KR20210053247A - Method and apparatus for assigning multiple tasks - Google Patents

Abstract

The present invention provides a method and apparatus for rapidly allocating a plurality of workers to a plurality of tasks based on a mixed integer programming (MIP) method. A method of allocating tasks according to the present invention includes the steps of: generating a task vector (B) by projecting a plurality of tasks; generating W cluster vectors (D_1, ..., D_W) corresponding to W clusters each including at least one worker; generating a dictionary matrix (D) by combining the W cluster vectors (D_1, ..., D_W); calculating a sparse code (c) using sparse optimization for the task vector (B) and the dictionary matrix (D); selecting J clusters from among the W clusters based on the dictionary matrix (D) and the sparse code (c); and allocating workers included in the J clusters to each of the plurality of tasks.

Description

TECHNICAL FIELD [Method and apparatus for assigning multiple tasks]

The present invention relates to a task assignment method and apparatus. More specifically, it relates to a method and apparatus for quickly assigning a plurality of workers to a plurality of tasks based on a mixed integer programming (MIP).

When a situation occurs in which multiple ballistic missiles or fighters are flying from the enemy force toward a friendly force, it will be necessary to effectively shoot down the enemy's weapons using the defense weapons that the team possesses, such as surface-to-air missiles. In this case, in order to effectively remove the enemy's weapons, the friendly defense weapons must be effectively assigned to the enemy's weapons. This can be solved by the allocation problem between multiple workers and multiple tasks based on the mixed integer programming (MIP). Here, the plurality of tasks may correspond to the weapons of the enemy army, and the plurality of workers processing the plurality of tasks may correspond to the defense weapons of the friendly force.

However, the problem of allocating multiple tasks based on the mixed integer programming (MIP) has a problem in that the computational complexity rapidly increases as the number of tasks and the number of workers increase. It is known that the computational complexity increases in combination with the number of tasks and the number of workers, and the time required for computation is proportional to the computational complexity. In an urgent situation where enemy weapons are flying into the ally, it is necessary to minimize the time to allocate workers to tasks in order to minimize damage to the ally.

The problem to be solved by the present invention is to provide a method and apparatus for allocating workers to tasks based on mixed integer programming (MIP).

As a technical means for achieving the above-described technical problems, the task assignment method according to an aspect of the present invention is performed by a computing device. The task assignment method includes generating a task vector (B) by projecting a plurality of tasks, W cluster vectors (D ₁ , ..., D _W ) corresponding to W clusters each including at least one worker A step of generating a _{dictionary matrix (D) by combining the W cluster vectors (D 1} , ..., D W ), the task vector B and the dictionary matrix D Calculating a sparse code (c) using sparse optimization for ), based on the dictionary matrix (D) and the sparse code (c), J clusters among the W clusters And selecting, and allocating workers included in the J clusters to each of the plurality of tasks.

^m)에서 정의되어 제1 내지 제m 원소(b₁, ... , b_m})의 값들을 가질 수 있다. 상기 태스크 벡터(B)의 제i 원소(b_i)(i ∈ {1, ... , m})의 값은 상기 복수의 태스크들 각각의 제i 속성 값을 누적한 값일 수 있다.According to an example, the task vector B is an m-dimensional real space (B ∈

^It is defined in m) and may have values of the first to mth elements (b ₁ , ..., b _{m }).} The value of the i-th element b _i (i ∈ {1, ..., m}) of the task vector B may be a value obtained by accumulating an i-th attribute value of each of the plurality of tasks.

^m)에서 정의될 수 있다. 상기 W개의 클러스터 벡터(D₁, ... , D_W) 중 제w 클러스터 벡터(D_w)(w ∈ {1, ... , W})의 제i 원소(d_wi)(i ∈ {1, ... , m})의 값은 제i 속성에 대하여 상기 제2 클러스터 벡터(D_w)에 포함되는 적어도 하나의 워커가 처리할 수 있는 크기일 수 있다.According to another example, each of the W cluster vectors (D ₁ , ..., D _W ) is the m-dimensional real space (D ₁ , ..., D _W ∈

^m ) can be defined. Of the W cluster vectors (D ₁ , ..., D _W ), the i-th element (d wi) (i ∈ {) of the _w- th cluster vector (D _w ) (w ∈ {1, ..., W}) The value of 1, ..., m}) may be a size that can be processed by at least one worker included in _{the second cluster vector D w with respect to the i-th attribute.}

^m×W)에서 정의되고 D = [D₁ | D₂ | ... | D_w]에 따라 생성될 수 있다.According to another example, the dictionary matrix (D) is a (m×W) dimensional real space (D ∈

^m×W ) and D = [D ₁ | D ₂ | ... | It can be created according to D _{w ].}

에 따라 산출되고, 제1 내지 제W 값들을 포함할 수 있다.According to another example, the sparse code (c) is

It is calculated according to, and may include first to Wth values.

