Function createMasterProblem

examples/branch-and-price.py:118–141

(columns: list)

#   0 <= \lambda_{k} <= 1, \foreach k                             // Can use each column at most once (can be fractional)
#
def createMasterProblem(columns: list):
    m = highspy.Highs()
    m.setOptionValue('output_flag', False)
    m.setOptionValue('random_seed', SEED)
    
    m.addVars(len(columns), [0.0]*len(columns), [1.0]*len(columns))
    
    # min \sum_{k} \lambda_{k}
    m.changeObjectiveSense(highspy.ObjSense.kMinimize)
    m.changeColsCost(len(columns), list(range(len(columns))), [1.0]*len(columns))
    
    #      \sum_{k \in K_i} \lambda_{k} == 1, \foreach i
    # 1 <= \sum_{k \in K_i} \lambda_{k} <= 1
    for i in range(NumberItems):
        K_i = [k for k, column in enumerate(columns) if i in column]
        m.addRow(1, 1, len(K_i), K_i, [1.0]*len(K_i))

    m.run() 

    solution = m.getSolution()
    vals = list(solution.col_value)
    duals = list(solution.row_dual)

    return m, vals, duals

#
# Solve the knapsack subproblem exactly with HiGHS