1

I another bug as you can see below:

Error at _cmdno 8 executing "solve" command
(file ./script/runConfiguration.run, line 5, offset 127):
error processing constraint c1a[2,'o1',1]:
unexpected type 0x14205 in ecopy()

I guess that the problem causing comparison with the index (element of set) variable in c1a constraint. Is it possible to avoid this bug?

My new ampl model:

#sets
#-------------------------------------------------------------------------------------
set K;              #index of nodes with group of clients
set N;              #nodes
set E;              #edges
set O;              #objects

#parameters
#-------------------------------------------------------------------------------------
param d {K,O};      #demands for object o
param t {K,O} symbolic;     #destination nodes
param r {N,K} binary;       #1 if node n is ancestor of node k, 0 otherwise

param a {N,E} binary;       #1 if edge begins in vertex, 0 otherwise
param b {N,E} binary;       #1 if edge ends in vertex, 0 otherwise

param c {E};        #cost of using an edge
param Hmax;         #available capacity for allocation object in proxy servers

#variables
#-------------------------------------------------------------------------------------
var f {N,O} binary;         #1 if object saved at node k, 0 otherwise
var x {E,K,O};              #value of the demand realised over edge for object
var s {K,O} symbolic in N;                #source nodes

#goal function
#-------------------------------------------------------------------------------------
#The function minimizes cost of routing
#By saving copies at CDN proxies we minimizing all traffic from all demands
#with all objects
minimize goal:
    sum{e in E}
    sum{k in K}
    sum{o in O}
        (x[e,k,o]*c[e]);

#constraints
#-------------------------------------------------------------------------------------
subject to c1a {k in K, o in O, n in N: n!=t[k,o]}:
(s[k,o]==n)
 ==>
        sum{e in E}
            (a[n,e]*x[e,k,o]) -
        sum{e in E}
            (b[n,e]*x[e,k,o]) =
                                d[k,o]*(1-f[k,o]);

subject to c1b {k in K, o in O, n in N: n!=t[k,o]}:
(s[k,o]!=n)
    ==>
        sum{e in E}
            (a[n,e]*x[e,k,o]) -
        sum{e in E}
            (b[n,e]*x[e,k,o]) =
                                0;

subject to c1c {k in K, o in O, n in N: n==t[k,o]}:
sum{e in E}
    (a[n,e]*x[e,k,o]) -
sum{e in E}
    (b[n,e]*x[e,k,o]) =
                            -d[k,o]*(1-f[k,o]);

subject to c2:
sum{k in K}
sum{o in O}
    f[k,o] <= Hmax;

subject to c3 {k in K, o in O}:
sum{n in N}
    r[n,k]*f[n,o] <= 2;

subject to c4 {o in O}:
    f[1,o]=1;

subject to c5 {k in K, o in O}:
    s[k,o]=
        2-sum{n in N}(r[n,k]*f[n,o])
        +(sum{n in N}
                (r[n,k]*f[n,o])-1)
        *(sum{i in K}(r[i,k]*f[i,o]*i));

subject to c0 {e in E, k in K, o in O}:
    x[e,k,o]>=0;

and here are very simple data:

#Data file for 'CDN allocation copies' problem simple example

#indices
set K := 2 3 4;               #index of nodes with group of clients
set N := 1 2 3 4;             #nodes
set E := 1_2 2_3 2_4;         #edges
set O := o1;                  #objects

#parameters
param d (tr):                  #demands for object o
        2       3       4    :=
o1      0       512     512;
#opt= 63 + 75 = 138

param t (tr):                  #destination nodes
        2       3       4    :=
o1      2       3       4;

param r (tr):                   #1 if node n is ancestor of node k, 0 otherwise
        1       2       3       4   :=  
2       1       0       0       0       
3       1       1       0       0
4       1       1       0       0;

param a (tr):                   #1 if edge begins in vertex, 0 otherwise
        1       2       3       4   :=
1_2     1       0       0       0
2_3     0       1       0       0
2_4     0       1       0       0;

param b (tr):                   #1 if edge ends in vertex, 0 otherwise
        1       2       3       4   :=
1_2     0       1       0       0
2_3     0       0       1       0
2_4     0       0       0       1;

param c :=      #cost of using an edge
1_2     3
2_3     1
2_4     1;

param Hmax := 1; #available capacity for allocation object in proxy servers

This data file describe network with 4 nodes with topology like this:

     1
     |
     2
    / \
    3 4

It is easy to guess that the best solution is to save only the content of the node 2. The object function = 1024 and f_2,o1=1.

