AN OPTIMIZATION MODEL AND ALGORITHM OF STUDENTS' PHYSICAL FITNESS TEST SEQUENCE

Transcription

1 28 th February 203. Vol JATIT & LLS. All rights reserved. ISSN: E-ISSN: AN OPTIMIZATION MODEL AND ALGORITHM OF STUDENTS' PHYSICAL FITNESS TEST SEQUENCE JINSONG ZHANG, 2 SHUWEI ZHANG, 2 Liaoning University of Technology, Jinzhou 200, Liaoning, China E-ail: zhangjs972@63.co, 2 zb58@63.co ABSTRACT In this paper, on the basis of full understanding of the odel and the algorith of solving cobinatorial atheatics bin-packing proble and production planning processes arrangeents, in accordance with the characteristics of the students' physical fitness test to deterine the two-stage ethod for solving the proble. The first stage, siplify the odel into a bin-packing proble, and thus get the iniu period, assign the class to each according to the total nuber of physical fitness test to the principle of the optial balance. The second stage, in order to siplify the calculation, take the student as little as possible total waiting as the objective function to siplify the proble into the process arrangeents odel, the odel for different rationality akes a better evaluation, adaptability is strong and have a certain value of popularization and application. Keywords: Physical Fitness Test, Waiting Tie, Approxiation Algorith, Bin-Packing Proble. INTRODUCTION In China at present, the school understand the student's physical condition though physical test ethods. The test including height and weight, standing long jup, vital capacity, grip and step test, the five all by electronic instruent autoatic easureent, record and store inforation [-5]. We assue that the school has 3 height and weight easuring instruents, standing long jup, vital capacity easureent instruent each, 2 grip strength and 2 step test easuring instruents [6-8]. Height and weight, standing long jup, vital capacity, the grip four s each instruent each student's average test (including students conversion) is 0 seconds, 20 seconds, 20 seconds, 5 seconds, and the step test each instruent test 5 students needs 3 inutes and 30 seconds. Before test each ite every student need to take an average of five seconds to record the personal inforation, that student nuber. Make sure that student nuber connected only need to input the one. School arrange for daily testing is 8:00 to 2:0 and 3:30 to 6:45[2]. The five tests is hold in sall places which contain a axiu of 50 students, the test has no fixed order of seniority [9-0]. The nuber of each class participate in physical fitness test seen Table. Under the conditions of the least entire test period, iniizing the waiting of students. And we put forward relevant suggestions for school physical test. Table : The Of Each Participate In Physical Fitness

2 28 th February 203. Vol JATIT & LLS. All rights reserved. ISSN: E-ISSN: PROBLEM ANALYSIS AND SYMBOLIC DESCRIPTION 2.. Proble Analysis This proble requires the sae class all students ust coplete the testing of all ites in the sae period of, and the required period the least nuber of conditions throughout the test, and iniize the students waiting. To this end, we put all participate in physical fitness test class section, idealized the conditions as uch as possible, as the class a unit, only to calculate rerecord between the classes. With the increasing of the nuber of classes, can be used to coplete the test will be reduced. Therefore, we use this relationship as a constraint condition to arrange the classes of the sae period, the process we give it to the coputer to coplete, specific procedures see attachent. After arrange the sae classes for arrange test order of the sae period class. According to various instruents with different instruents can be divided into different priority, first consider the high priority instruent arrangeent, in consideration of the back of the students to wait in front of the students in the testing process, in the back row of class to wait in front of the class, so these students can be arranged for other tests in waiting. The shortest waiting s forula can be calculated out, and then arrange personnel to coplete the test Sybol Description ts : The beginning of the period of ; te : The end of the period of ; tc : Each test needs ; r : Each instruent the nuber of each test; s : The nuber of test achine; tw : Each test iniizes wait : nuber*5; t : Period of equal to te-ts(s); w : The average class size is equal to [2036/56]; n : nuber; bend i, j : The end of classes i at the j instruent; bst, i j : The beginning of classes i at the j instruent; ark, i j : i student easuring at j instruent; C: Height and weight test instruent s; C2: Height and weight test 2 instruent s; C3: Height and weight test 3 instruent s; C4: The standing long jup test instruent s; C5: Vital capacity test instruent s; C6: Grip strength test instruent s; C7: Grip strength test 2 instruent s; C8: Step test instruent s; C9: Step test 2 instruent s. 3. MODEL ASSUMPTION Basic assuptions: After all the tests done, the students can leave the scene; do not need to wait all the students of the class finish test; No abnoral condition: No students were late, do not participate, the students strictly abide by the discipline according to plan arrangeent; In tests, all achines working properly; Other assuptions: To do the test, a class as a unit, according to the student nuber sequence test, do not allow this or any other class cut in line. The first students finish and arrange the student (according to the first hypothesis is actually the whole class) to other instruents do test. After all the tests done, the students can leave the scene, do not need to wait all the students of the class finish test. 4. THE ESTABLISHMENT OF THE MODEL AND THE SOLUTION 4.. The Whole Idea of Solving the Proble This proble is actually a plan proble, need to solve the following questions: Make sure all students coplete the physical fitness test with a iniu period of, and solve a iniu nuber of periods; Reasonably arrange the known classes (56 classes) for each period; In a period of, the physical fitness test class is known, the reasonable arrangeent of various classes of test as far as possible to ake the students iniu waiting. According to the above proble, we deterined that the two-stage solving ideas: First stage: Find out the iniu period, and put each class into each period according to the optiization odel. Second stage: On the known period and the period of required classes, constructing the solve odel, solving the operative class fitness test table for students as little as possible waiting s. 599

