TWI352933B - Scheduling method using meta-heuristics - Google Patents

Description

R1352933 IX. Description of the invention: 0 [Technical field to which the invention pertains] The present invention relates to a scheduling method using a heuristic algorithm, in particular, an ant group algorithm (Ant c〇1〇ny (10) Plus. , ACC)) is based on the method of scheduling the work schedules that meet the scheduling requirements. [Prior technology] 瘫, nowadays, such as nursing staff in medical institutions, factory production personnel, transportation industry drivers or catering industry service personnel, etc., usually must be pre-planned by the unit supervisor to schedule periodic work classes that meet relevant regulations. In order to successfully carry out regular work and provide sufficient human resources to cope with all kinds of situations. Take the current nursing staff (4) work schedules of various medical institutions as an example. Since the working characteristics of medical institutions are 24 hours a day, in general, the scheduling method of the unit supervisors usually takes the temple in advance. The nursing staff's seniority, work ability, legal requirements and other relevant limiting factors, etc., and then use the manual scheduling method to discharge each nursing staff into each duty class of the work shift table, so as to complete the planning schedule of the work shift table. Set the job. However, the above-mentioned traditional manual scheduling method still has many problems when it is actually carried out, and the nursing staff's scheduling method is taken as an example. Because during the course of the nursing staff's scheduling work, the unit's chief officer must still consider the basic hard limit scheduling rules (^ C〇nStraintS), for example: current government laws and regulations, medical institutions and trade unions. Class policy, etc.; or will also consider other soft restrictions on soft constraints, such as: individual care staff personal shift PK10330 07/06/11 1352933 * Good. Although the above-mentioned various scheduling restrictions are taken into account, the whole and shifting operations will become more complicated, which makes it difficult for the head of the unit to plan the work schedules of various scheduling requirements. Therefore, the work schedule established by the aforementioned conventional shift schedule cannot meet the fair and reasonable job assignment requirements. In addition, the manual planning of the work schedule will also waste a considerable amount of time and cost, so it is not in line with economic benefits. Furthermore, with reference to various related literatures that have been previously revealed at home and abroad, some scholars have tried to use mathematical programming models such as integer programming or secondary programming (qUadratic pr〇gramming) to seek platoons. The best solution on the class combination. However, the periodic work schedules such as the aforementioned caregivers belong to the Np__plete problem (Bartholdi proved in 1981), and it is not easy to use the linear algebra method to obtain a better solution. Therefore, the other-shift method is still not effective. Solve many problems that may arise in the planning and scheduling of the above work schedule. For the above reasons, it is necessary to further improve the above-mentioned various conventional scheduling methods. In view of the above, the present invention improves the shortcomings of the above-mentioned various conventional scheduling methods, which are based on the ant colony algorithm (Am Colony Optimization, Ac〇) in the heuristic algorithm, and pre-establish a constraint rule condition. In order to plan the schedule of a work shift, as a reference for updating the pheromone value of various shift routes, for quick planning of the work schedule meeting the scheduling requirements. SUMMARY OF THE INVENTION The main object of the present invention is to provide a scheduling method using a heuristic algorithm, which utilizes the positive feedback of the ant group algorithm to PK10330 07/06/11 ~ 6 - positive feedback. A computer system divides the number of staff members who want to be scheduled as a person-to-person ant, and then cooperates with updating the pheromone values of various shift routes as a reference for each manual _ 鸠 ' Completing a work; 疋 operation' makes the invention have the effect of greatly reducing the cost of the discharge and improving the applicability of the work schedule. A secondary object of the present invention is to provide a scheduling method using a heuristic algorithm, which is based on the method of saving the algorithm as the basis for selecting the scheduling of each artificial mother. The effect of A falling into the best solution in the region. I according to the present invention, the heuristic algorithm is used in the scheduling method, the package s class table 2 body slave step, the system uses the m thief according to the number of scheduling days and the number of workers to produce - silk individual; - scheduling path selection steps, The phylogenetic T ant group algorithm cooperates with the constraint rule condition, and finds the different age path in the class; the #洛隶 update step is to analyze the number of times the road k is opposite to the limit rule condition, to update the class ^ ^ _ pheromone value 'and through the pheromone value into - step selection ^ mouth, set the scheduling road ; S; and - I for the shift table output steps, the termination conditions of the cooperation ^ ^ into - work class table Planning and scheduling. The above and other objects, features, and advantages of the present invention will become more apparent from the description of the preferred embodiments of the invention. , the heuristic PK10330 07/06/11 of the preferred embodiment of the present invention

