Limited resource multi-task matching method based on greedy strategy

Abstract

The invention discloses a limited resource multi-task matching method based on a greedy strategy, and belongs to the field of scheduling optimization. The method comprises the following steps: screening all feasible solutions for task requirements from limited resources according to a multi-task requirement table, and constructing a multi-task feasible solution table; constructing a limited resource undirected weighted graph by using an adjacency list according to the multi-task feasible solution table; on the basis of a greedy strategy, traversing the multi-task feasible solution table to obtain a resource packet preliminary screening table; judging the number of feasible solutions required by each task in the resource packet preliminary screening table; and for task requirements of which matching is not completed, a breadth-first search algorithm is used for searching a channel in the limited resource undirected weighted graph and the multi-task feasible solution, and resource transfer and allocation are carried out. According to the method, the greedy strategy is ingeniously utilized for preliminary matching, and the problem scale is reduced; on the basis, the defect that a greedy strategy is prone to falling into a local optimal solution is overcome through a breadth-first search algorithm, and a global feasible solution can be found more efficiently.

Description

Technical Field

[0001] The invention relates to a limited resource multi-task matching method based on a greedy strategy, and belongs to the field of scheduling optimization. Background Art

[0002] Combinatorial optimization problems often occur in fields such as logistics and transportation, manufacturing and production, and human resource management. They are characterized by complexity, multiple objectives, multiple constraints, and combinatorial explosion.

[0003] At present, traditional solutions are divided into two categories: exact calculation and approximate calculation. Exact calculation includes dynamic programming, branch and bound method, linear programming and integer programming, etc.; approximate calculation includes meta-heuristic algorithm, deep learning method, etc. However, combinatorial optimization problems are usually NP-hard problems, which means that the complexity of solution will increase exponentially with the increase of problem scale. Exact calculation solution is difficult to calculate large-scale problems. And because combinatorial optimization problems have the characteristics of multiple objectives and multiple constraints, approximate calculation solution needs to introduce a large number of parameters, the algorithm parameter conditions are complex, and it is impossible to find the optimal solution.

[0004] For the above problem, how to directly find a global feasible solution without introducing a large number of parameters and polynomial time complexity, while making the solution simpler and faster becomes a problem that needs to be solved. Summary of the invention

[0005] The present invention provides a limited resource multi-task matching method based on a greedy strategy, which reduces the problem scale by cleverly using the greedy strategy for preliminary matching; on this basis, the deficiency of the greedy strategy that it is easy to fall into the local optimal solution is compensated by a breadth-first search algorithm, and a global feasible solution can be found more efficiently.

[0006] The technical solution of the present invention is:

[0007] According to a first aspect of the present invention, a method for matching multiple tasks with limited resources based on a greedy strategy is provided, comprising the following steps:

[0008] Step 1: For multiple task requirements under the resource scheduling project, a multi-task requirement table is constructed based on the task requirement number, the resource package attribute index of the task requirement, and the number of resource packages of the task requirement; the resource packages are combined according to a preset number of resources;

[0009] Step 2: According to the multi-task requirement table, select all feasible solutions for the task requirements from limited resources; construct a multi-task feasible solution table based on the task requirement number, the resource package attribute value of the task requirement, and the feasible solutions of the task requirement;

[0010] Step 3. Based on the multi-task feasible solution table, use the adjacency list to construct a limited resource undirected weighted graph. In the limited resource undirected weighted graph, the vertices represent different resources, the edges represent the combination of resources, and the edge weights represent the attribute values ​​of the resource packages.

[0011] Step 4. Establish priorities for multiple task requirements under the resource scheduling project; select task requirements in order of priority, and traverse the multi-task feasible solution table based on the greedy strategy to obtain the resource package preliminary screening table; judge the number of feasible solutions for each task requirement in the resource package preliminary screening table: when the number of feasible solutions for each task requirement in the resource package preliminary screening table meets the number of resource packages corresponding to the task requirement, use the feasible solution corresponding to the resource package preliminary screening table as the matching result of multiple task requirements under the resource scheduling project; otherwise, execute Step 5;

[0012] Step 5: For the unmatched task requirements in Step 4, use the breadth-first search algorithm to find paths in the limited resource undirected weighted graph and multi-task feasible solutions, and perform resource transfer and allocation.