에 따라 산출되고, 제1 내지 제W 값들을 포함할 수 있다. 상기 파라미터(λ)는 상기 스파스 코드(c)의 비제로(non-zero) 희소성을 결정할 수 있다.According to another example, the sparse code (c) is

It is calculated according to, and may include first to Wth values. The parameter λ may determine the non-zero sparsity of the sparse code c.

According to another example, each of the first to Wth values of the sparse code c may be 0 or 1.

According to another example, the J clusters may be determined by a matrix-vector product (D×c) of the dictionary matrix (D) and the sparse code (c).

According to another example, each of the first to Wth values of the sparse code c may be a real value of 0 or more and 1 or less.

According to another example, the selecting of the J clusters is a step of generating a modified sparse code rc by comparing the first to Wth values of the spark code c with a preset reference value, Each of the first to Wth values of the modified sparse code rc is 0 or 1, and determining the J clusters by multiplying the dictionary matrix D by the modified sparse code rc. Can include.

According to another example, the step of allocating workers included in the J clusters to each of the plurality of tasks includes obtaining the number K of the plurality of tasks, each of the first to Kth tasks and the J _Obtaining cost values (cv jk) (j ∈ {1, ..., J}, k ∈ {1, ..., K}) between each of the workers included in the clusters, and the cost value Using _{an integer programming (MIP) algorithm to which cv jk} is applied, calculating an allocation result (x) of allocating workers included in the J clusters to each of the plurality of tasks. The assignment result (x) is (J×K) elements (x _jk ) each having a value of 0 or 1 (j ∈ {1, ..., J}, k ∈ {1, ..., K }) can be included.

의 값이 상기 제j 클러스터에 포함되는 워커들의 개수 이하일 제1 조건, 및 상기 원소들(x_jk)에 대한

의 값이 1일 제2 조건을 만족하도록

에 따라 산출될 수 있다.According to another example, the assignment result (x) is for the elements (x _jk )

The first condition that the value of is less than or equal to the number of workers included in the j th cluster, and for the elements (x _jk )

So that the value of satisfies the second condition on day 1

It can be calculated according to.

A computer program according to an aspect of the present invention is stored in a medium in order to execute the above-described task allocation method using a computing device.

A task allocation apparatus according to an aspect of the present invention includes a memory and at least one processor. The at least one processor generates a task vector (B) by projecting a plurality of tasks, and W cluster vectors (D ₁ , ..., D _W ) corresponding to W clusters each including at least one worker _{And, by combining the W} cluster vectors (D ₁ , ..., D W ), a dictionary matrix (D) is generated, and the task vector (B) and the dictionary matrix (D) are For this, a sparse code (c) is calculated using sparse optimization, and J clusters are selected from the W clusters based on the dictionary matrix (D) and the sparse code (c). And allocating workers included in the J clusters to each of the plurality of tasks.

According to the present invention, a pruning step is performed before the allocation step of multitasks based on mixed integer programming (MIP) to reduce the computational complexity of the allocation problem between multiple workers and multiple tasks, thereby allocating workers to tasks. You can reduce the time to do it.

Although computational complexity is reduced due to the pruning step, sub-optimality may occur as a trade-off for this. However, the benefit of reducing allied damage from enemy weapons due to reduced computation time would be far greater than the damage of increased cost due to non-optimality.

In the pruning step, the sparse optimization (that is, LASSO) problem is a convex optimization problem and has a computational complexity independent of the number of tasks and the number of workers. Therefore, even if the number of tasks and the number of workers increase, the computational complexity of the pruning step will not increase, and the total computation time can be reduced.

1 is a flowchart illustrating a task assignment method according to an embodiment of the present invention.
2 is a flowchart illustrating a pruning stage of a method for assigning a task according to an embodiment of the present invention.
3A is a diagram illustrating an exemplary task vector B according to an embodiment of the present invention, and FIG. 3B is a diagram illustrating an exemplary dictionary matrix D according to an exemplary embodiment of the present invention.
4 illustrates an example in which workers included in clusters are allocated to tasks according to the present invention.
5 is a view for explaining the configuration and operation of a task assignment device according to an embodiment of the present invention.

Hereinafter, various embodiments will be described in detail with reference to the accompanying drawings so that those of ordinary skill in the art may easily implement the present disclosure. However, the technical idea of the present disclosure is not limited to the embodiments described in the present specification because it may be modified and implemented in various forms. In describing the embodiments disclosed in the present specification, when it is determined that a detailed description of a related known technology may obscure the gist of the technical idea of the present disclosure, a detailed description of the known technology will be omitted. The same or similar components are given the same reference numerals, and duplicate descriptions thereof will be omitted.

In the present specification, when an element is described as being "connected" with another element, this includes not only the case of being "directly connected" but also the case of being "indirectly connected" with another element interposed therebetween. When a certain element "includes" another element, it means that another element may be included in addition to the other element, not excluded, unless specifically stated to the contrary.

