A spacecraft system performance optimization method based on on-board resource configuration and scheduling

Abstract

The present invention belongs to the technical field of on-board resource configuration and scheduling system of spacecraft system, and specifically relates to a method for optimizing the performance of a spacecraft system based on on-board resource configuration and scheduling, establishing a TTPN model of the system, proposing mathematical models of cost optimization problem and completion time optimization problem and integrating them, and solving different problems by adjusting the parameters of the fusion model. A mathematical model based on TTPN is proposed according to the expression of the fusion model in combination with the TTPN model, and the model is further linearized to establish an integrated mixed integer linear programming model for on-board resource configuration and scheduling. The model can realize the reasonable configuration and scheduling of on-board resources of the spacecraft system, and realize cost minimization or completion time minimization.

Description

Technical Field

[0001] The present invention belongs to the technical field of on-board resource configuration and scheduling of a spacecraft system, and in particular relates to a spacecraft system performance optimization method based on on-board resource configuration and scheduling. Background Art

[0002] The performance of a spacecraft system (completion time, cycle time, and other indicators) is one of the key factors in determining its overall quality. A spacecraft system usually contains onboard resources such as infrared cameras and radars, and completes a series of tasks through onboard resources. Performance optimization through onboard resources may improve the efficiency of the system. System cost and efficiency may be weighed through appropriate onboard resource allocation. Insufficient onboard resources will lead to system instability and inefficiency, while allocating excess onboard resources will significantly increase the cost of resource allocation. In addition, reasonable onboard resource scheduling can optimize resource utilization and improve system performance under given resource allocation. Therefore, onboard resource allocation and scheduling problems have been widely studied in recent years.

[0003] Timed Petri Nets (TPNs) can effectively simulate the characteristics of most discrete event systems and can efficiently and accurately evaluate the cycle time of the system through linear programming methods. Therefore, TPN has become the main technology for resource allocation, especially for Timed Weighted Mark Graphs (TWMGs) and Timed Mark Graphs (TMGs); Mark optimization problems and cycle time optimization problems are the two main categories of performance optimization problems for TMGs and TWMGs. Mark optimization problems aim to find an initial mark that ensures the system output while minimizing the cost. Cycle time optimization problems target the initial mark that optimizes the system output under a limited budget.

[0004] In the prior art, resource scheduling problems have been studied more extensively and deeply than resource allocation problems, among which exact methods, heuristic methods, intelligent algorithms, and artificial intelligence algorithms have been developed successively. The most popular exact technique is the linear programming model, which transforms physical constraints into logical constraints; in addition, several techniques based on discrete graph optimization methods have been studied, such as multi-objective scheduling problems and scheduling problems considering traffic constraints; in order to solve larger-scale scheduling problems, heuristic methods based on rule-guided search directions have been proposed; in addition, there are some scheduling techniques for extremely complex projects in real-time workshop environments, such as Monte Carlo tree search, constraint programming, and beam search; intelligent algorithms, such as ant colony algorithms, genetic algorithms, simulated annealing algorithms, etc., are widely used because they can determine the global optimal solution more effectively than heuristic algorithms. At the same time, some hybrid algorithms have been proposed to improve the effectiveness or quality of solutions. With the advancement of artificial intelligence, deeper learning, machine learning and other technologies have been gradually applied to solve more complex scheduling problems, including dynamic real-time scheduling and time-related traffic environments. Due to the significant advantages of Petri nets, they are also used for resource scheduling. Simple sequential process and resource system (S3PR) ​​is the basis for modeling and implementing scheduling of systems. The constraint on this subclass is that each transformation can only require one resource, and only one in number.

