Optimization is a standard activity in everyday life. We use it consciously or unconsciously for almost all our daily jobs. When we try to find a way to finish an assignment in our professional life in less effort or time, it is an optimization procedure. Deciding the best way to reach the workplace from the time and distance
aspects, depending on the time of the day, is also an optimization. Many people in
this world try to reduce the daily cost of living for their survival. All these actions
have some amount of mental calculations behind it, and most of the time the
calculation is not that mathematical. The optimization process basically finds the
values of the variables those control the objective we need to optimize (i.e., minimize or maximize) while satisfying some constraints. This process becomes mathematical when we employ it in the professional sectors like finance, construction, manufacturing, etc. In those cases, the number of variables is quite high, and they are correlated in a complex way.
Mathematical optimization has various components. The first is the objective
function, which defines the attribute to be optimized in terms of the dependent
variables or design variables. For example, in manufacturing process, it describes
the profit or the cost or the product quality. The design variables are the variables
which control the value of the attribute, which is being optimized. The amounts of
different resources used and the time spent in a manufacturing process may be
considered as the design variables. The third important component in an optimization process is the constraint. It may be single or a set of constraints, which allow the process to take on certain values of the design variables but exclude others.