Fitting in the weekly timetables of a moderately big or complex school is not an easy task. This is well known to those who have faced sometimes this problem and, to a greater extent, to those who have the responsibility to make so every year; a real puzzle has to be solved. But if it is difficult to find a solution that meets the minimum requirements, finding the best solution seems like an impossible task. And this is precisely the question we ask: Is it possible to make perfect timetables?
Clearly, and unfortunately, we must say that the perfect timetable is impossible and there are several reasons to affirm it. The first and most obvious is that any model for expressing what is sought will have imperfections. Indeed, the mathematical model through which a weight function is calculated to obtain the optimum timetable and its application to the elements included in the timetable: students, teachers, class units, etc., will always be an approximation to reality which, at best, will be estimated precisely corresponding to what is sought.
The second reason, and this is not so obvious, is that the set of solutions is so high that exhaustive searching is impossible, even for the fastest computer in the world.
Do you remember the paradox of the legend of the inventor of chess?
According to legend, a Persian king, who liked the game of chess, commanded to call his inventor to reward him for his ingenuity. The king recklessly told him to ask for whatever he wanted and the inventor answered: I settle for 1 grain of wheat for the first square of the board, 2 for the second, 4 for the third, 8 for the fourth and so on up to the 64 square of the board. That is the sum of the series 1+2+4+8… until completing 64 terms in geometric progression. The king thought that what he was asking for was a trifle and ordered to prepare the prize requested but doing the calculations they realized that it was impossible to fulfill the order, because the sum of the grains of the 64 boxes was nothing less than the amount of 36,893,488,147,419,103,231 grains. If in each Kilogram of wheat approximately 25,000 grains fit, then the result would be about 1,475,739,525,896 tons. If the largest freighter could hold up to 186,000 net tons, it would take about 8 million huge freighters to transport all the wheat. More than 1000 times the annual world production of wheat.
This paradox also occurs with the problem of making academic timetables; it seems that it would be relatively easy to try all possible solutions with a computer but, in fact, it is impossible. The point is that the number of combinations grows exponentially and it would take years of calculation, even with the most powerful computer, to go through them all. The processes that solve this puzzle are studied through a mathematical and computational discipline that tries to give the best possible solution, in reasonable times, to excessively complex problems.
The Peñalara GHC Timetable Generator for Educational Institutions uses a software capable of finding solutions and making them optimal in an extraordinarily effective way in short enough periods of time even in the most complicated cases. The good news is that this type of intractable problems through exhaustive search processes can be solved to a large extent using intelligent algorithms. Finally, we can state with great satisfaction and relief for those who have the responsibility of making the timetables each course, that the ‘perfect’ timetables, in practice, are possible.
Thanks very nice blog!
Very good blog post. I certainly appreciate this site.
Thanks!
Weight is everyone of the most vital problems of the novel world. It has already reached wide-ranging proportions in some countries. In Russia, concerning 47% of men and 52% of women busy with overweight. Excess consequence is not just a fault in appearance. It can movement multitudinous physiological or subliminal disorders. To prepare e dress rid of essentials fat, you outset need to metamorphose your eating habits.
slim as a remedy for corpulence
What is the liable to be of grossness
Grossness is due to the fact that the amount of viands entering the heart of a up to the minute person significantly exceeds the amount needed for dash production. As a development, the left unaccustomed to even out is transformed into fat. The nobility of the food you sup also matters. If the slim is based on indubitably digestible carbohydrates, they force certainly be deposited in the bearing of ugly folds.
Excess http://nastuska-natuska.blogspot.com/2013/04/1.html charge should not be enchanted plainly as a visual disadvantage. It is a risk influence as the development of many diseases. The more adipose tissue grows, the stronger its bad essentially on the body.
Notice: patients with overweight are three times more likely to suffer from diabetes, twice as favourite to suffer from pathologies of the liver and the cardiovascular way, compared with people with normal weight.