[0005] Although there are many research results on resource allocation and resource scheduling, both have certain limitations, and joint optimization of the two is more advantageous than single optimization; however, both resource allocation and resource scheduling are NP-hard problems, which greatly increases the difficulty of joint optimization; currently, this problem has not been solved; in addition, due to the limited resources on board, resource allocation and scheduling are more important. Therefore, how to reasonably configure and schedule the resources in the spacecraft system to maximize the system performance has become an urgent problem to be solved. To this end, we propose a spacecraft system performance optimization method based on on-board resource allocation and scheduling. Summary of the invention

[0006] The purpose of the present invention is to provide a spacecraft system performance optimization method based on on-board resource allocation and scheduling, which uses the Transition Time-Delay Petri Net (TTPN) to model the resource allocation system, analyzes the mathematical models of two types of performance optimization problems, namely minimum cost and minimum completion time, and merges them, so as to reasonably allocate resources and schedule them.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A method for optimizing spacecraft system performance based on on-board resource configuration and scheduling comprises the following steps:

[0009] Step 1: Establish TTPN model;

[0010] Step 2: Establish and integrate the mathematical model of cost optimization and completion time optimization;

[0011] Step 3: Convert the mathematical model into a TPPN-based mathematical model;

[0012] Step 4: Linearize the TPPN-based mathematical model into a mixed integer linear programming model;

[0013] Step 5: Use LINGO to solve the optimal solution of the mixed integer linear programming model and output the mixed integer linear programming model;

[0014] Step 6: Use the mixed integer linear programming model to configure and schedule on-board resources.

[0015] Preferably, the step 1 is specifically as follows: N ={1, 2, ..., q} is a finite set of indices, defining a TTPN for on-board resource allocation and scheduling as: It consists of a set of subnets that share common on-board resources: Composition, including and are the starting place, the ending place, the active place and the on-board resource place respectively; for a given TTPN, the following conditions must be met: for any i,j∈I N (i≠j),

[0016] For any

[0017] For any t∈T, · t∩P R =t · ∩P R ;

[0018] is a transition and time mapping that specifies the deterministic token operation time δ of transition t t ,in represents the set of non-negative rational numbers;

[0019] In the formula, the TTPN system used for on-board resource allocation and scheduling is a pair of G =<N,M0> , where N is the TTPN and M0 is the initial identifier.

[0020] Preferably, the cost optimization problem is solved by establishing the following model:

[0021] min B·M0

[0022]

[0023] in:

[0024] B=[b1,b2,...,b n ] represents the cost vector, where b i M0(p i ) The cost of each token in

[0025] f(M0,ψ,M g ) is the initial identifier M0, the trigger sequence ψ and the target identifier M g The completion time of the relevant TTPN;

[0026] is a given positive real number, representing the upper bound of the completion time;

[0027] The completion time optimization problem is to find an initial identifier M0 under a given budget and formulate a trigger sequence ψ of transitions to minimize the completion time of the system; the completion time optimization problem is modeled as the following optimization problem:

[0028]

[0029] In the formula, B and f(M0,ψ,M g ) represents the cost vector and the completion time function; is a given positive real number, representing the budget; the above cost optimization problem and completion time optimization problem are integrated into the following mathematical model:

[0030]

[0031] In the formula, B and f(M0,ψ,M g ) represents the cost vector and the completion time function, and represents the upper bound and budget of the completion time; α and β are given 0-1 variables, when α=1, it is equivalent to the cost optimization problem, and when β=1, it is equivalent to the completion time optimization problem.

[0032] Preferably, the objective function of the mathematical model based on TTPN in step 3 is specifically based on the mathematical model of the fusion problem, and the objective function is expressed as:

[0033] minα·B·M0+β·f (2)

[0034] The transition enabling constraints of the mathematical model based on TTPN in step 3 are as follows: Assuming that the maximum number of stages required to reach the target identification is h, that is, M0[ψ1>M1[ψ2>M2…[ψ h >M g Indicates; Assuming the trigger completion time vector The emission completion time of the x-th stage transition t is:

[0035]

[0036] In the formula, σ x is the trigger sequence ψ x The emission count vector of x; the transition t in stage x y use The triggering times and completion times are expressed as and The enabling of a transition will be related to its trigger start time, expressed as:

[0037]

[0038] In the formula, the completion vector Indicates that change The count vector of all transitions completed at the start of the trigger, and the execution vector Transition The count vector of transitions being executed at the time the trigger starts.

