Large System Multi-objective Model of Optimal Allocation for Water Resources in Jiansanjiang Branch Bureau

Transcription

1 Large System Multi-obetive Model of Optimal Alloation for Water Resoures in Jiansaniang Branh Bureau Ping Lv, Dong Liu, Shool of Water Conservany & Civil Engineering, Northeast Agriultural University, Harbin Heilongiang , China Abstrat. Aording to the imbalane development and utilization of resoures, shortages and other issues in Saniang Plain, taing Jiansaniang branh bureau as an example, the multi-obetive optimal alloation model of resoures is established with goal of maximum eonomi and soial benefits. Only surfae, ground and transit are onsidered overall and different demands in industry, life and agriulture are satisfied an we realize the rational alloation of regional resoures. The large system deomposition-oordination theory and multiobetive geneti algorithm are applied to solve the model. The optimization results showed that, the shortage situation in Jiansaniang branh bureau is improved in planning years and surfae supply apaity an be inreased gradually and ground resoures an be effetively proteted. The optimal alloation model and solution method are effetive and feasible, and the optimal alloation results are reasonable. The researh an provide sientifi basis for rational development and utilization of resoures in Jiansaniang branh bureau and Saniang Plain. Keywords: Jiansaniang branh bureau; optimal alloation of resoures; multi-obetive geneti algorithm; large system deomposition-oordination 1 Introdution Optimal alloation of resoures refers to the sientifi and rational alloation of limited and different forms resoures, with both engineering and nonengineering measures in a partiular shed or region. The purpose is to ahieve the sustainable utilization of resoures, to oordinate the benefit onflit between eah region and use department, to improve the regional overall onsumption effiieny as muh as possible [1], to ensure the harmonious About the Author: Ping Lv (1985- ), Female, master, main researh diretion is agriulture and resoures system analysis and optimal using. pingping.85@163.om Corresponding author: Dong Liu (1972- ), Male, professor, dotor, main researh diretion is agriulture and resoures system analysis and optimal using. liu72dong@126.om.

2 development of soial eonomy, resoures and eologial environment to get the biggest integrative benefit whih inluding eonomi, environmental and soial benefits and other goals. Jiansaniang branh bureau loates in northeast of Heilongiang Provine and belongs to Saniang Plain,whih is an important grain prodution area in China. The total area is 12300m 2[2], with ultivated areage of hm 2[3], and the main grain rop is paddy. In reent years, the paddy is planted in mostly field as the eonomi benefits, then the demand of resoures for irrigation is inreasing rapidly. The issues suh as over-exploitation of ground and imbalane utilization of ground-surfae are serious in several areas [4]. It is neessary to optimize the resoures sientifially and reasonably, in order to utilize the limited resoures legitimately and develop sustainable agriultural and improve utilization effiieny of resoures. As the omplexity of resoures system and multi-obetive optimization problem, the traditional planning methods are diffiult to solve suh problems. The geneti algorithm has been onsidered to be the most suitable method for multiobetive optimization [5], so large system deomposition oordination theory and multi-obetive geneti algorithm are introdued into the solution of resoures optimal alloation model in this artile. 2 The Establishing of Multi-obetive Model of Optimal Alloation 2.1 Desription of the Deision Variables The regional soure whih based on the delivery range an be lassifying into publi and independent soures two types. Publi soure simultaneously supplies to two or more subareas, suh as mainstream transit. Independent soure only supplies to its own subareas, suh as loal interval runoff and ground [6]. Assuming that there are K subareas and M publi soures in the regional resoures system, and C() independent soures in subarea [7, 8]. So R r,the supply subarea has I()=C()+M supply soures. Define i m n and demand relationship matrix between soures and users in subarea; r, the supply-demand relation oeffiient between soures and users in the subarea;i=1 to m,different supply soures; =1 to n,different use departments. r =1 when there is the supply-demand relationship between the i soure i and the user, otherwise r i =0. Referring the supply quantity x i from soure i to user as the deision variable, then the deision variable in subarea is desribed as follow: i

