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Gams 结果输出解读

發表於 2019-07-25 更新於 2020-06-13 分類於 Gams 閱讀次數：
文章字數： 4.8k 所需閱讀時間 ≈ 4 分鐘

简介

GMAS的输出包含以下几部分： 1. 编译结果编译结果包含输入文件的打印，可能的错误提示以及GMAS对象和交叉引用图列表。 2. 执行结果执行结果包含展示声明的结果和可能的执行错误提示。 3. 模型生成该结果在模型生成过程给出，包含等式和变量列表以及模型统计和可可能的生成执行时的错误提示。 4. 解外部求解器程序处理模型时生成的解报告包括:求解总结，求解器的报告，解列表以及报告总结。 5. 解后输出输出的最后部分包括最终执行总结和文件总结。

模型示例

$Title A Quadratic Programming Model for Portfolio Analysis (ALAN,SEQ=124a)

$onsymlist onsymxref onuellist onuelxref

$Ontext
This is a mini mean-variance portfolio selection problem described in
'GAMS/MINOS:Three examples' by Alan S. Manne, Department of Operations
 Research, Stanford University, May 1986.
$Offtext

* This model has been modified for use in the documentation

Set i  securities   /hardware, software, show-biz, t-bills/;
alias (i,j);

Scalar target     target mean annual return on portfolio % /10/,
       lowyield   yield of lowest yielding security,
       highrisk   variance of highest security risk ;

Parameters  mean(i)  mean annual returns on individual securities (%)
      / hardware   8
        software   9
        show-biz  12
        t-bills    7 /

Table v(i,j)  variance-covariance array (%-squared annual return)
                  hardware  software  show-biz  t-bills
       hardware      4         3         -1        0
       software      3         6          1        0
       show-biz     -1         1         10        0
       t-bills       0         0          0        0 ;

lowyield = smin(i, mean(i)) ;
highrisk = smax(i, v(i,i)) ;
display lowyield, highrisk ;

Variables  x(i)       fraction of portfolio invested in asset i
           variance   variance of portfolio
Positive Variable x;

Equations  fsum    fractions must add to 1.0
           dmean   definition of mean return on portfolio
           dvar    definition of variance;

fsum..     sum(i, x(i))                     =e=  1.0;
dmean..    sum(i, mean(i)*x(i))             =e=  target;
dvar..     sum(i, x(i)*sum(j,v(i,j)*x(j)))  =e=  variance;

Model portfolio  / fsum, dmean, dvar / ;
Solve portfolio using nlp minimizing variance;
display x.l, variance.l;

1.编译输出

该结果在程序初始检查时生成。包括：输入文件的打印，符号引用图，符号清单图，特殊元素清单图和包含的文件总结。 ## 1.1 输入文件的打印基本就是把输入的模型文本重新打印一遍。

A Quadratic Programming Model for Portfolio Analysis (ALAN,SEQ=124a)
C o m p i l a t i o n

   2
   4
      This is a mini mean-variance portfolio selection problem described in
      'GAMS/MINOS:Three examples' by Alan S. Manne, Department of Operations
       Research, Stanford University, May 1986.
  10
  11  * This model has been modified for use in the documentation

12
 13  Set i  securities   /hardware, software, show-biz, t-bills/;
 14  alias (i,j);
 15
 16  Scalar target     target mean annual return on portfolio % /10/,
 17         lowyield   yield of lowest yielding security,
 18         highrisk   variance of highest security risk ;
 19
 20  Parameters  mean(i)  mean annual returns on individual securities (%)
 21        / hardware   8
 22          software   9
 23          show-biz  12
 24          t-bills    7 / ;
 25
 26  Table v(i,j)  variance-covariance array (%-squared annual return)
 27                    hardware  software  show-biz  t-bills
 28         hardware      4         3         -1        0
 29         software      3         6          1        0
 30         show-biz     -1         1         10        0
 31         t-bills       0         0          0        0 ;
 32
 33  lowyield = smin(i, mean(i)) ;
 34  highrisk = smax(i, v(i,i)) ;
 35  display lowyield, highrisk ;
 36
 37  Variables  x(i)       fraction of portfolio invested in asset i
 38             variance   variance of portfolio ;
 39  Positive Variable x ;
 40
 41  Equations  fsum    fractions must add to 1.0
 42             dmean   definition of mean return on portfolio
 43             dvar    definition of variance;
 44
 45  fsum..     sum(i, x(i))                     =e=  1.0;
 46  dmean..    sum(i, mean(i)*x(i))             =e=  target;
 47  dvar..     sum(i, x(i)*sum(j,v(i,j)*x(j)))  =e=  variance;
 48
 49  Model portfolio  / fsum, dmean, dvar / ;
 50  Solve portfolio using nlp minimizing variance;
 51  display x.l, variance.l;

1.2 符号引用图

Symbol Listing


SYMBOL      TYPE   REFERENCES

dmean        EQU   declared       42  defined       46 impl-asn       50      ref       49
dvar         EQU   declared       43  defined       47 impl-asn       50      ref       49
fsum         EQU   declared       41  defined       45 impl-asn       50      ref       49
highrisk     PARAM declared       18 assigned       34      ref       35
i            SET   declared       13  defined       13      ref       14       20       26       33     2*34
37     45     2*46     2*47  control       33       34       45       46       47
j            SET   declared       14      ref       26     2*47  control       47
lowyield     PARAM declared       17 assigned       33      ref       35
mean         PARAM declared       20  defined       21      ref       33       46
portfolio    MODEL declared       49  defined       49 impl-asn       50      ref       50
target       PARAM declared       16  defined       16      ref       46
v            PARAM declared       26  defined       26      ref       34       47
variance     VAR   declared       38 impl-asn       50      ref       47       50       51
x            VAR   declared       37 impl-asn       50      ref       39       45       46     2*47       51

头两列给出了符号的名字和类型。数据类型和简写如下:

Shorthand Symbol	GAMS Data Type
ACRNM	acronym
EQU	equation
FILE	put file
MODEL	model
PARAM	parameter
SET	set
VAR	variable

后面几列会给出符号在第几行声明(declared)，在第几行隐式的制定，第几行被引用。

1
2
3

declared       37
impl-asn       50
ref            39       45       46     2*47       51

完整的引用类型列表和对应的简写如下：

Shorthand Symbol	Reference Type	Description
declared	Declaration	The identifier is declared as to type. This must be the first appearance of the identifier.
defined	Definition	An initialization (for a table or a data list between slashes) or symbolic definition (for an equation) starts for the identifier.
assigned	Assignment	Values are replaced because the identifier appears on the left-hand side of an assignment statement.
impl-asn	Implicit Assignment	An equation or variable will be updated as a result of being referred to implicitly in a solve statement.
control	Control	A set is used as (part of) the driving index in an assignment, equation, loop or indexed operation.
ref	Reference	The symbol has been referenced on the right-hand side of an assignment or in a display, equation, model, solve statement or put statetement.
index	Index	Like control, but used only for set labels. Appears only in the cross reference map of unique elements. See section The Unique Element Listing Map for details.