一种基于改进遗传规划洪灾损失高精度的综合评价方法.pdf

Journal of Ocean University of China(Oceanic and Coastal Sea Research)ISSN 1672-5182,October 30,2006,Vol.5,No.4,pp.322-326 http:/ xbywbouc A High Precision Comprehensive Evaluation Method for Flood Disaster Loss Based on Improved Genetic Programming ZHOU Yuliang 1)*,LU Guihua 1),JIN Juliang 2),TONG Fang 1),and ZHOU Ping 1 1)College of Water Resources and Environment,Hohai University,Nanjing 210098,P.R.China 2)College of Civil Engineering,Hefei University of Technology,Hefei 230009,P.R.China(Received March 29,2006;accepted August 25,2006)Abstract Precise comprehensive evaluation of flood disaster loss is significant for the prevention and mitigation of flood disasters.Here,one of the difficulties involved is how to establish a model capable of describing the complex relation be-tween the input and output data of the system of flood disaster loss.Genetic programming(GP)solves problems by using ideas from genetic algorithm and generates computer programs automatically.In this study a new method named the evalua-tion of the grade of flood disaster loss(EGFD)on the basis of improved genetic programming(IGP)is presented(IGP-EGFD).The flood disaster area and the direct economic loss are taken as the evaluation indexes of flood disaster loss.Obvi-ously that the larger the evaluation index value,the larger the corresponding value of the grade of flood disaster loss is.Con-sequently the IGP code is designed to make the value of the grade of flood disaster be an increasing function of the index val-ue.The result of the application of the IGP-EGFD model to Henan Province shows that a good function expression can be obtained within a bigger searched function space;and the model is of high precision and considerable practical significance.Thus,IGP-EGFD can be widely used in automatic modeling and other evaluation systems.Key words automatic modeling;evaluation of flood disaster loss;genetic algorithm;genetic programming 1 Introduction Systems evaluation,which precedes system analysis and follows systems decision-making and analysis,is a hinge of the systems engineering theory and methodol-ogy(Jin et al.,2002).Comprehensive evaluation of the grade of flood disaster loss(EGFD)aims at evalu-ating the grade of disaster loss caused by flood based on the existing evaluation model of flood disaster loss and the indexes values.Precise evaluation result can provide a scientific decision-making basis for flood dis-aster management,which is very significant in region-al social economic and ecological environmental devel-opment.Because the evaluation results of single in-dexes in practical evaluation are often incompatible,the evaluation of flood disaster obtained by using flood disaster evaluation standard table directly lacks practi-cality.Hence many kinds of comprehensive evaluation models,such as the project pursuit method(Friedman and Turkey,1974;Jin et al.,2002),fuzzy compre-hensive evaluation method(Chen,1990),grey clus-tering method(Xia,2000)and logistic curve model(Jin et al.,2000)have been proposed successively.However,the complex mathematical expression desc-Corresponding author.Tel:0086-25-83787741 E-mail:zy154600 163.tom ribing the relation between the flood disaster evalua-tion indexes and the evaluation grade should be speci-fied in advance on the basis of the knowledge of the flood disaster system being studied when using those models,so they lack flexibility.Genetic programming,GP for short,as one of the automation wogramming techniques developing rapid-ly in recent years,is a kind of new evolutionary com-putation based on the extension and development of genetic algorithm;with the improvement on its theory and the application of its technique by efforts of many scholars,GP has successful applications in modelling,prediction and classification,designing,auto-design-ing of multi-agent systems and biomedicine(Koza et al.,1993,1994;Linet al.,1999;Chen et al.,2000;Whigham and Crapper,2001;Cornelis et al.,2004).The specific realization of IGP for the evalua-tion of flood disaster loss in this paper is presented on the basis of all the research achievements mentioned above.GP has been realized by Prof.J.R.Koza in the programming language of Lisp;in recent years,many scholars have realized programming GP in the languages of C,C+,Javal.1,Smalltalk 80,math-ematical,etc(Liu et al.,2001).For the sake of the practical engineering calculation,the IGP-EGFD mo-del in this paper is realized in the Fortran program-ming language.ZHOU Y.L.et al.:Evaluation for Flood Disaster Loss Based on Genetic Programming 323 2 Material and Methods The IGP-EGFD method includes six steps as fol-lows:Step 1 The standardization of the evaluation in-dexes set of the samples.Define the set of indexes as I(x,j)Ik=*,2,g;j=l,2,M,where N,M are the sample capacity and the number of the evaluation indexes,respectively.To make the model universal,the sample indexes are usually treated as follows:An index,which is of higher grade when its value is larger,can be treated with the following equation:x(i,j)=x (i,j)/xax(j),(1)x(i,j)=Ex(i,j)-7(j)/s(j).