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‎codes/Chapter 6/PYOMO_example_1.py

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# Filename: PYOMO_example_1.py
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# Description: An example of solving a linear
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# programming problem with Pyomo
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# Authors: Papathanasiou, J. & Ploskas, N.
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from pyomo.environ import *
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from pyomo.opt import SolverFactory
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import matplotlib.pyplot as plt
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import numpy as np
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# Create an object to perform optimization
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opt = SolverFactory('cplex')
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# Create an object of a concrete model
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model = ConcreteModel()
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# Define the decision variables
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model.x1 = Var(within=NonNegativeReals)
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model.x2 = Var(within=NonNegativeReals)
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# Define the objective function
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model.obj = Objective(expr = 60 * model.x1 +
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40 * model.x2)
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# Define the constraints
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model.con1 = Constraint(expr = 4 * model.x1 +
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4 * model.x2 >= 10)
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model.con2 = Constraint(expr = 2 * model.x1 +
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model.x2 >= 4)
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model.con3 = Constraint(expr = 6 * model.x1 +
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2 * model.x2 <= 12)
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# Solve the linear programming problem
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results = opt.solve(model)
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# Print the results
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print ("Status: ",
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results.solver.termination_condition)
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print("x1 = ", model.x1.value)
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print("x2 = ", model.x2.value)
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print ("The optimal value of the objective function "
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"is = ", model.obj())
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# Plot the results
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x = np.arange(0, 5)
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plt.plot(x, 2.5 - x, label = '4x1 + 4x2 >= 10')
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plt.plot(x, 4 - 2 * x, label= ' 2x1 + x2 >= 4')
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plt.plot(x, 6 - 3 * x, label = '6x1 + 2x2 <= 12')
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plt.plot(x, 2 - 2/3*x, '--')
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plt.annotate('Objective\n function', xy = (0.6, 1.6),
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xytext = (0.3, 0.8), arrowprops =
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dict(facecolor = 'black', width = 1.5, headwidth = 7))
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plt.annotate('Optimal\n solution\n(1.5, 1)',
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xy = (1.48, 0.98), xytext = (1, 0.5), arrowprops =
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dict(facecolor = 'black', width = 1.5, headwidth = 7))
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plt.plot(1.5, 1, 'wo')
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plt.text(0.1, 4, 'Feasible area', size = '12')
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# Define the boundaries of the feasible area in the plot
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a = [0, 1.5, 1.75, 0, 0]
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b = [4, 1, 0.75, 6, 4]
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plt.fill(a, b, 'grey')
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plt.xlabel("x1")
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plt.ylabel("x2")
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plt.title('LP Example 1')
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plt.axis([0, 3, 0, 6])
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plt.grid(True)
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plt.legend()
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plt.show()

‎codes/Chapter 6/PYOMO_example_2.py

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# Filename: PYOMO_example_2.py
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# Description: An example of solving a binary
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# linear programming problem with Pyomo
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# Authors: Papathanasiou, J. & Ploskas, N.
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from pyomo.environ import *
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from pyomo.opt import SolverFactory
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import matplotlib.pyplot as plt
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import numpy as np
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# Create an object to perform optimization
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opt = SolverFactory('cplex')
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# Create an object of a concrete model
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model = ConcreteModel()
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# Define the decision variables
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model.x1 = Var(within=Binary)
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model.x2 = Var(within=Binary)
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model.x3 = Var(within=Binary)
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model.x4 = Var(within=Binary)
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model.x5 = Var(within=Binary)
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model.x6 = Var(within=Binary)
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# Define the objective function
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model.obj = Objective(expr = model.x1 +
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model.x2 + model.x3 + model.x4 + model.x5 +
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model.x6)
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# Define the constraints
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model.con1 = Constraint(expr = model.x1 +
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model.x3 >= 2)
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model.con2 = Constraint(expr = model.x1 +
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model.x2 + model.x5 >= 2)
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model.con3 = Constraint(expr = model.x3 +
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model.x4 >= 1)
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model.con4 = Constraint(expr = model.x1 +
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model.x4 + model.x5 >= 1)
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model.con5 = Constraint(expr = model.x4 +
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model.x5 + model.x6 >= 1)
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# Solve the binary linear programming problem
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results = opt.solve(model)
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# Print the results
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print ("Status: ",
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results.solver.termination_condition)
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print("x1 = ", model.x1.value)
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print("x2 = ", model.x2.value)
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print("x3 = ", model.x3.value)
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print("x4 = ", model.x4.value)
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print("x5 = ", model.x5.value)
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print("x6 = ", model.x6.value)
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print ("The optimal value of the objective function "
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"is = ", model.obj())

