Public testing resource scheduling method based on multi-level random characteristic particle swarm optimization

Abstract

A public test resource scheduling method based on multi-level random characteristic particle swarm optimization comprises the steps of construction of a task scheduling model and a resource constraint model, design of a multi-level optimization structure, definition of a task dependency relationship and formulation of a resource allocation rule, and meanwhile an optimization algorithm used for public test resource scheduling is designed. According to the method, the efficient scheduling strategy is constructed by designing the multi-level random characteristic particle swarm optimization algorithm, reasonable allocation of resources in multi-task scheduling is achieved, and the project construction period is effectively shortened. Compared with a traditional method, the method has more advantages in the aspects of solving efficiency and scheduling quality, the total project construction period can be shortened, the resource utilization rate can be increased, and the method is very suitable for a complex multi-skill public measurement resource-limited project scheduling scene.

Description

Technical Field

[0001] The present invention relates to the field of project scheduling optimization, and in particular to a crowd-testing resource scheduling method based on multi-level random characteristic particle swarm optimization. Background Art

[0002] The skill diversity of resources and the resource allocation constraints of tasks are two real factors that are generally ignored in the existing research on the crowd-testing resource scheduling problem (MS-RCPSP). Few studies have conducted in-depth discussions on the project scheduling problem with crowd-testing resource constraints. However, the foundations of the project scheduling problem with crowd-testing resource constraints, such as the classic resource scheduling problem (RCPSP) and the crowd-testing resource allocation problem, have received widespread attention. In addition, particle swarm optimization (PSO) technology has been successfully applied to task scheduling problems and resource allocation optimization problems, which lays the foundation for solving the MS-RCPSP problem. In summary, it is urgent to design a new method to solve the crowd-testing resource scheduling problem. At the same time, it is feasible to use multi-level random characteristic particle swarm optimization (RND-PSO) technology to construct an optimization strategy to solve the MS-RCPSP problem. Summary of the invention

[0003] The present invention provides a crowd-testing resource scheduling method based on multi-level random characteristic particle swarm optimization, which aims to overcome the defects of insufficient processing of complex resource allocation and task dependency in existing crowd-testing resource problems by introducing a multi-level optimization strategy.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A crowd-testing resource scheduling method based on multi-level random characteristic particle swarm optimization includes the following steps:

[0006] Step 1: Build a dynamic and adaptive crowd-testing resource project scheduling model that integrates factors such as task dependency, resource constraints, and skill matching. Through the multi-objective design of optimizing resource allocation and shortening construction period, the model can not only reduce project construction period, but also improve resource utilization efficiency, effectively balancing the contradiction between "resource competition" and "task order";

[0007] Step 2: Introduce an adaptive inertia weight adjustment strategy. In the early iterations, use a higher inertia weight to achieve extensive search to ensure that the solution can fully cover the space and avoid missing the best solution; in the later stage, gradually reduce the weight so that particles gather and optimize near the current optimal solution. This strategy balances the exploration and convergence problems of the particle swarm algorithm, and dynamically adjusts parameters by monitoring fitness to better adapt to complex scheduling needs;

[0008] Step 3: Implement the random characteristic particle swarm optimization algorithm under the multi-level optimization framework. In the exploration phase, the potential optimal solutions are comprehensively screened by randomly initializing the particle positions; in the development phase, the scheduling solutions near the current optimal solution are optimized to gradually improve the scheduling quality. The multi-level collaboration improves the global search and local optimization capabilities of the algorithm.

[0009] Step 4: Generate and verify the scheduling plan. Determine the scheduling order of tasks by decoding particle positions, calculate the start and end time of tasks, and verify whether the plan meets the constraints such as resource allocation, task dependency, and skill matching. The optimization effect is evaluated by comparing with other methods to confirm its superiority and applicability in complex scenarios.

[0010] Step 1: Build and dynamically adjust the crowd testing resource scheduling model based on a multi-level optimization strategy. The specific steps are as follows:

[0011] Step 1.1, define the index, which includes four parts, namely task index j (j = 1, 2, ..., J), resource index r (r = 1, 2, ..., K), time index t, skill index k (k = 1, 2, ..., N), where task index j defines the index of each task in the task set, and the value range is j = 1, 2, ..., J; resource index r defines the index of each resource in the resource set, and the value range is r = 1, 2, ..., K; time index t defines the index of a time point, which is used to indicate the execution status of a task at a specific time; skill index k defines the index of each skill in the skill set, and the value range is k = 1, 2, ..., N;

[0012] Step 1.2: Define the model parameters, which include six parts: resource set R, task set J, skill plan S, task quantity J, resource quantity K, and skill quantity N. The resource set R includes all available resources; the task set J includes all tasks that need to be scheduled; the skill plan S includes all skills required for task execution; the task quantity J is the total number of tasks in the project; the resource quantity K is the total number of resources in the project; and the skill quantity N is the total number of skills in the project.