[0039] Preferably, the completion time constraint of the mathematical model based on TTPN in step 3 is specifically:

[0040] According to the trigger completion time τ x Definition, assuming that the global clock starts at 0, the completion time is defined as the maximum completion time of all tasks, that is, the maximum value of the maximum emission completion time of all transitions, which can be expressed as:

[0041]

[0042] The target identification constraint of the mathematical model based on TTPN in step 3 is specifically as follows: the target task is expressed by the target identification, and the initial state and the final state of the system are expressed as follows according to the Petri net state equation:

[0043]

[0044] Preferably, in step 3, combining equations (1) to (6), the mathematical model based on TTPN is expressed as:

[0045]

[0046] Preferably, (7a) is transformed into the following linear constraint, specifically:

[0047]

[0048] In the formula, H1 satisfies The extremely large constant.

[0049] Preferably, (7a) is transformed into the following linear constraint, specifically: for formula (7b), for the transition Define a completion matrix ζ x,y ∈{0,1} m×h satisfy:

[0050]

[0051] In the formula, ζ {x,y} (y',x')=1 indicates a transition is triggered and changes Completed when start triggers; transition The completion vector It is expressed as:

[0052] Furthermore, formula (9) is transformed into the following linear constraint:

[0053]

[0054] In the formula, For the corresponding x,y (y′, x′) is a 0-1 Boolean variable, ε is a very small number, and H2 satisfies The extremely large constant.

[0055] Definition Change The execution matrix ξ x,y ∈{0,1} m×h satisfy:

[0056]

[0057] Then change The execution vector It is expressed as: Then equation (11) is transformed into the following linear constraint:

[0058]

[0059] In the formula, For the corresponding x,y (y′, x′) is a 0-1 Boolean variable, ε is a very small number, and H3 satisfies The extremely large constant.

[0060] Preferably, equation (7c) is transformed into the following linear constraint:

[0061]

[0062] In the formula, Indicates completion time.

[0063] Preferably, the fourth step is to convert the linearization of the mathematical model based on TPPN into a mixed integer linear programming model as follows:

[0064] Combining equations (7), (8), (10), (12), and (13), the mixed integer linear programming model for system performance optimization of on-board resource allocation and scheduling is expressed as:

[0065]

[0066] The technical effects achieved by the present invention are:

[0067] In the present invention, first, a TTPN model is established; then a mathematical model of cost optimization and completion time optimization is established and integrated; then, the mathematical model is converted into a mathematical model based on TPPN; then, the mathematical model based on TPPN is linearized and converted into a mixed integer linear programming model; then, the optimal solution of the mixed integer linear programming model is solved in LINGO, and the mixed integer linear programming model is output; finally, the mixed integer linear programming model is used to configure and schedule on-board resources, so that the present invention can reasonably configure on-board resources and schedule them to achieve system performance optimization, and provide theoretical and practical guidance for factory construction, production scheduling and other issues by adjusting parameters to solve cost optimization problems and completion time optimization problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flowchart of the method of the present invention.

[0069] Figure 2 It is the TTPN model of the embodiment.

[0070] Figure 3 It is the Gantt chart of on-board resource scheduling. DETAILED DESCRIPTION

[0071] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0072] like Figure 1 As shown, a method for optimizing spacecraft system performance based on on-board resource configuration and scheduling includes the following steps:

[0073] Step 1: Establish TTPN model;

[0074] Specifically, the above process flow, optional operations, and operation time are as follows:

[0075] Order IN ={1,2,…,q} is a finite set of indices; a TTPN for on-board resource allocation and scheduling is defined as It consists of a group of subnets that share common on-board resources. Composition, of which and They are the starting place, the ending place, the active place and the on-board resource place. For a given TTPN, the following conditions must be met:

[0076] For any i,j∈I N (i≠j),

[0077] For any i∈I N ,

[0078] For any t∈T, · t∩P R =t · ∩P R ;

[0079] is a transition and time mapping that specifies the deterministic token operation time δ of transition t t ,in represents the set of non-negative rational numbers;

[0080] In addition, the TTPN system used for on-board resource allocation and scheduling is a pair of G=<N,M0> , where N is the TTPN and M0 is the initial identifier.

