The Search Objective

Consider n types of modules with m options per module. There would be run possible module options, and m possible product variants. Clearly, the search space for creating the optimal product family would be very large if n or /n is large. To better organize this search, the company may maintain a knowledge base of a selective few modules, components, product variants, production and assembly processes, and customer-segments. The stmctured form of such a library is called the platform as mentioned earlier. 

Consider a product family comprising three products A, B, C. As shown in Fig. 3.4, product A comprises p unique modules, and it shares r and r-i modules with products C and B, respectively. Products B and C comprise p2 and p unique modules, respectively, and share 3 modules. Finally, r4 modules are shared by all the three products. We use the notation r, to denote the identity as well as the number of modules. 

Without the structore of a platform, all the modules of a product must be identified and then assembled to create that product. This must be done independently of other two products. For example, to build product A, the number of modules that the designer would need to search and evaluate would equal Pi + + r2 + r. Similarly, 

The simplest platform that can be built would possess the knowledge base for building modules given that this set is common to all three products, so that no search is involved for using this knowledge base. This implies that every product will have the module-options in built into them ex ante, reducing the search space to S = Pi + p2 + P3 + 2ri + 2v2 + 2r2, Pi + P2+ Ps searches are performed outside the platform and 2(ri + r2 + r ) searches are performed inside the platform. 

consider enlarging the platform to include the module options in the sets ri, f2, t 3, and r. The module options will be builtin all products ri earmarked for products A and C r2 for A and B, and rj, for C and B. The search space outside the platform will equal Pi + P2 + Ps, as before. Note that to build product A, the company needs to search and eliminate rj, modules. Therefore the search space for the three products inside the platform will equal ri + r2 + rj,. Hence the total search space will equal S = pi + p2 + P3 + ri + r2 + r. If the company decides to reduce variety by cutting out product C, it can build a platform comprising V2 and r, and the search space will equal S = pi + p2 + r2 + r.  

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Practical Bounding of the Subject. A practical method of bounding the search subject is to make a list of questions which, if answered in the abstract of each item entered, fully cover the intended subject area and feed into the search objectives. 

Everyone will agree that a searcher, like any other investigator, should be competent in his own specialty-searching. A good searcher decides on the relative value of the references he finds for the search objectives, and states his evaluation in the search report. 

To illustrate, let us assume that a searcher reads that a chemical compoimd has a certain effect on a chromium catalyst. He cannot vouch for the scientific validity of this. However, he can say, assuming the statement to be true, that it has considerable, some, or little bearing on the search objectives. If his task is to locate information pertinent to patent validity, he may say, "This information may anticipate claim 5, U.S. patent. . . . Lawyers later may agree or disagree with his statement, but it has called their attention to the possible usefulness of the reference. Such highlighting is what is meant by saying the search abstract should be interpretive relative to the search objectives. 

Ideally, a complete 6-dimensional search would involve an inner exhaustive translational search for every rotational setting. At each such configuration of the search object some measure of the quality of fit has to be calculated. Given the limited computer resources available, this measure is often simply the sum of the electron density at each of the n atomic locations, for any given configuration of the search object,... 

Feature Search is performed parallel and enables to immediately identify an object that distinguishes itself from the distractor objects in one distinct feature (e.g. a red circle in a field of blue circles). Treisman and Gelade s studies identified several kinds of such distinctive features color, intensity, direction of lighting, orientation, size, motion direction, and disparity. The response times for feature search is below 200 ms and independent of the number of distractors. The latter indicates a parallel search, whereas the low response times support the assumption of unconscious processing, which directly highlights the searched object (see Fig. 12). 

In the earlier part of the sixteenth century Paracelsus gave a new direction to alchemy by declaring that its true object was not the making of gold but the preparation of medicines. This union of chemistry with medieine was one characteristic goal of iatrochemists, of whom he was the predeeessor. The search for the elixir of life had usually... 

Nonlinear Programming The most general case for optimization occurs when both the objective function and constraints are nonlinear, a case referred to as nonlinear programming. While the idea behind the search methods used for unconstrained multivariable problems are applicable, the presence of constraints complicates the solution procedure. 

To overcome the limitations of the database search methods, conformational search methods were developed [95,96,109]. There are many such methods, exploiting different protein representations, objective function tenns, and optimization or enumeration algorithms. The search algorithms include the minimum perturbation method [97], molecular dynamics simulations [92,110,111], genetic algorithms [112], Monte Carlo and simulated annealing [113,114], multiple copy simultaneous search [115-117], self-consistent field optimization [118], and an enumeration based on the graph theory [119]. 

However, conflicts between the fulfillment of different objectives and aspiration levels may prevent any feasible zone of the decision space from leading to satisfactory joint performances. If the search procedure fails to uncover at least one feasible final solution, X, consistent with y, a number of options are available to the decisionmaker to try to overcome this impasse. Namely, the decisionmaker can revise the initial problem definition, by either... 

Here (j is the CG update parameter. In the above equations, e = e (tj) o vector notation for the discretized electric field strength, = g (fj) o objective functional J with respect to the field strength (evaluated at a field strength of e t) and dk = d (t ) o search direction at the feth iteration. The time has been discretized into N time steps, such as that tj=jx )t, where j = 0,1,2, , N. Different CG methods correspond to different choices for the scalar (j. ... 

The RDM s are therefore much simpler objects than the A-electron Wave Function (WF) which depends on the variables of N electrons. Unfortunately, the search for the 7V-representability conditions has not been completed and this has hindered the direct use of the RDM s in Quantum Chemistry. In 1963 A. J. Coleman [4] defined the A -representability conditions as the limitations of an RDM due to the fact that it is derived by contraction from a matrix represented in the N-electron space. In other words, an antisymmetric A-electron WF must exist from which this RDM could have been derived by integrating with respect to a set of electron variables. 

What type of objective function should we minimize This is the question that we are always faced with before we can even start the search for the parameter values. In general, the unknown parameter vector k is found by minimizing a scalar function often referred to as the objective function. We shall denote this function as S(k) to indicate the dependence on the chosen parameters. 

In this method the search vector is the negative of the gradient of the objective function and is given by the next equation... 

Hitchcock, Ethan Allen. Remarks upon alchemy and the alchemists, indicating a method of discovering the true nature of Hermetic philosophy and showing that the search after the Philosopher s Stone had not for its object the discovery of an agent for the transmutation of metals. Being also an attempt to rescue from undeserved opprobrium the reputation of a class of extraordinary thinkers in past ages. 2nd ed., 1865 or 1866. 

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