3 x 11 x12 x1, J ( ) x 21 x22 x2, J ( ) X (1) xi ( ),1 xi ( ),2 xi ( ), J ( ) Where, I(),the number of supply soures in subarea;j(),the number of use departments(inluding domesti, industrial, agriultural and other departments)in subarea. x is orresponding to the oeffiient r. r =0, soure i does not i supply to department in subarea, so to department in subarea, then x 0. i i i i x =0; r =1, soure i supplies i 2.2 Obetive Funtion The artile follows the regional sustainable development ideology, taing the regional eonomi and soial benefits as goals to establish the optimal alloation model [9-11]. (1) Eonomi goal. The eonomi net benefits produed by different use departments of region are maximum in the target year. K J ( ) I ( ) 1 ( x) max ( bi i ) 1 1 i1 max f x (2) Where, x,the supply quantity from soure i to user in i subarea (10 4 m 3 ); b,the benefit oeffiient of supply from soure i to i user in subarea (10 4 Yuan/ m 3 );,the ost oeffiient of supply from i soure i to user in subarea (10 4 Yuan/ m 3 );,the supply order oeffiient of soure i in subarea;,the use fair oeffiient of user in subarea. (2) Soial goal. The total shortage quantity of region is minimum in the target year. K J ( ) I ( ) max f2( x) min D xi (3) 1 1 i Where, D,the demand quantity of user in subarea (10 4 m 3 ). i i i 2.3 Constraints The onstraints of resoures optimal alloation model is mainly onsidering the supply apaity onstraints of supply system and demand apaity onstraints of use system of region.

4 (1) Water supply onstraints Where, x and Publi soure: J ( ) 1 K 1 Independent soure: m x W m m W W m m J ( ) x 1 W x,the supply quantity form publi soure m and independent soure to user in subarea (10 4 m 3 ); W and m (4) (5) W,the supply apaity of publi soure m and independent soure in subarea (10 4 m 3 );W m,the supply apaity of publi soure m (10 4 m 3 ). (2) Water demand onstraints Where, L and L I ( ) x i1 i H H, the lower and the upper limit of demand department in subarea (10 4 m 3 ). (3) Nonnegative variable onstraints x 0 (7) i (6) 3 Mode Solution 3.1 The Proess of Large System Deomposition-oordination Large system deomposition-oordination theory an be applied to establish the large system multi-obet optimal alloation model for above large-sale resoures system with multi-soure and multi-user [12]. Aording to the theory of large system deomposition-oordination and the atual ondition of resoures supply and demand, two-stage hierarhial multi-obetive optimization model is established [13]. The related onstraint variables also are the regional publi resoures are alloated in advane whih mae the system divided into K independent subsystems by the model oordination method. Then the distribution amount is oordinated repeatedly until the best integrated goal of system is ahieved (Figure.1).

5 Total resoures of region D 1 2 F F D D 2 X D F Subarea 1 Subarea 2 Subarea X X The seond level (System oordination ) The first level (Subarea optimization) Fig. 1. The level transfer deomposition-oordination struture of resoures optimal alloation Figure.1 shows that the model after large system deomposition-oordination is atually going to ahieve two-level optimizations, whih are the alloation of soures between different users in eah subarea and quantity between subareas [14]. (1) The optimization of first level subsystem The region is divided into K subareas based on the natural geographial or administrative onditions in the first level. Eah subarea optimize inside independently, under the premise of a given resoures amount from the seond level (oordination level), whih satisfied K D 1 W. The optimization of subarea is still a multi-obetive optimal alloation model whih solved by aelerated multiobet geneti algorithm. The internal optimal solution in eah subarea and the orresponding fitness value are not neessarily the best balaned solution of region. Therefore, we need to feed ba the optimal solution X ( D ) and the target value F ( X, D ) in eah subarea that got from the first level to the seond level, and do the seond level system oordination. (2) The oordination of seond level system The tas of the seond level oordination is to get the optimal alloation of publi resoures in subareas, to oordinate the partial optimal solution of eah subarea to find the best balaned solution of the entire region. The solution of the seond level oordination is still solved by aelerated multi-obet geneti algorithm. The main steps are as follows: 1 Produing the pre-alloated resoures D, and transferring them to eah subarea in the first level. 2 Optimizing the first level subsystem, and getting the feedba value of the first level. 3 Doing the geneti operation based on the feedba information, and getting the new pre-alloated proet. 4 Cyle alulation until the solution satisfied the termination requirement or the number of evolution generation, and getting the optimal alloation of resoures. 3.2 Multi-obetive Geneti Algorithm The geneti algorithm does not require the problem with the requirements of linearity, ontinuation, onvexity and others, and it has high omputation effiieny, global