The 1352933 I algorithm scheduling method is based on a computer system (not shown) connecting at least one database (not shown) as an execution architecture, and based on Ant Colony Optimization (ACO). The method includes the following steps: an individual setting step S1, a scheduling path selection step, a pheromone value updating step S3, and a work shifting step s4. Therefore, the present invention uses the heuristic algorithm to arrange the scheduling method, which can be applied to the planning of periodic work schedules such as nursing staff, factory production personnel, transportation industry, or people in the transportation industry. Schedule the job. The above-mentioned database is used for pre-storage through a complete data collection and collection operation - "Limited Warships", which refers to laws and regulations, work orders or scheduling rules stipulated by the trade unions, etc. Scheduling rules, as well as other soft scheduling rules such as personal preferences of staff. For example, the international I face e Takeshi and other scholars have proposed: with = 1 student = system conditions 'including the general prohibition of the shift limit π stop 4 Li Renbei personal shift restrictions, etc. The library also establishes a limit number of times 辂 J is outside The blted table of the invention is used to record the number of times in the course of the number of violations, and the number of violations of the above-mentioned restrictions rule is ρ (Prohibited); The Prohibited Table is used to make the A name. Furthermore, (10) the library (4) reference information for the route search, such as the class of each staff member: (10) can be used as a reference for the scheduling work. Please refer to Figures 1 and 2, and the preferred embodiment of the present invention is shown in the table PK10330 07/06/11 1352933. The individual is set to step si, which is to set the work to be scheduled. The number of personnel and the number of shift days, in order to generate a table individual 1 by one display interface of the computer system, the size of the individual table is the matrix of the number of staff members multiplied by the number of shift days. In the embodiment shown in the figure, the abscissa of the individual 1 of the shift table can be set as the shift date, and the ordinate is preferably set to the name or code of the staff member. The duty classes that can be selected by each staff member include off-duty, night shift, big night shift and vacation (the code is set to D, N, Μ and H in order). g, and referring to Figures 1 and 2, the scheduling path selection step S2 of the preferred embodiment of the present invention is performed by the computer system to set each worker to be scheduled as an artificial ant, each artificial The initial ants are randomly selected as one starting point of the shift schedule of the individual 1 of the shift table as a starting point. After each artificial worm is selected to complete a starting point, the department must separately select other scheduling dates - the duty shift class And finally back to _ starting point. As shown in the figure: Assume that an artificial squad (worker's staff) selects the 2nd night shift (M) as the starting point, which must be on the date of each shift outside the 2nd (1st, 3rd to Days) Then select a duty shift class, and finally return to the starting point of the 2nd night shift (M). When an artificial stalk completes a shift path, it is called a cycle 11 (cycle). In addition, each artificial phoenix completes a cycle of 11 (cycle), which is called an evolutionary generation (that is, 70% of the work schedule of a work schedule). Zeng and Tu said that the above-mentioned artificial ants must be based on an ant ethnic group to find out the number of violations of the above-mentioned "restriction rule conditions" to complete an evolutionary generation. Among them, each artificial ant preferably can be determined by PK10330 07/06/11: according to the selection basis of the scheduling path, the roulette plays p(u,v)=—the aforementioned health algorithm is public, u represents the person The value of the shift class on which the μ ant is currently located; V represents the next shift day (four) silk class selected by the labor (4); CGnneet (8) represents the value that has been selected, and the class is connected to the next one. The collection of the class; r (four) represents the value of the duty class u and the duty class Vm; α represents the value of the value of the artificial Wei's duty bans (by the user to set the illusion according to the needs; 3 represents The manually selected class is subject to the waiting time _ impact value (by the user according to their own needs); c W represents the value of the diligent U to the next _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ The formula is equivalent to the following: ^ φ)=--- 1 + Frequency (ν') In addition, in order to avoid the possibility of applying the r-wheel algorithm alone, the probability of falling into the optimal solution of the region is increased, and each artificial_ It can be based on the "round method" and is used together with the "saving algorithm" as the selection of its scheduling. The "time of use of the "round (4) algorithm" and the "L algorithm" is set in advance in the computer system - "the door is set by the user according to the requirements". Each artificial ant wants to select the next one - 1035 07/06/11 - 10 1352933. The computer system can be randomly generated with a probability value. When the probability value is less than the threshold value, Using the above-mentioned "rotation of the roulette method" to obtain the scheduling path of the artificial ant ant 'when the probability value is greater than the threshold value', the above-mentioned "saving algorithm" is used to obtain the scheduling route of the artificial ant, the saving The algorithm formula is preferably defined as follows: · p\{u^v) = Min{Frequency{f) + Frequency(w) + Frequency[c)} Please refer to Figure 3 for the block A representation.