Some embodiments may be described with functional block configurations and various processing steps. Some or all of these functional blocks may be implemented with various numbers of hardware and/or software components that perform a specific function. For example, the functional blocks of the present disclosure may be implemented by one or more microprocessors, or may be implemented by circuit configurations for a predetermined function. Functional blocks of the present disclosure may be implemented in various programming or scripting languages. The functional blocks of the present disclosure may be implemented as an algorithm executed on one or more processors. Functions performed by a function block of the present disclosure may be performed by a plurality of function blocks, or functions performed by a plurality of function blocks in the present disclosure may be performed by a single function block. In addition, the present disclosure may employ conventional techniques for electronic environment setting, signal processing, and/or data processing.

1 is a flowchart illustrating a task assignment method according to an embodiment of the present invention.

Referring to FIG. 1, the task assignment method includes a pruning stage S100 and a mixed integer programming (hereinafter referred to as “MIP”) stage S200. The task allocation method of the present invention may be performed by a computer device having a memory and at least one processor.

A task assignment method according to an embodiment of the present invention relates to a method of quickly allocating a plurality of tasks based on a mixed integer programming (MIP). The pruning stage S100 is a step in which some workers judged to be less likely to be assigned to a plurality of tasks are removed and only some remaining workers are selected. The MIP stage S200 is a step of allocating the workers selected in the pruning stage S100 based on the MIP to a plurality of tasks. The MIP stage S200 is performed after the pruning stage S100.

In the present specification, a'task' corresponds to a target that exists in multiple numbers, such as an enemy ballistic missile or a fighter. Enemy ballistic missiles or fighters will have to be intercepted by friendly defense weapons (eg, interceptor guided missiles, surface-to-air missiles, etc.). In the present specification, a'worker' is a target to be assigned to a'task' in order to process a'task', and may correspond to, for example, a defense weapon of a friendly force. 'Workers' may be grouped into a plurality of clusters. For example, a cluster may correspond to a missile unit or missile launcher capable of launching a plurality of missiles. Each of the clusters includes at least one worker.

According to the present invention, information on the number and property of workers and clusters may be stored in advance. Information about the properties of tasks may be obtained in the pruning stage S100 using, for example, radar equipment, analysis equipment, and the like. Information about the location of each of the tasks may be obtained in the MIP stage S200. For example, in the pruning stage S100, approximate location information of the tasks may be obtained, and then in the MIP stage S200, information on the exact location and number of tasks may be obtained through additional analysis.

Optimization algorithms such as mixed integer programming (MIP) greatly increase the time complexity as the problem size increases. The present invention proposes a method of efficiently reducing the size of a problem for fast execution of such an optimization algorithm. First, it is assumed that there are a plurality of tasks and a plurality of workers capable of processing them. According to the present invention, unpromising workers are removed in the pruning stage S100 without directly solving the task assignment problem using MIP. Selected workers remaining in the MIP stage S200 are allocated to a plurality of casts.

Hereinafter, the pruning stage S100 will be described in more detail with reference to FIGS. 2 to 3A and 3B.

2 is a flowchart illustrating a pruning stage of a method for assigning a task according to an embodiment of the present invention. 3A is a diagram illustrating an exemplary task vector B according to an embodiment of the present invention, and FIG. 3B is a diagram illustrating an exemplary dictionary matrix D according to an exemplary embodiment of the present invention.

2, 3A, and 3B, workers that do not seem suitable for processing a plurality of tasks are preferentially removed in the pruning stage according to an embodiment of the present invention. According to an example, sparse optimization may be used in the pruning stage. Sparse optimization can be implemented using the LASSO regression analysis algorithm.

^m)에서 정의될 수 있으며, 제1 내지 제m 원소(b₁, ... , b_m})의 값들을 가질 수 있다. 여기서, m은 미리 설정된 자연수이다. m은 태스크들이 가질 수 있는 속성들의 총 개수에 기초하여 미리 설정될 수 있다. m의 크기는 태스크들의 속성을 어떻게 정의하느냐에 따라 결정될 수 있다.A task vector B may be generated by projecting a plurality of tasks (S110). The plurality of tasks may be projected onto an m-dimensional task vector B. The task vector (B) is the m-dimensional real space (B ∈

^m ), and may have values of the first to mth elements (b ₁ , ..., b _{m }).} Here, m is a preset natural number. m may be preset based on the total number of attributes that tasks may have. The size of m can be determined according to how the properties of tasks are defined.

와 같이 표현될 수 있다. b_i,t는 T개의 태스크들 중에서 제t 태스크의 제i 속성 값을 나타낸다.Among the m dimensions of the task vector (B), the i-th dimension corresponds to the i-th property of the tasks, and the value of the ith element (b _i ) (i ∈ {1, ..., m}) of the task vector (B) May be a value obtained by accumulating an i-th attribute value of each of a plurality of tasks. If the number of tasks is known as T, the ith element (b _i ) of the task vector (B) is

It can be expressed as b _i,t represents the i-th attribute value of the t-th task among T tasks.