3 28 th February 203. Vol JATIT & LLS. All rights reserved. ISSN: E-ISSN: The First Stage of Basic Model and Conclusion The first stage of the basic odel can be siplified as: Known for each period ing and ending, each instruent average test and entry conversion of not consecutive nuber of the students' inforation, find the iniu nuber of period and the class arrangeents for each period. Conclusion : Morning arrangeent nuber up to 70, the nuber of arrangeent in the up to 550 people. Conclusion testifies: According to each physical testing s and equipent nuber, we get the following Table 2: Table 2: The Of Testing Students In Test Project Of Full Load Work Each Period Project Height and Weight Standing long Vital Miniu Grip Step test jup capacity Full load work in the orning Full load work in the Consider inforation recorded orning Consider inforation recorded in the Above data calculation forula: Full load work in the orning: [5000/tc]*r*s. Full load work in the : [700/tc]*r*s. Consider inforation recorded orning :w*n [(5000- n*5)/tc]*r*s Obtained the iniu nuber of classes *w. Consider inforation recorded in the : w*n [(700-n*5)/tc]*r*s Obtained the iniu nuber of classes *w. Thus we have the conclusion that orning can accoodate up to 70 people, the for 550. The physical testing is a total 2036 people, if all the in the orning, so, the ideal situation for the iniu nuber 3 (orning); taking into account of the actual situation, working arrangeents is as days for the unit, the period ust be continuous, and therefore, we ust use 2 day four to arrange the above personnel finish fitness test. So, we have the following conclusion: Conclusion2: The proble of fitness test at least for 2 days at least four periods (Continuous orning and each 2 s). In order to ore accurately deterine the nuber of periods and class arrangeents, we constructed the following atheatical odel. Box odel: (The atheatical odel of segent nuber and the class period arrangeent). According to the sequence of each can accoodate the nuber of people: zr, zr2, zr3,... br br, br,..., class:, The nuber of each, 2 3 br, Arrange classes to zr, zr2,..., zrk the period are, Get the iniu segents K. The proble is actually a bin-packing proble, so we called box proble. It is as if the different sizes of stones in order of different size box, each box with a different nuber of stones, solve the iniu nuber of boxes. This proble is a NP coplete proble, we use the approxiate algorith to calculate the least nuber of segents and arrange the class. Box odel approxiation algorith: Step: Divide the class according to the nuber of descending sort, assue br br2 br3... br Step 2:According i=,2, sequence test class with each period, The principle of the i period arrangeent as following: scan one of br, br2, br3,..., br, If the class has been arranged or arrangeents to go into ore than the total nuber of the class, so don't arrange the class, otherwise arrange for the class to the period. According to this algorith we use Turbo C prograing relevant procedures, operating results as follows Table3: 600

