Every step in engineering leads to optimization in some way. So it plays substantial role in engineering.

Optimization allows you to get the most out of a given system. In a way it is the minimization of waste. Optimization can be applied to a single discipline or multi-disciplinary systems. Very often optimization can shed new light in design when considering the coupling of multiple systems.

By the way I would argue that you cannot do multi-objective optimization. Multiple objectives are often in conflict with one another, e.g. you can't design a battery that has maximum power AND maximum energy. You can only optimize one objective while constraining the other.

In my opinion, optimization is the future, since the investment cost, efficiency, energy savings, etc. are critical are critical aspects. In particular, engineering disciplines need to develop mathematical and computational optimization methods to improve the efficiency of the processes.

I disagree with Nansi Xue in reference to the imposibility of applying multi-objective optimization to engineering problems. Of course it is possible, and I would say that desirable, to apply multi-objective optimization to problems having conflicting objectives. In fact, Pareto-based multi-objective optimization methos allow to generate a front of non-dominated solutions that can be later used by the decision maker. You can read several papers dealing with multi-objective optimization in peer-reviewed international journals, such as Engineering Optimization.

I agree with Raul that the optimization is the future. And let me rephrase my point about multi-objective optimization. I am not saying that one cannot obtain a Pareto-front where multiple objectives are considered (in fact I have generated Pareto-fronts myself). My point is that a single solution cannot be optimal in more than one objective. In determining the final design, the decision maker has to either consider all the objectives as a weighted aggregate or maximize one objective while constraining all others. In either case the problem reduces to a single-objective optimization problem. Having said that, I do understand that not all engineering problems are clearly defined, and a Pareto-front to such a problem can be very valuable in providing different options to the decision maker.

Dear leno, Optimization may be defined as a process or a methodology of making something as perfect, functional, or effective as possible. This is particularly true in the aspect of mathematical procedures for maximizing or minimizing the objective function. In engineering that involved designing, systems and decision making, optimization is essential in producing the best design subjects the whatever constraints, the optimum systems and many more. In practice the role of optimization are plenty but not well recognized.

Iam also in line with Nansi Xue

In engineering optimization is always necessary.By optimization we can gain maximum efficiency and it give perfect solution in designing and operation.

The term optimization suggests to design a product or process to its ultimate perfection, its optimum, which is in most cases hardly achieved at all. Here I agree to Rauls more modest desciption describing this process as aiming to improve the efficiency of a process or product.

As the discussion points out, "the optimization" depends on the objectives to be considered. The "best result" can be quite different, depending on the target function to be optimized and the method and function can result only in an intermediate optimum rather than the absolut one. In this sense, I would rather follow Nansi Xue's view on multi-objective optimization, that the constraints require to accept compromises on some parameters in order to achieve an improvement in terms of the objective function one is looking at in its analysis.

This is an interesting discussion. I must remark that I am not saying that single-objective constrained formulations of engineering optimization problems are incorrect, but I consider that using multi-objective formulations are more suitable for most real applications because they avoid the inconvenience of establishing the constraints, which in most case are subjective. I will try to explain my point of view using an example:

Let us suppose that a group of motor design engineers aim to optimize the design a new motor according to n input parameters (dimensions of windings or magnets, communication angles, etc.) with the aim of maximizing its power (horsepower, hp), and minimizing its fuel consumption (litres/kilometer). Both formulations are discussed:

i) A SINGLE-OBJECTVE CONSTRAINED formulation would be, for example, to maximize the horsepower (hp) subject to a maximum consumption of 6 litres/kilometer (l/km). Let us consider that a deterministic or stochastic optimization method is applied, which obtains, among others, two configurations of this motor:

Motor A) 150 hp and 5.99 l/km.

Motor B) 170 hp and 6.01 l/km.