[0081] In this embodiment, the system consists of four subnets: N ={1,2,3,4}, It consists of a group of subnets that share common on-board resources. Composed of and They are the starting place, the ending place, the active place and the on-board resource place respectively; taking i=1 as an example, T 1 ={t1,t2,t3};

[0082] Step 2: Establish and integrate the mathematical model of cost optimization and completion time optimization;

[0083] The cost optimization problem aims to find an initial identifier M0, i.e., on-board resource allocation, to minimize the cost, and formulate a trigger sequence ψ, i.e., on-board resource scheduling, to achieve the target identifier M g That is, the completion time of the final state of the system is lower than a given threshold; the cost optimization problem is modeled as the following optimization problem:

[0084] min B·M0

[0085]

[0086] Where: B = [b1, b2, ..., b n ] represents the cost vector, where b i M0(p i ) The cost of each token in

[0087] f(M0,ψ,M g ) is the initial identifier M0, the trigger sequence ψ and the target identifier M g The completion time of the relevant TTPN;

[0088] is a given positive real number, which represents the upper bound of the completion time. The completion time optimization problem is to find an initial identifier M0 under a given budget and formulate a trigger sequence ψ of transitions to minimize the completion time of the system. The completion time optimization problem is modeled as the following optimization problem:

[0089] min f(M0,ψ,M g )

[0090]

[0091] Where: B and f(M0,ψ,M g ) represents the cost vector and the completion time function; is a given positive real number, representing the budget; the above cost optimization problem and completion time optimization problem are integrated into the following mathematical model:

[0092]

[0093] Where: B and f(M0,ψ,M g ) represents the cost vector and the completion time function, and represents the upper bound and budget of the completion time; α and β are given 0-1 variables, when α=1, it is equivalent to the cost optimization problem, and when β=1, it is equivalent to the completion time optimization problem;

[0094] like Figure 1-3 As shown, step three: convert the mathematical model into a mathematical model based on TPPN:

[0095] Objective function: According to the mathematical model of the fusion problem, the objective function is expressed as:

[0096] minα·B·M0+β·f (2)

[0097] Transition enabling constraint: Assume that the maximum number of stages required to reach the target identity is: H;

[0098] That is, M0[ψ1>M1[ψ2>M2…[ψ h >M g ; Assume that the trigger completion time vector represents the emission completion time of the x-th stage transition t, where:

[0099]

[0100] Where: x is the trigger sequence ψ x The emission count vector of . We will transform the transition t in stage x y use The triggering times and completion times are expressed as and Since the time factor is taken into account, the enabling of the transition will be related to its trigger start time, expressed as:

[0101]

[0102] In the formula, the completion vector Indicates that change The count vector of all transitions completed at the start of the trigger, and the execution vector Transition The count vector of transitions being executed at the time the trigger starts.

[0103] Completion time constraint: According to the trigger completion time τ x Definition, assuming that the global clock starts at 0, the completion time is defined as the maximum completion time of all tasks, that is, the maximum value of the maximum emission completion time of all transitions, which can be expressed as:

[0104]

[0105] Target identification constraint: The target task is expressed by the target identification. According to the Petri net state equation, the initial state and final state of the system are expressed as:

[0106]

[0107] Mathematical model based on TTPN, combined with equations (1)-(6), the mathematical model based on TTPN is expressed as:

[0108]

[0109] Its essence is to complete the time function f(M0,ψ,M g ) is mathematically expressed (i.e., equations (7a)-7(c)).

