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Topic: Objective function

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Optimization (mathematics)

Linear programming

Numerical analysis

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	[No title] (Site not responding. Last check: 2007-10-26)
		The objective function is to minimize the file transmission costs of running the tasks given the constra int that the sum of the sizes of a set of files on a node must be less then or equal to the capacity of the node.
		In accordance with the primary aspect of the present invention, the objective function for a storage system is determined, the workload units are selected and their standards are determined.
		An extension of the Toyoda gradient function is to composite it with the objective function of supporting the greatest number of workload units on the cheapest set of storage devices.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=00/31640.000602&ELEMENT_SET=DECL (4515 words)

	Fitness function (Site not responding. Last check: 2007-10-26)
		A fitness function (sometimes referred to as an objective function) quantifies the optimality of a solution (that is, a chromosome) in a genetic algorithm so that that particular chromosome may be ranked against all the other chromosomes.
		The fitness function is used to calculate the elevation of a point on the fitness landscape corresponding to that particular chromosome.
		PHP Function Table Handy PHP function reference which helps to quickly locate a desired function, to learn which PHP version it available in, and if it is documented.
	www.serebella.com /encyclopedia/article-Fitness_function.html (450 words)

	Objective Function (Site not responding. Last check: 2007-10-26)
		The objective function is the actual function which needs to be minimised in order for an optimal choice or a solution to be picked from the many alternatives offered.
		The function is most heavily based on similarity measures as briefly explained earlier, but it allows this measure to be extended in some way.
		Objective functions are built to encapsulate in a concise and effective way everything that is repeatedly evaluated.
	www.schestowitz.com /Research/Literature_Report/HTML/node27.html (281 words)

	Linear Programming Models
		Objective function: Mathematical function of the decision variables that converts a solution into a numerical evaluation of that solution.
		Additivity means the total value of the objective function and each constraint is the sum of the individual contributions from each variable.
		The marginal change in the optimal objective function value that occurs if the right-hand side of a constraint is changed (for example, if it increased by one unit).
	www.pages.drexel.edu /~isp22/pom300/lpsolver.html (864 words)

	5.9 Other objective functions
		A direct comparison of the different variance-like objective functions is made in figure 5.7.
		The mean values of the objective functions are plotted in figure 5.7a, which shows them to behave similarly, with the positions of the minima being almost indistinguishable.
		The standard deviations of the objective functions are plotted in figure 5.7b, and here the differences are more pronounced.
	www.physics.uc.edu /~pkent/thesis/pkthnode42.html (235 words)

	Optimization Theory (Site not responding. Last check: 2007-10-26)
		Seemingly, the next step to minimizing the objective function is to set the derivatives with respect to each quantity to zero and then solve the resulting pair of equations.
		As this objective function is strictly convex, the objective function's sole stationary point is its global minimum.
		When the objective function depends on a vector-valued quantity x, the evaluation of the function's stationary points is a simple extension of the scalar-variable case.
	cnx.rice.edu /content/m11240/latest (1308 words)

	Models - Operations Research Models and Methods
		This is called a quadratic, separable function because the highest order of the nonlinear terms is 2, and each term is a function of only one variable.
		We note that the objective function Z is a concave function of the decision variables P, Q and R.
		For a maximization problem, when the objective function is concave and the constraints form a convex feasible region, we can be sure that the solution obtained is a global maximum (i.e., no other feasible solution provides a greater objective value).
	www.me.utexas.edu /~jensen/ORMM/models/unit/nonlinear/subunits/manufacture/concave.html (481 words)

	GAlib: overview (Site not responding. Last check: 2007-10-26)
		The objective function is used to evaluate the genome.
		The objective score is the value returned by your objective function; it is the raw performance evaluation of a genome.
		Each objective function returns a single value that represents the objective score of the genome that was passed to the objective function.
	www.sis.pitt.edu /~shirtle/galibnotes.html (1691 words)

	Minimum value of objective function..
		The minimum value of the objective function can be thought of as the overall error in the prediction of drug concentrations based upon observed data.
		Comparing the objective function value usually comes into play when when you are trying to evaluate hierarchal models to see which model produced the smallest sum of weighted squared residuals.
		If a nested model with fewer parameters has an objective function value lower by an amount larger than the critical chi square value than the "larger" model, than it is the "better" model.
	www.cognigencorp.com /nonmem/nm/99oct052001.html (512 words)

	5.8 Limitation of outlying energies
		It is highly undesirable for an objective function to have a large variance.
		A larger variance implies that a greater number of configurations is required to determine the objective function to a given accuracy.
		In this graph the standard deviations of the objective functions are plotted as error bars.
	www.physics.uc.edu /~pkent/thesis/pkthnode41.html (604 words)