[0013] Step 1.3: Define model variables, which include eight parts: resource R r 、Task T j , Skill S k , task duration d j , task start time s j , Skill Requirement Proficiency jk , Resource Mastery Level Q rk , the set of pre-tasks P j , where resource R r represents the rth resource, which is a specific resource in the resource set; task Tj represents the jth task, which is a specific task in the task set; skill S k represents the kth skill, which is a specific skill in the skill set; the task duration d j It is task T j The execution duration of the task; the task start time s j It is task T j Starting time; skill proficiency required jk It is task T j Skill S k Proficiency requirements; resource mastery level Q rk It is a resource R r Skill S k The mastery level and the set of pre-tasks P j It is task T j The set of pre-tasks;

[0014] Step 1.4: Define the decision variables, which include two parts: assigning variables x jr and execute variable y jrt :

[0015]

[0016] Assign variable x jr is a binary decision variable used to indicate whether task T j Assigned to resource R r ; Execute variable y jrt Used to represent the resource R at time t r Whether to execute task T j ;

[0017] Step 1.5: Construct the objective function. The core of this step is to optimize the project's make span by constructing the objective function. The objective function is used to describe the maximum completion time of all tasks in the project, that is, the total duration. The specific definition is as follows:

[0018] Minimize max{s j +d j ,j∈J}

[0019] In the exploration and development stages, the task priority weights are adjusted according to the importance of the tasks, so that the optimization objectives are more adapted to the optimization needs of different stages:

[0020]

[0021] Where w1+w2=1, and w1 and w2 are adjusted dynamically according to the stage;

[0022] Step 1.6: Construct constraints. In the model, a series of constraints need to be introduced to ensure the feasibility of task scheduling and the rationality of resource allocation. These constraints include the following categories:

[0023] The task priority constraints are as follows:

[0024]

[0025] This constraint ensures that task T j Only in all its predecessor tasks T j After completion, start

[0026] The skill matching constraints are as follows:

[0027]

[0028] This constraint ensures that the allocated resource R r Must meet the task T j Required skills k The proficiency requirements

[0029] The unique assignment constraints are as follows:

[0030]

[0031] This constraint stipulates that each task can only be assigned to one resource for execution.

[0032] The resource usage restrictions are as follows:

[0033]

[0034] This constraint ensures that each resource can only process one task at a time.

[0035] The variable value range constraints are as follows:

[0036]

[0037] These constraints define the range of values ​​that the variables can take, making the construction of the solution reasonable;

[0038] Step 1.7: Setting of multi-level optimization strategy. In order to improve the performance of the algorithm, the multi-level optimization strategy is optimized for different goals in the exploration phase and the development phase, as follows:

[0039] Exploration phase settings: The goal of the exploration phase is to fully search the solution space to prevent the algorithm from falling into the local optimum. In this phase, the position and speed of the particle swarm are initialized, where each particle represents a possible task scheduling order, the position of the particle reflects the task order, and the speed indicates the direction and magnitude of the change in the scheduling order; a higher inertia weight (w) is set, usually between 0.8 and 1.2, so that the particles move in a larger range, and the cognitive coefficient (c1) and social coefficient (c2) can be set to smaller values ​​(such as 1.0 and 1.2) to reduce the possibility of over-convergence to the local or global optimum; each particle updates its speed and position according to its own historical optimal position (pbest) and global optimal position (gbest). The particle speed and position update formulas are as follows. Through the above formulas, particles can perform diversified searches in different areas, thereby improving the initial exploration capabilities of the algorithm:

[0040] v i+1 =ω·v i +c1·r1·(p local -x i )+c2·r2·(p global -x i )

[0041] x i+1 =x i +v i+1

[0042] Development phase settings: After the exploration phase is completed, the algorithm enters the development phase, focusing on optimizing the area near the current solution. The specific settings are as follows: Use a linear decreasing strategy to gradually reduce the inertia weight (w), usually between 0.4 and 0.6, to encourage particles to gather near the optimal solution. The formula is as follows:

[0043]

[0044] Gradually increase the social coefficient and cognitive coefficient (for example, c1=2.0, c2=2.5) to strengthen the ability of particles to move toward the local optimal and global optimal solutions. In the development stage, constrain the particle speed to avoid excessive fluctuations that lead to deviations from the current optimal solution. Each particle updates its position and speed based on the reduced inertia weight (w) and the improved cognitive and social coefficients, gradually converges to the optimal solution, and records the current global optimal value to ensure the stability and efficiency of the final solution.