In this way, by projecting the tasks onto a task vector B having a fixed dimension m, a task vector B independent of the number of tasks may be generated.

Fig. 3A shows an image of an exemplary task vector B. The diagram of FIG. 3A includes m cells, and the cells correspond to properties of tasks, respectively. The brightness of each cell represents the cumulative value of the corresponding attribute of the tasks.

According to another embodiment, a task vector B may be generated from the drawing shown in FIG. 3A. For example, when enemy weapons appear in a detection image such as a radar image or a sonar image, a task vector B may be generated from the image. The pixels of the detection image may be grouped into m groups, and the m groups may correspond to the m dimension of the task vector B. _{The value of the i-th element b i} of the task vector B may be determined based on brightness, size, and analysis results of pixels in the i-th group.

W cluster vectors (D ₁ , ..., D _W ) corresponding to the W clusters may be generated (S120). Each of the W clusters includes at least one worker. As described above, if a worker responds to an anti-aircraft missile, the cluster may respond to a missile base. The number of workers and the number of clusters is known in advance. It is assumed that there are W clusters.

^m)에서 정의될 수 있다.Each of the W cluster vectors (D ₁ , ..., D _W ) corresponds to the task vector (B), and each of the W cluster vectors (D ₁ , ..., D _W ) is the same as the task vector (B). M-dimensional real space (D ₁ , ..., D _W ∈

^m ) can be defined.

Of the W cluster vectors (D ₁ , ..., D _{W ), the ith element (d w,i} )(i ∈) of the wth cluster vector (D _w )(w ∈ {1, ..., W}) The value of {1, ..., m}) may mean a size that can be processed by at least one worker included in _{the w-th cluster vector D w with respect to the i-th attribute. That is, the value of the ith element (d w,i} ) (i ∈ {1, ..., m}) of the wth cluster vector (D _w ) (w ∈ {1, ..., W}) is zero. It means that at least one worker included in the w cluster vector D _w can process as much as _{d w,i} for the i-th attribute of the task vector B.

^m×W)에서 정의될 수 있다. 사전 행렬(D)은 D = [D₁ | D₂ | ... | D_w]와 같이 생성될 수 있으며, W개의 클러스터 벡터들(D₁, ... , D_W)은 사전 행렬(D)의 열 벡터들에 해당한다. 즉, 제w 클러스터 벡터(D_w)는 사전 행렬(D)의 w번째 열 벡터이다.A dictionary matrix (D) may be generated by combining the _W cluster vectors (D ₁ , ..., D W) (130). The lexicographic matrix (D) is a (m×W) dimensional real space (D ∈

^m×W ). The dictionary matrix (D) is D = [D ₁ | D ₂ | ... | D _w ] can be generated, and the W cluster vectors (D ₁ , ..., D _W ) correspond to the column vectors of the dictionary matrix (D). That is, the w- _{th cluster vector D w} is the w-th column vector of the dictionary matrix D.

FIG. 3B is a diagram illustrating an image of first and second cluster vectors D ₁ , D ₂ , ... combined by a prior matrix D. In FIG. Each of the first and second cluster vectors D ₁ and D ₂ of FIG. 3B includes m cells. The m cells also correspond to m properties, respectively. In a diagram in which the first cluster vector D ₁ is imaged, the brightness of each cell indicates a size at which at least one worker included in the first cluster can process a corresponding attribute.

에 따라 산출될 수 있다. 스파스 코드(c)는 스파스 최적화에서 구하고자 하는 결정 변수(decision variable)로서, 비제로(non-zero) 요소의 개수가 작아지도록 최적화에서 고려된다. 스파스 코드(c)는 w차원 실수 공간(c ∈

^w)에서 정의되어 W개의 값들, 즉, 제1 내지 제W 값들을 포함할 수 있다. 스파스 코드(c)의 제1 내지 제W 값들은 0 이상 1 이하의 실수 값일 수 있다. 예컨대, 제1 내지 제W 값들은 0 또는 1일 수 있다.The sparse code c may be calculated using sparse optimization for the task vector B and the dictionary matrix D (S140). According to one example, the sparse code (c) is

It can be calculated according to. The sparse code (c) is a decision variable to be obtained in sparse optimization, and is considered in optimization so that the number of non-zero elements decreases. The sparse code (c) is the w-dimensional real space (c E

^It is defined in w) and may include W values, that is, first to W-th values. The first to Wth values of the sparse code c may be real values of 0 or more and 1 or less. For example, the first to Wth values may be 0 or 1.