(2)On the other hand,for an index,which is of higher grade when its value is smaller,the following equation is used:x(i,j)=l.O-x(i,j)/Xma(j),(3)where,x(j),Xmin,j,X.j and s(j)are the mean,minimum value,maximum and the standard deviation of the jth evaluation index,respectively.The aim of GP is to find an optimal function expression G(c,xl,x2,XM)to make the following equation a minimum:N minf=G(c,xk,1,2Ck,M)-Yk ,(4)where,c is a constant,Yk is the grade value of flood disaster,is for taking the absolute value.Step 2 Encoding.Find the terminal set T and the function set F.The elements of the terminal set T are usually variable x,constant c,functions without parameters(including self-defined functions without parameters),etc.The elements of the function set are usually arithmetic operations,e.g.,/+,-,x,/I,logical operations,e.g.,AND,OR,NOT t,ele-mentary functions,e.g.,t sin,cos,tan,exp,ln l,and self-defined functions with parameters.Both the terminal set T and the function set F being discrete sets,their union D can be encoded with a subset of natural numbers:D=T.J F(Yun,2000).The error presented in equation(4)is taken as the driving force of evolution;hence the corresponding solution may not be consistent with the physical significance of the studied problem.For example,for equation ax2+bx+c=0,although the solutionx=(-b+b2-4ac)/2a+lO-labc is acceptable by GP,it can not be a correct solution for the equation.To ensure that the solution has physical significance and to reduce proba-bility of assembler explosion of GP(Pan et al.,1998;Im et al.,2000),an encoding scheme(making the grade value of flood disaster an increasing function of the index value of flood disaster)shown in Table 1 is presented based on Zhou et al.(2004).Table 1 An encoding scheme of genetic programming Element of D cl X+exp(x)xc2 Encoding value 0 1 2 3 4 5 Step 3 The initialization of the parental generation group.Define the group scale as n,i.e.the number of trees is n,and the maximum depth of these trees(i.e.the number of layers)should be smaller integers(e.g.,4-6),so that it is convenient to analyze and explain the optimal function expression searched by GP and to prevent against the problem of assembler explosion during calculation(Lu et al.,2000).When producing the initial group-the n trees,the root knot of each tree can be randomly selected from the corresponding encoding values of the function set F,and the middle knots and leaf knots can be ran-domly selected from the corresponding encoding values of the union set D and the terminal set T.For in-stance,in the encoding scheme shown in Table 1,the encoding value of the root knot of each tree has been placed in array IA(n),the selected values(encoding values)being 2 or 3,and the maximum depth of the tree has been defined as d+1=6 layers to prevent a-gainst the appearance of hue trees during the crossover operation.Beyond the root knot layer,there remains 5 layers below,whose codes can be placed into array IB(n,d,/),where/is the number of leaf knots lo-cated in the last layer.For instance,it is obvious that l=2 d=32 with a 2-cross tree.The encoding value of the lower layer should correspond to that of the upper layer,i.e.,if the upper layer is the/th knot,and the encoding value of knot/of the upper layer is 2 or 3,then the values of the(2l-1)th and 2/th knots of its lower layer can be selected arbitrarily from the corre-sponding encoding set of the union set D;if the en-coding value is 4,then the value of the(2/-1)th knot of its lower layer can be selected arbitrarily from the corresponding encoding set of the union set D,whereas the value of the 2/th knot can be 1(which means no operation);if the encoding value of the up-per layer is 5,then the(2l-1)th knot of its lower layer can be randomly selected from the corresponding encoding set of the union set D,whereas the value of the 2!th knot can only be 0(which means the expo-nent);if the encoding value of the upper layer is 0,1 or 1,then the encoding values of both the(2l-1)th and the 2/th knots will be 1.Thus,the n trees can be expressed withthe arrays IA(n)and IB(n,d,l).Step 4 The decoding of the parental generation and the evaluation of the fitness of the individuals.Define an array bb(j,l)to store the function values of the sub-tree corresponding to the lower part of the 324 Journal of Ocean lth knot in the j th layer,i.e.if the encoding value of the/th knot in thejth layer is 4,then bb(j,l)=exp(bb(j+1,2l-1)When reaching the 2nd lay-er,bb(2,1)and bb(2,2)are obtained,then the cor-responding function expression is G=bb(1,1)=bb(2,1)bb(2,2),where j,l are the serial numbers of layer and knot,respectively.The detailed realiza-tion process can be seen in Zhou et al.(2004).Sub-stitution of the expression G into Eq.