General Procedure for Solving Optimization Problems

No single method or algorithm of optimization can be applied efficiently to all problems. The method chosen for any particular case depends primarily on (1) the character of the objective function and whether it is known explicitly, (2) the nature of the constraints, and (3) the number of independent and dependent variables. 

Remember, the general objective in optimization is to choose a set of values of the variables subject to the various constraints that produce the desired optimum response for the chosen objective function. 

Steps 1, 2, and 3 deal with the mathematical definition of the problem, that is, identification of variables, specification of the objective function, and statement of the constraints. We devote considerable attention to problem formulation in the remainder of this chapter, as well as in Chapters 2 and 3. If the process to be optimized is very complex, it may be necessary to reformulate the problem so that it can be solved with reasonable effort. 

Step 4 suggests that the mathematical statement of the problem be simplified as much as possible without losing the essence of the problem. First, you might 

Analyze the process itself so that the process variables and specific characteristics of interest are defined that is, make a list of all of the variables. 

---