[0110] like Figure 1-3 As shown, step 4: linearize the mathematical model based on TPPN into a mixed integer linear programming model;

[0111] In equation (7), there are nonlinear constraints in equations (7a)-7(c), and the model is less solvable, so it needs to be further linearized;

[0112] Formula (7a) is transformed into the following linear constraint:

[0113]

[0114] In the formula, H1 satisfies The extremely large constant.

[0115] The above (7a) is transformed into the following linear constraint, specifically: For formula (7b), for the transition Define a completion matrix ζ x,y ∈{0,1} m×h satisfy:

[0116]

[0117] In the formula, ζ {x,y} (y',x')=1 indicates a transition is triggered and changes Completed when start triggers; transition The completion vector It is expressed as:

[0118] Furthermore, formula (9) is transformed into the following linear constraint:

[0119]

[0120] In the formula, For the corresponding x,y (y′, x′) is a 0-1 Boolean variable, ε is a very small number, and H2 satisfies The extremely large constant.

[0121] Definition Change The execution moment x,y ∈{0,1} m×h satisfy:

[0122]

[0123] Then change The execution vector It is expressed as: Then equation (11) is transformed into the following linear constraint:

[0124]

[0125] In the formula, For the corresponding x,y (y′, x′) is a 0-1 Boolean variable, ε is a very small number, and H3 satisfies The extremely large constant.

[0126] Equation (7c) is transformed into the following linear constraint:

[0127]

[0128] In the formula, Indicates completion time.

[0129] The fourth step is to convert the linearization of the mathematical model based on TPPN into a mixed integer linear programming model:

[0130] Combining equations (7), (8), (10), (12), and (13), the mixed integer linear programming model for system performance optimization of on-board resource allocation and scheduling is expressed as:

[0131]

[0132] like Figure 1-3 As shown, step five: use LINGO to solve the optimal solution of the mixed integer linear programming model and output the mixed integer linear programming model;

[0133] In this embodiment, assuming that the cost vector B = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1], each task needs to be completed once, that is, M g =[0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0], respectively considering the cost optimization problem (i.e., α = 1) and the completion time optimization problem (i.e., β = 1), and setting different upper bounds for the completion time and budget The results are shown in Tables 1 and 2. Further analysis of on-board resource scheduling, with α = 1, For example, the Gantt chart is as follows Figure 3 shown.

[0134] Table 1 Cost optimization problem

[0135]

[0136]

[0137] Table 2 Completion time optimization problem

[0138]

[0139] Step 6: Use the mixed integer linear programming model to configure and schedule on-board resources.

[0140] The invention can reasonably allocate on-board resources and schedule them to achieve system performance optimization. It can adjust parameters to solve cost optimization and completion time optimization problems, providing theoretical and practical guidance for factory construction, production scheduling and other issues.

