Hill-climbing

Like simulated annealing, tabu search is a technique designed to avoid the problem of becoming trapped in local optima. The procedure is basically hill-climbing, which commences at an initial solution and searches the neighbourhood for a better solution. However, the process will recognize, and avoid areas of the solution space that it has already encountered, thus making these areas tabu . The tabu moves are kept in a finite list, which is updated as the search proceeds. 

For maximum vehicle acceleration, the driver depresses the accelerator pedal to the floorboard and the engine operates with a tvide-open throttle. The power required curve traces the power needed by the car as a function of vehicle velocity when it is operated at constant speed in still air on a level road. At any given speed, the difference between these curves, Pa-Pr in Equation 1, is available for accelerating and hill climbing. 

High yield, high selectivity (HY/HS) catalysts, 20 536, 537, 544 Hildebrand-Scatchard hypothesis, 23 97 Hill climbing, 7 400... 

Battery system efficiency can also be increased by using flywheels to equalize power demands on batteries during acceleration and hill climbing. 

On the other hand, the optimal control problem with a discretized control profile can be treated as a nonlinear program. The earliest studies come under the heading of control vector parameterization (Rosenbrock and Storey, 1966), with a representation of U t) as a polynomial or piecewise constant function. Here the mode is solved repeatedly in an inner loop while parameters representing V t) are updated on the outside. While hill climbing algorithms were used initially, recent efficient and sophisticated optimization methods require techniques for accurate gradient calculation from the DAE model. 

Figure 24.12 Measured Trms values (a) for successive feedback control steps during closed-loop control of the 50-kilowatt forced combustor at China Lake, feedback was based on a simplex hill-climbing algorithm which is adjusting the phase between the primary and secondary air drivers to maximize Trms values (6) illustrates representative power spectra with and without control...

Fitting model predictions to experimental observations can be performed in the Laplace, Fourier or time domains with optimal parameter choices often being made using weighted residuals techniques. James et al. [71] review and compare least squares, stochastic and hill-climbing methods for evaluating parameters and Froment and Bischoff [16] summarise some of the more common methods and warn that ordinary moments matching-techniques appear to be less reliable than alternative procedures. References 72 and 73 are studies of the errors associated with a selection of parameter extraction routines. 

For the optimization of, for instance, a tablet formulation, two strategies are available a sequential or a simultaneous approach. The sequential approach consists of a series of measurements where each new measurement is performed after the response of the previous one is knovm. The new experiment is planned according to a direction in the search space that looks promising with respect to the quality criterion which has to be optimized. Such a strategy is also called a hill-climbing method. The Simplex method is a well known example of such a strategy. Textbooks are available that describe the Simplex methods [20]. 

One can consider product optimization as a type of "hill climbing." The product models in Table 4 each represent a hill or a surface, with one hill or surface for each attribute. 

EXAMPLE OF HILL CLIMBING OPTIMIZATION TO MAXIMIZE PURCHASE Best Formulation (Viz Highest Purchase) At Each Iteration... 

It is a characteristic of most iterative methods that their performance is strongly correlated with the values chosen for adjustable parameters. Thus, the step size in a hill-climb must be selected with care (and perhaps adjusted as the calculation proceeds) to ensure that movement across the search landscape is neither so languid that the task of locating the maximum is unreasonably drawn out, nor so volatile and unpredictable that the search is unable to settle on a maximum. Mathematical recipes sometimes exist which specify how the values of adjustable parameters in iterative algorithms should be chosen, or how they can be optimised as the calculation proceeds. 

Fig. 2 Searches across a colour wheel a random search b exhaustive search c hill-climbing d evolutionary search...

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