Frequency(f), the block B represents Frequency(w); the block c represents Frequency(c); the block D represents v of the above formula. The schedule dates covered by the blocks A and B are set according to the actual needs of the users. The "saving algorithm" mainly calculates the number of violations of the "restriction rule conditions" for all other duty classes v that have not been selected for the duty class u where the artificial sacrifice is currently located, so as to select among the duty classes v. The number of violations of the "restriction rule conditions" is the least, as the next duty class to be selected for the manual code. Referring to FIGS. 1 and 2 again, the pheromone value updating step S3 of the preferred embodiment of the present invention repeats the foregoing evolution generation and analyzes the different scheduling paths in each evolved generation to violate the "restriction rule". The number of conditions is used as the main reference for updating the pheromone value of the scheduling route of each artificial ant. That is to say, the number of shifts that violate the "restricted rule conditions" is relatively small, and the pheromone value must be relatively increased, so that the artificial ants can continuously accumulate experience, so as to gradually select the scheduling route that meets the rules, and then complete its PK10330. 07/06/11 —11 — Work schedule. Review " Wenping S' when the artificial ants select a duty shift and move to the next duty shift, that is, the pheromone value for the shift shift from the duty shift to another duty shift For the regional update operation, the pheromone region update formula is preferably defined as follows: t{u, v) = (1 - p) · ν) + Δτ(^, ν) in the aforementioned pheromone region update formula , ρ represents the attenuation value of the pheromone concentration (set by the user according to the demand), that is, after a predetermined time, after the interval, the pheromone value remaining by the artificial ant after the scheduling path will be ^= Volatilization, the volatilization rate is expressed by ρ, and the value of ρ is preferably set to " between 〇 and 1', that is, G< Ρ <1. △τ(χι,ν) represents the updated intensity value of the shift, that is, the reciprocal of the number of violations of the "off-rule conditions" + 1, that is, the number of violations of the "restriction rule condition" is less. The path has a relatively high pheromone value, and its formula is preferably defined as follows:

At{u,v)= —____ 1 + Frequency (ν ) Furthermore, when each artificial ant selects the duty shift of each shift date to establish a shift path p (8) belonging to each artificial ant, each The artificial ant will return the starting point along the scheduling path Path(k) to complete a cycle n (cycle). #中人工4| sacrifice in the process of returning to the starting point to match the pheromone value. # Each artificial township has completed two PK10330 07/06/11 —12 — after the cycle (that is, complete an evolutionary generation), the computer system is: according to each of the artificial ants established the scheduling path pa_, Select one of the least frequent shift paths for the number of times

Path(k), and then compare the shift path path(k) with all other generations of anti-“restricted rules” Wei’s sinister age p'ath(k), and then - Best scheduling path Path(8). Finally, the Giobd Update is the best definition for the most comprehensive path (k). The pheromone global update formula is defined as follows:

Q~ p) r(u,v) ,when (μ} ν) g Path{k) This pheromone value global update formula represents the pheromone delta value, which is a whole shift path Path (k) The reciprocal of the total number B (Path(k)) of the number of violations of the "restriction rule conditions" is taken as the value of the heart (7). The formula is preferably defined as follows:

