An optimum ( Latin optimum , neuter from optimus 'best', 'outstanding', superlative from bonus 'good') is understood to mean the best achievable result in the sense of a compromise between different parameters or properties under the aspect of an application, use or one Target. In contrast to this stands the ideal , which denotes the best thinkable. The search for the optimum under given conditions and objectives is called optimization .
Mathematically speaking, it is an extremum of a function which, depending on any parameters, in some way represents bad or good. Whether the optimum is a minimum or a maximum depends on the context of the problem, namely on whether the bad should be minimized or the good should be maximized.
Many technical problems cannot be optimized with the help of purely mathematical methods. Although there is usually a mapping of a set of input parameters to one or more evaluation criteria, the differentiability of the evaluation function, which is necessary for many purely mathematical optimization methods, is not given. If the evaluation is calculated as part of a simulation, a numerical quality can be specified for each valid parameter set, but this is calculated by a computer program. Due to the lack of differentiability, treatment is e.g. B. only approximately possible with gradient methods. The differential quotient of a gradient descent can thus be replaced by a differential quotient, which, however, implies risks for the accuracy due to the finite step size. Methods of stochastic optimization such as evolutionary algorithms then offer a way out .
Operations Research provides mathematical-theoretical methods, especially for business and economics .
If the quality of a solution can be judged from different points of view and a good performance in one area leads to a deterioration in another, one can start looking for a Pareto optimum .
In computer science, improving the efficiency of a computer program is called program optimization or code optimization .
The basis of the optimization is the program analysis . In addition to program code that only the programmer can optimize himself ( human design ), code optimization can also improve compilation (see Compiler: Program Optimization ) or optimize the executed code itself at runtime (see Dynamic Optimization ).
When making a decision, optimization means looking for alternatives until the best possible solution to a problem is found. Colloquially, one usually means an improvement of a process or condition with regard to one aspect such as quality, costs, speed, efficiency and effectiveness, sometimes at the expense of another aspect.
Results that do not achieve the specifications or expectations of the optimum, but which are by no means to be assessed as real failures , are referred to as suboptimal (from the Latin sub 'under'). However, the term is often used with an ironic undertone or as a euphemism when describing an actually catastrophic result. In 2005, the term suboptimal was voted 8th in the choice of the word of the year by the Society for German Language. The occasion was an intoxicated appearance by the then Federal Chancellor Gerhard Schröders on the evening of the Bundestag election in 2005 , which he himself described as suboptimal and which was criticized by the media and politics for a long time as extremely embarrassing and remembered as a historical misstep.