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In statistics, an optimality criterion [1] provides a measure of the fit of the data to a given hypothesis, to aid in model selection.A model is designated as the "best" of the candidate models if it gives the best value of an objective function measuring the degree of satisfaction of the criterion used to evaluate the alternative hypotheses.
Best-Fit (BF), too, keeps all bins open, but attempts to place each new item into the bin with the maximum load in which it fits. Its approximation ratio is identical to that of FF, that is: B F ( L ) ≤ ⌊ 1.7 O P T ⌋ {\displaystyle BF(L)\leq \lfloor 1.7\mathrm {OPT} \rfloor } , and there is a family of input lists L for which B F ( L ...
Mathematically, shape optimization can be posed as the problem of finding a bounded set, minimizing a functional (),possibly subject to a constraint of the form =Usually we are interested in sets which are Lipschitz or C 1 boundary and consist of finitely many components, which is a way of saying that we would like to find a rather pleasing shape as a solution, not some jumble of rough bits ...
The resulting value can be compared with a chi-square distribution to determine the goodness of fit. The chi-square distribution has ( k − c ) degrees of freedom , where k is the number of non-empty bins and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the distribution plus one.
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
Topology optimization has a wide range of applications in aerospace, mechanical, bio-chemical and civil engineering. Currently, engineers mostly use topology optimization at the concept level of a design process. Due to the free forms that naturally occur, the result is often difficult to manufacture.
This topology allows all particles to communicate with all the other particles, thus the whole swarm share the same best position g from a single particle. However, this approach might lead the swarm to be trapped into a local minimum, [ 29 ] thus different topologies have been used to control the flow of information among particles.
Let be a set and a nonempty family of subsets of ; that is, is a nonempty subset of the power set of . Then is said to have the finite intersection property if every nonempty finite subfamily has nonempty intersection; it is said to have the strong finite intersection property if that intersection is always infinite.