[0045] Phase transition criteria: The transition between the exploration phase and the development phase can be carried out dynamically based on the number of iterations, the fitness change rate and the dynamic adjustment mechanism. Based on the number of iterations, the system can automatically switch to the development phase when the total number of iterations reaches half; based on the fitness change rate, if the fitness value does not change significantly after multiple consecutive iterations, the system can enter the development phase in advance; the dynamic adjustment mechanism is to flexibly determine the switching time by analyzing the fitness distribution and change trend of the particles to ensure the adequacy of the search in the exploration phase.

[0046] Step 2: Introduce an adaptive inertia weight adjustment strategy. In the early iterations, use a higher inertia weight to achieve extensive search to ensure that the solution can fully cover the space and avoid missing the best solution; in the later stage, gradually reduce the weight so that particles gather and optimize near the current optimal solution. This strategy balances the exploration and convergence problems of the particle swarm algorithm, and dynamically adjusts parameters by monitoring fitness to better adapt to complex scheduling needs. The specific steps are as follows:

[0047] Step 2.1. Dynamic adjustment formula of inertia weight: At each iteration, the inertia weight (w) is adjusted according to the following formula:

[0048] where w max and w min are the initial and minimum inertia weights respectively; t is the current iteration number, T max is the total number of iterations; α is the exponential parameter that controls the decreasing speed, which determines the decreasing rate of the inertia weight;

[0049] Step 2.2, adaptive adjustment scheme: In the initial stage of the algorithm, the inertia weight is set to a higher value to encourage the particle swarm to conduct a comprehensive search in a broad solution space, enhancing diversity and exploration capabilities. As the iterations progress, the inertia weight will gradually decrease in a linear or nonlinear decreasing manner, approaching a smaller value, thereby enhancing the convergence performance of the particles and making them more focused on optimization and refinement near the current solution. At the same time, in order to adapt to the current solution distribution of the particle swarm, by monitoring the change in fitness, the update rule of the inertia weight is adaptively and dynamically adjusted to ensure that the change in the inertia weight can match the convergence requirements of the solution and the balance of exploration depth, thereby effectively improving the quality of the solution and optimization efficiency.

[0050] Step 3: Implement the random characteristic particle swarm optimization algorithm under the multi-level optimization framework. In the exploration phase, the potential optimal solutions are comprehensively screened by randomly initializing the particle positions; in the development phase, the scheduling schemes near the current optimal solution are optimized to gradually improve the scheduling quality. The multi-level collaboration improves the global search and local optimization capabilities of the algorithm. The specific steps are:

[0051] Step 3.1: Initialize the particle swarm: randomly generate the initial position and velocity of each particle. The position represents the scheduling order of the tasks, and the velocity represents the rate at which the scheduling order changes. Set the initial inertia weight w max , cognitive coefficient (c1) and social coefficient (c2), provide sufficient flexibility for the initial search of particles;

[0052] Step 3.2, update particle speed and position: The speed update formula is as follows:

[0053]

[0054] v id represents the velocity of the particle on the i-th task, x id represents the position of the particle on the i-th task, pbest and gbest are the local optimal and global optimal positions respectively.

[0055] The position update formula is as follows: Through the position update formula, particles gradually move closer to the optimal solution area, improving optimization efficiency;

[0056] Step 3.3: Update local optimum and global optimum: If the current fitness of a particle is better than the historical optimum, update the local optimal position of the particle; if the local optimal value of all particles is better than the current global optimum, update the global optimal position.

[0057] Step 4: Generate and verify the scheduling plan. Determine the scheduling order of tasks by decoding particle positions, calculate the start and end time of tasks, and verify whether the plan meets the constraints such as resource allocation, task dependency, and skill matching. The optimization effect is evaluated by comparing with other methods to confirm its superiority and applicability in complex scenarios. The specific steps are:

[0058] Step 4.1, generate a scheduling plan: In this stage, according to the final position of the particle, decode the task scheduling order and calculate the start and completion time of each task. The final position of each particle represents the execution order of the task; according to the scheduling order, calculate the start time s of each task one by one j and completion time f j =s j +d j , ensure that the timing of all tasks meets the initial conditions;

[0059] Step 4.2, verify the constraints: Resource constraint check: Check whether the allocation of each resource meets its capacity constraints at any time point t; ensure that the resource usage does not exceed its available amount, that is: Task dependency check: Verify whether the start time of a task meets the finish time requirements of its predecessor tasks.