6 searh ability and strong robustness [15,16] ompared with other traditional algorithms. The population in geneti algorithm is made up of individuals, in whih eah individual orresponds to a basi supply alloation program in the resoures system. The size of population is determined by the number of individuals. The greater the population or the more individuals, the more pre-alloated programs. Aording to the features of resoures multi-obetive optimization, the alulation method of fitness that based on the sort in the paper only depends on the multi-obetive itself. Therefore, we an ran all individuals in the population separately by their responds to different obetive funtions, and alulate the total fitness. Thus, an individual in the geneti algorithm population is a alloation program of resoures, and eah program reflets multi-obetive funtion values [17]. f (i) (i=1 to n)stands for the obetive funtion, n is the number of target, N is the total number of individual. For eah goal i, every individual will generate a sorting sequene X of feasible solution based on the quality of funtion value. The i overall performane of individuals to all obetive funtions an be got after sorting eah goal. Aording to the sorting of the individual alulated the fitness: 2 ( N Yi ( X )) Yi ( X ) 1; Fi ( X ) i 1,2,, n (8) 2 N Yi ( X ) 1; n F( X ) Fi ( X ) 1,2,, n i1 Where,n,the total number of obetive funtion;n,the total individual number; X,the individual of the population; Y X ),the serial number of i ( X to the target i in the population; F X ),the fitness of X to target i; i ( F ( X ),the omprehensive fitness of X to all targets;k,a onstant between 1 and 2, whih is used to inrease the fitness when the funtion value of individual is optimal. The above formula shows that, the better the individual represent the greater fitness it will get, and aquire more opportunities of involving in the evolution [18]. The individual that has the optimal overall performane is the best program for the multiobetive funtion in all solutions. (9) 4 Case study 4.1 Model parameters Jiansaniang branh bureau is divided into 15 subareas aording to its administrative division of farms, they are Farm Bawuiu, Shengli, Qixing, Qindeli, Daxing, Qinglongshan, Qianin, Chuangye, Hongwei, Qianshao, Qianfeng, Honghe, Yalvhe,

7 Erdaohe and Nongiang. Eah subarea has ground, surfae and transit three forms of soures. Ground and surfae are independent soures, and transit is publi soures. In this plan, we only onsider domesti, agriultural and industrial use departments. The planning years are 2010, 2015 and In this plan, in order to protet loal limited ground resoures, to improve eologial environment, we should gradually ontrol the exploitation of ground and improve the utilization of surfae resoures. Therefore onforming the ground exploitation extent of eah farm are 50%(moderate intensity), 40%(moderate intensity) and 30%(moderate intensity), and the supply of surfae are 10%, 15% and 20% of the multi-year average surfae resoures. Heilong River and Ussuri River are the main transit resoures in the region, in the future, Heilong River an supply m 3, m 3 and m 3, and Ussuri River an supply m 3, m 3 and m 3. The industrial and domesti demand are alulated aording to the development goals of prodution value, industrial use quota, the development sale of population and the per apita use quota. The agriultural demand is alulated based on the irrigation quota, the area of rops and the utilization oeffiients of irrigation. 4.2 Results and analysis The alulation parameters of geneti algorithm are as follows: the population size N=200, the rossover probability P =0.8, mutation probability P m =0.2, the random number of mutation diretion required M=10 and the aeleration times C i =10. Due to the length limitations, the resoures optimal alloation results of Farm Qixing in the future years are listed only in this artile (Table 1). Table 1. The resoures optimal alloation results of Farm Qixing (Unit: 10 4 m 3 ) Year Water onsumption department Domesti Agriultural Industrial Ground Water resoures Surfae Transit Water supply Water demand Water shortage Total Domesti Agriultural Industrial Total Domesti Agriultural

