Famously in 1962 the mathematician Richard Hamming stated that 'The purpose of computing is insight, not numbers'. A similar statement, with "computing" replaced by "mathematical programming", was repeated in 1976 by Arthur Geoffrion, further emphasizing that true insight learnt from research has to with "why?" rather than "what?". What Hamming and Geoffrion were trying to tell us was, of course, that we cannot only focus on producing results, but to understand their consequences, and to put them in perspective by learning more about the nature of the system we are studying. Geoffrion asks us to reduce the complexity of the system until we do understand it, so that the output can be deduced to be a reasonable consequence of the input. Whenever a system or model is extended from a previous one, in which we have good knowledge, such studies are necessary. A further giant among scientists, active in transportation science, also contributed many years ago by stating that entire journals devoted to transportation science merely produce papers full of numbers without any REAL problem having been solved. So several voices have spoken out about the poor state of scientific research.
As it turns out much research, which is nowadays being performed and articles being written as a consequence, is the result of not much thought. To take an example from numerical analysis, a new algorithm for a known problem is claimed to be X% faster than an earlier one, where the claim stems from the result of tests on a small set of, seemingly, arbitrary numerical examples for which we do not really know the background, or degree of realism. From such studies conclusions are drawn which - to be perfectly honest - cannot be drawn with significance, because the numerical analysis is almost always far too weak to be credible, and it is based on too few or too unrealistic cases. Even more seriously, very few who produce these articles seem to be *really* interested in a credible answer to the question - it has come too far from practical applications, and to establish a strong relation between, say, two algorithms on the same problem would take far too much work for anyone to bother.
I fear that research publications are turning away from trying to actually answer an important question, and that we all are turning into lab mice running the treadmill. And seriously - even the guys in lab coats observing us - i.e., the reviewers and editors of journals - buy what we do, since they apparently need to fill their volumes with something. Does anyone want to contradict me, or provide further insights into this? I think it is a hard question, and it eats at the conscience of at least some researchers.
I think that I can agree on some of your thoughts. Yes indeed everyone chooses-quietly-a subset of the reality, particulary that with the best fitting property for his/her algorithm. When I was developing my ESE & EDE methods (see http://arxiv.org/abs/1206.5478v2 ) I was tryimg to capture even the most hard cases of curves. After reading literature, not for inflection point investigation, I realised that they took just one case (for example a parabolic curve) and presented the 'so better fit' of their algorithm...
I think it is a kind of 'cover fraud' to present an algorithm with numerical experiments that only fit your method: If you want to be honest you have to include the greatest possible set of cases.
Your question has a second part too. The concept of 'insight' has been lost many years since now, because the publishing industry cares only for creating classes of methods and not solving problems globally.
Dear Michael Patriksson,
I want to present my answer to your consideration by commenting your key phrase
"But as it turns out much research, which is nowadays being performed and articles being written as a consequence, is the result of much less thought. A new algorithm for a known problem is claimed to be X% faster than an earlier one, as a result of tests on a small set of, seemingly, arbitrary numerical examples for which we do not really know the background, or degree of realism. From such studies we can seldom draw any real conclusions, not only because the numerical analysis is almost always too weak to be credible, but more importantly because no-one is *really* interested in the answer to the question - it has come too far from practical applications."
In my opinion, the 21st century must be the century of developments. From this point of view, at least in Computer Science, A PAPER MUST BE PRESENTED AS A FUNCTIONAL SITE. In order words, need to move from the Traditional Paper (e.g. in .pdf) to the Online Tool (e.g. in ASP.NET) in the Internet. This tool should be available to all people (researchers, practitioners, users) to solve their tasks (for personal data) just by clicking the link. Thus, your question can be solved completely by presenting functional sites that will solve the all problems you mentioned.
Let's assume you presented your functional site in the Internet. Then
1. If I'm a researcher and I'm interested to know about your Theory (Methodology, Solution Approach, Algorithm, and so on) in detail, then I will read your paper (e.g. in .pdf) from your site.
2. If I'm a practitioner and I'm interested to use your program in order to solve my task (for personal data), then I will use your tool.
3. If I'm a researcher and I'm interested to compare your output to my output for the same input data, then I will use your tool.
I want to observe, that the point "3." is very important to evaluate quality of your tool for arbitrary input data. This point must answer completely to your phrase "From such studies we can seldom draw any real conclusions, not only because the numerical analysis is almost always too weak to be credible, but more importantly because no-one is *really* interested in the answer to the question - it has come too far from practical applications."
In conclusion, I want address you to the link http://www.fedulov.ge/MIC_2011/Conception.pdf to read about my proposals a little bit more. This draft was written in Russian but you can use Google Translator ( https://translate.google.com/ ) to translate into English.
Dear Gennady, a suitable website for such a task is CRAN repository:
http://cran.r-project.org/web/packages/
For example I have the .pdf file for my theory (http://arxiv.org/abs/1206.5478v2 or https://www.researchgate.net/publication/228059400 )
and I have the package 'inflection' for its implementation:
http://cran.r-project.org/web/packages/inflection/index.html
Is there any reason to accept broadly the .asp standard?
Can you point out to us a full example of your proposal?
Thank you.
Article Developing methods for identifying the inflection point of a...
Dear Demetris,
a functional site can be consedered as a commercial or non-commercial Online Product for all people (researchers, students, practitioners, and usual users without any special knowledge). In other words, this product must be a conenient tool for all people but only for researchers. You can use any tool to create Online Product in the Internet. As example, I use ASP.NET as a very power tool to develp Online Product. At the moment, I have my "Bin Packing Online Tool" on the link http://www.fedulov.ge . This product was developed 2,5 years ago and has many disadvantages. But now I deveolped two commercial products on the links http://www.gpsline.ge and http://www.taxi.gpsline.ge . Now, I'm very interested to update essentially my Research Bin Packing Online Tool using accumulated knowledge and experience.
Dear Michael
Unfortunately I just saw this discussion today (by ref. from Gennady).
I absolutely agree with you all the way. Your comment is also much in line with the excellent article of Kenneth Sörensen about use of metaphors in meta-heuristics.
But my main aim here with this comment is to make you aware of some resent work by Australian professor Kate Smith-Miles. I heard her presentation at PATAT-2014 in York. That presentation was the high-point of the conference. Her idea: We can use statistics tools to evaluate and gain knowledge about (meta-heuristic) algorithms. Her work focus on evaluating the quality of meta-heuristics, which in my opinion is where the problems are greatest. I have attached the article.
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