution set continuously improves or remains unchanged during the iteration process.

[0107] Step 8) specifically includes the following steps:

[0108] 8.1 Iteration Termination Condition The iteration stops when at least one of the following termination conditions is met.

[0109] First, the number of iterations reaches the preset maximum number of iterations. ,Right now:

[0110] Second, continuous The change in the current optimal overall fitness value within a generation is less than the preset convergence threshold. ,Right now:

[0111] in, Indicates the preset number of consecutive iterations. This indicates the preset convergence threshold. Indicates the first The current optimal overall fitness value at the next iteration. Indicates the first The current optimal overall fitness value at the next iteration.

[0112] Third, the current optimal overall fitness value is less than or equal to the preset target value. ,Right now:

[0113] in, This represents the preset target fitness value.

[0114] 8.2 Output Results: The final output is the optimal scheduling scheme:

[0115] in, This is the final optimal scheduling scheme; The feasible solution space is the set of solutions that satisfy all scheduling constraints. This is the comprehensive fitness function used to evaluate the scheduling scheme when the algorithm terminates; This represents the number of iterations at which the algorithm terminates.

[0116] Through the above steps, this invention constructs a scheduling optimization method that integrates multi-objective optimization, dynamic weight adjustment, constraint penalty and swarm intelligence search mechanism, which can achieve efficient and stable multi-task collaborative scheduling under complex constraints.

[0117] Example 2: Another embodiment of the present invention provides a multi-task cooperative scheduling and resource optimization system based on slime mold algorithm, comprising: The data input module is used to acquire task information, resource information, and related constraint parameters; The scheduling modeling module is used to build a task-resource coordination model and establish a matching relationship between tasks and resources; The decision encoding module is used to generate scheduling decision vectors and construct candidate solution sets; The performance evaluation module is used to evaluate the performance of scheduling schemes based on a multi-objective evaluation mechanism. The optimization solution module is used to iteratively optimize the candidate solution set based on the slime mold algorithm and to achieve solution space search through fitness-driven approach. The constraint management module is used to detect whether the scheduling scheme meets the constraints and to handle them through repair or penalty strategies. The results output module is used to output the optimized scheduling scheme and corresponding performance indicators.

[0118] Example 3: Figure 2 As shown, in this task-resource matching model, the task set Each task in Based on task requirements Execution time window Execution time and priority Describe its task requirements parameters; resource set Each resource in Resource capacity constraints and unit usage cost Characterize its resource capacity parameters. The relationship between tasks and resources is established through 0-1 decision variables. To achieve matching, when When, it indicates a task. Allocate to resources ;when When, it indicates a task. Unallocated to resources .

[0119] Determining the matching relationship includes: based on task requirements. Resource capacity constraints Determine if the capacity is sufficient; based on the task execution time window. Is it compatible with the time-based resource scheduling availability status determination? Based on task priority. Order of task execution Determine whether priority constraints are met. Through the above method, the correspondence between task requirement parameters and resource capability parameters can be clearly defined, and a closed-loop scheduling and matching relationship between task requirements and resource capabilities can be formed.

[0120] Example 4: Figure 3 As shown, the scheduling decision vector Candidate scheduling schemes are characterized from three aspects: task allocation, task execution order, and resource occupancy status.

[0121] in, Assign a variable matrix to the task to represent the task. With resources The allocation and attribution relationship between them; when When, it indicates a task. Allocate to resources ,when When, it indicates a task. Unallocated to resources .

[0122] This is a variable representing the task execution order, used to indicate the scheduling logic between tasks; where, Indicates task The execution order position in the scheduling sequence is used to determine whether priority constraints are met.

[0123] This is a resource occupancy state variable used to represent resources. The occupancy status during the scheduling process includes resource capacity occupancy status and resource time occupancy status; wherein, resource capacity occupancy status is used to determine whether resource capacity constraints are met, and resource time occupancy status is used to determine whether time window constraints and resource conflict constraints are met.

[0124] Task Start execution time and completion time It is not used as an independent scheduling decision variable, but rather as a task allocation variable. Task execution order variables and resource usage state variables Confirmed. Specifically, when the task... Assigned to resources Then, based on resources Existing time occupancy status, tasks Execution order position And tasks The execution time window is used to determine the task. Start execution time And according to the formula Define the task Completion time .

[0125] By combining the above three types of variables, the specific location of a candidate scheduling scheme in the solution space can be determined.

[0126] Example 5: Figure 7 As shown, set the task set This represents the delivery tasks to be completed. Each task includes delivery requirements, service time window, execution duration, and priority information; a resource set is also defined. This represents the transportation resources available for executing the task, each resource having capacity limitations and unit operating costs. The spatial distribution of tasks and their demand parameters are randomly generated, and the availability and operational capabilities of the resources are initialized.

[0127] First, without optimizing the scheduling, the scheduling process is executed using the baseline scheduling strategy to obtain baseline performance indicators, including total system completion time, resource usage cost, and overall energy consumption level.