4 28 th February 203. Vol JATIT & LLS. All rights reserved. ISSN: E-ISSN: Periods of The first day orning The first day orning Table 3: Preliinary Section Tie Schedule The of 54,33,44,45,02,3,4 5,50,03,04,06,6,37,8 47,07,4,46,49,5,0 3,48,42,9,34,25 40,53,0,2,22,39,,38,24,28,43,26,20,3 0,32,29,23,05,2,08 Capacity of Students ,7,27,35,36,52,55, We can see fro the Table3: Physical fitness test can be arranged for 2 days 4 s, and the fourth nearly two-thirds of the surplus. Therefore, we have the following conclusion: Conclusion 3: The iniu period of for physical fitness test is 2 days 4 s. The above arrangeent of each class has obvious shortcoings as follows: The first period has the largest nuber of people and the classes of ost people are concentrated in the period of, so if classes are not divided, venues axiu seating capacity of 50 people, is not conducive to optiize specific testing for each class. Much difference the degree of saturation of each period, 70 people test the first, alost require full load, while the 4th period, alost has 2/3 free. In order to solve the above proble, we put forward the odified odel and algorith The First Phase of the Iproved Matheatical Model and Algorith The iproved odel: (class arrangeent atheatical odel) According to the sequence known four periods, it can hold the nuber of students are: zr, zr2, zr3, zr4, existing classes, the nuber of students are: br, br2, br3,..., br, arrange classes to zr the period of, zr2, zr3, zr4, Make the students quantity rate ost close for each period. Balance than calculation forula: The period of can accoodate nuber-arrangeent. The period of can accoodate nuber Balance nuber rate is close; the fact is the work saturation close. Solution of odel algorith: Step: Divide the class according to the nuber of descending sort, assue br br2 br3... br. Step2: Divide parts: br br br... br 2 3 into four s = { br, br5, br9,...}, s 2 = { br2, br6, br0,...}, s 3 = { br3, br7, br,...}, s 4 = { br4, br8, br2,...}, then, s,s3 reordering according to the ascending. Step 3:According i=,2, sequence test class with each period, The principle of the i period arrangeent as following: scan one of br, br2, br3,..., br, If the class has been arranged or arrangeents to go into ore than the total nuber of the class, so don't arrange the class, otherwise arrange for the class to the period. The algorith is practical in the case of ensure the least period, collocate the classes of big difference in students quantity with each other together, so that ake the reaining of each period ore closer. According to the algorith, divide the original arranged into four parts, the first and third sections are arranged in ascending order, the fourth and the second part are arranged in descending order, and in the progra use the total inus 800 seconds to obtain a progra (considering occupied by rerecording the nuber of s the aount of to the actual ipleentation). Use TURBO C run the progra and gets the following group results Table 4: 60

5 28 th February 203. Vol JATIT & LLS. All rights reserved. ISSN: E-ISSN: Periods of The first day orning The first day orning Table 4: section schedule The of Capacity of Students 36,33,55,45,09,3,27,5,2 03,28,06,8,37,23,07,20, ,32,5,,3,43,42,0,34 22, ,2,40,39,0,38,48,26,4 30,49,29,6,25, ,50,04,08,02,7,4,35,54 52,44, Results: To observe the results found that the nuber of four arrangeent is close, and each the nuber of classes with a neat, each the reaining is average The Second Stage Matheatical Model and Algorith The second stage of the odel can be siplified as: Known the period and arranged classes, solving students waiting as short as possible actionable classes physical fitness test schedule. () Basic sybol and assuptions Assue that the paraeters: : ts, end : te, Period of : t=te-ts (seconds for the unit); Set the class nuber is, the nuber of br br, br,..., br, 3 ; each class respectively are 2 nuber test ites according to the following ways: q: Height and weight test: Three instruents C,C2,C3, every person, the average test 0 seconds; q2: The standing long jup test: One instruent C4, every person, the average test 20 seconds; q3: Vital capacity test: One instruent C5, every person, the average test 20 seconds; q4: Grip strength test: Two instruents C6, C7, every person, the average test 5 seconds; q5: Step test: Two instruents C8,C9,every 5 person, the average test 20 seconds. 602 The instruent of the average test : test, test2, test 3 = 0, test 4 = 20, test 5 = 20, test6, test 7 = 5, test8, test 9 = 42 Deterine the : The of the class students whose nuber is test on a single instruent, after these students test one, iediately into another test. Deterine the end : The end is the class last student finish the test on one instruent, after the class last student finishing the test, the instruent can be used by other students. (2) The calculation of class waiting The basic calculation forula: Students waiting = Students coplete the last the students enter test Test = s waiting = the class every student waiting In accordance with the above assuptions, we can get the class waiting calculation forula: The i class waiting : wait = (ax{ bend } in{ bst })* br w Aong the, (test ) i i, j i, j i i j 9 j 9 bri ( bri ) * testk k is the end of the apparatus nuber, k 7 w = 2 i br0i ( br0i ) bri + 4 * testk br0i = =, k 8,9 2 5 So, the total waiting is: Swait = i= wait i (3) The class arrangeent of solving odel: Known the nuber of each class and the physical testing, satisfy the following conditions, find out the class, so that iniize the su of the class waiting, naely Swait = Min{ wait i i= } The necessary satisfy condition: (a)feasibility conditions: Any the sae bst jk, bstik, end jk, orbst, k bst end j, k i, k

