Considering i have the algorithms implemented in c language.,what could be the next step of comparing the algorithms. Id like to measure its efficiency .
You need to create, or assemble from existing sources, a large selection of (known) test problems with a variation in size, complexity, and (I guess) application areas. The test set instances that you create have to "span" the territory of problems that you are interested in, with respect to size, variations in data, and so on. Depending on the type of problem you are interested in you may have to assemble data from practice, or at least make your very best efforts to create randomized test cases that span the problem instance domain as well as possible. (There is no way that you can publish a paper based on numerical experiments, if the test problems and algorithms are not VERY well selected, thought through, and are in the best possible way representing a set of problems that researchers are also INTERESTED in.) When you report your findings you also need to be very careful, so that you do not make any unsupported claims. (It's partly for that reason the your test cases need to be very well designed.)
How would you then present your results, one might wonder? First, as you are dealing with heuristics, there is a potential problem in comparing the algorithms that you will implement. If you do not also utilize a deterministic, and globally optimizing, code for your problem, you will have no idea whatsoever how far the output from your solvers are from being optimal, and hence your conclusions will be worth nothing at all (except to say, perhaps, that algorithm A "appears" to be better than algorithm B on your test cases). That kind of conclusion is not valid, and is also rather uninteresting. What you need to do is to let more algorithms - from a variety of territories and domains - compete. Then, you will be able to tell whether the heuristics that you implemented are, for example, ten times faster in reaching a "good enough" solution to your problem than a branch-and-bound solver (for example).
This business is quite tricky, and you do want readers to feel that you have done a very solid work.
Good luck!
compare the results in terms of converging speed, accuracy, NFE, time etc
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