에 따라 산출될 수 있다. 여기서, 파라미터(λ)는 스파스 코드(c)의 비제로(non-zero) 희소성을 결정하는 값으로서, 미리 설정될 수 있다. 스파스 코드(c)는 W개의 값들, 즉, 제1 내지 제W 값들을 포함할 수 있다. 스파스 코드(c)의 제1 내지 제W 값들은 0 이상 1 이하의 실수 값일 수 있다. 예컨대, 제1 내지 제W 값들은 0 또는 1일 수 있다.According to another example, the sparse code (c) is

It can be calculated according to. Here, the parameter λ is a value that determines the non-zero sparsity of the sparse code c, and may be set in advance. The sparse code c may include W values, that is, first to Wth values. The first to Wth values of the sparse code c may be real values of 0 or more and 1 or less. For example, the first to Wth values may be 0 or 1.

As the parameter λ increases, the non-zero sparsity of the sparse code c increases, so among the W values of the sparse code c, the number of elements having a value of 0 increases. In this case, the number of clusters selected from the W clusters decreases. Accordingly, the allocation speed between the multiple workers and the multiple tasks increases, but the amount of information to be lost also increases, so the optimality decreases. Conversely, when the parameter λ becomes smaller, the non-zero sparsity of the sparse code c decreases, and among the W values of the sparse code c, elements having a value of 0 decrease. In this case, the number of clusters selected from the W clusters increases. The parameter λ may be set in advance in consideration of a trade-off relationship between execution speed and optimality.

)에서, 첫 번째 항은 데이터-일관성 촉진항(Data-Consistency-promoting term)으로서, 사전 행렬(D) 내의 클러스터 벡터들(D₁, ... , D_W) 중에서 태스크 벡터(B)에 최적 적합(optimal fit)한 최적의 클러스터 벡터들을 선택하도록 촉진한다. 두 번째 항은 희소성 촉진항(Sparsity-promoting term)으로서, 스파스 코드(c)의 비제로(non-zero) 요소의 개수를 작게 하는 클러스터 벡터들을 선택하도록 촉진한다. 파라미터(λ)는 비제로(non-zero) 요소의 희소성의 정도를 결정할 수 있다. 스파스 코드(c)의 비제로 요소가 적을수록, 적은 수의 클러스터 벡터들이 최종적으로 선택될 것이며, 이는 이후 MIP 스테이지(S200)에서 계산복잡도를 낮출 것이다. 그러나, 비제로 요소의 희소성이 커질수록, 즉, 프루닝의 정도가 커질수록, 비최적성(sub-optimality)도 커지는 트레이드 오프 문제가 발생한다.The objective function to find the sparse code (c) (

), the first term is a data-consistency-promoting term, which is optimal for the task vector (B) among _{the cluster vectors (D 1} , ..., D _{W) in the dictionary matrix (D).} Facilitates the selection of optimal fit cluster vectors. The second term is a sparsity-promoting term, which promotes selection of cluster vectors that reduce the number of non-zero elements of the sparse code (c). The parameter λ may determine the degree of sparsity of a non-zero element. As the number of non-zero elements of the sparse code c decreases, a small number of cluster vectors will be finally selected, which will lower the computational complexity in the MIP stage S200 later. However, as the scarcity of the non-zero element increases, that is, the degree of pruning increases, a trade-off problem arises in which the sub-optimality also increases.

At least one of the W clusters may be selected based on the dictionary matrix D and the sparse code c (S150). According to an example, the first to Wth values of the sparse code c may be 0 or 1. In this case, the cluster selected in step S15 is referred to as a selection cluster. The selection cluster may be determined by the product of the dictionary matrix (D) and the sparse code (c), that is, D×c. Among the first to Wth cluster vectors D ₁ , ..., D _W included in the dictionary matrix D, a cluster corresponding to a value that is one of the first to Wth values of the sparse code c Clusters corresponding to vectors may be selected as selection clusters. It is assumed that the number of selection clusters is J. J is a natural number less than W.

According to another example, each of the first to Wth values of the sparse code c may be a real value of 0 or more and 1 or less. In this case, the first to Wth values of the spark code c may be compared with a preset reference value. The preset reference value may be 0.5. The preset reference value may be, for example, 0.3. Similar to the parameter λ, the preset reference value may determine the degree of sparsity of the non-zero element. Exemplary numerical values of the preset reference values do not limit the present invention. Among the first to Wth values of the sparse code c, values smaller than a preset reference value may be determined as 0, and values greater than the preset reference value may be determined as 1. Through this process, the sparse code c can be transformed into a modified sparse code rc. Each of the first to Wth values of the modified sparse code rc is 0 or 1.

The selection cluster may be determined by the product of the dictionary matrix D and the modified sparse code rc, that is, D×rc. Among the first to Wth cluster vectors (D ₁ , ..., D _W ) included in the dictionary matrix D, a value corresponding to one of the first to Wth values of the modified sparse code rc Clusters corresponding to cluster vectors may be selected as selection clusters. It is assumed that the selection cluster is J. J is a natural number less than W.