[0060] Advantages and beneficial effects of the present invention

[0061] The present invention proposes a crowd-testing resource scheduling method based on a multi-level random characteristic particle swarm optimization algorithm. Aiming at the characteristics of the crowd-testing resource scheduling problem, combined with the multi-level particle swarm optimization technology, an optimization algorithm including exploration and development stages is designed. The method comprehensively considers the impact of multiple factors such as resource allocation, task dependency, and skill matching on the scheduling effect, aiming to improve project scheduling efficiency and shorten project duration (makespan). The present invention is suitable for scenarios such as complex project management, engineering scheduling, and manufacturing system optimization, and can achieve more efficient resource utilization and project execution effects, providing effective technical support for improving productivity and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flow chart of a crowd-test resource scheduling method of a multi-level random characteristic particle swarm optimization algorithm of the present invention;

[0063] Figure 2 It is a topological diagram of task dependencies and resource constraints in crowd-testing resource scheduling. DETAILED DESCRIPTION

[0064] The present invention is described in detail below with reference to the accompanying drawings and examples.

[0065] A crowd-test resource scheduling method based on a multi-level random characteristic particle swarm optimization algorithm is constructed according to a crowd-test resource scheduling problem with 5 task nodes and several dependencies (the structure information is shown in Table 1). The multi-level optimization method is used to solve the optimal scheduling plan of resources and tasks within a limited time unit. The specific implementation plan includes the following contents and steps:

[0066] Table 1 Structural information of a crowd-testing resource scheduling

[0067]

[0068]

[0069]

[0070] Step 1: Build and dynamically adjust the crowd testing resource scheduling model based on a multi-level optimization strategy. The specific steps are as follows:

[0071] Step 1.1, define the index, which includes four parts, namely task index j (j = 1, 2, ..., J), resource index r (r = 1, 2, ..., K), time index t, skill index k (k = 1, 2, ..., N), where task index j defines the index of each task in the task set, and the value range is j = 1, 2, ..., J; resource index r defines the index of each resource in the resource set, and the value range is r = 1, 2, ..., K; time index t defines the index of a time point, which is used to indicate the execution status of a task at a specific time; skill index k defines the index of each skill in the skill set, and the value range is k = 1, 2, ..., N;

[0072] Step 1.2: Define the model parameters, which include six parts: resource set R, task set J, skill plan S, task quantity J, resource quantity K, and skill quantity N. The resource set R includes all available resources; the task set J includes all tasks that need to be scheduled; the skill plan S includes all the skills required for task execution; the task quantity J is the total number of tasks in the project; the resource quantity K is the total number of resources in the project; and the skill quantity N is the total number of skills in the project.

[0073] Step 1.3: Define model variables, which include eight parts: resource R r 、Task T j , Skill S k , task duration d j , task start time s j , Skill Requirement Proficiency jk , Resource Mastery Level Q rk , the set of pre-tasks P j , where resource R r represents the rth resource, which is a specific resource in the resource set; task T j represents the jth task, which is a specific task in the task set; skill S k represents the kth skill, which is a specific skill in the skill set; the task duration d j It is task T j The execution duration of the task; the task start time s j It is task T j Starting time; skill proficiency required jk It is task T j Skill S k Proficiency requirements; resource mastery level Q rk It is a resource R r Skill S k The mastery level and the set of pre-tasks P j It is task T j The set of pre-tasks;

[0074] Step 1.4: Define the decision variables, which include two parts: assigning variables x jr and execute variable y jrt , assign variable x jr is a binary decision variable used to indicate whether task T j Assigned to resource R r ; Execute variable y jrt Used to represent the resource R at time t r Whether to execute task T j :

[0075]

[0076] Step 1.5: Construct the objective function. The core of this step is to optimize the project's make span by constructing the objective function. The objective function is used to describe the maximum completion time of all tasks in the project, that is, the total duration. The specific definition is as follows:

[0077] Minimize max{s j +d j ,j∈J}

[0078] In the exploration and development stages, the task priority weights are adjusted according to the importance of the tasks, so that the optimization objectives are more adapted to the optimization needs of different stages:

[0079]

[0080] Among them, w1+w2=1, and w1 and w2 are adjusted dynamically according to the stage.

[0081] Step 1.6: Construct constraints. In the model, a series of constraints need to be introduced to ensure the feasibility of task scheduling and the rationality of resource allocation. These constraints include the following categories:

[0082] The task priority constraints are as follows:

[0083]

[0084] This constraint ensures that task T j Only in all its predecessor tasks T j Start after you finish.

[0085] The skill matching constraints are as follows:

[0086]

[0087] This constraint ensures that the allocated resource R r Must meet the task T j Required skillsk proficiency requirements.

[0088] The unique assignment constraints are as follows:

[0089]

[0090] This constraint states that each task can only be assigned to one resource for execution.