8 Industrial Total Table 1 shows that, along with the population growth and soio-eonomi development, domesti and industrial supply both represent the trend of steady inrease, agriultural supply dereased eah year in Farm Qixing. The variation trend is same as the demand predition. The soures supply struture of eah use department shows that, domesti is mainly supplied by ground, agriultural and industrial supply are shared by ground, surfae and transit. In this alloation, transit resoures gradually assume the most demand, whih remits the shortage situation of ground supply and protet the loal ground resoures effetively. Volume of shortage (10 4 m 3 ) Bawuiu Shengli Qixing Qindeli Daxing Qinglongshan Qianin Chuangye Hongwei Qianshao Qianfeng Honghe Yalvhe Erdaohe Nongiang Farms 2010 Agriultural shortage 2010 Total shortage 2015 Agriultural shortage 2015 Total shortage 2020 Agriultural shortage 2020 Total shortage Fig. 2. The omparison between agriultural shortage and total shortage in Jiansaniang branh bureau in future years Under the ondition of total supply an not satisfied the demand, agriultural shortage is the main representation (Figure.2). The reasons on the one hand, the paddy area is inreasing massively to meet the food prodution demand, but the supply annot quily satisfy the irrigation requirements. On the other hand, the quantity and quality of irrigation and onservany failities annot follow the inrement speed of irrigation demand. From the omparison results of shortages we an see that, along with the gradually onstruting of onservany proet, the ondition of shortage improving gradually, and the volume of shortage dereasing yearly. 5 Conlusions This paper onsidering the multi-obet harater in the optimization of resoures system, established the resoures system multi-obetive optimization model in Jiansaniang branh bureau, taing the eonomi and soial maximum benefits as the obetive funtion, the supply apaity, demand apaity of use system and variable non-negative as the onstraints. The large system deomposition-oordination theory is applied and the model is solved by the real oding based aelerating geneti algorithm, the resoures optimal alloation results of eah use department in 2010, 2015 and 2020 are obtained.

9 The optimization results show that, the ondition of shortage improving gradually, the utilization effiieny of surfae resoures is inreasing and the loal ground resoures are effetively proteted in planning years. Thus the optimal alloation model and solution method are effetive and feasible, and the optimal alloation results are reasonable. The results an support sientifi evidene for resoures optimization in Jiansaniang branh bureau in the future. On the other hand, the shortage of agriulture is still severe. In order to solve this problem, we should ontrol the growth rate of paddy planting, inrease the utilization effiieny of irrigation and redue the irrigation quota. Anowledgments. Thans to the support of the National Natural Siene Foundation of China (No ), Postdotoral Siene Foundation of China (No ), Postdotoral Siene Foundation Speial Funds of China (No ), Speialized Researh Foundation of Colleges and Universities Dotoral Program (No ), National Natural Siene Foundation of Heilongiang Provine (No.C201026), Siene and Tehnology Researh Proet of the Eduation Bureau in Heilongiang Provine (No ) and Dotoral Start-up Foundation of Northeast Agriultural University (No.2009RC37). Referenes 1. Xinyi Xu, Hao Wang, Hong Gan, et al: Maro-eonomi resoures planning theory and method in North China. Yellow River Water Conservany Press, Zhengzhou (1997) 2. Lei Guo, Keming Ma, Yi Zhang: Landsape assessment on wetland degradation during thirty years in Jiansaniang region of Saniang Plain, Northeast China. Ata Eologia Sinia, 29(6), (2009) 3. Qing Zhao: Researh on the trend of underground hange in Jiansaniang area based on gray predition. Journal of Water Resoures and Water Engineering, 20(5), , 134 (2009) 4. Hongyan Li, Ruiqiang An, Yongxia Wei: Applying of the GM(1,1) model to foreast the ground movement in Jiansaniang land relamation area. Journal of Agriultural Mehanization Researh, (3), (2007) 5. Xiangqing Lu, Yingun Tan: Study on multi-obetive geneti algorithm. Journal of Nanyang Teahers College, 3 (9), (2004) 6. Caiqiong Deng: Study on model and it s appliation of regional resoures optimal alloation. Wuhan University, Wuhan (2005) Smith, T.F., Waterman, M.S.: Identifiation of Common Moleular Subsequenes. J. Mol. Biol. 147, (1981) 7. Deshan Tang: A model of multiobetive optimal alloation of resoures in Yellow River Basin. Journal of Hohai University(Natural Sienes), (1), (1994) 8. Beifang Hei: An optimum model of large sale system for optimum alloation of regional resoures. Journal of Wuhan University of Hydrauli and Eletri Engineering, (5), (1988) 9. Hipel Keith, W.: Multiple Obetive Deision Maing in Water Resoure. Water Resoure Bulletin, 28(1), (1992) 10. Buras, N.: Operation of a Complex Water Resoure Utilization System, Intern. Conf. Water for Peae, Washington D.C. (1967)

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