At. (u, v) - _1 _ B {Path^k)) Referring again to FIG. 1, the work shift table of the preferred embodiment of the present invention outputs step S4, which is terminated by a predetermined condition. Complete the planning and scheduling of the work schedule. The termination condition can be set such that each artificial ant must complete a predetermined number of evolutionary generations, for example, one time 渖 PK10330 07/06/11 - 13 - 1352933 generation. Or by analyzing the work schedule obtained by each generation = whether the number of "restriction rule conditions" is lower than a standard value, for example, although a work shift table is generated, the number of violations of the restriction rule condition is lower than When the standard value is 50, the execution steps of the present invention are terminated. The above-mentioned termination conditions can be used as the main basis for determining whether or not to complete the work of the work schedule, so as to quickly plan the work schedule that meets the scheduling requirements.

In order to prove that the present invention uses the heuristic algorithm to perform the scheduling method, it has the advantage that the execution time is greatly dependent on the relatively small amount of money for the anti-"provisional job" and the work schedule that meets the scheduling requirements can be obtained. The present invention is applied to the scheduling method of the nursing staff by the present invention, and several experimental results are listed. The rhyme device includes cpu [ Ime] penti^ 2.8GHz], memory [512RAM], and is used as the implementation language of the algorithm. Moreover, the overall test process mainly uses various test conditions as shown in the following table to experimentally test the effectiveness of the present invention for nursing staff to perform shifting operations.

Furthermore, the related parameter setting of the present invention is based on the ant group algorithm, and the evolution generation is set to 1000 generations, the artificial ant is set to be the buckle, and the artificial sacs select the path length of each duty class as the nursing PK10330. 07/06/11 丄妁2933 The total number of personnel and the number of shift days, the pheromone attenuation value p is set to 0.45, the parameter of r (U, v) is determined to be 0.45, the decision; 7 (v) parameters The /5 is set to 0.65, and the test comparison results are as follows:

This hair two ~~~

Spend time ___(#)

Far anti-limit rule

According to the results of the two-step test, the reference table L of the present invention can be used for a short period of time regardless of the date, the number of caregivers and the department (Table 2 of Table 2). The completion of the work class rules stop = 4 and the towel can be used to reduce the number of periodic work schedules. pKl〇33〇°7/〇6/n as described above. Compared with the work done by f scheduling method~15 — and the requirement 1 is based on the ant restriction group algorithm, and the condition is “' and cooperates with the “rotation algorithm” or "Save the algorithmic formula, for each artificial ant to find a row of shifts separately. Then \ by the knife to analyze the limits of the restrictions on the storage of the various conditions, the money, the best, the new lion path The pheromone value, as an important basis for each person to select the tank selection = the prescribed shift path, can quickly plan out: a good work schedule. Although the invention has been disclosed using the above preferred embodiment, it is not used In order to limit the invention, any person skilled in the art without departing from the spirit and scope of the invention The various modifications and changes to the above-described embodiments are still within the technical scope of the present invention. Therefore, the scope of the present invention is defined by the scope of the appended claims. PK10330 07/06/11 —16 — 1352933 BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic diagram of a flow of a heuristic algorithm in accordance with a preferred embodiment of the present invention. FIG. 2 is a perspective view of a preferred embodiment of the present invention using a heuristic algorithm. A schematic diagram of the generated individual of the shift table. Fig. 3 is a schematic diagram of an individual using the heuristic algorithm in conjunction with the saving method in the preferred embodiment of the present invention. • [Major component symbol description] 1 shift table individual 11 cycle S1 Individual schedule setting step ί'ν-'λ S2 Shift path selection step ~~ S3 pheromone value update step S4 Work shift table output step • . PK10330 07/06/11 —17 —

Claims (1)