[0091] The resource usage restrictions are as follows:

[0092]

[0093] This constraint ensures that each resource can only process one task at a time.

[0094] The variable value range constraints are as follows:

[0095]

[0096] These constraints define the range of values ​​that the variables can take, making the construction of the solution reasonable.

[0097] Step 1.7: Setting of multi-level optimization strategy. In order to improve the performance of the algorithm, the multi-level optimization strategy is optimized for different goals in the exploration phase and the development phase, as follows:

[0098] Exploration phase settings: The goal of the exploration phase is to fully search the solution space to prevent the algorithm from falling into the local optimum. In this phase, the position and speed of the particle swarm are initialized, where each particle represents a possible task scheduling order, the position of the particle reflects the task order, and the speed represents the direction and magnitude of the change in the scheduling order; a higher inertia weight (w) is set, usually between 0.8 and 1.2, so that the particles move in a larger range, and the cognitive coefficient (c1) and social coefficient (c2) can be set to smaller values ​​(such as 1.0 and 1.2) to reduce the possibility of over-convergence to the local or global optimum; each particle updates its speed and position according to its own historical optimal position (pbest) and global optimal position (gbest). The particle speed and position update formulas are shown below. Through the above formulas, particles can perform diversified searches in different areas, thereby improving the initial exploration ability of the algorithm.

[0099] v i+1 =ω·v i +c1·r1·(p local -x i )+c2·r2·(p global -x i )

[0100] x i+1 =x i +v i+1

[0101] Development phase settings: After the exploration phase is completed, the algorithm enters the development phase, focusing on optimizing the area near the current solution. The specific settings are as follows; use a linear decreasing strategy to gradually reduce the inertia weight (w), usually between 0.4 and 0.6, to encourage particles to gather near the optimal solution. The formula is as follows

[0102]

[0103] Gradually increase the social coefficient and cognitive coefficient (for example, c1=2.0, c2=2.5) to strengthen the ability of particles to move toward the local optimal and global optimal solutions. In the development stage, constrain the particle speed to avoid excessive fluctuations that lead to deviations from the current optimal solution. Each particle updates its position and speed based on the reduced inertia weight (w) and the improved cognitive and social coefficients, gradually converges to the optimal solution, and records the current global optimal value to ensure the stability and efficiency of the final solution.

[0104] Phase transition criteria: The transition between the exploration phase and the development phase can be carried out dynamically based on the number of iterations, the fitness change rate and the dynamic adjustment mechanism. Based on the number of iterations, the system can automatically switch to the development phase when the total number of iterations reaches half; based on the fitness change rate, if the fitness value does not change significantly after multiple consecutive iterations, the system can enter the development phase in advance; the dynamic adjustment mechanism is to flexibly determine the switching time by analyzing the fitness distribution and change trend of the particles to ensure the adequacy of the search in the exploration phase.

[0105] Step 2: Introduce an adaptive inertia weight adjustment strategy. In the early iterations, use a higher inertia weight to achieve extensive search to ensure that the solution can fully cover the space and avoid missing the best solution; in the later stage, gradually reduce the weight so that particles gather and optimize near the current optimal solution. This strategy balances the exploration and convergence problems of the particle swarm algorithm, and dynamically adjusts parameters by monitoring fitness to better adapt to complex scheduling needs. The specific steps are as follows:

[0106] Step 2.1. Dynamic adjustment formula of inertia weight: At each iteration, the inertia weight (w) is adjusted according to the following formula:

[0107] where w max and w min are the initial and minimum inertia weights respectively; t is the current iteration number, T max is the total number of iterations; α is the exponential parameter that controls the decreasing speed, which determines the decreasing rate of the inertia weight.

[0108] Step 2.2, adaptive adjustment scheme: In the initial stage of the algorithm, the inertia weight is set to a higher value to encourage the particle swarm to conduct a comprehensive search in a broad solution space, enhancing diversity and exploration capabilities. As the iterations progress, the inertia weight will gradually decrease in a linear or nonlinear decreasing manner, approaching a smaller value, thereby enhancing the convergence performance of the particles and making them more focused on optimization and refinement near the current solution. At the same time, in order to adapt to the current solution distribution of the particle swarm, by monitoring the change in fitness, the update rule of the inertia weight is adaptively and dynamically adjusted to ensure that the change in the inertia weight can match the convergence requirements of the solution and the balance of exploration depth, thereby effectively improving the quality of the solution and optimization efficiency.