[0128] Subsequently, the scheduling scheme is optimized according to the method proposed in this invention. First, the task-resource allocation relationship is encoded and represented, and an initial set of candidate scheduling schemes is constructed. Then, the scheduling scheme is iteratively optimized based on the slime mold algorithm. During the optimization process, a multi-objective evaluation mechanism, dynamic weight adjustment, constraint penalty strategy, random perturbation, and diversity preservation mechanism are combined to continuously improve the scheduling scheme.

[0129] After multiple iterations, the optimal scheduling scheme is output, including task allocation relationships, execution order and resource usage, and the corresponding optimized performance indicators are calculated, such as the optimized total completion time, resource usage cost and system energy consumption.

[0130] By comparing the performance indicators before and after optimization, it can be verified that the method of the present invention can effectively reduce the total system completion time, reduce resource usage costs, and reduce overall energy consumption under the premise of meeting task constraints and resource constraints, thereby significantly improving the overall operating efficiency and resource utilization efficiency of the scheduling system.

[0131] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A multi-task cooperative scheduling and resource optimization method based on slime mold algorithm, characterized in that, Includes the following steps: 1) Construct a task-resource collaboration model: Obtain the task set in the target system. and resource collection Each task Includes task requirements Execution time window Execution time and priority , can be represented as: Each resource Including resource capacity constraints Unit usage cost , ; Assign variables through tasks Indicates task With resources The matching relationship between them ,in Indicates task Allocate to resources , Indicates task Unallocated to resources ; 2) Generate scheduling decision representation: Define and encode scheduling decision vectors ,in, Assign a variable matrix to the task. For task execution order variables, Indicates task The execution order position in the scheduling sequence; For resource occupancy state variables, Representing resources The occupancy status during the scheduling process includes resource capacity occupancy status and resource time occupancy status; task Start execution time and completion time Instead of being used as an independent scheduling decision variable, it is determined based on the task allocation variable A, the task execution order variable O, and the resource occupancy status variable U; the combined values ​​of the above task allocation variable, task execution order variable, and resource occupancy status variable uniformly represent the solution space location corresponding to different candidate scheduling schemes; 3) Initialize the candidate scheduling scheme set: Based on the task set, resource set, and constraints such as time window, resource capacity, priority, and resource conflict, generate multiple candidate scheduling schemes using a combination of random and heuristic generation methods to form an initial candidate scheduling scheme set. Where P is the total number of candidate scheduling schemes, the random generation method is used to randomly determine the task allocation relationship, task execution order and resource occupancy status, and the heuristic generation method generates candidate scheduling schemes according to preset heuristic rules, which include at least one of nearest resource priority, low-cost resource priority, or high-priority task priority; the ratio of the number of random generation schemes to the number of heuristic generation schemes is determined by a preset control ratio parameter ρ, where the value of ρ ranges from 0 < ρ < 1, and the number of randomly generated candidate scheduling schemes is... The number of candidate scheduling schemes generated heuristically is When the generated candidate scheduling scheme does not meet the constraints, it is repaired or regenerated to obtain the initial candidate solution set. 4) Establish a scheduling performance evaluation mechanism: Construct a multi-dimensional performance evaluation system around three indicators: total completion time, resource usage cost, and system energy consumption, and use it to measure the merits of different scheduling schemes; 5) Perform search optimization based on slime mold algorithm: By simulating the adaptive search behavior of slime mold in the environment, the candidate scheduling scheme is iteratively updated, and the individual distribution is dynamically adjusted according to the fitness evaluation results to achieve continuous optimization of the solution space; 6) Introducing an optimization and enhancement mechanism: During the iterative update of candidate scheduling schemes, fitness-based weight updates, random perturbations, diversity preservation, and retention of the current best individual are performed. Among them, fitness-based weight updates are used to adjust the search weights according to the comprehensive fitness value of the candidate scheduling schemes, random perturbations are used to increase the diversity of the candidate solution set, diversity preservation is used to avoid premature convergence of the candidate solution set, and retention of the current best individual is used to prevent the current best scheduling scheme from being lost during the iteration process. 7) Perform individual selection and population update: After each iteration, compare the comprehensive fitness values ​​of the candidate scheduling schemes before and after the update, and use a greedy selection strategy to select; when the comprehensive fitness value of the candidate scheduling scheme after the update is less than or equal to the comprehensive fitness value of the candidate scheduling scheme before the update, replace the candidate scheduling scheme before the update with the candidate scheduling scheme after the update, otherwise retain the candidate scheduling scheme before the update. 8) Output scheduling optimization results: Stop iteration when the preset termination condition is met, and output the scheduling scheme with the best comprehensive fitness value and that meets the constraints; the preset termination condition includes at least one of the following: the number of iterations reaches the preset maximum number of iterations, the change of the best comprehensive fitness value within a consecutive preset number of generations is less than the preset convergence threshold, and the best comprehensive fitness value reaches the preset target value.

