HIERARCHICAL CLUSTERING APPROACH WITH HYBRID GENETIC ALGORITHM FOR COMBINATORIAL OPTIMIZATION PROBLEMS

Engineering field has inherently many combinatorial optimization problems which are hard to solve in some definite interval of time especially when input size is big. Although traditional algorithms yield most optimal answers, they need large amount of time to solve the problems. A new branch of algorithms known as evolutionary algorithms solve these problems in less time. Such algorithms have landed themselves for solving combinatorial optimization problems independently, but alone they have not proved efficient. However, these algorithms can be joined with each other and new hybrid algorithms can be designed and further analyzed. In this paper, hierarchical clustering technique is merged with IAMB-GA with Catfish-PSO algorithm, which is a hybrid genetic algorithm. Clustering is done for reducing problem into sub problems and effectively solving it. Results taken with different cluster sizes and compared with hybrid algorithm clearly show that hierarchical clustering with hybrid GA is more effective in obtaining optimal answers than hybrid GA alone.

Interval criterion for stability analysis of discrete-time nonlinear systems with partial state saturation nonlinearities

A generalization of sufficient conditions for global asymptotic stability of the equilibrium of discrete-time nonlinear systems with saturation non linearity's on part of the states in the case of interval uncertainties is considered. When using quadratic form Lyapunov functions, sufficient conditions based on the positive definite interval matrices are presented. In order to check this, a recently proposed method for determining the outer bounds of eigenvalues ranges is used. A numerical example illustrating the applicability of the method suggested is solved in the end of the paper.

Memoirs: The Physiology of Ecdysis in Rhodnius Prolixus (Hemiptera). II. Factors controlling Moulting and ‘Metamorphosis’

The five nymphal stages of Rhodnius prolixus are more or less alike. The adult differs markedly from the nymphs. There are thus two phenomena to be considered: simple moulting and moulting coupled with metamorphosis. 1. Causation of Moulting. Moulting occurs at a definite interval after feeding, only one meal being necessary in each stage. There is a ‘critical period’ in the moulting cycle (about 7 days after feeding in the fifth nymph, about 4 days in the earlier nymphs) and removal of the head of the insect before this period prevents moulting. The critical period corresponds with the time when mitotic divisions in the epidermis begin. The blood of insects that have passed the critical period contains a factor or hormone which will induce moulting in insects decapitated soon after feeding. It is suggested that this moulting hormone may be secreted by the corpus allatum, since the cells of this gland show signs of greatest secretory activity during the critical period. Stretching of the abdominal wall provides the stimulus which causes secretion of the moulting hormone. This stimulus is conveyed by nerves to the brain: moulting is prevented by section of the nerve-cord in the prothorax. Section of the nerves between the brain and the corpus allatum appears to prevent moulting; but these experiments were inconclusive. Insects sharing the same blood moult simultaneously. The whole process of growth must therefore be co-ordinated by chemical means; the factors concerned being produced presumably by the growing cells themselves. 2. Causation of Metamorphosis. If fourth or even first nymphs, decapitated soon after feeding, receive the blood from moulting fifth nymphs, they suffer a precocious metamorphosis and develop adult characters. Metamorphosis is therefore brought about by chemical differences in the blood. If fifth nymphs decapitated soon after feeding receive blood from moulting fourth nymphs, they also moult; showing that the moulting factor is the same at all stages. The absence of metamorphosis in normal nymphs before the fifth stage must therefore be due to an inhibitory factor or hormone in the blood. This is proved by the fact that if a fifth nymph decapitated soon after feeding receives the blood from a moulting fourth nymph (not deprived of its head) it develops characters much more like those of a nymph than an adult. The inhibitory hormone is normally produced in such small quantities that simple dilution of the blood of a moulting fourth nymph with that of another fourth nymph (decapitated soon after feeding) causes them both to suffer metamorphosis. The head is necessary for the secretion of the inhibitory hormone. This hormone seems to be secreted after the moulting hormone. Thus if series of fourth, third, second, or first nymphs are decapitated around the critical period, some of them show more or less complete metamorphosis. Others show characters intermediate between those of nymphs and adults. The bearing of these results on the phenomena of diapause and prothetely is discussed.