[0013] Furthermore, according to the multi-task requirement table, all feasible solutions for the task requirements are screened from limited resources, specifically: resource packages in different combinations are obtained by combining limited resources according to a preset number of resources, and all combined resource packages are screened, and all resource packages whose "resource package attribute values" meet the resource package attribute indicators of the current task requirements are taken as feasible solutions to the current task.

[0014] Furthermore, the resource package attribute value is obtained by combining the attribute values ​​of each resource in the resource package according to a combination method; the combination method is:

[0015] ;

[0016] In the formula, Indicates the resource pack attribute value; Indicates the resource package resource attribute value, Indicates the resource package The determination coefficient of a resource.

[0017] Furthermore, the Step 4 is specifically as follows:

[0018] Create and initialize the resource package initial screening table;

[0019] Establish priorities for multiple task requirements under the resource scheduling project; select task requirements in order of priority and put the task requirement numbers into the resource package initial screening table;

[0020] Determine whether the number of feasible solutions required by the current task in the resource package initial screening table meets the number of resource packages required by the task or whether the multi-task feasible solution table has been accessed:

[0021] If it is satisfied, select the next task requirement;

[0022] If not, a feasible solution is selected from the multi-task feasible solution table: if any resource in the resource package corresponding to the feasible solution already exists in the resource package preliminary screening table, the feasible solution is skipped; if not, the feasible solution is released into the resource package preliminary screening table; until the number of feasible solutions required by the current task in the resource package preliminary screening table meets the number of resource packages required by the task or the multi-task feasible solution table is accessed.

[0023] Furthermore, the limited resource multi-task matching method based on the greedy strategy is used for electrolyte resource scheduling.

[0024] According to a second aspect of the present invention, a limited resource multi-task matching system based on a greedy strategy is provided, comprising a module of any one of the above-mentioned limited resource multi-task matching methods based on a greedy strategy.

[0025] According to a third aspect of the present invention, a processor is provided, the processor being used to run a program, wherein the program, when running, executes any one of the above-mentioned limited resource multi-task matching methods based on a greedy strategy.

[0026] The beneficial effects of the present invention are as follows: the present invention utilizes the advantages of the greedy strategy to select as many required resources for multiple tasks as possible at one time during the initial matching, without the need for overly complex prediction and judgment, and without the need to exhaustively enumerate every possible solution, thereby avoiding the situation of combinatorial explosion and reducing the time and space overhead of the computer; on this basis, the present invention further introduces a breadth-first search BFS algorithm, which can not only determine whether the multiple matching problem has a globally feasible solution, but also find a path in the resource graph within a polynomial time complexity, and transfer and allocate limited resources. Each matching does not need to consider the impact of the current choice on the future, thus solving the problem of after-effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a flow chart of the present invention;

[0028] Figure 2 This is an example of a resource map. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other arbitrarily without conflict.

[0030] Example 1: Figure 1-2 As shown, according to a first aspect of an embodiment of the present invention, a limited resource multi-task matching method based on a greedy strategy includes the following steps:

[0031] Step 1: For multiple task requirements under the resource scheduling project, a multi-task requirement table is constructed based on the task requirement number, the resource package attribute index of the task requirement, and the number of resource packages of the task requirement; the resource packages are combined according to a preset number of resources;

[0032] Step 2: According to the multi-task requirement table, select all feasible solutions for the task requirements from limited resources; construct a multi-task feasible solution table based on the task requirement number, the resource package attribute value of the task requirement, and the feasible solutions of the task requirement;

[0033] Step 3. Based on the multi-task feasible solution table, use the adjacency list to construct a limited resource undirected weighted graph. In the limited resource undirected weighted graph, the vertices represent different resources, the edges represent the combination of resources, and the edge weights represent the attribute values ​​of the resource packages.