Obesity is a systemic http://server974265.nazwa.pl/kadraknurow/index.php/forum/cras-ut-turpis-libero/1507-podstawy-wlasciwego-karmienia-dla-utraty-wagi virus, it can influence the masterpiece of all internal organs.
Among the diseases that instigate http://elka54.ru/forum/?PAGE_NAME=profile_view&UID=97339 overindulgence force:
hypertension;
Alzheimer’s disease;
strokes;
arthritis;
manful helplessness;
phlebeurysm;
angina;
respiratory pathology;
depression;
beauty sleep apnea (abrupt cessation of breathing during sleep);
heart attack;
gallbladder pathology;
osteoarthritis;
diseases of the digestive sermon;
atherosclerosis;
menstrual irregularities.
It has been scientifically proven that paunchiness increases the strong of developing cancer of the heart and thyroid glands, colon, gallbladder, and kidneys. The relationship between over-abundance force and malignant neoplasms of the esophagus, as well as the endometrium, is most evidently traced. On usual, heart bulky reduces a person’s life expectancy on 12-15 years.
The picture is aggravated past the details that obese people bear a metabolic breach of the peace – this slows down the process of losing weight. But the condition is reversible. Exact the heaviest weight can be “lost”. To do this, you opening paucity to interchange the diet. The cardinal mistake tons people make is that they try to thoroughly pass by food. As a result, fasting periods are replaced close breakdowns. Consequence returns in true level greater volumes, health problems arise. The number of a fast inasmuch as an obese person should be handled by a professional nutritionist.
Weight is everyone of the most necessary problems of the novel world. It has already reached pestilence proportions in some countries. In Russia, beside 47% of men and 52% of women actual with overweight. Excessive consequence is not just a blemish in appearance. It can issue myriad physiological or unconscious disorders. To get rid of body paunchiness, you first extremity to metamorphose your eating habits.
diet for grossness
What is the peril of size
Bulk is anticipated to the details that the amount of food entering the heart of a up to the minute личность significantly exceeds the amount needed for dash production. As a follow-up, the unused balance is transformed into fat. The nobility of the food you eat also matters. If the abstain is based on indubitably digestible carbohydrates, they resolution certainly be deposited in the bearing of ugly folds.
Excess http://ciitcluster.blogspot.com/2016/09/how-to-add-responsive-head-slider-to.html charge should not be taken plainly as a visual disadvantage. It is a hazard aspect for the situation of diverse diseases. The more adipose chain grows, the stronger its bad essentially on the body.
Notice: patients with overweight are three times more proper to suffer from diabetes, twice as suitable to suffer from pathologies of the liver and the cardiovascular organized whole, compared with people with common weight.
Obesity is a systemic https://zhshops.com/home.php?mod=space&uid=9843 virus, it can influence the masterpiece of all internal organs.
Total the diseases that encourage http://www.tvoidom.galaxyhost.org/forums.php?m=posts&q=25305&n=last#bottom overindulgence weight:
hypertension;
Alzheimer’s ailment;
strokes;
arthritis;
man’s debilitation;
phlebeurysm;
angina;
respiratory pathology;
dent;
sleep apnea (brisk cessation of breathing during sleep);
heart begin;
gallbladder pathology;
osteoarthritis;
diseases of the digestive tract;
atherosclerosis;
menstrual irregularities.
It has been scientifically proven that plumpness increases the distinct possibility of developing cancer of the knocker and thyroid glands, colon, gallbladder, and kidneys. The relationship between remaining burden and harmful neoplasms of the esophagus, as indeed as the endometrium, is most undoubtedly traced. On average, substance fat reduces a person’s life expectancy at hand 12-15 years.
The situation is aggravated by the fact that obese people comprise a metabolic clutter – this slows down the change of losing weight. But the place is reversible. Even the heaviest value can be “puzzled”. To do this, you first paucity to interchange the diet. The ranking misapprehension various people set upon is that they strive to thoroughly repudiate food. As a conclusion, fasting periods are replaced via breakdowns. Weight returns in equable greater volumes, haleness problems arise. The number of a slim on an chubby личность should be handled by means of a mavin nutritionist.