Obviously, using the single-objective constrained formulation, the solution B would be considered unfeasible, and therefore rejected.

ii) A Pareto-based MULTI-OBJECTIVE formulation would consider both objectives as equally important, which is why the front of non-dominated solutions obtained could include, among others, both solutions (A and B). Later, the decision maker would select solution A or B according to any criterion. In this particular case, probably, the decision maker would select solution B because it increase the power significantly with respect to solution A, while the increase in fuel consumption is very reduced.

Something similar would be said in the case commented by Nansi Xue, where the battery power must be maximized and the energy consumption minimized.

Part of the difficulty in this discussion is that optimization in engineering applications is not the same as optimization in mathematics. Most of the practicing engineers that I have met (building space systems) use the term optimization to mean using the mathematical methods to do as well as is feasible, not as well as is possible. The other difficulty with the term is that optimal values are very fragile; the slightest change in the original conditions (or the slightest error in problem formulation caused by uncertainty) can change the computed optimum value wildly (matrix theory has good examples of this). What is actually desired for practical problems is a robust (large) region containing a very good solution, not exactly the optimum. This notion (and the reasons mentioned above) lead directly to the need for multi-criterion optimization, which allows the trade-offs to be considered explicitly from the solutions along the Pareto boundary.

In my opinion, optimization is how to get best solution for any kind of problems in engineering disciplines. Examples are at what production quantity your profit will me maximum or at what capacity your company maintaining the service level should be 95% etc. Some engineering models we can convert to mathematical models and use several optimization techniques to get the best results.

@Nansi: we can use techniques like goal programming to solve multi objective optimization problems. Even now a days some heuristics also used for solving the similar kind of problems.

Every genuine engineering problem is an optimization problem, that is to say, try to get the best balance of contradictory effects.

Optimization is a natural concept. Its essentially a philosophical concept that found its way into science and engineering. If we can understand the working of a system in general, we can as well describe the system by a set of mathematical equation or function (response surface methodology). When we have an equation, we can simulate the whole system in a computer. Optimization helps us here, since any mathematical function will involve arbitrary coefficients in the fitted function, which when adjusted properly gives the systems behaviour accurately. This is the god like power that we scientists harnessed in the past few centuries !!!

Its exactly how the whole universe works. Hidden parameters are associated with almost all processes in this universe. For example, the string theory and other equivalents work only at a particular parameter values which they optimized to fit the experimental and few theoretical results. Since, we are developing faster in understanding these processes through theory, experimentation and simulation, the need to understand various optimization techniques becomes imperative.

I do not agrie with N Xue. The sentence a single solution cannot be optimal in more than one objective is meaningles in multicriteria optimization. It is not necessarily true that a designer has to either aggregate the objectives to select a solution or constrain all objectives and optimize one. The generation of the Pareto front if possible, or at least of non-dominated solutions provide the designer with multiple answers, and typically, it is other criteria that were not considered that support the decision process. The ability to see multiple pareto optimal solutions (solutions such as an improvement in one objective necessarily means a decrease in one or more other objectives) enable the designer to make trrade-offs, and to decide on how much he or she is willing to accept degradation in an objective to gain in another. Seeing the solutions is what the designer wants.

I believe a general definition of optimization would be a process in which an object or a system is being changed, so that a property or a function of multiple properties would reach a maximal (or minimal) value, according to the desire of the optimizer.

In engineering it is done usually so that a system would reach maximal efficiency and/or minimal chance of failure, and is considered a large part of the work of engineers.

A large part of optimizing is realising the best method for the problem at hand, and realising what is the function one wants to bring to maximum, since it is rarely a single property.

Optimization in engineering is about getting the best design n processes that will optimise profits within the well defined constraints and limitations. Its role is to improve engineering decisions.

I believe a general definition of optimization concerns with use of resourses effectively by using any method  which  may be qualitative or quantitative.

Optimization is the quintessence of engineering itself. After engieers have found a solution for a specific problem, then there comes optimization which is the choice of a solution requiring the least resources but still complying with the problem specifications.

We can say that best choice of decision maker for get highest level of satisfaction, which provides the balance between system parameters and contradictory responses.