Chapter 14 – Overview of Optimization

Publisher Summary This chapter provides an overview of the tool of optimization and how it aids in in the systematic solution of process integration problems. Optimization refers to the identification of the “best” solution from among the set of candidate solutions. An optimization formulation typically involves the minimization or maximization of an objective function subject to a number of constraints. Mathematical programming deals with the formulation, solution, and analysis of optimization problems or mathematical programs. The vector x is referred to as the vector of optimization variables, and if it satisfies all the constraints, it is called a feasible point. An optimization problem in which the objective function as well as all the constraints are linear is called a linear program (LP); otherwise, it is termed a nonlinear program (NLP). To formulate an optimization model it is necessary to determine the objective function, develop constraints, and improve formulation. In properly formulating an optimization problem, it is necessary to establish a model that accurately describes the task using mathematical relationships that capture the essence of the problem. When the solution of a mathematical program is implemented using computer-aided tools, it is possible to effectively examine what-if scenarios and conduct sensitivity analysis. LINGO is an optimization software that solves linear, nonlinear, and mixed integer linear and nonlinear programs. If the line for minimizing or maximizing an objective function is not included, LINGO will solve the model as a set of equations provided that the degrees of freedom are appropriate. The use of set formulations is attractive in dealing with large problems with repetitive constraints. The generic set formulation is developed once different scenarios can be run by altering the data.