[Python] Use tupla(i,j) instead of a single variable(j)

I want to create a tupla variable for this model p(i,j) instead of only variable p(j). I have to change it here and on the variables that impacts it.

Current model example

Code


def buildBaseModel():
global nVars,nClauses,kbRulesLit,kbRulesProbMin,kbRulesProbMax,kbRulesCard,Q
# Create Model
m = pulp.LpProblem("Profit maximising problem",pulp.LpMaximize)

nPsatVars = 2 ** nVars

# Create variables p_i -->HERE SHOULD BE p_[j]
p = {}
for j in range(nPsatVars):
p[j]=pulp.LpVariable(lowBound=0,cat='Continuous',name='p_'+str(j))

#m += sum([p[j] for j in range(nPsatVars)]) --> HERE CHANGE OBJECTIVE FUNCTION

# Create variables pai_i
pai = {}
for j in range(1,Q + 1):
#pai[j] = kbRulesProb[j]
pai[j]= pulp.LpVariable(lowBound=kbRulesProbMin[j],upBound=kbRulesProbMax[j],cat='Continuous',name='pai_'+str(j))
for j in range(Q + 1,nClauses + 1):
pai[j]= pulp.LpVariable(lowBound=0,cat='Continuous',name='pai_'+str(j))

# Create variables qp_i
qp = {}
for j in range(1,Q+1): #not first rule
qp[j]=pulp.LpVariable(lowBound=0,cat='Continuous',name='qp_'+str(j))

# Create variables qn_i
qn = {}
for j in range(1,Q+1): #not first rule
qn[j]=pulp.LpVariable(lowBound=0,cat='Continuous',name='qn_'+str(j))

#construct the matrix A
A=np.array([[1] * nPsatVars] * (nClauses + 1))#0
x = {}
for j in range(nVars):
x[j] = 0
for i in range(1,nClauses + 1):
for j in range(nPsatVars):
r = j
#the value of x is the assignment of the Var,such as [0,1,1,0,0,0]
for k in range(nVars):
x[k] = (r >> k)%2
t = 0
for k in kbRulesLit:
if k == 0 and x[0] == 1:
t = 1
if k > 0 and x[k] == 1:
t = 1
if k < 0 and x[-k] == 0:
t = 1
if t == 1:
A[j] = 0

#constrict
m+=sum([p[j] for j in range(nPsatVars)])== 1.0

#constrict
for i in range(1,Q + 1):
m+=sum([p[j]*A[j] for j in range(nPsatVars)])-qp <= kbRulesProbMax

for i in range(1,Q + 1):
m+=sum([p[j]*A[j] for j in range(nPsatVars)])+qn >= kbRulesProbMin

for i in range(Q + 1,nClauses + 1):
m+=sum([p[j] * A[j] for j in range(nPsatVars)]) - pai == 0

#USE GUROBI
m.solve(pulp.GUROBI())
pulp.LpStatus[m.status]

if(m.status==-1):
print("there is no solution for the CONDSAT problem")
else :
print("find solution\n")

varsdict = {}
for v in m.variables():
print(v.name,"=", v.varValue)
m.writeLP('c.lp')


Final Model that the code should do So at final model we will have p_i_j instead of p_j like this code generate today.

besides this, I need help to change the objective function of the model is to add an objective function that maximize the sum of all variables p(i,j) (that needs to be done after the first change)

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