As the pruning stage steps shown in FIG. 2 are performed, only the workers included in the J selection clusters remain among the workers included in the W clusters, thereby reducing the size of the MIP problem and reducing the computational complexity.

Referring back to FIG. 1, in the MIP stage S200, workers included in J selection clusters may be allocated to each of a plurality of tasks. Clusters corresponding to non-zero elements are selected through the sparse code c calculated in the pruning stage S100. In the MIP stage S200, only workers included in the selection clusters selected in the pruning stage S100 are included in the MIP problem, thereby reducing the size of the problem and reducing the complexity of MIP calculation.

In order to allocate workers included in the J clusters to each of the plurality of tasks, the number of the plurality of tasks may be obtained. It is assumed that the number of tasks is K, and the K tasks are first to Kth tasks.

_{Cost values (cv jk} ) between each of the first to Kth tasks and each of the workers included in the J clusters (j ∈ {1, ..., J}, k ∈ {1, ..., K} ) Can be obtained. The cost value cv _jk refers to a cost required to allocate one of the workers included in the jth cluster among the first to Jth clusters to the kth task among the first to Kth tasks. Here, j is a natural number of 1 or more and J or less, and k is a natural number of 1 or more and K or less. Even if a plurality of workers are included in the j th cluster, there is no difference in _{cost value (cv jk) between workers included in the j th cluster.}

³)라고 하고, 제k 태스크의 위치를 p_k (p_k ∈

³)라고 하면, 제k 태스크를 제j 클러스터에 포함되는 하나의 워커를 할당하는 비용값(cv_jk)은

와 같이 유클리디안 거리의 제곱 값으로 정의될 수 있다. 그러나, 이는 예시적이며, 주어진 조건, 상황 등에 따라 비용값(cv_jk)은 다르게 정의될 수 있다.According to an example, the location of the j th cluster is p _j (p _j ∈

³ ), and the location of the kth task is p _k (p _k ∈

³ _{), the cost value (cv jk} ) for allocating one worker included in the jth cluster for the kth task is

It can be defined as the squared value of the Euclidean distance. However, this is exemplary, and the cost value cv _jk may be defined differently according to a given condition, situation, and the like.

Using an integer programming (MIP) algorithm to which cost values cv _jk are applied, an allocation result (x) of allocating workers included in J clusters to each of K tasks may be calculated. The assignment result (x) is (J×K) elements (x _jk ) each having a value of 0 or 1 (j ∈ {1, ..., J}, k ∈ {1, ..., K} ) Can be included. If the value of the element (x _jk ) of the assignment result (x) is 1, it means that one worker included in the j-th cluster is assigned to the k-th task, and the element (x _jk ) of the assignment result (x) is If the value is 0, it means that workers included in the jth cluster are not allocated to the kth task.

와 같이 정식화(Formulation)할 수 있다. 이때, 제j 클러스터에 포함되는 워커들의 개수를 초과하여 태스크들에 할당될 수 없으므로, 원소들(x_jk)에 대한

의 값이 제j 클러스터에 포함되는 워커들의 개수 이하이어야 한다. 또한, 태스크들 각각에 하나의 워커가 할당되어야 할 경우, 원소들(x_jk)에 대한

의 값이 1이어야 한다. 다른 예에 따라서, 태스크들 각각에 예컨대 2개 이하의 워커가 할당되는 것이 허용되는 조건이라면, 원소들(x_jk)에 대한

의 값이 2이하라는 조건이 만족하도록 변형될 수도 있다.In order to calculate the allocation result (x) of allocating workers included in J clusters to each of K tasks, applying the cost values (cv _jk ) to the integer programming (MIP) algorithm,

It can be formulated like this. In this case, since the number of workers included in the j th cluster cannot be exceeded and cannot be allocated to tasks, the elements (x _jk ) are

The value of must be less than or equal to the number of workers included in the j th cluster. In the case to be a single worker assigned to the task, respectively, to the elements (x _jk)

Must have a value of 1. According to another example, if it is a condition that each of the tasks is allowed to be assigned, for example, two or less workers, then for the elements (x _jk )

It may be modified to satisfy the condition that the value of is 2 or less.

4 illustrates an example in which workers included in clusters are allocated to tasks according to the present invention. x ₂₃ =1 means that one worker included in the second cluster is assigned to the third task. In addition, Capacity ₀ = 3 means that there are 3 workers included in the 0th cluster, and Capacity ₁ = 5 means that there are 5 workers included in the first cluster.

5 is a view for explaining the configuration and operation of a task assignment device according to an embodiment of the present invention.

In an embodiment, the task allocation device 100 may include a memory 110, a processor 120, a communication module 130, and an input/output interface 140.

