274
Y. Xu et al.
q i
refers to the flowrate of each CSs, m3/h
p max
i
refers to the maximum design pressure of a pipe network, MPa
p min
i
refers to the minimum pressure of a pipe network, MPa
P max
i
refers to the maximum operation power of CSs, kw
P min
i
refers to the minimum operation power of CSs, kw
M
is a sufficiently large positive constant
MI
is a sufficiently small positive constant
Decision variables
D P
i,j
is a binary variable, if one pipeline start from node i to node j was chosen,
then D P
i,j = 1, and D P
i,j = 0 otherwise.
D i,j,d
is a binary variable, if one size of pipe starts from node i to node j was chosen,
then D i,j,d = 1, and D i,j,d = 0 otherwise
D C
i
is a binary variable, if compressors would be constructed, then D C
i = 1 and
D C
i = 0 otherwise
NP
upper
i
is a binary variable, if the pressure exceeds the upper pressure limitation, then
NP
upper
i
= 1, and NP
upper
i
= 0 otherwise
NP blow
i
is a binary variable, if the pressure exceeds the upper pressure limitation, then
NP blow
i
= 1, and NP blow
i
= 0 otherwise
NP
upper
i
is a binary variable, if the pressure exceeds the lower pressure limitation, then
NP
upper
i
= 1, and NP
upper
i
= 0 otherwise
P c
refers to the power of compressors in original CSs, kw
P C
refers to the power of newly built compressors, kw
P T
refers to the power of throttle loss in CSs, kw
References
1. Afshar, M.H.: A new transition rule for ant colony optimization algorithms: application to
pipe network optimization problems. Eng. Optimiz. 37(5), 525–540 (2005)
2. Afshar, M.H.: Penalty adapting ant algorithm: application to pipe network optimization. Eng.
Optimiz. 40(10), 969–987 (2008)
3. de Wolf, D., Bakhouya, B.: Optimal dimensioning of pipe networks: the new situation when
the distribution and the transportation functions are disconnected. Oper. Res. Proc. 2011,
369–374 (2012)
4. De Wolf, D., Smeers, Y.: The gas transmission problem solved by an extension of the simplex
algorithm. Manag. Sci. 46(11), 1454–1465 (2000)
5. El-Mahdy, O.F.M., et al.: Computer aided optimization of natural gas pipe networks using
genetic algorithm. Appl. Soft Comput. 10(4), 1141–1150 (2010)
6. He, G., et al.: A methodology for the optimal design of gathering pipeline system in old
oilfield during its phased development process. Comput. Ind. Eng. 130, 14–34 (2019)
7. Hong, B., et al.: An integrated MILP method for gathering pipeline networks considering
hydraulic characteristics. Chem. Eng. Res. Des. 152, 320–335 (2019)
Y. Xu et al.
q i
refers to the flowrate of each CSs, m3/h
p max
i
refers to the maximum design pressure of a pipe network, MPa
p min
i
refers to the minimum pressure of a pipe network, MPa
P max
i
refers to the maximum operation power of CSs, kw
P min
i
refers to the minimum operation power of CSs, kw
M
is a sufficiently large positive constant
MI
is a sufficiently small positive constant
Decision variables
D P
i,j
is a binary variable, if one pipeline start from node i to node j was chosen,
then D P
i,j = 1, and D P
i,j = 0 otherwise.
D i,j,d
is a binary variable, if one size of pipe starts from node i to node j was chosen,
then D i,j,d = 1, and D i,j,d = 0 otherwise
D C
i
is a binary variable, if compressors would be constructed, then D C
i = 1 and
D C
i = 0 otherwise
NP
upper
i
is a binary variable, if the pressure exceeds the upper pressure limitation, then
NP
upper
i
= 1, and NP
upper
i
= 0 otherwise
NP blow
i
is a binary variable, if the pressure exceeds the upper pressure limitation, then
NP blow
i
= 1, and NP blow
i
= 0 otherwise
NP
upper
i
is a binary variable, if the pressure exceeds the lower pressure limitation, then
NP
upper
i
= 1, and NP
upper
i
= 0 otherwise
P c
refers to the power of compressors in original CSs, kw
P C
refers to the power of newly built compressors, kw
P T
refers to the power of throttle loss in CSs, kw
References
1. Afshar, M.H.: A new transition rule for ant colony optimization algorithms: application to
pipe network optimization problems. Eng. Optimiz. 37(5), 525–540 (2005)
2. Afshar, M.H.: Penalty adapting ant algorithm: application to pipe network optimization. Eng.
Optimiz. 40(10), 969–987 (2008)
3. de Wolf, D., Bakhouya, B.: Optimal dimensioning of pipe networks: the new situation when
the distribution and the transportation functions are disconnected. Oper. Res. Proc. 2011,
369–374 (2012)
4. De Wolf, D., Smeers, Y.: The gas transmission problem solved by an extension of the simplex
algorithm. Manag. Sci. 46(11), 1454–1465 (2000)
5. El-Mahdy, O.F.M., et al.: Computer aided optimization of natural gas pipe networks using
genetic algorithm. Appl. Soft Comput. 10(4), 1141–1150 (2010)
6. He, G., et al.: A methodology for the optimal design of gathering pipeline system in old
oilfield during its phased development process. Comput. Ind. Eng. 130, 14–34 (2019)
7. Hong, B., et al.: An integrated MILP method for gathering pipeline networks considering
hydraulic characteristics. Chem. Eng. Res. Des. 152, 320–335 (2019)