[0034] Step 4. Establish priorities for multiple task requirements under the resource scheduling project; select task requirements in order of priority, and traverse the multi-task feasible solution table based on the greedy strategy to obtain the resource package preliminary screening table; judge the number of feasible solutions for each task requirement in the resource package preliminary screening table: when the number of feasible solutions for each task requirement in the resource package preliminary screening table meets the number of resource packages corresponding to the task requirement, use the feasible solution corresponding to the resource package preliminary screening table as the matching result of multiple task requirements under the resource scheduling project; otherwise, execute Step 5;

[0035] Step 5: For the unmatched task requirements in Step 4, use the breadth-first search algorithm to find paths in the limited resource undirected weighted graph and multi-task feasible solutions, and perform resource transfer and allocation.

[0036] Furthermore, according to the multi-task requirement table, all feasible solutions for the task requirements are screened from limited resources, specifically: resource packages in different combinations are obtained by combining limited resources according to a preset number of resources, and all combined resource packages are screened, and all resource packages whose "resource package attribute values" meet the resource package attribute indicators of the current task requirements are taken as feasible solutions to the current task.

[0037] Furthermore, the resource package attribute value is obtained by combining the attribute values ​​of each resource in the resource package according to a combination method; the combination method is:

[0038] ;

[0039] In the formula, Indicates the resource pack attribute value; Indicates the resource package resource attribute value, Indicates the resource package It should be noted that the resource package is combined according to a preset number of resources, and the preset number can be selected according to the determination coefficient. For example, for the electrolyte resource scheduling project, the determination coefficient is , that is, the volume of electrolyte. The determination coefficient of each resource is about 2.3t. The terminal device that performs the task can grab 4.6t of resources at a time. Therefore, the preset number is set to 2, that is, 2 electrolytic cells are combined into an electrolyte package as a resource package.

[0040] Furthermore, the Step 4 is specifically as follows:

[0041] Create and initialize the resource package initial screening table;

[0042] Establish priorities for multiple task requirements under the resource scheduling project; select task requirements in order of priority and put the task requirement numbers into the resource package initial screening table;

[0043] Determine whether the number of feasible solutions required by the current task in the resource package initial screening table meets the number of resource packages required by the task or whether the multi-task feasible solution table has been accessed:

[0044] If it is satisfied, select the next task requirement;

[0045] If not, a feasible solution is selected from the multi-task feasible solution table: if any resource in the resource package corresponding to the feasible solution already exists in the resource package preliminary screening table, the feasible solution is skipped; if not, the feasible solution is released into the resource package preliminary screening table; until the number of feasible solutions required by the current task in the resource package preliminary screening table meets the number of resource packages required by the task or the multi-task feasible solution table is accessed.

[0046] By applying the above technical solution, it can be seen that the present invention utilizes the advantages of the greedy strategy to select as many required resources for multiple tasks as possible at one time during the initial matching, without the need for overly complex prediction and judgment, and without the need to exhaustively enumerate every possible solution, thereby avoiding the combinatorial explosion and reducing the time and space overhead of the computer. On this basis, the present invention further introduces a breadth-first search algorithm, which can not only determine whether the multiple matching problem has a global feasible solution (i.e., if no path can be found for tasks that are not fully matched, it can be determined that there is no global feasible solution), but can also find the path of the resource graph within the polynomial time complexity, and transfer and allocate limited resources. Each matching does not need to consider the impact of the current choice on the future, solving the problem of aftereffect.

