第四讲 多目标规划

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,多目标规划问题,BY CAO,Multiobjective,Optimization,OPtim,_,tb,.,pdf,P131140,选做作业：,1,）,MATLAB,中的多目标优化思路！,2,）多目标优化算法讨论,3,）有关多目标优化实例分析,Algorithm Improvements for Goal Attainment Method,x=,fgoalattain,(fun,x0,goal,weight),x=,fgoalattain,(fun,x0,goal,weight,A,b),x=,fgoalattain,(fun,x0,goal,weight,A,b,Aeq,beq,),x=,fgoalattain,(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,),x=,fgoalattain,(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon,),x=,fgoalattain,(fun,x0,goal,weight,A,b,Aeq,beq,.,lb,ub,nonlcon,options),x=,fgoalattain,(fun,x0,goal,weight,A,b,Aeq,beq,.,lb,ub,nonlcon,options,P1,P2,.),x,fval,=,fgoalattain,(.),x,fval,attainfactor,=,fgoalattain,(.),x,fval,attainfactor,exitflag,=,fgoalattain,(.),x,fval,attainfactor,exitflag,output=,fgoalattain,(.),x,fval,attainfactor,exitflag,output,lambda=,fgoalattain,(.),The arguments passed into the function are described in Table 4-1.The arguments returned by the function are described in Table 4-2.Details relevant to,fgoalattain,are included below for fun,goal,nonlcon,options,weight,attainfactor,exitflag,lambda,and output.,The function to be minimized.fun takes a vector x and returns a vector F of the objective functions evaluated at x.You can specify fun to be an inline object.For example,fun=inline(sin(x.*x);,Alternatively,fun can be a string containing the name of a function(an M-file,a built-in function,or a MEX-file).If fun=,myfun,then the M-file function,myfun,.m would have the form,function F=,myfun,(x),F=.%Compute function values at x,To make an objective function as near as possible to a goal value,(i.e.,neither greater than nor less than)set options.,GoalsExactAchieve,to the number of objectives required to be in the neighborhood of the goal values.Such objectives,must,be partitioned into the first elements of the vector F returned by fun.,If the gradient of the objective function can also be computed,and,options.,GradObj,is on,as set by options=,optimset,(,GradObj,on),then the function fun must return,in the second output argument,the gradient value G,a matrix,at x.Note that by checking the value of,nargout,the function can avoid computing G when,myfun,is called with only one output argument(in the case where the optimization algorithm only needs the value of F but not G):,function F,G=,myfun,(x),F=.%compute the function values at x,if,nargout,1%two output arguments,G=.%gradients evaluated at x,end,The gradient is the partial derivatives,dF,/,dx,of each F at the point x.If F is a vector of length m and x has length n,then the gradient G of F(x)is an n-by-m matrix where G(i,j)is the partial derivative of F(j)with respect to x(i)(i.e.,the,jth,column of G is the gradient of the,jth,objective function F(j).,goal,Vector of values that the objectives attempt to attain.The vector is the same length as the number of objectives F returned by fun.,fgoalattain,attempts to minimize the values in the vector F to attain the goal values given by goal.,nonlcon,The function that computes the nonlinear inequality constraints c(x)2%,nonlcon,called with 4 outputs,GC=.%gradients of the inequalities,GCeq,=.%gradients of the equalities,end,If,nonlcon,returns a vector c of m components and x has length n,then the gradient GC of c(x)is an n-by-m matrix,where GC(i,j)is the partial derivative of c(j)with respect to x(i)(i.e.,the,jth,column of GC is the gradient of the,jth,inequality constraint c(j).,Likewise,if,ceq,has p components,the gradient,GCeq,of,ceq,(x)is an n-by-p matrix,where,GCeq,(i,j)is the partial derivative of,ceq,(j)with respect to x(i)(i.e.,the,jth,column of,GCeq,is the gradient of the,jth,equality constraint,ceq,(j).,options,Optimization parameter options.You can set or change the values of these parameters using the,optimset,function.,DerivativeCheck,Compare user-supplied derivatives(gradients of objective or constraints)to finite-differencing derivatives.,Diagnostics Print diagnostic information about the function to be minimized or solved.,DiffMaxChange,Maximum change in variables for finite-difference gradients.,DiffMinChange,Minimum change in variables for finite-difference gradients.,Display Level of display.off displays no output;,iter,displays output at each iteration;final displays just the final output.,GoalExactAchieve,Specifies the number of goals to“just”achieve,that is,do not try to over-or underachieve.,GradConstr,Gradient for the constraints defined by user.See the description of,nonlcon,under the,Arguments,section above to see how to define the gradient in,nonlcon,.,GradObj,Gradient for the objective function defined by user.See the description of fun under the,Arguments,section above to see how to define the gradient in fun.The gradient,must,be provided to use the large-scale method.It is optional for the medium-scale method.,MaxFunEvals,Maximum number of function evaluations allowed.,MaxIter,Maximum number of iterations allowed.,MeritFunction,Use goal attainment/,minimax,merit function if set to,multiobj,.Use,fmincon,merit func