Table 1:

Framework for the solution of multiobjective mixed-integer linear optimization problems.

Step 1: Reformulate the general multiobjective mixed-integer linear optimization problem of the form of Problem (1) to the form shown in Problem (2) using the ∊-constraint method.

Step 2: Calculate the lower and upper bounds for the ∊ parameters of the ∊-constraint formulation by minimizing the individual objectives for the lower bounds, and by evaluating the value of the other objectives and selecting the maximum value for the upper bounds.

Step 3: Reformulate Problem (2) to a multiparametric programming problem (3).

Step 4: Solve the resulting multiparametric programming problem using the algorithm proposed by Acevedo and Pistikopoulos.40

Step 5: Identify weakly Pareto solutions and the corresponding critical regions if at least one objective function is not a parametric function of all ∊ parameters.

Step 6: Obtain the Pareto front and the optimal solution as an explicit function of the ∊ parameters.