[0109] Step 3: Implement the random characteristic particle swarm optimization algorithm under the multi-level optimization framework. In the exploration phase, the potential optimal solutions are comprehensively screened by randomly initializing the particle positions; in the development phase, the scheduling schemes near the current optimal solution are optimized to gradually improve the scheduling quality. The multi-level collaboration improves the global search and local optimization capabilities of the algorithm. The specific steps are:

[0110] Step 3.1: Initialize the particle swarm: randomly generate the initial position and velocity of each particle. The position represents the scheduling order of the tasks, and the velocity represents the rate at which the scheduling order changes. Set the initial inertia weight w max , cognitive coefficient (c1) and social coefficient (c2), provide sufficient flexibility for the initial search of particles;

[0111] Step 3.2, update particle speed and position: The speed update formula is as follows:

[0112]

[0113] v id represents the velocity of the particle on the i-th task, x id represents the position of the particle on the i-th task, pbest and gbest are the local optimal and global optimal positions respectively.

[0114] The position update formula is as follows: Through the position update formula, particles gradually approach the optimal solution area, improving the optimization efficiency.

[0115] Step 3.3, update local optimum and global optimum: if the current fitness of a particle is better than the historical optimum, update the local optimum position of the particle; if the local optimum value of all particles is better than the current global optimum, update the global optimum position;

[0116] Step 4: Generate and verify the scheduling plan. Determine the scheduling order of tasks by decoding particle positions, calculate the start and end time of tasks, and verify whether the plan meets the constraints such as resource allocation, task dependency, and skill matching. The optimization effect is evaluated by comparing with other methods to confirm its superiority and applicability in complex scenarios. The specific steps are:

[0117] Step 4.1, generate a scheduling plan: In this stage, according to the final position of the particle, decode the task scheduling order and calculate the start and completion time of each task. The final position of each particle represents the execution order of the task; according to the scheduling order, calculate the start time s of each task one by one j and completion time f j =s j +d j , ensuring that the timing of all tasks meets the initial conditions.

[0118] Step 4.2, verify the constraints: Resource constraint check: Check whether the allocation of each resource meets its capacity constraints at any time point t; ensure that the resource usage does not exceed its available amount, that is: Task dependency check: Verify whether the start time of a task meets the finish time requirements of its predecessor tasks.

Claims

1. A crowd-testing resource scheduling method based on multi-level random characteristic particle swarm optimization includes the following steps: Step 1: Build a dynamically adaptive multi-skill resource-constrained project scheduling model that integrates factors such as task dependency, resource constraints, and skill matching. Through the multi-objective design of optimizing resource allocation and shortening construction period, the model can not only reduce project construction period, but also improve resource utilization efficiency, effectively balancing the contradiction between "resource competition" and "task order"; Step 2: Introduce an adaptive inertia weight adjustment strategy. In the early iterations, use a higher inertia weight to achieve extensive search to ensure that the solution can fully cover the space and avoid missing the best solution; in the later stage, gradually reduce the weight so that particles gather and optimize near the current optimal solution. This strategy balances the exploration and convergence problems of the particle swarm algorithm, and dynamically adjusts parameters by monitoring fitness to better adapt to complex scheduling needs; Step 3: Implement the random characteristic particle swarm optimization algorithm under the multi-level optimization framework. In the exploration phase, the potential optimal solutions are comprehensively screened by randomly initializing the particle positions; in the development phase, the scheduling solutions near the current optimal solution are optimized to gradually improve the scheduling quality. The multi-level collaboration improves the global search and local optimization capabilities of the algorithm. Step 4: Generate and verify the scheduling plan. Determine the scheduling order of tasks by decoding particle positions, calculate the start and end time of tasks, and verify whether the plan meets the constraints such as resource allocation, task dependency, and skill matching. The optimization effect is evaluated by comparing with other methods to confirm its superiority and applicability in complex scenarios.