The memory 110 is a computer-readable recording medium and may include a permanent mass storage device such as a random access memory (RAM), a read only memory (ROM), and a disk drive. In addition, a program code for controlling the task allocation device 100 may be temporarily or permanently stored in the memory 110. The memory 110 may temporarily or permanently store information about workers and clusters, such as the number and location of clusters, the number of workers included in each of the clusters, properties of workers, properties of clusters, etc. have. In addition, information on the properties of the task may be temporarily stored in the memory 110.

The processor 120 may be configured to process instructions of a computer program by performing basic arithmetic, logic, and input/output operations. Instructions may be provided to the processor 120 by the memory 110 or the communication module 130. For example, the processor 120 may be configured to execute a command received according to a program code stored in a recording device such as the memory 110. In one embodiment, the processor 120 of the task allocating device 100 projects a plurality of tasks to generate a task vector B, and W cluster vectors corresponding to W clusters each including at least one worker ( D ₁ , ..., D _W ) is generated, and the W cluster vectors (D ₁ , ..., D _W ) are combined to generate a dictionary matrix (D), and the task vector ( A sparse code (c) is calculated using sparse optimization for B) and the dictionary matrix (D), and based on the dictionary matrix (D) and the sparse code (c), the It may be configured to select J clusters from W clusters and allocate workers included in the J clusters to each of the plurality of tasks.

The communication module 130 may provide a function for communicating with an external server through a network. As an example, a request generated by the processor 120 of the task allocation device 100 according to a program code stored in a recording device such as the memory 110 may be transmitted to an external server through a network under the control of the communication module 130. I can. Conversely, control signals, commands, contents, files, etc. provided according to the control of the processor of the external server may be received by the task assignment device 100 through the communication module 130 via a network. For example, control signals or commands of an external server received through the communication module 130 may be transmitted to the processor 120 or the memory 110, and the task assignment device 100 further includes contents or files. It can be stored in a storage medium capable of.

According to an example, the processor 120 of the task assignment apparatus 100 may receive information on properties of tasks and information on the number and location of tasks through the communication module 130. The communication method is not limited, and not only a communication method using a communication network (for example, a mobile communication network, a wired Internet, a wireless Internet, a broadcasting network), but also a short-range wireless communication between devices may be included. For example, the network is a personal area network (PAN), a local area network (LAN), a campus area network (CAN), a metropolitan area network (MAN), a wide area network (WAN), a broadband network (BBN), the Internet, etc. May include any one or more of the networks of. In addition, the network may include any one or more of a network topology including a bus network, a star network, a ring network, a mesh network, a star-bus network, a tree, or a hierarchical network, but is not limited thereto. .

The communication module 130 may communicate with an external server through a wireless network. The communication method is not limited, but the network may be a local area wireless communication network. For example, the network may be a Bluetooth, Bluetooth Low Energy (BLE), or Wifi communication network.

The input/output interface 140 may be a means for an interface with an input/output device. For example, the input device may include a device such as a keyboard or a mouse, and the output device may include a device such as a display for displaying a communication session of an application. As another example, the input/output interface 140 may be a means for interfacing with a device in which input and output functions are integrated into one, such as a touch screen. For example, the processor 120 of the task allocation apparatus 100 may display a data processing result generated by processing a command of a computer program loaded from the memory 110 on the display through the input/output interface 140.

The processor 120 may control the task assignment device 100 to perform the task assignment method described above with reference to FIGS. 1 and 2. For example, the processor 120 and the components of the processor 120 may be implemented to execute an instruction according to the code of the operating system included in the memory 110 and the code of at least one program. Here, the components of the processor 120 are expressions of different functions of the processor 120 performed by the processor 120 according to an instruction provided by the program code stored in the task assignment device 100. I can.

The various embodiments described in the present specification are exemplary, and are not to be performed independently as they are distinguished from each other. The embodiments described in the present specification may be implemented in combination with each other.

The various embodiments described above may be implemented in the form of a computer program that can be executed through various components on a computer, and such a computer program may be recorded in a computer-readable medium. In this case, the medium may be one that continuously stores a program executable by a computer, or temporarily stores a program for execution or download. In addition, the medium may be a variety of recording means or storage means in a form in which a single piece of hardware or several pieces of hardware are combined. The medium is not limited to a medium directly connected to a computer system, but may be distributed on a network. Examples of media include magnetic media such as hard disks, floppy disks and magnetic tapes, optical recording media such as CD-ROMs and DVDs, magneto-optical media such as floptical disks, And there may be ones configured to store program instructions, including ROM, RAM, flash memory, and the like. In addition, examples of other media include an app store that distributes applications, a site that supplies or distributes various software, and a recording medium or a storage medium managed by a server.

In the present specification, a "unit", a "module", etc. may be a hardware component such as a processor or a circuit, and/or a software component executed by a hardware configuration such as a processor. For example, "unit", "module", etc. are components such as software components, object-oriented software components, class components and task components, processes, functions, properties, It can be implemented by procedures, subroutines, segments of program code, drivers, firmware, microcode, circuits, data, databases, data structures, tables, arrays and variables.