Whis model try to solve Strorage Capacity Allocation problem, which I described in another my post: Bug when solving CDN allocation rule

4

1 回答 1

0

我和我的朋友找到了重新定义 CDN SCAP 问题的解决方案,如下所示,适用于 CPLEX 解析器:

#Model for 'CDN allocation copies' problem

#sets
#-------------------------------------------------------------------------------------
set K;              #index of nodes with group of clients
set N;              #nodes
set E;              #edges
set O;              #objects

#parameters
#-------------------------------------------------------------------------------------
param d {K,O};      #demands for object o
param t {K,O} symbolic;     #destination nodes
param r {N,K} binary;       #1 if node n is ancestor of node k, 0 otherwise

param a {N,E} binary;       #1 if edge begins in vertex, 0 otherwise
param b {N,E} binary;       #1 if edge ends in vertex, 0 otherwise

param c {E};        #cost of using an edge
param Hmax;         #available capacity for allocation object in proxy servers

#variables
#-------------------------------------------------------------------------------------
var f {N,O} binary;         #1 if object saved at node k, 0 otherwise
var x {E,K,O} >= 0;              #value of the demand realised over edge for object
var s {K,O} binary;                #source nodes

#goal function
#-------------------------------------------------------------------------------------
#The function minimizes cost of routing
#By saving copies at CDN proxies we minimizing all traffic from all demands
#with all objects
minimize goal:
    sum{e in E}
    sum{k in K}
    sum{o in O}
        (x[e,k,o]*c[e]);

#constraints
#-------------------------------------------------------------------------------------

subject to c1a {k in K, o in O, n in N: n==1}:
s[k,o] = 0
  ==>       
        sum{e in E}
            (a[n,e]*x[e,k,o]) -
        sum{e in E}
            (b[n,e]*x[e,k,o]) -
                                d[k,o]*(1-f[k,o]) = 0
else
        sum{e in E}
            (a[n,e]*x[e,k,o]) -
        sum{e in E}
            (b[n,e]*x[e,k,o]) =
                                0;


subject to c1b1 {k in K, o in O, n in N: n!=t[k,o] and n!=1}:      
        sum{e in E}
            (a[n,e]*x[e,k,o]) -
        sum{e in E}
            (b[n,e]*x[e,k,o]) -
                                r[n,k]*d[k,o]*(1-f[k,o]) <= 0;

subject to c1b2 {k in K, o in O, n in N: n!=t[k,o] and n!=1}:
        sum{e in E}
            (a[n,e]*x[e,k,o]) - 
        sum{e in E}
            (b[n,e]*x[e,k,o]) -
                                r[n,k]*d[k,o]*s[k,o] <= 0;

subject to c1b3 {k in K, o in O, n in N: n!=t[k,o] and n!=1}:    
        sum{e in E}
            (a[n,e]*x[e,k,o]) -
        sum{e in E}
            (b[n,e]*x[e,k,o]) -
                                r[n,k]*d[k,o]*f[n,o] <= 0;

subject to c1c {k in K, o in O, n in N: n==t[k,o]}:
sum{e in E}
    (a[n,e]*x[e,k,o]) -
sum{e in E}
    (b[n,e]*x[e,k,o]) =
                            -d[k,o]*(1-f[k,o]);

subject to c2:
sum{k in K}
sum{o in O}
    f[k,o] <= Hmax;

subject to c3 {k in K, o in O}:
sum{n in N}
    r[n,k]*f[n,o] <= 2;

subject to c4 {o in O}:
    f[1,o]=1;

subject to c5 {k in K, o in O}:
    s[k,o]=sum{n in N}(r[n,k]*f[n,o])-1;
于 2013-05-15T13:02:32.883 回答