2. According to claim 1, a multi-skill resource-constrained project scheduling method based on a multi-level random characteristic particle swarm optimization algorithm is characterized by: The construction of a dynamically adaptive multi-skill resource-constrained project scheduling model described in step 1 integrates factors such as task dependency, resource constraints, and skill matching. Through the multi-objective design of optimizing resource allocation and shortening construction period, the model can not only reduce project construction period, but also improve resource utilization efficiency, and effectively balance the contradiction between "resource competition" and "task sequence". The specific steps are as follows: Step 1.1, define the index, which includes four parts, namely task index j (j = 1, 2, ..., J), resource index r (r = 1, 2, ..., K), time index t, skill index k (k = 1, 2, ..., N), where task index j defines the index of each task in the task set, and the value range is j = 1, 2, ..., J; resource index r defines the index of each resource in the resource set, and the value range is r = 1, 2, ..., K; time index t defines the index of a time point, which is used to indicate the execution status of a task at a specific time; skill index k defines the index of each skill in the skill set, and the value range is k = 1, 2, ..., N; Step 1.2: Define the model parameters, which include six parts: resource set R, task set J, skill plan S, task quantity J, resource quantity K, and skill quantity N. The resource set R includes all available resources; the task set J includes all tasks that need to be scheduled; the skill plan S includes all the skills required for task execution; and the task quantity J is the total number of tasks in the project. The number of resources K is the total number of resources in the project; the number of skills N is the total number of skills in the project; Step 1.3: Define model variables, which include eight parts: resource R r 、Task T j , Skill S k , task duration d j , task start time s j , Skill Requirement Proficiency jk , Resource Mastery Level Q rk , the set of pre-tasks P j , where resource R r represents the rth resource, which is a specific resource in the resource set; task T j represents the jth task, which is a specific task in the task set; skill S k represents the kth skill, which is a specific skill in the skill set; the task duration d j It is task T j Execution duration; task start time s j It is task T j Starting time; skill proficiency required jk It is task T j Skill S k Proficiency requirements; resource mastery level Q rk It is a resource R r Skill S k The mastery level and the set of pre-tasks P j It is task T j The set of pre-tasks; Step 1.4: Define the decision variables, which include two parts: assigning variables x jr and execute variable y jrt : Assign variable x jr is a binary decision variable used to indicate whether task T j Assigned to resource R r ; Execute variable y jrt Used to represent the resource R at time t r Whether to execute task T j ; Step 1.5: Construct the objective function. The core of this step is to optimize the project's make span by constructing the objective function. The objective function is used to describe the maximum completion time of all tasks in the project, that is, the total duration. The specific definition is as follows: Minimize max{s j +d j ,j∈J} In the exploration and development stages, the task priority weights are adjusted according to the importance of the tasks, so that the optimization objectives are more adapted to the optimization needs of different stages: Where w1+w2=1, and w1 and w2 are adjusted dynamically according to the stage; Step 1.6: Construct constraints. In the model, a series of constraints need to be introduced to ensure the feasibility of task scheduling and the rationality of resource allocation. These constraints include the following categories: The task priority constraints are as follows: This constraint ensures that task T j Only in all its predecessor tasks T j After completion, start The skill matching constraints are as follows: This constraint ensures that the allocated resource R r Must meet the task T j Required skills k The proficiency requirements The unique assignment constraints are as follows: This constraint stipulates that each task can only be assigned to one resource for execution. The resource usage restrictions are as follows: This constraint ensures that each resource can only process one task at a time. The variable value range constraints are as follows: These constraints define the range of values ​​that the variables can take, making the construction of the solution reasonable; Step 1.7: Setting of multi-level optimization strategy. In order to improve the performance of the algorithm, the multi-level optimization strategy is optimized for different goals in the exploration phase and the development phase, as follows: Exploration phase settings: The goal of the exploration phase is to fully search the solution space to prevent the algorithm from falling into the local optimum. In this phase, the position and speed of the particle swarm are initialized, where each particle represents a possible task scheduling order, the position of the particle reflects the task order, and the speed represents the direction and magnitude of the change in the scheduling order; a higher inertia weight (w) is set, usually between 0.8 and 1.2, so that the particles move in a larger range, and the cognitive coefficient (c1) and social coefficient (c2) can be set to smaller values ​​(such as 1.0 and 1.2) to reduce the possibility of over-convergence to the local or global optimum; each particle updates its speed and position according to its own historical optimal position (pbest) and global optimal position (gbest). The particle speed and position update formulas are shown below. Through the above formulas, particles can perform diversified searches in different areas, thereby improving the initial exploration ability of the algorithm. v i+1 =ω·v i +c1·r1·(p best -x i )+c2·r2·(g best -x i ) x i+1 =x i +v i+1 Development phase settings: After the exploration phase is completed, the algorithm enters the development phase, focusing on optimizing the area near the current solution. The specific settings are as follows: Use a linear decreasing strategy to gradually reduce the inertia weight (w), usually between 0.4 and 0.6, to encourage particles to gather near the optimal solution. The formula is as follows: Gradually increase the social coefficient and cognitive coefficient (for example, c1=2.0, c2=2.5) to strengthen the ability of particles to move toward the local optimal and global optimal solutions. In the development stage, constrain the particle speed to avoid excessive fluctuations that lead to deviations from the current optimal solution. Each particle updates its position and speed based on the reduced inertia weight (w) and the improved cognitive and social coefficients, gradually converges to the optimal solution, and records the current global optimal value to ensure the stability and efficiency of the final solution. Phase transition criteria: The transition between the exploration phase and the development phase can be carried out dynamically based on the number of iterations, the fitness change rate and the dynamic adjustment mechanism. Based on the number of iterations, the system can automatically switch to the development phase when the total number of iterations reaches half; based on the fitness change rate, if the fitness value does not change significantly after multiple consecutive iterations, the system can enter the development phase in advance; the dynamic adjustment mechanism is to flexibly determine the switching time by analyzing the fitness distribution and change trend of the particles to ensure the adequacy of the search in the exploration phase.

