Optimization is the act of obtaining the best result under given circumstances. the word ‘optimum’ is taken to mean ‘maximum’ or ‘minimum’ depending on the circumstances. In design, construction, and maintenance of any engineering system, engineers have to take many technological and managerial decisions at several stages. The ultimate goal of all such decisions is either to minimize the effort required or to maximize the desired benefit. Since the effort required or the benefit desired in any practical situation can be expressed as a function of certain decision variables, so optimization can be defined as the process of finding the conditions that give the maximum or minimum value of a function
The optimum searching methods are also known as mathematical programming techniques and are generally studied as a part of operations research. Operations research is a branch of mathematics concerned with the application of scientific methods and techniques to decision making problems and with establishing the best or optimal solutions.
ENGINEERING APPLICATIONS OF OPTIMIZATION
Optimization, in its broadest sense, can be applied to solve any engineering problem e.g.
1. Running a business to maximize profit, minimize loss, maximize efficiency, or minimize risk.
2. It might mean designing a bridge to minimize weight or maximize strength. It might mean selecting a flight plan for an aircraft to minimize time or fuel use.
3. Design of water resources systems for maximum benefit
4. Planning the best strategy to obtain maximum profit in the presence of a competitor
5. Planning of maintenance and replacement of equipment to reduce operating costs
The power of optimization methods to determine the best case without actually testing all possible cases comes through the use of a modest level of mathematics and at the cost of performing iterative numerical calculations using clearly defined logical procedures or algorithms implemented on computing machines.
Design Vector
Any engineering system or component is defined by a set of quantities some of which are viewed as variables during the design process. In general, certain quantities are usually fixed at the outset and these are called pre-assigned parameters. All the other quantities are treated as variables in the design process and are called design or decision variables xi , i = 1, 2, . . . , n. The design variables are collectively represented as a design vector X = {x1, x2, . . . , xn}T.
Design Constraints
In many practical problems, the design variables cannot be chosen arbitrarily; rather, they have to satisfy certain specified functional and other requirements. The restrictions that must be satisfied to produce an acceptable design are collectively called design constraints.
Objective Function
The conventional design procedures aim at finding an acceptable or adequate design that merely satisfies the functional and other requirements of the problem. In general, there will be more than one acceptable design, and the purpose of optimization is to choose the best one of the many acceptable designs available. Thus a criterion has to be chosen for comparing the different alternative acceptable designs and for selecting the best one. The criterion with respect to which the design is optimized, when expressed as a function of the design variables, is known as the criterion or merit or objective function. The choice of objective function is governed by the nature of problem. The objective function for minimization is generally taken as weight in aircraft and aerospace structural design problems. In civil engineering structural designs, the objective is usually taken as the minimization of cost. The maximization of mechanical efficiency is the obvious choice of an objective in mechanical engineering systems
Constraints
Any optimization problem can be classified as constrained or unconstrained, depending on whether or not constraints exist in the problem. A problem that does not entail any equality or inequality constraints is said to be an unconstrained optimization problem.
