Originally posted by: DannyYoung

Please assist, I am a new user of Cplex.

I am trying to code a problem (see attached file) which has 24 nodes and 38 lines (arcs).

Below is what I could come up with but my solution is giving zeros for all decision variables.

Please help check if my coding has issues. Thanks

 

//parameters

int B=...; //number of nodes
int L=...; //number of lines

range nodes =1..B;
range lines =1..L;

float cost_generation [nodes]= ...;
float cost_shedding [nodes]= ...;
float max_generation[nodes]= ...;
float load_demand[nodes] = ...;

float cost_transmission [lines]= ...;
float max_power_flow[lines] = ...;
float Mmatrix[1..38][1..24] = ...;

//Variables

dvar float+ G[nodes];
dvar float+ D[nodes];
dvar float+ F[lines];

minimize sum (i in nodes, k in lines)
(cost_generation[i]*G[i] + cost_transmission[k]*F[k] -     cost_shedding[i]*D[i]);

subject to {
forall (i in nodes)
0<=G[i]<=max_generation[i];

forall (i in nodes) 
-load_demand[i]<=-D[i]<=0;

forall (k in lines)
-max_power_flow[k]<=F[k]<=max_power_flow[k];

forall (k in lines, i in nodes)
 F[k]==Mmatrix[k][i]*(G[i]-D[i]);
  }

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

can you also attach your .dat ?

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks alot.
Below is the .dat file, I also attached the data and a snapshot of the solution in Cplex.

 

B=24;
L=38;

SheetConnection my_sheet("Area 1.xls");

cost_generation from SheetRead(my_sheet,"cost_generation");
cost_shedding from SheetRead(my_sheet,"cost_shedding");
cost_transmission from SheetRead(my_sheet,"cost_transmission");
max_generation from SheetRead(my_sheet,"Max_generation");
load_demand from SheetRead(my_sheet,"Load_demand");
max_power_flow from SheetRead(my_sheet,"maxi_power_flow");
Mmatrix from SheetRead(my_sheet,"M_matrix");

 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

instead of

forall (k in lines, i in nodes)
 F[k]==Mmatrix[k][i]*(G[i]-D[i]);
  }

could you rather try

forall (k in lines)
 F[k]==sum(i in nodes) Mmatrix[k][i]*(G[i]-D[i]);
  }

?

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks a million, it worked but I have some issues with the solution.
Why is the value for each generator (G) zero and the loads (D) have values.

Each generator represents a source while the loads are the sinks.

I expect each generator (G) that has max value to have values, since it is the source that supplies the sink.

Please assist, Many thanks.

 

 

 

 

 

 

 

 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

first instead of

dvar float+ F[lines];

do not you want to try

dvar float F[lines];

?

Second you may try to add

sum(i in nodes) D[i]==sum(i in nodes) G[i];

if you want to have sums of D and G equal.

regards

 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Many thanks for your help. The value of each generator (G) is still zero.

I also tried to introduce a parameter to represent (G[i]-D[i]) as shown below but generators (G) are all zero

 

forall (i in nodes)
 P[i]==(G[i]-D[i]);

forall (k in lines)
 F[k]==sum(i in nodes) Mmatrix[k][i]*P[i];
  }
 

Please assist. Thanks.

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

have you added

sum(i in nodes) D[i]==sum(i in nodes) G[i];

too ?

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks. I added
sum(i in nodes) D[i]==sum(i in nodes) G[i];

but all decision variables are zero,

I have attached a screenshot of the solution.

Please assist.

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

if I add

execute
  {
  writeln("D=",D);
  writeln("G=",G);  
  }

in the postprocess I get

// solution (optimal) with objective -558.520625305391
D= [0 0 36.264 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 27.405 0 0 0 0 0]
G= [0 0 0 0 0 0 0 0 0 0 0 0 63.669 0 0 0 0 0 0 0 0 0 0 0]

regards

 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks, but I see that it is only one generator that has a value.

 

Is it not possible for all the generators that have maximum value to have value for G?

 

Thanks,

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi

forall (i in nodes)
G[i]==max_generation[i];

would do that

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks alot Alex, you've been so helpful.

However, the research restricts the constraint to G[i]<=max_generation[i];

Just like any other network problem, the source should be within the range of a lower bound and an upper bound

Please is there any other way around it?

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Please, is there anything I can do to ensure that each generator G has value its value and still maintain the constraint

G[i]<=max_generation[i];

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

So simply keep

forall (i in nodes)
0<=G[i]<=max_generation[i];

 

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks,

I'm still getting zero for all the G[i] and the objective function is still negative.