(4),gives the object function value f(i)corresponding to each indi-vidual.Then arrange f(i)in increasing order of their values,meanwhile arrange the corresponding ar-rays IA(i)and IB(i,d,l)in the same order,and the first several individuals are named the optimal in-dividuals.Define the fitness value F(i)of the i th parental individual F(i)as(Jin and Ding,2002)F(i)=l/(f(i)f(i)+O.O01).(5)Obviously,the larger the value of the fitness function,the smaller the object function value is.Step 5 Perform operations of selection,cross-over and mutation on the parental generation to generate the filial generation group.In this step,GP carries out the 3 evolutionary operations mentioned above.Define the selection,crossover and mutation operation probabilities as p.,Pc and Pm=1-p,-Pc,respec-tively.A uniform random number u is generated within the interval 0,I.If up,then a selection operation is performed;if p,u (Ps+Pc),then a crossover operation is performed;and if u p,+Pc,then a mutation operation is performed.Carry out these operations repeatedly for 0.95 Popsize times to complete one evolutionary iteration(0.05 Popsize indi-viduals are preserved from the optimal individuals of the parental generation group).The detailed operation process can be seen in Jin and Ding(2002)and Zhou et al.(2004).Step 6 Define the filial generation group as the parental generation group,return to step 4,and carry out the above operations repeatedly until the number of the evolutionary iterations is larger than the prede-termined value,or the object function value has reached the predetermined value.The optimal individu-al of the present group is taken as the final result of the IGP model.3 Results and Discussion Case Study of Using the IGP-EGFD Method In Jianget a/.(1996),the disaster area x (1,k)and di-rect economic loss cr*(2,k.)were taken as the indexes of the flood disaster loss.Frequency analysis was per-formed using 41 years real flood disaster data from 1950 to 1990 in Henan Province,and the evaluation criteria of flood disaster in Henan Province were ob-tained and shown in Table 2.Five random values of University of China Vol.5,No.4,2006 Table 2 The assessment criteria of flood disaster in Henan Province,China Assessment index Ordinary Fairly great Great disaster Super Flood disaster area/(krn 2)283.3 Directeconomieloss/108 85.0 The table is taken from Jiang et al.(1996).flood disaster indexes for each grade are generated by using 5 uniform random numbers,then with the cor-responding flood disaster grade,the standard sample series is obtained,and the standard samples are Nos.1-23 shown in Table 3.Now try to search the optimal function expression between the evaluation indexes and the evaluation grade.During the standardization according to Eq.(1),23.5,4.5 and 700210 are cho-sen as the minimum and maximum of the evaluation indexes x*(1,k)and x (2,k),respectively.The group scale of IGP-EGFD is 100,the selection,cross-over and mutation operation probabilities are 0.15,0.6 and 0.25 respectively,and the encoding of the con-stants Cl,c2 in this case should be expressed with the tree whose structure is the same with the function ex-pression tree(there should be a one-to-one relation be-tween the two trees),all the values of the knots in the tree are real numbers,and the values of the knots that are corresponding to the codes Cl,c2 have been chosen in the intervals 0,6 and 0,1 with uniform ran-dom numbers respectively.The calculation result(the result of the 32th iteration of the IGP-EGFD model)is shown in Table 3.The searched optimal function expression with the corresponding iteration numbers of IGP-EGFD and the values of Eq.(4)are shown in Table 4.As shown in Table 3,the values of object function expressed in Eq.(4)for the PP and LOG model are 5.133 and 4.76,respectively;the corresponding value of the IGP-EGFD model established in this paper is 4.503.The IGP-EGFD model is thus of higher precision and can better reflect the complex relation between the disaster evaluation indexes and the grade,and it needs smaller iteration numbers than the GP model in searching the optimal function expression,which can also be seen in Zhou et al.(2004).The 9 real flood disasters in 41 years,which are selected from flood disasters over the period in Henan Province,are also shown in Table 3,and their evaluation results can be seen from No.1950 to No.1984 in Table 3.The cal-culation results of flood disasters in Henan Province have proved that the capability and precision of IGP in searching out the mapping relation between the output and input data of the system are strong and high.IGP can search out the complex mapping relation with sev-eral variables without knowing the general relation a-mong these data;moreover,the model developer does not need to have a solid knowledge of the background of the problem,and more than one optimal models can be provided by IGP for selection at the same time.ZHOU Y.L.et al.:Evaluation for Flood Disaster Loss Based on Genetic Programming Table 3 Comparison results between IGP-EGFD and other methods for evaluating the grade of flood disaster 325 No.Eva.I t Grade of flo