The above description of the present invention is for illustrative purposes only, and those of ordinary skill in the art to which the present invention pertains will be able to understand that other specific forms can be easily modified without changing the technical spirit or essential features of the present invention. will be. Therefore, it should be understood that the embodiments described above are illustrative in all respects and are not limiting. For example, each component described as a single type may be implemented in a distributed manner, and similarly, components described as being distributed may also be implemented in a combined form.

The scope of the present invention is indicated by the claims to be described later rather than the detailed description, and all changes or modified forms derived from the meaning and scope of the claims and their equivalent concepts should be construed as being included in the scope of the present invention. do.

Claims (14)

A method for assigning tasks performed by a computing device, comprising:
Generating a task vector (B) by projecting a plurality of tasks;
Generating _{W cluster vectors (D 1} , ..., D W) corresponding to W clusters each including at least one worker;
Generating a dictionary matrix ( _{D) by combining the W} cluster vectors (D ₁ , ..., D W );
Calculating a sparse code (c) using sparse optimization for the task vector (B) and the dictionary matrix (D);
Selecting J clusters from among the W clusters based on the dictionary matrix (D) and the sparse code (c); And
And allocating workers included in the J clusters to each of the plurality of tasks. The method of claim 1,
The task vector (B) is an m-dimensional real space (B ∈

^m ) has values of the first to mth elements (b ₁ , ..., b _m }),
The value of the i-th element (b _i ) (i ∈ {1, ..., m}) of the task vector B is a value obtained by accumulating the i-th attribute values of each of the plurality of tasks. The method of claim 2,
Each of the W cluster vectors (D ₁ , ..., D _W ) is the m-dimensional real space (D ₁ , ..., D _W ∈

^m ),
Of the W cluster vectors (D ₁ , ..., D _{W ), the i-th element (d w,i} )(i) of the wth cluster vector (D _w )(w ∈ {1, ..., W}) The value of ∈ {1, ..., m}) is a size that can be processed by at least one worker included in _{the w-th cluster vector (D w) for the i-th attribute.} The method of claim 3,
The prior matrix (D) is a (m×W) dimensional real space (D ∈

^m×W ) and D = [D ₁ | D ₂ | ... | The task assignment method generated according to D _{w ].} The method of claim 1,
The sparse code (c) is

The task allocation method is calculated according to the method and includes first to Wth values. The method of claim 1,
The sparse code (c) is

It is calculated according to, and includes first to Wth values,
The parameter (λ) is a task assignment method for determining the non-zero sparsity of the sparse code (c). The method according to claim 5 or 6,
Each of the first to Wth values of the sparse code (c) is 0 or 1. The method of claim 7,
The J clusters are determined by a product (D×c) of the dictionary matrix (D) and the sparse code (c). The method according to claim 5 or 6,
Each of the first to Wth values of the sparse code (c) is a real value of 0 or more and 1 or less. The method of claim 9,
Selecting the J clusters,
Generating a modified sparse code rc by comparing the first to Wth values of the spark code c with a preset reference value, wherein the first to Wth values of the modified sparse code rc Each is 0 or 1; And
And determining the J clusters by multiplying the dictionary matrix (D) by the modified sparse code (rc). The method of claim 1,
Allocating workers included in the J clusters to each of the plurality of tasks,
Obtaining the number (K) of the plurality of tasks;
_{Cost values (cv jk} ) between each of the first to Kth tasks and each of the workers included in the J clusters (j ∈ {1, ..., J}, k ∈ {1, ..., K }) obtaining; And
Using an integer programming (MIP) algorithm to which the cost values (cv _jk ) are applied, calculating an allocation result (x) of allocating workers included in the J clusters to each of the plurality of tasks,
The assignment result (x) is (J×K) elements (x _jk ) each having a value of 0 or 1 (j ∈ {1, ..., J}, k ∈ {1, ..., K }), including task assignment method. The method of claim 11,
The assignment result (x) is for the elements (x _jk )

The first condition that the value of is less than or equal to the number of workers included in the j th cluster, and for the elements (x _jk )

So that the value of satisfies the second condition on day 1

Task allocation method calculated according to. A computer program stored in a medium for executing the method of claim 1 using a computing device. Memory; And
A task vector (B) is generated by projecting a plurality of tasks, and W cluster vectors (D ₁ , ..., D _W ) are generated corresponding to W clusters each including at least one worker, and the W Cluster vectors (D ₁ , ..., D _W ) are combined to generate a dictionary matrix (D), and sparse optimization (Sparse) for the task vector (B) and the dictionary matrix (D) Optimization) to calculate the sparse code (c), based on the dictionary matrix (D) and the sparse code (c), select J clusters from the W clusters, and each of the plurality of tasks Task assignment apparatus comprising at least one processor configured to allocate workers included in the J clusters to.

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