‎codes/Chapter 6/classicalGP.py

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# Filename: classicalGP.py
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# Description: Classical Goal Programming method
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# Authors: Papathanasiou, J. & Ploskas, N.
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from pyomo.environ import *
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from pyomo.opt import SolverFactory
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# Create an object to perform optimization
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opt = SolverFactory('cplex')
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# Create an object of a concrete model
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model = ConcreteModel()
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# Define the decision variables
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model.x1 = Var(within = NonNegativeIntegers)
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model.x2 = Var(within = NonNegativeIntegers)
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# Define the deviational variables
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model.n1 = Var(within = NonNegativeIntegers)
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model.p1 = Var(within = NonNegativeIntegers)
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model.n2 = Var(within = NonNegativeIntegers)
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model.p2 = Var(within = NonNegativeIntegers)
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model.n3 = Var(within = NonNegativeIntegers)
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model.p3 = Var(within = NonNegativeIntegers)
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model.n4 = Var(within = NonNegativeIntegers)
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model.p4 = Var(within = NonNegativeIntegers)
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# Define the objective function
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model.obj = Objective(expr = model.p1 + model.p2 +
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model.n3 + model.p4)
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# Define the constraints
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model.con1 = Constraint(expr = 2 * model.x1 +
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4 * model.x2 + model.n1 - model.p1 == 600)
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model.con2 = Constraint(expr = 5 * model.x1 +
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3 * model.x2 + model.n2 - model.p2 == 700)
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model.con3 = Constraint(expr = 100 * model.x1 +
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90 * model.x2 + model.n3 - model.p3 == 18000)
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model.con4 = Constraint(expr = 2 * model.x1 +
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2 * model.x2 + model.n4 - model.p4 == 380)
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model.con5 = Constraint(expr = model.x1 +
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model.x2 <= 200)
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model.con6 = Constraint(expr = model.x1 >= 60)
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model.con7 = Constraint(expr = model.x2 >= 60)
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# Solve the Goal Programming problem
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opt.solve(model)
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# Print the values of the decision variables
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print("x1 = ", model.x1.value)
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print("x2 = ", model.x2.value)
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# Print the achieved values for each goal
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if model.n1.value > 0:
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print("The first goal is underachieved by ",
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model.n1.value)
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elif model.p1.value > 0:
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print("The first goal is overachieved by ",
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model.p1.value)
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else:
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print("The first goal is fully satisfied")
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if model.n2.value > 0:
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print("The second goal is underachieved by ",
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model.n2.value)
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elif model.p2.value > 0:
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print("The second goal is overachieved by ",
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model.p2.value)
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else:
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print("The second goal is fully satisfied")
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if model.n3.value > 0:
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print("The third goal is underachieved by ",
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model.n3.value)
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elif model.p3.value > 0:
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print("The third goal is overachieved by ",
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model.p3.value)
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else:
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print("The third goal is fully satisfied")
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if model.n4.value > 0:
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print("The fourth goal is underachieved by ",
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model.n4.value)
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elif model.p4.value > 0:
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print("The fourth goal is overachieved by ",
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model.p4.value)
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else:
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print("The fourth goal is fully satisfied")