1352933 The computer system is shunned by the staff of the artificial ants based on an ant group interpretation method. 'Generation, its: then::: the class individual; take a number of rows == with the knife to make up - the scheduling path and complete an evolution 2 people ^ ants use - roulette algorithm as a basis for scheduling, its The formula is defined as follows: , P(u,v) = ^J^Y±?(^ Σ [^ν)]^[η(ν)]β Connect(ii) ^ ” U represents the duty class of the manual _ current scheduling date; v represents the duty class of the τ__ class date selected by the artificial ant, Connect (u) represents the selected duty class connected to the next - a set of duty classes (4) to be selected; t(u, v) represents the "montage" between the duty class uf duty class V; α represents the pheromone value of the duty class selected by the artificial mom ant The impact value; 々 represents the value of the waiting time of the class selected by the artificial ant; represents the reciprocal of the frequency (F) of the duty class u to the next selected duty class that violates the condition of the restriction rule, Gu Hai - 18 - September 29, 100 revised replacement page Frequency (v) formula is defined as follows; And analyzing the violation of the limit of each shift path to correspondingly update one of the shift paths, repeating the execution of the evolution generation, the number of times of the rule condition, and the selection of the scheduling path of the payment; and matching a preset The termination condition completes an assignment. Lomon value, for each person to call the ants based on the pheromone value accumulation experience and 7G into a work schedule, according to the scope of application of the scope of application of the heuristic algorithm of the scheduling method, Each artificial ant system uses the selection basis of the one-shift path, and the Qing Qian algorithm calculates the number of times that all other unsuccessful duty classes violate the conditions of the restriction rule for one of the duty classes, so as to be used in each duty class. Select the one with the least number of violations of the restriction rule as the next class to be selected by the artificial ant. 'According to the scheduling method using the heuristic algorithm described in item 2 of the patent application scope, wherein the roulette algorithm and the saving algorithm use timing, a threshold is set in the computer system, and a random generation is generated The probability value, the probability value is less than the threshold value, and the robin algorithm is used to obtain the scheduling route of the artificial ant, and the probability value is greater than the threshold, and the saving algorithm is used to obtain the scheduling route of the artificial ant. According to the application method of the heuristic algorithm described in the second, second or third patent application scope, wherein the artificial ants select a duty class and a monument c'month>1b;, the positive replacement page 100 In the process of moving to the next duty shift in the year 9 ^ zy day, the pheromone value area update operation is performed for the duty shift of the duty shift to another duty shift. 'The pheromone value The region update formula is defined as follows: T(u, v) = (1 - . T(u, v) + At(u, v) where Δrhv) is expressed as: Ατ(μ,ν)= 1 \ + Frequency { y) Further 'Ρ represents the attenuation value of the pheromone concentration, and 〇< ρ <1 ; Δ7: (u,v) represents the pheromone intensity value at which the shift path is updated. The scheduling method using the heuristic algorithm described in item 4 of the patent application scope, wherein the computer system performs pheromones on the scheduling path Path(k) with the least number of violations of the "restriction rule condition" in each evolutionary generation. Value global update 'The pheromone global update formula is defined as follows p)-r(ii,v) + ^Af.(ii,v) ,when (u,v) e Path{k) ^) r(ii, v) , when (u}v) ^ Path(k) △ τ i(u,v) represents the pheromone delta value, which is a path(k) anti-restriction rule condition number of times B (Path( The reciprocal of k)) is taken as the value of Δ ri(u,v), and the formula is Δ r , · («, v ) =__I B (Path (k)). According to the method of applying the heuristic custody method described in claim 1, 2 or 3, the termination condition is set such that each artificial slay must complete a predetermined number of evolutionary generations. There is no right or wrong page positive-laid 1 pV (100 years according to the application for the fifth round of the inspection method must be completed, the termination condition is set to the artificial (four) method of a predetermined number of evolutions Generation. According to the application of the heuristic method described in the scope of patent application 1, 2 or 3, the method 'the termination condition is analyzed by the second: the obtained guard class is a violation of the number of regulations. The value is based on the low-level application method of the heuristic algorithm described in item 5 of the patent scope, in which the secret condition is analyzed by analyzing the work schedule obtained by the evolutionary generation. The second standard value, as the basis for its termination, is lower than the scheduling method of the Yunlin hair-type performance method described in Sections 2, 3 or 3 of the application. The Prohibited Table is used to record the number of violations of the conditions of the restriction rule as a reference for searching for the scale.