Ideal objective vector

In MOO, ideal and nadir objective vectors are occasionally used. The ideal objective vector contains the optimum values of the objectives, when each of them is optimized individually disregarding the other objectives. The ideal objective vector denoted by superscript (i.e., [/i /2 J) is shown in Figure 1.2a along with the nadir objective vector denoted by superscript N (i.e., [/i /2 ]). Here,/i is the value of /i(x) when /2(x) is optimized individually, and is the value of /2(x) when /i(x) is optimized individually. Components of the nadir objective vector are the upper bounds (i.e., most pessimistic values) of objectives in the Pareto-optimal set. In case of two objectives, as shown in Figure 1.2a, they correspond to the value of one objective when the other is optimized individually. This may not be the case if there are more than two objectives (Weistroffer, 1985). The ideal objective vector is not realizable unless the objectives are non-conflicting in which case the MOO problem has only a unique solution, namely, ideal objective vector. However, it tells us the best possible value for each of the... 

No Preference Methods (e.g., global criterion and neutral compromise solution) These methods, as the name indicates, do not require any inputs from the decision maker either before, during or after solving the problem. Global criterion method can find a Pareto-optimal solution, close to the ideal objective vector. 

The DM may find information about the ranges of feasible Pareto optimal objective vectors useful. Lower bounds form a so-called ideal objective vector z G R. Its components zf are obtained by minimizing each ob-... 

In the initialization phase of the NIMBUS method, the ranges in the Pareto optimal set, that is, the ideal and the nadir objective vectors are computed to give the DM some information about the possibilities of the problem. The starting point of the solution process can be specified by the DM or it can be a neutral compromise solution located approximately in the middle of the Pareto optimal set. To get it, we set + z )/2 as a reference point and solve (6.4). 

Strictly speaking, a symmetry-translation is only possible for an infinitely extended object. An ideal crystal is infinitely large and has translational symmetry in three dimensions. To characterize its translational symmetry, three non-coplanar translation vectors a, b and c are required. A real crystal can be regarded as a finite section of an ideal crystal this is an excellent way to describe the actual conditions. 

Part of the process of infection and tumor formation requires the insertion of the Tj plasmid of the bacterium into the genome of the plant, a characteristic that makes the Tj plasmid an ideal vector for the introduction of foreign DNA into the plant. The DNA of interest is spliced into the T plasmid, and then the whole segment is inserted into a plant chromosome. To achieve this objective, some modifications must be made to the Ti plasmid—for example, its attenuation (deletion of tumor-inducing genes), the insertion of cloning sites so that the DNA of interest can be inserted easily into the vector, and the addition of selectable genes. 

High-resolution transmission electron microscopy can be understood as a general information-transfer process. The incident electron wave, which for HRTEM is ideally a plane wave with its wave vector parallel to a zone axis of the crystal, is diffracted by the crystal and transferred to the exit plane of the specimen. The electron wave at the exit plane contains the structure information of the illuminated specimen area in both the phase and the amplitude.. This exit-plane wave is transferred, however affected by the objective lens, to the recording device. To describe this information transfer in the microscope, it is advantageous to work in Fourier space with the spatial frequency of the electron wave as the relevant variable. For a crystal, the frequency spectrum of the exit-plane wave is dominated by a few discrete values, which are given by the most strongly excited Bloch states, respectively, by the Bragg-diffracted beams. 

Fuzzy goal programming uses the ideal values as targets and minimizes the maximum normalized distance from the ideal solution for each objective. An ideal solution is the vector of best values of each criterion obtained by optimizing each criterion independently ignoring other criteria. In this example, ideal solution is obtained by minimizing price, lead-time, and quality independently. In most situations, the ideal solution is an infeasible solution since the criteria conflict with one another. 

Ideal solution is the vector of individual optima obtained by optimizing each objective function separately ignoring all other objectives. 

An ideal solution is the vector of individual optima obtained by optimizing each objective function separately, ignoring all other objectives. In Example 2.4, the maximum value of Zj, ignoring Zj, is 26 and occurs at point D. Similarly, maximum Zj of 15 is obtained at point C. 

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