The behaviour of crystals and lenses of fats on the surface of water.—Part II. The effect of temperature on the equilibrium pressure

In Part I a study was made of the rate of spread and unimolecular nature of films of fatty substances, containing a long hydrocarbon chain and a polar “head,” over a surface of pure water or of N/100 HC1. It was shown that after a definite interval of time, the surface became saturated with a unimolecular film in equilibrium with either a crystal or a lens of the substance in question, and that the time taken to attain equilibrium as well as the equilibrium surface tension was a function of the temperature. In the present paper the effect of increasing temperature on the two-dimensional equilibrium pressure is considered in detail.

Magnetic storms of March 7-8 and August 15-16, 1918, and their discussion

§1. A recent paper described the records obtained at Kew and Eskdalemuir Observatories of a world-wide magnetic storm which occurred on December 16-17, 1917. The outstanding feature was the much larger size of the disturbance at the more northern station. This seems a general fact, of which the two magnetic storms discussed in the present paper afford further evidence. They were two of the principal storms of 1918. Their joint discussion affords an opportunity of emphasising the variety in the phenomena exhibited by storms of the same class. The results differ so much from some which Dr. S. chapman has given in a recent paper as representative of world-wide magnetic storms, that it may not be amiss to explain that the two storms were selected before the appearance of Dr. Chapman’s paper. The storm of March 7-8 was suggested by the kindness of the Director of the Meteorological Service of Canada in sending me, unasked, copies of the D (declination), H (horizontal force), and V (vertical force) curves from Agincourt (near Toronto). Eskdalemuir curves for that date and also for the second storm, which occurred on August 15-16, were kindly supplied by Dr. Crichton Mitchell. The Eskdalemuir magnetographs record N (north component) and W (west component), instead of H and D as at Kew and Agincourt. The simplest way to a comparison was to calculate H and D changes at Eskdalemuir from the observed N and W changes. The two storms are undoubtedly of the kind discussed by Dr. Chapman, according to whom “apparently all great world-wide magnetic storms commence simultaneously to within a few seconds, over the whole earth, although small local fluctuations may sometimes mask the commencement at particular stations.” All I think we can really say is that the particular form of disturbance known as a “sudden commencement,” or Sc, which precedes a considerable number of world-wide storms, appears simultaneously at all stations, to the degree of accuracy with which time can be measured on ordinary curves. This conclusion has been reached independently by several recent investigators, including Dr. Chapman and myself.§ Accuracy to half-a-minute in time measurements is a high claim, and tlie instant at which a movement becomes visible is not wholly independent of the sensitiveness of the instrument. If Dr. Chapman is correct in stating that all world-wide storms commence simultaneously, we must I think suppose that all have Sc s. If so, these must be “masked” more often than not. The existence of an Sc is important in relation to the question whether storms recur after a definite interval. When Mr. W. Maunder* claimed to have established a 27.3-day recurrence period, this aspect of the case was dealt with in a review of his paper which I contributed to “Terrestrial Magnetism.” Of the 276 storms in Mr. Maunder’s list for the period 1882 to 1903 only 77, or 28 per cent., were credited by him with an Sc. In many cases of world-wide storms disturbance seems to originate gradually. The storm of December 16-17, 1917, is a case in point. On that occasion the growth of disturbance was so rapid that I concluded “ its commencement may be accepted without hesita­tion as occurring between 8 h. and 9 h.” Often, however, differences of several hours occur in the estimate of the time of commencement made at different stations. Also, an Sc is only sometimes immediately followed by large disturbance. Often a comparatively quiet time intervenes between the Sc—which possesses at most stations a characteristic form—and the large movements, which in the absence of an Sc would be recognised as a storm. In some cases there is room for doubt whether there is a real connection between the Sc and the subsequent storm. There is all the more reason for hesitation on this point because, in a considerable number of cases, the Sc itself is the principal movement. It is followed in some instances by what I have described as a “crest.” In low or mean latitudes the Sc is mainly an H movement and is seldom visibly oscillatory, H undergoing a considerable rise in the course of a few minutes. The “crest” consists essentially in the maintenance of the enhanced value of H, the curve presenting a nearly level ridge for a considerable time, which may amount to several hours. A rapid fall, somewhat like an inversion of the original Sc, then ensues, and there may be no further disturbance worth mentioning.