[0141] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A method for optimizing spacecraft system performance based on on-board resource configuration and scheduling, characterized in that: The following steps are involved: Step 1: Establish TTPN model; The step 1 is specifically as follows: N ={1, 2, ..., q} is a finite set of indices, defining a TTPN for on-board resource allocation and scheduling as: It consists of a set of subnets that share common on-board resources: Composition, including and are the starting place, the ending place, the active place and the on-board resource place respectively; for a given TTPN, the following conditions must be met: for any i,j∈I N (i≠j), For any For any t∈T, · t∩P R =t · ∩P R ; is a transition and time mapping that specifies the deterministic token operation time δ of transition t t ,in represents the set of non-negative rational numbers; In the formula, the TTPN system used for on-board resource allocation and scheduling is a pair of G =<N,M0> , where N is the TTPN and M0 is the initial identifier; Step 2: Establish and integrate the mathematical model of cost optimization and completion time optimization; The cost optimization problem is solved by building the following model: minB·M0 Where: B = [b1, b2, ..., b n ] represents the cost vector, where b i M0(p i ) The cost of each token in f(M0,ψ,M g ) is the initial identifier M0, the trigger sequence ψ and the target identifier M g The completion time of the relevant TTPN; is a given positive real number, representing the upper bound of the completion time; The completion time optimization problem is to find an initial identifier M0 under a given budget and formulate a trigger sequence ψ of transitions to minimize the completion time of the system; the completion time optimization problem is modeled as the following optimization problem: In the formula, B and f(M0,ψ,M g ) represents the cost vector and the completion time function; is a given positive real number, representing the budget; the above cost optimization problem and completion time optimization problem are integrated into the following mathematical model: In the formula, B and f(M0,ψ,M g ) represents the cost vector and the completion time function, and represents the upper bound and budget of the completion time; α and β are given 0-1 variables, when α=1, it is equivalent to the cost optimization problem, and when β=1, it is equivalent to the completion time optimization problem; Step 3: Convert the mathematical model into a TPPN-based mathematical model; The objective function of the mathematical model based on TTPN in step 3 is specifically based on the mathematical model of the fusion problem, and the objective function is expressed as: minα·B·M0+β·f(2) The transition enabling constraints of the mathematical model based on TTPN in step 3 are as follows: Assuming that the maximum number of stages required to reach the target identification is h, that is, M0[ψ1〉M1[ψ2>M2…[ψ h >M g Indicates; Assuming the trigger completion time vector The emission completion time of the x-th stage transition t is: In the formula, σ x is the trigger sequence ψ x The emission count vector of x; the transition t in stage x y use The triggering times and completion times are expressed as and The enabling of a transition will be related to its trigger start time, expressed as: In the formula, the completion vector Indicates that change The count vector of all transitions completed at the start of the trigger, and the execution vector Transition The count vector of transitions being executed at the time the trigger starts; The completion time constraint of the mathematical model of TTPN in step 3 is specifically: According to the trigger completion time τ x Definition, assuming that the global clock starts at 0, the completion time is defined as the maximum completion time of all tasks, that is, the maximum value of the maximum emission completion time of all transitions, which can be expressed as: The target identification constraint of the mathematical model based on TTPN in step 3 is specifically as follows: the target task is expressed by the target identification, and the initial state and the final state of the system are expressed as follows according to the Petri net state equation: In step 3, combining equations (1) to (6), the mathematical model based on TTPN is expressed as: The (7a) is transformed into the following linear constraint, specifically: In the formula, H1 satisfies The maximum constant of The above (7a) is transformed into the following linear constraint, specifically: For formula (7b), for the transition Define a completion matrix ζ x,y ∈{0,1} m×h satisfy: In the formula, ζ {x,y} (y',x')=1 indicates transition is triggered and changes Completed when start triggers; transition The completion vector It is expressed as: Formula (9) is transformed into the following linear constraint: In the formula, For the corresponding x,y (y′, x′) is a 0-1 Boolean variable, ε is a very small number, and H2 satisfies The maximum constant of Definition Change The execution moment x,y ∈{0,1} m×h satisfy: Then change The execution vector It is expressed as: Then equation (11) is transformed into the following linear constraint: In the formula, For the corresponding x,y (y′, x′) is a 0-1 Boolean variable, ε is a very small number, and H3 satisfies The maximum constant of Equation (7c) is transformed into the following linear constraint: In the formula, Indicates the completion time; Step 4: Linearize the TPPN-based mathematical model into a mixed integer linear programming model; The fourth step is to convert the linearization of the mathematical model based on TPPN into a mixed integer linear programming model: Combining equations (7), (8), (10), (12), and (13), the mixed integer linear programming model for system performance optimization of on-board resource allocation and scheduling is expressed as: Step 5: Use LINGO to solve the optimal solution of the mixed integer linear programming model and output the mixed integer linear programming model; Step 6: Use the mixed integer linear programming model to configure and schedule on-board resources.

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