A guess value is more commonly called a starting value or initial value. These are necessary for most optimization

Optimization (mathematics)

In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....

 problems which use search algorithms, because those algorithms are mainly deterministic

Deterministic algorithm

In computer science, a deterministic algorithm is an algorithm which, in informal terms, behaves predictably. Given a particular input, it will always produce the same output, and the underlying machine will always pass through the same sequence of states...

 and iterative, and they need to start somewhere. One common type of application is Nonlinear regression

Nonlinear regression

In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables...

.

The quality of the initial values can have a considerable impact on the success or lack of such of the search algorithm. This is because the fitness function

Fitness function

A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims....

 or objective function (in many cases a sum of squared errors (SSE

SSE

-Computing:*Server-sent events, a technology to push content to web clients*Simple Sharing Extensions, a specification that extends RSS from unidirectional to bidirectional information flows*SPARQL Syntax Expressions*Microsoft SQL Server Express Edition...

)) can have difficult shapes. In some parts of the search region, the function may increase exponentially, in others quadratically, and there may be regions where the function asymptotes to a plateau

Plateau (mathematics)

A plateau of a function is a part of its domain where the function has constant value.More formally, let U, V be topological spaces. A plateau for a function f: U → V is a path-connected set of points P of U such that for some y we havefor all p in P....

. Starting values that fall in an exponential region can lead to algorithm failure because of arithmetic overflow

Arithmetic overflow

The term arithmetic overflow or simply overflow has the following meanings.# In a computer, the condition that occurs when a calculation produces a result that is greater in magnitude than that which a given register or storage location can store or represent.# In a computer, the amount by which a...

. Starting values that fall in the asymptotic plateau region can lead to algorithm failure because of "dithering". Deterministic search algorithms may use a slope function to go to a minimum. If the slope is very small, then underflow errors can cause the algorithm to wander, seemingly aimlessly; this is dithering.

Guess values can be determined a number of ways. Guessing is one of them. If one is familiar with the type of problem, then this is an educated guess or guesstimate

Guesstimate

Guesstimate is an informal English contraction of guess and estimate, first used by American statisticians in 1934 or 1935. It is defined as an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture...

. Other techniques include linearization

Linearization

In mathematics and its applications, linearization refers to finding the linear approximation to a function at a given point. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or...

, solving simultaneous equations

Simultaneous equations

In mathematics, simultaneous equations are a set of equations containing multiple variables. This set is often referred to as a system of equations. A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations...

, reducing dimensions

Dimensions

Dimensions is a French project that makes educational movies about mathematics, focusing on spatial geometry. It uses POV-Ray to render some of the animations, and the films are release under a Creative Commons licence....

, treating the problem as a time series

Time series

In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...

, converting the problem to a (hopefully) linear

Linear

In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

 differential equation

Differential equation

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

, and using mean

Mean

In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

 values.

Other methods for determining starting values and optimal values in their own right come from stochastic

Stochastic

Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...

 methods, the most commonly known of these being evolutionary algorithms and particularly genetic algorithms.