[0047] According to the second aspect of an embodiment of the present invention, a system for matching multiple tasks of limited resources based on a greedy strategy is provided, including a module of any one of the above-mentioned methods for matching multiple tasks of limited resources based on a greedy strategy. Specifically, it includes: a first module for executing Step 1: for multiple task requirements under a resource scheduling project, a multi-task requirement table is constructed according to the number of the task requirement, the attribute index of the resource package of the task requirement, and the number of resource packages of the task requirement; the resource package is combined according to a preset number of resources; a second module for executing Step 2: according to the multi-task requirement table, all feasible solutions for the task requirements are screened from limited resources; a multi-task feasible solution table is constructed according to the number of the task requirement, the attribute value of the resource package of the task requirement, and the feasible solutions of the task requirement; a third module for executing Step 3: according to the multi-task feasible solution table, an undirected weighted graph of limited resources is constructed using an adjacency list, in which vertices in the undirected weighted graph of limited resources represent different resources, edges represent combinations of resources, and the weights of edges represent resources. Source package attribute value; the fourth module is used to execute Step 4: establish priorities for multiple task requirements under the resource scheduling project; select task requirements in order of priority, and traverse the multi-task feasible solution table based on the greedy strategy to obtain the resource package preliminary screening table; judge the number of feasible solutions for each task requirement in the resource package preliminary screening table: when the number of feasible solutions for each task requirement in the resource package preliminary screening table meets the number of resource packages corresponding to the task requirements, the feasible solution corresponding to the resource package preliminary screening table is used as the matching result of multiple task requirements under the resource scheduling project; otherwise, execute the fifth module; the fifth module is used to execute Step 5, for the task requirements that have not been matched in the fourth module, use the breadth-first search algorithm to find a path in the limited resource undirected weighted graph and the multi-task feasible solution, and transfer and allocate resources. For the parts not described in detail in the above for each module, please refer to the relevant description of the embodiment.

[0048] According to a third aspect of an embodiment of the present invention, a processor is provided, wherein the processor is used to run a program, wherein the program executes any one of the above-mentioned limited resource multi-task matching methods based on a greedy strategy when running.

[0049] In order to verify the effectiveness and feasibility of the invention, the following experiments are designed for verification:

[0050] An electrolyte resource scheduling project P has a total of 3 downstream production line task requirements and 20 electrolytic cells. The electrolyte in each electrolytic cell has 6 different metal element ratios and electrolyte volumes. Each downstream production line task requirement requires 2 electrolytic cells to be combined into an electrolyte package, and the element ratio value of each electrolyte package needs to meet the downstream production line task requirements. The number of electrolyte packages and metal element ratio indicators required by each downstream production line task are given in Table 1, and the corresponding data of the 20 electrolytic cells are given in Table 2.

[0051] Table 1 Experimental data example (number of electrolyte packages required by downstream production line tasks and metal element proportion indicators)

[0052]

[0053] Table 2 Experimental data examples (electrolyte volume and metal element ratio in 20 electrolytic cells)

[0054]

[0055] The specific steps of the method are as follows:

[0056] Step 1. For the three downstream production line task requirements, the task requirements are numbered T1, T2, and T3. The resource attributes of the task requirements include six different metal elements. The resource package attribute index of the task requirements is the proportion index of the six different metal elements. Based on the combination of two electrolytic cells into one electrolyte package as a resource package, the number of resource packages required for the three downstream production line task requirements is 2, 6, and 2 respectively. Based on the number of the task requirement, the attribute index of the resource package of the task requirement, and the number of resource packages of the task requirement, a multi-task requirement table as shown in Table 3 is constructed (the first column in Table 3 is the number of the task requirement, the second to seventh columns are the attribute index of the resource package of the task requirement, and the eighth column is the number of resource packages of the task requirement);

[0057] Table 3

[0058]

[0059] Step 2. The limited resources known in the project are 20 electrolytic cells; resource packages in different combinations are obtained by combining 2 of the 20 electrolytic cells, and all the resource packages in these combinations are screened, and all resource packages whose "resource package attribute values" meet the resource package attribute indicators of the current task requirement are taken as feasible solutions to the current task. Exemplarily, as shown in Table 4, taking task requirement T1 as an example: resource packages in different combinations are obtained by combining 2 of the 20 electrolytic cells, and all the resource packages in these combinations are screened, and all the resource packages whose "resource package attribute values" meet the "resource package attribute indicators" of task requirement T1 are taken as feasible solutions to the current task. As can be seen from the first row of Table 4, the "resource package attribute values" in the second to seventh columns of the first row of Table 4 meet the "resource package attribute indicators" of the second to seventh columns of the first row of Table 3 regarding task requirement T1, so the resource package formed by the resource combination (E1, E2) corresponding to the "resource package attribute values" in the first row of Table 4 is a feasible solution to task requirement T1.

[0060] According to the task requirement number, the resource package attribute value of the task requirement, and the feasible solution of the task requirement, a multi-task feasible solution table is constructed as shown in Table 4:

[0061] Table 4

[0062]

[0063] It should be noted that the resource package attribute value is obtained by combining the attribute values ​​of each resource in the resource package. The attribute values ​​of each resource are shown in Table 2.