	Solver Advanced Tutorial - Gradients, Linearity, and Sparsity
		In mathematical terms, 75 is the partial derivative of the objective function with respect to variable x1, and 50 is its partial derivative with respect to x2.
		Similarly, each constraint function has a gradient, which is a vector consisting of the partial derivatives of that function with respect to each decision variable.
		For example, the objective function changes by 75 units, whether x1 moves from 0 to 1 or from 100 to 101.
	www.solver.com /tutorialadv.htm (811 words)

	Oct 29 Lecture (Site not responding. Last check: 2007-10-26)
		In the language of optimization theory, the quantity being minimized is referred to as the objective function.
		To minimize a function with respect to a variable, the standard protocol is to use calculus.
		We differentiate the function with respect to the variable of interest, set the result equal to zero, and then solve for the variable of interest.
	www.unc.edu /courses/2003fall/biol/145/001/docs/lectures/Oct29.html (1529 words)

	Fitness Function
		The fitness function measures the (potential for) reproductive success of any individual in a given environment.
		(Note: A Genetic Algorithm is an optimization algorithm that makes use of a population of artificially reproducing test solutions and works by enforcing the condition that the fitness function, in sense 1, for this population is equal to the objective function.
		Note that the objective function is input to the genetic algorithm, while process of forcing the fitness function, in sense 1, to be equal to the objective function is a part of the algorithm itself.
	www.iscid.org /encyclopedia/Fitness_Function (145 words)

	iTOUGH2 Minimization Algorithms
		The choice depends on the characteristics of the objective function, the number of parameters to be estimated, and the efficiency with which the forward problem can be solved.
		After local linearization of the objective function with respect to the parameters to be estimated, the Levenberg-Marquardt algorithm performs initially small, but robust steps along the steepest descent direction, and switches to more efficient quadratic Gauss-Newton steps as the minimum is approached.
		Evaluating the objective function on a grid in the entire parameter space is prohibitively expensive for higher dimensional parameter spaces.
	esd.lbl.gov /ITOUGH2/Minimization/minalg.html (514 words)

	Objective Function and Derivatives
		Sometimes the objective function cannot be computed for all points of the specified feasible region; for example, the function specification may contain the SQRT or LOG function, which cannot be evaluated for negative arguments.
		If the function module takes the square root or the log of an intermediate result, you can use nonlinear constraints to try to avoid infeasible function evaluations.
		If the Hessian matrix G of the objective function f has a large proportion of zeros, you may save computer time and memory by specifying a sparse Hessian of dimension nn ×3 rather than a dense n ×n Hessian.
	www.dnr.state.ak.us /ssd/whtest/sashtml/iml/chap11/sect7.htm (1520 words)

	Objective Function (SAP Library - Automated Production Planning and Optimization) (Site not responding. Last check: 2007-10-26)
		The weighting that you apply to the various times or costs when defining the objective function reflect the importance of each problem for your schedule.
		For example, if a very important scheduling objective of yours is to have low setup costs, you weight the setup costs in the objective function particularly highly.
		Due to the fact that the various scheduling objectives generally compete with one another, it is often not possible to achieve all of the objectives to the same extent.
	help.sap.com /saphelp_apo/helpdata/en/68/bf75395da86236e10000000a114084/content.htm (185 words)

	Optimization Algorithms
		Each optimizer constructs an objective function from the design goals and then employs a unique algorithm to minimize the object function.
		The objective function formulated for this optimizer, similarly to Minimax, facilitates improving the design margin when all specifications are satisfied (design centering).
		Therefore, their performance in handling their objective functions is likely to be far superior over any other optimizer.
	eesof.tm.agilent.com /docs/adsdoc2002/mom/momD5.html (569 words)

	Graphing LPs - Example 2 (Site not responding. Last check: 2007-10-26)
		We want to minimize our objective function, so we would like to find solutions with an objective value of less than 1.
		We could look for solutions with an objective value of 0, but we'll be ambitious and look for solutions with an objective value of -1.
		We then pushed the objective function as far as we could before leaving the feasible region.
	www.cob.ohio-state.edu /~croxton_4/tutorial/Geometry/graphing4.html (315 words)

	Point-wise Wind Retrieval :: MERS -- BYU
		The forward model function accepts as inputs: wind speed, relative azimuth angle (or the angle between the instrument azimuth and the wind direction), incidence angle, instrument frequency, and instrument polarization.
		For a fixed incidence, frequency, and polarization, sigma-0 is shown as a function of wind direction (x axis) and wind speed (labeled on each curve.) Note that in general, higher wind speeds generate more surface roughness and therefore higher sigma-0 values.
		To generate a statistical model for use in estimation, each measurement is assumed to be a realization of a Gaussian random variable dependent on the wind speed and wind direction.
	www.ee.byu.edu /ee/mers/wind/pointwise.html (916 words)

	iTOUGH2 Objective Function (Site not responding. Last check: 2007-10-26)
		The objective function measures the misfit between the data and the corresponding modeling result.
		The standard method is weighted least squares, i.e., the objective function to be minimized is the sum of the residuals weighted by the inverse of the measurement error.
		However, if the residuals are not normally distributed, a different objective function should be chosen, or the parameters are not maximum-likelihood estimates.
	www-esd.lbl.gov /iTOUGH2/Objective/of.html (142 words)

