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surface (one that can be approximated locally by a convergent power series) having hills that must be climbed More sophisticated implementations go further, commonly assuming that the fitness function can be well approximated locally by a quadratic form If a fitness function satisfies this assumption, then much faster convergence to a solution can be achieved However, when the fitness surface has many irregularly shaped bills and valleys, quadratic forms often fail to provide a good approximation In such cases, the more sophisticated methods break down entirely or their performance seriously degrades Worse than degraded performance is the problem of local solutions Almost all analytic methods, whether elementary or sophisticated, are easily trapped by local maxima: they generally fail to locate the globally best solution when there are many hills and valleys in the fitness surface.

Members who shop only in the deli and not in the produce department will get a special certi cate giving them $1 to spend in the produce department This will get luncheon shoppers to buy stuff to take home This $1 is awarded only to the deli-only shoppers Other certi cates will get produce shoppers to use the deli Lapsed members who spent a lot but who have stopped buying for 6 weeks will get a special offer to encourage them to come back to the store..

Least-squares, neural network predictive modeling gives rise to fitness surfaces that, although clearly analytic, are full of bumps, troughs, and other irregularities that lead standard analytic techniques (including back-propagation, a variant on steepest ascent) astray Local maxima and other hazards that accompany such fitness surfaces can, however, be sidestepped by cleverly marrying a genetic algorithm with an analytic one For titness surfaces amenable to analytic optimization, such a combined algorithm can provide the best of both worlds: fast, accurate solutions that are also likely to be globally optimal Some fitness surfaces are simply not amenable to analytic optimization More specifically, analytic methods cannot be used when the fitness surface has flat areas or discontinuities in the region of parameter space where a solution is to be sought Flat areas imply null gradients, hence the absence of a preferred direction in which to take a step.

Shoe stores, dress stores, department stores, bookstores, and other types of stores have used loyalty programs with some success. Here, however,

At points of discontinuity, the gradient is not defined; again, a stepping direction cannot be determined Even if a method does not explicitly use gradient information, such information is employed implicitly by the optimization algorithm Unfortunately, many fitness functions of interest to traders-including, for instance, all functions that involve net profit, drawdown, percentage of winning trades, risk-to-reward ratios, and other like items-have plateaus and discontinuities They are, therefore, not tractable using analytic methods Although the discussion has centered on the maximization of fitness, everything said applies as well to the minimization of cost Any maximization technique can be used for minimization, and vice versa: Multiply a fitness function by - 1 to obtain an equivalent cost function; multiply a cost function by - 1 and a fitness function is the result.

Malignant cells can spread, or metastasize, to other parts of the body through the lymphatic system or bloodstream If they are not stopped, the malignant cells of metastatic cancer can migrate and infiltrate the brain, lungs, liver, bone marrow, and other vital organs Benign tumors, although they are not classified as cancer because they do not invade other tissues, have been known to progress to cancer or become malignant Typically, benign tumors are not a threat to life unless they arise in the brain or other vital organs In the United States, skin, lung, colon, prostate, and breast are the most common types of cancer The number of new cases of cancer in this country is increasing each year People of all ages get cancer However, middle-aged and elderly people are most often affected because of the long latency period of cancer (ten to thirty years).

the process is more complicated and often less rewarding than it is for supermarkets or travel-related businesses Let s take the DSW Shoe Warehouse I bought four pairs of shoes from its store in Fort Lauderdale The store gave me a DSW paper card that I could use to get further bene ts I have never used it since after all, I am not the shopper in our house Helena is But what has happened is that I now think of DSW when I think about shoes It is because of the card, I think I am sure that this card does affect customer behavior in a positive way The rewards to the retailer are: Some people will return and use the cards to buy more products Some will remember the store because of the card, and may buy more products.

If a minimization algorithm takes your fancy, but a maximization is required, use this trick to avoid having to recode the optimization algorithm Linear Programming.