[0064] Step 3. Based on the multi-task feasible solution table, use the adjacency list to construct a finite resource undirected weighted graph. The vertices in the finite resource undirected weighted graph represent different resources, the edges represent the combination of resources, and the edge weights represent the attribute values ​​of the resource packages.

[0065] For example, according to the feasible solution table of the task shown in Table 4, an undirected weighted graph with limited resources is constructed using an adjacency list, where vertices represent different electrolytic cells, edges represent combinations of electrolytic cells (i.e., electrolyte packages), and weights represent the proportion of metal elements in the electrolyte package, such as Figure 2 Some vertices and edges are displayed.

[0066] Step 4. Create and initialize a resource package screening table; establish a priority order of T1, T2, and T3 for multiple task requirements under the resource scheduling project; select task requirements in order of priority, initially select the highest priority task requirement, i.e., T1, and put the task requirement number into the resource package screening table; select feasible solutions from the multi-task feasible solution table, first select (E1, E2), and then put them into the resource package screening table. At this time, the number of feasible solutions for the current task requirement in the resource package screening table is 1, so the number of resource packages that do not meet the task requirement (i.e., the number of 2), and the multi-task feasible solution table has not been accessed at this time; then select the feasible solution (E1, E3) from the multi-task feasible solution table, but E1 already exists in the resource package preliminary screening table, so skip this feasible solution; after skipping multiple feasible solutions, find (E3, E4), any resource in the resource package corresponding to the feasible solution (E3, E4) does not exist in the resource package preliminary screening table, and put the feasible solution (E3, E4) into the resource package preliminary screening table; similarly, filter the feasible solutions for the next priority task requirements, as shown in Table 5, which is an example of the resource package preliminary screening table. In the example shown in Table 5, the number of feasible solutions obtained for task requirement T3 is less than the number of resource packages required for task requirement 3, so the next step is executed.

[0067] Table 5

[0068]

[0069] Step 5. Use the breadth-first search algorithm to find a path for the unmatched downstream production line tasks in the limited resource undirected weighted graph and the multi-task feasible solution. After all downstream production line tasks on the path release the corresponding electrolyte packages step by step, they are assigned to the unmatched downstream production line tasks until all downstream production line task requirements are met or there is no path, and the algorithm ends. Example: T3 needs electrolyte package (E19, E20), but electrolyte package (E19, E20) is occupied by T2 and according to the multi-task feasible solution table, T2 has other electrolyte packages (E7, E8) that can be occupied, then T2 releases electrolyte package (E19, E20) to T3 and occupies electrolyte package (E7, E8). The above process is automatically completed in the resource graph and multi-task feasible solution using the breadth-first search algorithm. The results are shown in Table 6:

[0070] Table 6

[0071]

[0072] It should be noted that the problem of matching multiple tasks with limited resources in combinatorial optimization is often solved using backtracking and bipartite graph methods. The essence of the backtracking method is to traverse all possibilities through brute force search until a feasible solution or optimal solution is found. In the problem of matching multiple tasks with limited resources, its time complexity is O(n!). The essence of the bipartite graph method is to divide resource packages and task requirements into two types of vertices, namely, the K point set is all feasible packages after the electrolytic cell combination, and the U point set is the task requirements.<K,U> The edges are all feasible combinations that meet the task requirements. Therefore, the model only needs to use a specific algorithm to find the maximum matching of the U point set. In the problem of limited resource multi-task matching, the Push-Relabel algorithm is often used to find the maximum matching of the U point set, with a time complexity of O(V 2 ·E). The present invention has been described, and the time complexity is O(V+E). In the above, V and E represent the scale of vertices and edges in the graph respectively. In order to prove the time advantage of the present invention, two experiments are designed, each experiment is carried out ten times, and the average value is taken as the final result. Experiment 1: an electrolyte resource scheduling project P, a total of 3 downstream production line task requirements, 20 electrolytic cells; Experiment 2: an electrolyte resource scheduling project P, a total of 30 downstream production line task requirements, 200 electrolytic cells; the results are shown in Table 7 below:

[0073] Table 7

[0074]

[0075] It can be seen from Table 7 that, compared with the traditional optimization method, the present invention utilizes the characteristics of the greedy strategy and breadth-first search algorithm to solve the computational complexity caused by the large scale of the problem, greatly reduces the time complexity, and makes the optimization process simpler and faster.