I want a solution where the G[i] with defined upper bound will have values and the objective will be positive.

Please, can I specify that in my model?

Many thanks for your assistance so far.

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

 

Thanks Alex,

 

I used the model to solve a network with 5 nodes and 5 lines.

The same problem was observed, G[i] is zero for each and the obj function is negative.

Please what can I do to get my desired solution.

Thanks

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Please what can be done to ensure that generators have values and get a positive objective function?

Kindly assist, thanks.

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

if you want the G not to be too low with regards the max of generation you may try

forall (i in nodes)
G[i]>=0.5*max_generation[i];

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks alot. I really appreciate.

I observe that my results were not copied to the I excel sheet when I used the code below

 

G to SheetWrite(my_sheet,"resultg");
D to SheetWrite(my_sheet,"resultd");
P to SheetWrite(my_sheet,"resultp");
F to SheetWrite(my_sheet,"resultf");

Are the codes wrong.

Thanks

 

#DecisionOptimization
#OPLusingCPLEXOptimizer

This looks good.

Can you post .mod, .dat and .xls ?

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks, please find below and attached as requested.

I also observed another problem, when I tried to change the max power flow values to zero in the excel, the model still run using the previous data.

 

Please help.

 

//parameters

int B=...; //number of nodes
int L=...; //number of lines

range nodes =1..B;
range lines =1..L;

float cost_generation [nodes]= ...;
float cost_shedding [nodes]= ...;
float max_generation[nodes]= ...;
float load_demand[nodes] = ...;

float cost_transmission [lines]= ...;
float max_power_flow[lines] = ...;
float Mmatrix[1..38][1..24] = ...;

//Variables

dvar float+ G[nodes];
dvar float+ D[nodes];
dvar float P[nodes];
dvar float F[lines];

minimize sum (i in nodes, k in lines)
(cost_generation[i]*G[i] + cost_transmission[k]*F[k] - cost_shedding[i]*D[i]);

subject to {
forall (i in nodes)
0.5*max_generation[i]<=G[i]<=max_generation[i];

forall (i in nodes)
-load_demand[i]<=-D[i]<=0;

forall (k in lines)
-max_power_flow[k]<=F[k]<=max_power_flow[k];

forall (i in nodes)
 P[i]==G[i]-D[i];
 
forall (k in lines)
 F[k]==sum (i in nodes)Mmatrix[k][i]*P[i];

 }

 

 

B=24;
L=38;

SheetConnection my_sheet("Area.xlsx");

cost_generation from SheetRead(my_sheet,"cost_generation");
cost_shedding from SheetRead(my_sheet,"cost_shedding");
cost_transmission from SheetRead(my_sheet,"cost_transmission");
max_generation from SheetRead(my_sheet,"Max_generation");
load_demand from SheetRead(my_sheet,"Load_demand");
max_power_flow from SheetRead(my_sheet,"max_powerflow");
Mmatrix from SheetRead(my_sheet,"Mmatrixx");

G to SheetWrite(my_sheet,"resultg");
D to SheetWrite(my_sheet,"resultd");
P to SheetWrite(my_sheet,"resultp");
F to SheetWrite(my_sheet,"resultf");

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

I see the results in the spreadsheet.

In order to see change in the result when you change the input do not forget to save the xls file

regards
 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks a million, Alex.

I saved it and I can now see the results. Thanks alot.

 

Please how do I include the below in my constraint,

sum of all lines F[k] connected to a node equals the P[i] of that same node.

For example F[1], F[2] & F[3] are connected to node 1.

So F[1]+F[2]+F[3] = P[1]

 

Pleas assist. Thanks

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Please how do I include the below in my constraint,

sum of all lines F[k] connected to a node equals the P[i] of that same node.

For example F[1], F[2] & F[3] are connected to node 1.

So F[1]+F[2]+F[3] = P[1]

 

Pleas assist. Thanks

#DecisionOptimization
#OPLusingCPLEXOptimizer

You could try something like

forall(i in nodes) ct:sum(k in lines:abs(Mmatrix[k][i])>=0.01)F[k]==P[i];

if Mmatrix describes whether a line is connected to a node

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: DannyYoung

Thanks.

 

However, Mmatrix does not describe whether a line  is connected to a node.

I input your codes in my model but didn't get the needed result.

is there any other way it can be represented.

sum of all arcs connected to a node == the output of the node

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi

if

int connect[1..38][1..24]=...;

describes connection then you could try something such as

 forall(i in nodes) sum(k in lines:connect[i][k]==1) F[k]==G[i];

regards

 

#DecisionOptimization
#OPLusingCPLEXOptimizer