6 28 th February 203. Vol JATIT & LLS. All rights reserved. ISSN: E-ISSN: achine can t have ore than two classes of students in the test, so that does not exist i, j ake: (b)test requireents: Each student ust do five different tests, and don't allow a test to do ore than twice. Such as class i do the test on the j instruent. ark i, j =, otherwise, test requireents is: 9 j= ark ark i i, j, j = 0 = 5, then, the (c)site conditions: Any t, no ore than 50 students on the test. Define class i field h (t) function i : h ( t) i 0 in{ bst } t ax{ bend i, j = j 9 j 9 others i, j Then, site conditions can be expressed as follows: i= br h ( t) 50 i So as to obtain the atheatical odel: The atheatical odel of class s arrangeent at the period of : Swait = wait i Min{ i= }. (4) Solution of the odel algorith This is siilar to the arrangeents of production planning process, is an NP-coplete proble which can only be solved by approxiate algorith, we design a siulation algorith, set the selective priority, high priority during the siulation priority greedy principle. i Algorith principle:()order each test fro slow to fast, ust ensure that the slowest equipent } isn t idle, and then ensure slower, arrangeents for the test priority; (2)When a class the first personal finish, then the student can arrange for the second ; (3)The class ust be entirety into the test site. Siulation algorith: Siulate the entire testing process, choose the priority greedy algorith. Step : Divide the class into two groups and ake the total nuber of two groups close. (Graph theory has a special algorith). And order the two groups of people according to the nuber fro sall to large,, 2 groups of each class are fixed to the,2 device on the 5 test Step 2:Initial arrangeent: The two classes order front the group and 2 respectively arranged to do the test in 5 individual test ites,2 device, under the preise of the total nuber is lower 50 and the rest of class 2 coponents as possible as equally, according to the 's priority to arrange other classes to test. Step 3: When a class personal done a test, can arrange the class to do the second test, choose the second test principle is: According to the priority, first do the high priority (achine of slow test speed), only if high priority of waiting enough to all our students finish a lower priority, so, choose the lower priority s as the next priority. Step 4: When students have finished copute the quantity of students, when the nuber reaches to a class without waiting, then select a class with step sort order and ensure two groups have siilar reaining nuber. The new entering class uses the step3 principle select test. Final results () The classes arrangeent Table 5: Table 5: Section Tie Schedule Periods of The Capacity of of Students The first day orning 36,33,55,45,09,3,27,5,2 03,28,06,8,37,23,07,20, The first day 46,32,5,,3,43,42,0,34,22, ,2,40,39,0,38,48,26,4,30,49,29,6,2 orning 5, ,50,04,08,02,7,4,35,54,52,44, (2) The first orning Table 6, Table 7, the second day orning Table 8 Table 9: 603