	Labor Economics (Site not responding. Last check: 2007-10-26)
		Objective function – Links the level of several choice variables to the ultimate goal of the problem
		Given a function f(x,y) subject to a constraint g(x,y) = k (a constant), a new function F can be formed by:
		The lagrange multiplier l approximates the marginal impact on the objective function caused by a small change in the constant of the constraint
	garnet.acns.fsu.edu /~fdv3471/math11.html (307 words)

	SPSA Algorithm (Site not responding. Last check: 2007-10-26)
		There has recently been much interest in recursive optimization algorithms that rely on measurements of only the objective function to be optimized, not on direct measurements of the gradient (derivative) of the objective function.
		This contrasts with algorithms requiring direct measurements of the gradient of the objective function (which are often difficult or impossible to obtain).
		SPSA is generally used in nonlinear problems having many variables where the objective function gradient is difficult or impossible to obtain.
	www.jhuapl.edu /SPSA (1641 words)

	Chapter 4 Notes (Site not responding. Last check: 2007-10-26)
		The general rule is if the objective function measures a benefit, the decision maker seeks to maximize this benefit and is solving a maximization problem.
		Objective function may be a function of more than one activity.
		The objective function is the total benefit function and the constraint is the total cost function.
	www.gardner-webb.edu /intra/negbenebor/chapter4.htm (1166 words)

	GEATbx: Tutorial 5 Overview of GEA Toolbox Structure
		All options not defined are set automatically inside the main function geamain2 by calling geaoptset, checking the validity of the options at the same time.
		The high-level initialization function initpop handles all aspects of population size, additional randomization or inclusion of randomly generated individuals.
		Instead of writing an objective function file and passing the name of the function, the objective function can be passed directly in a string to the main function as well.
	www.geatbx.com /docu/tutindex-04.html (1503 words)

	Optimizing With COOOL (Site not responding. Last check: 2007-10-26)
		numbers from its standard input, computes the function value or gradient vector according to the request, and writes that to its standard output; finally, the optimization routine captures the objective function value or gradients via its own standard input and then decides how to update the model.
		A key point is that the communication between the optimization routine and the objective function is transparent to the user.
		If you want to use one of the optimization methods on your own objective function, all you have to do is write the objective function as a stand-alone program which reads a flag followed by a model from standard input and writes a number to standard output-until an end-of-file is reached.
	www.cwp.mines.edu /html_reports/coool/node4.html (534 words)

	ipedia.com: Linear programming Article (Site not responding. Last check: 2007-10-26)
		Due to the geometry of these kinds of linear constraints and the linear objective function, LP problems are "convex", which means that there are no local optima (aside from the global optimum).
		Barring these two pathological conditions (which are often ruled out by resource constraints integral to the problem being represented, as above) it is possible to have either a point optimal solution, at a vertex of the polytope of admissible values, or a set of optimal solutions covering an edge or face of that polytope.
		The simplex algorithm solves LP problems by constructing an admissible solution at a vertex of the polytope, and then walking along edges of the polytope to vertices with successively higher values of the objective function until the optimum is reached.
	www.ipedia.com /linear_programming.html (698 words)

	Getting Started
		The linearly constrained Betts function (Hock & Schittkowski 1981) is defined as
		The Rosen-Suzuki problem is a function of four variables with three nonlinear constraints on the variables.
		The OPTN vector is passed to the subroutine as the opt input argument.
	www.asu.edu /sas/sasdoc/sashtml/iml/chap11/sect2.htm (845 words)

	Untitled Document
		Usually the objective will apply to all periods in the planning horizon but it is possible for the objective to only be calculated over a smaller period range.
		To maximise the objective over a smaller period range, click the box labelled ALL next to the selected objective so that the ‘tick’ disappears and then specify the first and last periods in the next two boxes.
		Visually, the only change to the objectives and constraints screen is the inclusion of regeneration lag.
	www.mang.canterbury.ac.nz /courseinfo/msci/msci480/LOGHtml/objective.html (390 words)

	Function
		There are two kinds of restraints, static and dynamic, that both contribute to the objective function as indicated in Eq.
		The dynamic pairs list is not necessarily re-generated each time the objective function is evaluated, although the contribution of the restraint to the objective function is calculated in each call to the objective function routine with the current values of the Cartesian coordinates.
		Sum the contributions of all violated restraints to the objective function and the derivatives (routine
	web.ics.purdue.edu /~xiaoc/Software/Modeller/manual/node153.html (841 words)

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