Context independent problem solving

Each solution is represented symbolically, so the user has no contextual clues as to what the problem is that he is attempting to solve. This is done in order to create a context independent interface that can be used for a wide variety of problems and algorithms. The only information to which the user has access is similarities between solutions (as shown by similarities in symbols) and the value of each solution. Once the user selects a set of solutions, he picks the type of variation operators to apply to the solutions and then presses GO to have the algorithm, as shown in Figure 8.1, create a new set of solutions. Dembski s work implies that even with only this information it is possible for the user to be able to provide active information to the search algorithm because a prior external source of information is unnecessary to add active information to the search since the user is an intelligent agent. 

In Section 1.5 we briefly discussed the relationships of equality and inequality constraints in the context of independent and dependent variables. Normally in design and control calculations, it is important to eliminate redundant information and equations before any calculations are performed. Modem multivariable optimization software, however, does not require that the user clearly identify independent, dependent, or superfluous variables, or active or redundant constraints. If the number of independent equations is larger than the number of decision variables, the software informs you that no solution exists because the problem is overspecified. Current codes have incorporated diagnostic tools that permit the user to include all possible variables and constraints in the original problem formulation so that you do not necessarily have to eliminate constraints and variables prior to using the software. Keep in mind, however, that the smaller the dimensionality of the problem introduced into the software, the less time it takes to solve the problem. 

Consider the stress distribution in such a problem. Let us subtract from this the applied stresses at infinity, thus giving the distribution for the problem where the stresses tend to zero at infinity and have uniform applied stresses, of the same magnitude and opposite sign, on the open crack faces. It is clear that this distribution also obeys the dynamical equation (1.8.17), since the applied stresses, which are independent of position, contribute nothing. This latter problem is more convenient in the context of the methodology introduced in the present chapter, and will be adopted as the statement of the problem. The stress distribution of final interest may be deduced trivially, once the problem is solved. 

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