Algorithms worst-case algorithm

Table 9.7. Comparison of Nominal and Worst-case Algorithm Based Optimum Design of Operating Policies (Open Loop Strategy)...

Determining Computational Complexity Development of (Efficient) Algorithms Worst-Case Analysis of Heuristics... 

The complexity analysis shows that the load is evenly balanced among processors and therefore we should expect speedup close to P and efficiency close to 100%. There are however few extra terms in the expression of the time complexity (first order terms in TV), that exist because of the need to compute the next available row in the force matrix. These row allocations can be computed ahead of time and this overhead can be minimized. This is done in the next algorithm. Note that, the communication complexity is the worst case for all interconnection topologies, since simple broadcast and gather on distributed memory parallel systems are assumed. 

In the worst case, the backtracking algorithm will form a search tree of depth n, where n is the number of atoms in the query graph. Also, in this case a separate sub-tree search process for each atom of the target graph will be initiated. That is why the linear multiplier m is apphed to Eq. (7). 

When the planning algorithms are run on this plant no MSVS is found since, in the worst-case state, there are no valves that will prevent hydrogen cyanide and formaldehyde from mixing in the region of overlap. Thus the computer will try to use the methodology described in the... 

The algorithm CREATE-PURGE-ROUTE described earlier is run under the worst-case scenario of the original EDTA plant with the added... 

Predictive methods of exposure assessment often rely on single values for input parameters to the exposure model that represent one point on the distribution curve of all possible values for this parameter. This point value can range from a 50th percentile, mean, median, or typical value to a worst-case estimate. In the predictive exposure assessment, a number of parameters are integrated through an algorithm to produce an output such as the predicted environmental concentration (PEC). If many worst-case values are involved, this integration can result in a PEC that has a... 

Fletcher and Ley ffer (1994) studied the worst-case performance of GOA in an attempt to present the potential limitations that the outer approximation algorithm of Duran and Grossmann (1986a) may exhibit despite the encouraging experience obtained from application to engineering problems. 

Section 6.7 presents the Generalized Outer Approximation GOA approach. After a brief discussion on the problem formulation, the primal and master subproblem formulations are developed, and the GOA algorithm is stated in section 6.7.4. In Section 6.7.5, the worst case analysis of GOA is discussed, while in section 6.7.6 the Generalized Outer Approximation with exact Penalty GOA/EP and its finite convergence are discussed. 

As illustrated in the above example, equation 1 represents the simplest algorithm to express a room air concentration by dividing the amount by the room volume (EU, 2003). Equation 2 makes the model for estimating the room concentration more complex and time dependent. Equation 1 is used only for worst-case and low-tier assessments. Equation 2 is nearer to reality. If, however, the variables in the model are uncertain, total uncertainty of the results revealed by this model may be increased. These examples show that complexity of algorithms may introduce different qualitative and quantitative uncertainties into an assessment. 

Walsh et al. (1995) used a simplified BREAD process model in conjunction with a parameterised uncertainty description to predict the performance. Worst-case design algorithm of Walsh (1993) was used to systematically determine the optimal operating policies that allow performance constraints to be met over a bounded set of uncertain parameters. 

Figure 9.15. Worst-case Design using Outer Approximation Algorithm.

Table 9.8 shows the results of base case (case 1) optimisation with nominal values of operating parameters and those obtained by using worst-case design algorithm (case 2). The profit in Case 2 is based on weighted average of 20.5 nominal and 13.5 worst-case scenarios. Figure 9.17 shows nominal (optimum) and worst-case (optimum) temperature profile. 

As a last point we note that the present author and his coworkers [36] devised an algorithm for the calculation of matrix elements of the overlap and Hamiltonian based upon the PAf operator that is n5 in its worst case,... 

The estimated analyte concentrations in each of the three mixtures, with added random errors of a standard deviation equal to 10% of the mean value of S2, are summarized in Table 12.1. The results are presented for prediction with each of the three standards for each of the three mixtures utilizing the GRAM algorithm with concatenated (Table 12.1a) and added (Table 12.1b) samples. Similarly, the squared correlation coefficients between the true and estimated X-way and Y-way profiles are presented in Table 12.2. Figure 12.5 presents the best-case and worst-case examples for estimating the X-way and Y-way profiles with GRAM. In the worst-case scenario (p2x = 0.9938, p2y = 0.9987), there is very little discernible variation between the true and estimated profiles. In most cases, the true and estimated profiles... 

Overall accuracy of a data acquisition system is determined by the worst-case error of all its components. One should be aware of the fact that most system errors come neither from transducers (0.5%i-l%i accuracy) nor from A/D converters (0.025%i accuracy) but from the software analyzing the data (round-off errors, improper sampling rate, or algorithms). 

The general structure of an outer-approximation algorithm for worst-case design is as follows... 

None of the methods reviewed provides a complete solution to the type of problems of interest. They suffer either from making assumptions that are not likely to be satisfied or from relying on a computationally unrealistic degree of brute force. This review has, however, highlighted a number of methods that could usefully be exploited in an algorithm for worst-case design. 

The new worst-case design algorithm is discussed further below following the general outer-approximation algorithm structure constraint maximization, initialization, and multi-mode design. 

Prett and Garcia (1988) pose the validation problem as a discrete time linear optimal control problem under uncertainty. The uncertainty is defined by simple bounds, giving a polyhedral set of uncertain parameters V. For this problem, certain forms of uncertainty, e.g., in gains only, together with a quadratic performance index can be shown to satisfy the convexity requirements for the worst-case parameters to lie at vertices of V. This allows the algorithm of Gross-mann et al, based on examination only of vertices of V, to be applied (see Section II.A.l). The mathematical formulation is... 

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