3. According to claim 1, a multi-skill resource-constrained project scheduling method based on a multi-level random characteristic particle swarm optimization algorithm is characterized by: Step 2 introduces the adaptive inertia weight adjustment strategy. In the early iterations, a higher inertia weight is used to achieve extensive search to ensure that the solution can fully cover the space and avoid missing the optimal solution; in the later stage, the weight is gradually reduced to make the particles gather and optimize near the current optimal solution. This strategy balances the exploration and convergence problems of the particle swarm algorithm, and dynamically adjusts parameters by monitoring fitness to better adapt to complex scheduling requirements. The specific steps are as follows: Step 2.

1. Dynamic adjustment formula of inertia weight: At each iteration, the inertia weight (w) is adjusted according to the following formula: where w max and w min are the initial and minimum inertia weights, respectively; t is the current iteration number, T max is the total number of iterations; α is the exponential parameter that controls the decreasing speed, which determines the decreasing rate of the inertia weight; Step 2.2, adaptive adjustment scheme: In the initial stage of the algorithm, the inertia weight is set to a higher value to encourage the particle swarm to conduct a comprehensive search in a broad solution space, enhancing diversity and exploration capabilities. As the iterations progress, the inertia weight will gradually decrease in a linear or nonlinear decreasing manner, approaching a smaller value, thereby enhancing the convergence performance of the particles and making them more focused on optimization and refinement near the current solution. At the same time, in order to adapt to the current solution distribution of the particle swarm, by monitoring the change in fitness, the update rule of the inertia weight is adaptively and dynamically adjusted to ensure that the change in the inertia weight can match the convergence requirements of the solution and the balance of exploration depth, thereby effectively improving the quality of the solution and optimization efficiency.

4. According to claim 1, a multi-skill resource-constrained project scheduling method based on a multi-level random characteristic particle swarm optimization algorithm is characterized by: Step 3 implements the random characteristic particle swarm optimization algorithm under the multi-level optimization framework. In the exploration phase, the potential optimal solutions are comprehensively screened by randomly initializing the particle positions; in the development phase, the scheduling schemes near the current optimal solution are optimized to gradually improve the scheduling quality. The multi-level collaboration improves the global search and local optimization capabilities of the algorithm. The specific steps are as follows: Step 3.1: Initialize the particle swarm: randomly generate the initial position and velocity of each particle. The position represents the scheduling order of the tasks, and the velocity represents the rate at which the scheduling order changes. Set the initial inertia weight w max , cognitive coefficient (c1) and social coefficient (c2), provide sufficient flexibility for the initial search of particles; Step 3.2, update particle speed and position: The speed update formula is as follows: v id represents the velocity of the particle on the i-th task, x id represents the position of the particle on the i-th task, pbest and gbest are the local optimal and global optimal positions respectively. The position update formula is as follows: Through the position update formula, particles gradually move closer to the optimal solution area, improving optimization efficiency; Step 3.3: Update local optimum and global optimum: If the current fitness of a particle is better than the historical optimum, update the local optimal position of the particle; if the local optimal value of all particles is better than the current global optimum, update the global optimal position.

5. According to claim 1, a multi-skill resource-constrained project scheduling method based on a multi-level random characteristic particle swarm optimization algorithm is characterized by: Step 4 generates and verifies the scheduling plan. The scheduling order of tasks is determined by decoding the particle positions, the start and end times of the tasks are calculated, and the plan is verified to meet the constraints such as resource allocation, task dependency, and skill matching. The optimization effect is evaluated by comparing with other methods to confirm its superiority and applicability in complex scenarios. The specific steps are as follows: Step 4.1, generate a scheduling plan: In this stage, according to the final position of the particle, decode the task scheduling order and calculate the start and completion time of each task. The final position of each particle represents the execution order of the task; According to the scheduling order, calculate the start time s of each task one by one j and completion time f j =s j +d j , ensure that the timing of all tasks meets the initial conditions; Step 4.2, verify the constraints: Resource constraint check: Check whether the allocation of each resource meets its capacity constraints at any time point t; ensure that the resource usage does not exceed its available amount, that is: Task dependency check: Verify whether the start time of a task meets the finish time requirements of its predecessor tasks.

Images