[0076] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A limited resource multi-task matching method based on a greedy strategy, characterized in that: The following steps are involved: Step 1: For multiple task requirements under the resource scheduling project, a multi-task requirement table is constructed based on the task requirement number, the resource package attribute index of the task requirement, and the number of resource packages of the task requirement; the resource packages are combined according to a preset number of resources; Step 2: According to the multi-task requirement table, select all feasible solutions for the task requirements from limited resources; construct a multi-task feasible solution table based on the task requirement number, the resource package attribute value of the task requirement, and the feasible solutions of the task requirement; Step 3. Based on the multi-task feasible solution table, use the adjacency list to construct a limited resource undirected weighted graph. In the limited resource undirected weighted graph, the vertices represent different resources, the edges represent the combination of resources, and the edge weights represent the attribute values ​​of the resource packages. Step 4. Establish priorities for multiple task requirements under the resource scheduling project; select task requirements in order of priority, and traverse the multi-task feasible solution table based on the greedy strategy to obtain the resource package preliminary screening table; judge the number of feasible solutions for each task requirement in the resource package preliminary screening table: when the number of feasible solutions for each task requirement in the resource package preliminary screening table meets the number of resource packages corresponding to the task requirement, use the feasible solution corresponding to the resource package preliminary screening table as the matching result of multiple task requirements under the resource scheduling project; otherwise, execute Step 5; Step 5: For the unmatched task requirements in Step 4, use the breadth-first search algorithm to find paths in the limited resource undirected weighted graph and multi-task feasible solutions, and perform resource transfer and allocation.

2. The limited resource multi-task matching method based on greedy strategy according to claim 1 is characterized in that: The method of screening all feasible solutions to the task requirements from limited resources according to the multi-task requirement table is as follows: combining a preset number of resources from limited resources to obtain resource packages in different combinations, screening all combined resource packages, and taking all resource packages whose "resource package attribute values" meet the resource package attribute indicators of the current task requirement as feasible solutions to the current task.

3. The limited resource multi-task matching method based on greedy strategy according to claim 1 is characterized in that: The resource package attribute value is obtained by combining the attribute values ​​of each resource in the resource package according to a combination method; the combination method is: ； In the formula, Indicates the resource pack attribute value; Indicates the resource package resource attribute value, Indicates the resource package The determination coefficient of a resource.

4. The limited resource multi-task matching method based on greedy strategy according to claim 1 is characterized in that: The Step 4 is specifically as follows: Create and initialize the resource package initial screening table; Establish priorities for multiple task requirements under the resource scheduling project; select task requirements in order of priority and put the task requirement numbers into the resource package initial screening table; Determine whether the number of feasible solutions required by the current task in the resource package initial screening table meets the number of resource packages required by the task or whether the multi-task feasible solution table has been accessed: If it is satisfied, select the next task requirement; If not, a feasible solution is selected from the multi-task feasible solution table: if any resource in the resource package corresponding to the feasible solution already exists in the resource package initial screening table, the feasible solution is skipped; If it does not exist, the feasible solution will be released into the resource package preliminary screening table; until the number of feasible solutions required by the current task in the resource package preliminary screening table meets the number of resource packages required by the task or the multi-task feasible solution table is accessed.

5. The limited resource multi-task matching method based on greedy strategy according to claim 1 is characterized in that: The limited resource multi-task matching method based on greedy strategy is used for electrolyte resource scheduling.

6. A limited resource multi-task matching system based on a greedy strategy, characterized in that: A module comprising the limited resource multi-task matching method based on a greedy strategy as described in any one of claims 1-5.

7. A processor, characterized in that: The processor is used to run a program, wherein the program, when running, executes the limited resource multi-task matching method based on a greedy strategy as described in any one of claims 1 to 5.

Images