‎codes/Chapter 6/lexicographicGP.py

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# Filename: lexicographicGP.py
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# Description: Lexicographic Goal Programming
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# method
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# Authors: Papathanasiou, J. & Ploskas, N.
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from pyomo.environ import *
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from pyomo.opt import SolverFactory
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# Create an object to perform optimization
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opt = SolverFactory('cplex')
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# Create an object of a concrete model
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model = ConcreteModel()
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# Define the decision variables
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model.x1 = Var(within = NonNegativeIntegers)
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model.x2 = Var(within = NonNegativeIntegers)
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# Define the deviational variables
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model.n1 = Var(within = NonNegativeIntegers)
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model.p1 = Var(within = NonNegativeIntegers)
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model.n2 = Var(within = NonNegativeIntegers)
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model.p2 = Var(within = NonNegativeIntegers)
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model.n3 = Var(within = NonNegativeIntegers)
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model.p3 = Var(within = NonNegativeIntegers)
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model.n4 = Var(within = NonNegativeIntegers)
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model.p4 = Var(within = NonNegativeIntegers)
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# Define the objective function of the
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# first priority level
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model.obj = Objective(expr = model.p4)
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# Define the constraints
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model.con1 = Constraint(expr = 2 * model.x1 +
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4 * model.x2 + model.n1 - model.p1 == 600)
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model.con2 = Constraint(expr = 5 * model.x1 +
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3 * model.x2 + model.n2 - model.p2 == 700)
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model.con3 = Constraint(expr = 100 * model.x1 +
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90 * model.x2 + model.n3 - model.p3 == 18000)
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model.con4 = Constraint(expr = 2 * model.x1 +
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2 * model.x2 + model.n4 - model.p4 == 380)
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model.con5 = Constraint(expr = model.x1 +
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model.x2 <= 200)
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model.con6 = Constraint(expr = model.x1 >= 60)
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model.con7 = Constraint(expr = model.x2 >= 60)
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# Solve the Goal Programming problem of the
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# first priority level
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opt.solve(model)
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# Retrieve the value of the first priority level
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p4 = model.p4.value
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# Define the objective function of the
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# second priority level
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model.obj = Objective(expr = model.n3)
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# Add a constraint for the value of the first
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# priority level
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model.con8 = Constraint(expr = model.p4 == p4)
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# Solve the Goal Programming problem of the
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# second priority level
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opt.solve(model)
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# Retrieve the value of the second priority level
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n3 = model.n3.value
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# Define the objective function of the
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# third priority level
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model.obj = Objective(expr = model.p1 + model.p2)
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# Add a constraint for the value of the second
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# priority level
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model.con9 = Constraint(expr = model.n3 == n3)
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# Solve the Goal Programming problem of the
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# third priority level
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opt.solve(model)
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# Print the values of the decision variables
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print("x1 = ", model.x1.value)
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print("x2 = ", model.x2.value)
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# Print the achieved values for each goal
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if model.n1.value > 0:
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print("The first goal is underachieved by ",
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model.n1.value)
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elif model.p1.value > 0:
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print("The first goal is overachieved by ",
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model.p1.value)
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else:
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print("The first goal is fully satisfied")
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if model.n2.value > 0:
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print("The second goal is underachieved by ",
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model.n2.value)
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elif model.p2.value > 0:
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print("The second goal is overachieved by ",
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model.p2.value)
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else:
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print("The second goal is fully satisfied")
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if model.n3.value > 0:
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print("The third goal is underachieved by ",
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model.n3.value)
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elif model.p3.value > 0:
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print("The third goal is overachieved by ",
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model.p3.value)
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else:
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print("The third goal is fully satisfied")
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if model.n4.value > 0:
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print("The fourth goal is underachieved by ",
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model.n4.value)
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elif model.p4.value > 0:
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print("The fourth goal is overachieved by ",
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model.p4.value)
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else:
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print("The fourth goal is fully satisfied")

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