The objective function has the form: u = f(x1, x2,..., xn), where u is the area of decision-making (goal) for a particular set of design parameters (x), each of which has a dimension (n). The construction of this function needs to perform economic and engineering calculations, for example, to calculate the strength or mass of the structure, plant capacity, volume of production, cost of freight, profits, etc.
If the task involves selection of optimal solutions or the comparison of two alternative solutions, in this case, can not do without some dependent variable, determined by the design parameters. It is this value and is the objective function. When solving optimization problems to find such design parameters, when the objective function has a minimum or maximum. Thus, the function is a model of optimality, which describes the economic or engineering problems.
If there is one design parameter, when n = 1, the objective function has one variable, and its graph is taken some curve lying on the plane. If n = 2, the function has two variables and its graph will be a surface in three-dimensional space.
The objective function is not necessarily represented as a formula. In those cases, when it takes only discrete values can be set in a table. Anyway, in all cases, it is an unambiguous function of design parameters.
Construction of the objective function is a required step in the solution of optimization problems. Optimization is the process of selecting the most suitable option possible. For example, when performing engineering calculations method optimization to determine which design option is best, as rationally allocate resources.
The solution of optimization problems involves finding the optimal values that define the task. In the engineering tasks they are called project parameters, and economic parameters of the plan. As design parameters can be the values of the object's size, temperature, mass, etc.
For the solution of certain problems is to build multiple objective functions. For example, in the design process of engineering products it is necessary to find the optimum values for maximum reliability, minimum material, maximum volume, etc.