By Dr. Zbigniew Michalewicz, Dr. David B. Fogel (auth.)
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Extra info for How to Solve It: Modern Heuristics
All it "knows" is the information that you provide in the evaluation function, the representation that you use, and the manner in which you sample possible solutions. If your evaluation function doesn't correspond with the objective, you'll be searching for the right answer to the wrong problem! The point x that satisfies the above condition is called a global solution. Finding such a global solution to a problern might be very difficult. , the SAT, TSP, and NLP), but sometimes finding the best solution is easier when we can concentrate on a relatively small subset of the total (feasible or perhaps also infeasible) search space.
It seems that all three cases are reasonable and all three values found for p make sense! Yet they're all different! How can this be? Still, all of these possible solutions are correct. It just depends on how you model the possibilities for how you'll generate a random line. The reason is that each model makes implicit assumptions about the way in which a line is "thrown" at the circle. Can you make them explicit in each case? We'll give you the answer for the first possibility: the assumption is that the midpoint of the line L can occur at any interior point of R, and that no points or regions are favored over any others.
Why Are Some Problems Difficult to Solve? The travel time depends on many factors. For example, you might be lucky and make all of the green traffic lights along the way. Or you might be unlucky and not only hit the red lights but also get stuck behind a slow-moving truck. Worse, you might get a flat tire, which would add a significant amount of time to your trip. All of these possibilities, and an unimaginable number of other outcomes including the weather, road conditions, traffic accidents, emergency vehicles requiring you to pull aside, a train on tracks crossing your path, and so forth, can be described under the heading of noise or randomness.