2. The multi-task cooperative scheduling and resource optimization method based on slime mold algorithm according to claim 1, characterized in that: The task requirement parameters include task requirements. Execution time window Execution time and priority The resource capability parameters include resource capacity constraints. and unit usage cost The matching relationship between tasks and resources is represented by the 0-1 decision variables, and is determined according to task requirements. Does it meet resource capacity constraints? Task execution time window Does it meet the requirements for resource scheduling availability and task priority? Determine whether the task execution order requirements are met and whether the task can be allocated to the corresponding resource.

3. The multi-task cooperative scheduling and resource optimization method based on slime mold algorithm according to claim 1, characterized in that: In step 2), the scheduling decision vector X is represented using a parameterized encoding method, and X = [A, O, U]; where, Assign a variable matrix to the task. Used to define tasks Should resources be allocated? ; For task execution order variables, Used to define tasks The execution order position in the scheduling sequence; For resource occupancy state variables, Used to define resources The occupancy status includes resource capacity occupancy status and resource time occupancy status. Different scheduling decision vectors are formed by taking different combinations of values ​​for task allocation variables, task execution order variables and resource occupancy status variables. Each scheduling decision vector corresponds to a candidate scheduling scheme, thereby realizing the description of the position of different scheduling strategies in the solution space.

4. The multi-task cooperative scheduling and resource optimization method based on slime mold algorithm according to claim 1, characterized in that: The scheduling scheme must simultaneously satisfy the following constraints: Unique task allocation constraint: Each task is assigned to a resource; Resource capacity constraints: The task requirements allocated to the same resource shall not exceed the capacity limit of that resource; Time window constraint: The start and finish times of each task are located within their corresponding execution time windows; Priority constraints: The task execution order meets the task priority requirements; Resource conflict constraints: The same resource is not occupied by multiple conflicting tasks within the same time period. The start and finish times of a task are determined based on task allocation variables, task execution order variables, and resource occupancy status variables.

5. The multi-task cooperative scheduling and resource optimization method based on slime mold algorithm according to claim 4, characterized in that: When a candidate scheduling scheme does not meet the constraints, the constraint violation degree V(X) of the candidate scheduling scheme is calculated. The constraint violation degree V(X) includes the resource capacity violation degree, time window violation degree, priority conflict degree, and resource conflict degree, and is expressed as: Among them, the degree of resource capacity violation is determined by the portion of the actual resource usage exceeding the resource capacity limit; the degree of time window violation is determined by the portion of the task start time exceeding the lower limit of the time window or the task completion time exceeding the upper limit of the time window; the degree of priority conflict is determined by the number of conflicts between task priority and task execution order; and the degree of resource conflict is determined by the situation where the same resource is occupied by multiple conflicting tasks in the same time period. The probability of infeasible candidate scheduling schemes being selected is reduced by repair processing or by adding a penalty term to the comprehensive fitness function.

6. The multi-task cooperative scheduling and resource optimization method based on slime mold algorithm according to claim 1, characterized in that: The scheduling performance evaluation mechanism constructed in step 4) uses task completion time as the core indicator and combines resource usage cost and system energy consumption to construct a multi-objective evaluation function. The total completion time objective function is: The objective function for resource utilization cost is: The system energy consumption objective function is: Normalize the k-th objective function: The dynamic weights corresponding to the k-th objective function are defined as follows: A comprehensive fitness function is formed through a dynamic weight allocation strategy: This guides the optimization and evolution process of the candidate solution set.

7. The multi-task cooperative scheduling and resource optimization method based on slime mold algorithm according to claim 1, characterized in that: In steps 5) to 7), the current optimal scheduling scheme is first determined based on the comprehensive fitness value, and the search weight is determined based on the comprehensive fitness value of the candidate scheduling schemes. Then, based on the current optimal scheduling scheme, randomly selected candidate scheduling schemes, and the search weights, an updated candidate scheduling scheme is generated; subsequently, random perturbation and constraint repair are performed on the updated candidate scheduling schemes, and the current optimal scheduling scheme is directly retained to the next generation of candidate solution set; finally, greedy selection is performed according to the comprehensive fitness value to complete the candidate solution set update.

8. A multi-task collaborative scheduling and resource optimization system based on slime mold algorithm, characterized in that, include: The data input module is used to acquire task information, resource information, and related constraint parameters; The scheduling modeling module is used to build a task-resource coordination model and establish a matching relationship between tasks and resources; the decision encoding module is used to generate scheduling decision vectors and build a candidate solution set; and the performance evaluation module is used to evaluate the performance of scheduling schemes based on a multi-objective evaluation mechanism. The optimization and solution module is used to iteratively optimize the candidate solution set based on the slime mold algorithm and to achieve solution space search through fitness-driven approach; the constraint management module is used to detect whether the candidate scheduling scheme meets the constraint conditions and to process it through repair or penalty strategies. The results output module is used to output the optimized scheduling scheme and corresponding performance indicators.

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