7 28 th February 203. Vol JATIT & LLS. All rights reserved. ISSN: E-ISSN: Table 6: The First Day Morning 8:00-2:0 Testing Tie Schedule (8:00 And 3:30 Recorded As 0 Moent) First test Second test Third test Fourth test Fifth test waiting 36 C8 0 C5 420 C4 955 C7 45 C C C 3470 C C5 520 C C3 0 C6 20 C4 855 C8 345 C C C C C C C5 0 C4 655 C6 995 C9 505 C C C 8470 C C5 20 C C 55 C7 685 C C C C7 955 C5 240 C 2575 C C C9 0 C4 325 C5 745 C 820 C C C7 605 C 6780 C C C7 955 C5 240 C 2575 C C C C C C C C C C C C C8 0 C5 420 C4 955 C7 45 C C C7 605 C 6780 C C C C 8470 C C5 20 C C C C C C C9 0 C4 325 C5 745 C 820 C Table 7: The First Day Afternoon 3:30-6:45 Testing Tie Schedule (8:00 And 3:30 Recorded As 0 Moent) First test Second test Third test Fourth test Fifth test waitin g 46 C3 25 C7 685 C C C C8 0 C7 25 C2 220 C5 535 C C 2625 C C C C C9 0 C6 25 C 230 C4 540 C C3 595 C6 975 C 265 C C C2 925 C C4 295 C C C7 0 C2 85 C4 45 C5 680 C C5 0 C4 405 C7 65 C9 830 C C 55 C7 685 C C C C4 595 C5 975 C 265 C C C7 0 C2 85 C4 45 C5 680 C Table 8: The Second Day Morning 8:00-2:0 Testing Tie Schedule (8:00 And 3:30 Recorded As 0 Moent) No. First test Second test Third test Fourth test Fifth test waiting 9 C9 0 C4 325 C5 745 C 820 C C 55 C7 685 C C C C7 955 C5 240 C 2575 C C C8 0 C5 420 C4 955 C7 45 C C C C C C C4 0 C8 355 C C2 025 C C C 3470 C C5 520 C C2 425 C C5 545 C C C5 0 C4 655 C6 995 C9 505 C C C C C C C3 0 C6 20 C4 855 C8 345 C C C7 605 C 6780 C C C C C C 9450 C C C4 C5 205 C C C C C5 925 C9 650 C

8 28 th February 203. Vol JATIT & LLS. All rights reserved. ISSN: E-ISSN: Table 9: The Second Day Afternoon 3:30-6:45 Testing Tie Schedule (8:00 And 3:30 Recorded As 0 Moent) First test Second test Third test Fourth test Fifth test waiting 05 C7 0 C2 85 C4 45 C5 680 C C 440 C4 855 C C C C4 595 C5 975 C 265 C C C6 0 C 55 C5 45 C4 660 C C C C C C C5 0 C4 405 C7 65 C9 830 C C2 925 C C4 295 C C C4 3:00 C5 405 C6 65 C8 830 C C7 855 C C C4 35 C C9 3:00 C6 25 C 230 C4 540 C C5 785 C C C 3645 C C8 3:00 C7 25 C2 220 C5 535 C The total waiting : Through the calculation get total waiting : 5986s=44.2h. 5. CONCLUSION The advantage of this odel is that it grasps the relationship between the nuber of classes and total, and obtains reasonable section and class distribution by using the relationship. Another highlight of the odel is using the greedy algorith sort classes for the sae period in the second stage of the odel. Moreover, it akes a better evaluation of the reasonableness of the different progras, strong adaptability and better integrated with the objective reality. REFERENCES: [] Liang Kaifu, Study on properties of knapsack proble, Matheatical theory and applications, Vol. 20, 2, 2000, pp [2] Sun Jinguang, Design and analysis of knapsack proble, Journal of Liaoning Technical University, Vol. 4, 2002, pp [3] Christian H. S et al, Arena Football das neue Gesicht des Aerican Football in Europa, Sport-Orthopädie - Sport-Trauatologie - Sports Orthopedics and Trauatology, Vol.27, 2, 202, pp [4] Richard G. E, The National Football League and Concussion: Leading a Culture Change in Contact Sports, World Neurosurgery, Vol.74, 6, 200, pp [5] Hongju Shi, Xifeng Qu, The principle and application of reasonable defense in football gaes, Science & Technology Inforation, Vol.2, 2009, pp [6] Binfeng Huang, On the Defensive Statics in Modern Soccer Copetition, Science & Technology Inforation, Vol. 5, 200, pp [7] Gang Yi, Football Players' Overall Mixed Defense Ability in Colleges of Heilongjiang Area, The Science Education Article Collects, Vol.5, 200, pp [8] Xiaolu Zhang, Gang Lu, A Review of the Studies on Modern Football s Defensive Tactical Syste fro Multidiensional Perspectives, Journal of Zhao tong Teacher s College, Vol.34, 5, 202, pp [9] Ziyong Ling, Zeyong Hu, To See Modern Football Defensive Pattern fro the goals Conceded of the 9th World Cup, Sports Science Research, Vol.5, 6, 20, pp [0] Jian Huang, Xuezhen Ge, Wei Li, The Application of Defensive Tactics in the Football Match, Journal of Gannan Medical University, Vol.5, 2009, pp