Chill-Block Melt Spin Technique: Theories & Applications
In this connection use is made of the established process of melt spinning. Traditionally amorphous metals in the form of macroscopic bands are produced. In the present invention the melt spinning process is modified in the following ways: - the nozzle geometry is especially selected to reduce and control the quantity of molten metal falling onto the circumferential surface of the rotating wheel per unit axial width of the circumferential surface,.
The surface topography of the wheel, the forces which arise due to surface tension and in particular the high centtrifugal forces bring about the control of the de-wetting laterally of the wheeel surface and perpendicular to the axis of rotation. Different process parameters result in different thicknesses and thickness distributions of the metal fibres.
In this connection the reduction of the deposition rate of the metallic melt onto the wheel by a smaller nozzle width, by an appropriate applied pressure to expel the metal melt from the crucible and an increase in the peed of rotation of the wgheel lead to a significant reduction of the fibre thicknes. The smaller theoutlet width of the nozzle the finer are the fibres produced. EP-A-1 is directed to the manufacture of magnetic ribbon by the melt spin process.
For good magnetic material oxidation must be prevented. For this reason the process is operated under inert gas. This inert gas disturbs the process of making uniform layer thicknesses, which are in turn important for the magnetic properties of the material. It is important to note that EP-A-1 discloses a nozzle with a circular orifice. The EP document utilizes a technique by which the gas is directed away from the ribbon on the roll. For this purpose grooves are provided on the wheel. The generally circumferential grooves have an average depth in the range 0.
No real information is given on the width of the ribbons. JP-A discloses a similar concept for removing air from the forming ribbon, but here the grooves are arranged in chevron form V form on the surface of the wheel. So far as can be seen there is no discussion in either of these patent specifications that the ribbons should be constrained laterally widthwise nor any suggestion as to how this can be done. In both documents JP-A and EP-A-1 the inventors are concerned with recesses in the surface of the wheel to lead gas away from the wheel surface and the metal and to increase the contact area between the wheel surface and the metal EP-A-1 [, ] and JP-A EP-A-1 explicitly states that the grooves should have a depth of 0.
This is a clear indiction to the person skilled in the art that he should not increase the groove depth beyond the value quoted. That this can be achieved can be seen from the median values and the standard deviation values entered in Fig. Neither reference suggests that recesses could be exploited to generate a lateral constriction of the ribbons, so that fibres are formed. Both references show relatively wide ribbons with a width much greater than their thickness, see EP-A-1 , Fig. EP-A-1 admittedly gives no accurate value for the width of the ribbons, however one can conclude from Fig.
Furthermore, the Figs. The apertured surface structure in Fig. Wider spacings allegedly lead to a poorer removal of the air and thus to a poorer result. In both documents the manufacture of the powdery magnetic particles is based on a comminution process which follows the melt spinning process. This has nothing to do with the melt spinning process itself. It is a completely different application of the melt spinning process and the prior art references are simply not concerned with the prepara- tion of fibres to which the present application is directed.
EP-A-0 describes the coiling of a wire which is created by extrusion through a nozzle in a melt spinning apparatus. The Liebermann reference "Liebermann h. The structured circumferential surface of the wheel may also comprise peripherally circumferentially extending lands, each land being disposed between two circumferen- tially extending recesses. The presence of such lands forms a reservoir of melt material between the circumferentially extending edges and this material can be concentrated into the metal strands by the capillary action generated at the edges. Thus the presence of the lands and their width can be selected to influence the width of the metal strands that are produced.
The lands typically have widths of I mm or less. The lands also provide surface area for additional heat removal from the molten metal and can thus also influence the size of the strands produced, since the size does not change after solidification has taken place. The cross-sectional shape of the recesses does not appear to be critical. Thus the recesses can have a cross-sectional shape selected from the group comprising semi-circular, symmetrically v-shaped, asymmetrically v-shaped, rectangular and trapezoidal.
The volume of the recesses is, however, another important criteria determining the width and thickness of the metal strands that are produced. For the sake of completeness reference should also be made to two further prior art documents: DE describes a method of making a round wire by a melt spinning process. In that method the circumferential surface of a rotatable wheel is provided with a groove extending in the direction of rotation and a plurality of nozzles aligned in series along the groove are used to deposit molten metal into the groove as the wheel rotates. This document does not disclose the function of utilizing the edges formed by the groove to separate a stream of molten metal into thin strands or ribbons of material by appropriate choice of the operating parameters such as the surface speed of the wheel.
US patent 6,, describes a way of making metal fibres by "dropping a metal plate vertically onto the blades of a rotary disc thereby extracting metal fibre therefrom". The metal plate passes through a pair of induction coils which has a melting function but there is no description of molten metal being dispensed onto the blades of the rotary disc. The structure and dimension of the blades are not indicated in the above mentioned patent.
The reference does not discuss the use of a nozzle of defined geometry which is an important feature of the present invention, nor does it discuss the use of a profiled circumferential surface having a defined structure or geometry, another important feature of the present invention. Also there is no discussion of the metal plate being completely melted. In contrast, the melting of the metal upstream of a nozzle is another important feature of the invention as it allows a controlled gas pressure to dispense the molten metal through a nozzle of defined geometry, which is not present in the reference.
The nozzle geometry and amount of pressure applied to the liquid metal regulates controls the amount of liquid metal material which passes through the nozzle and hits the rotating wheel. This control is critical for obtaining small fibre width dimensions and controlling the geometry as well as the distribution of geometry dimensions small distribution! Certainly it is not clear that the referenced operates with liquid metal.
Although the word "melt" is used it seems to be more important for the authors of the reference that a solid metal plate is in contact with the blade, although the end of the plate might be in a melted or softened state. The reference also does not disclose the inventive concept of separating the solid metal from the liquid metal.
The reference does not disclose the concept of dispensing a drop of molten metal and does not provide any way of controlling the volume of metal brought into contact with the rotating blade. There certainly does not seem to be any disclosure of the controlling of the amount of metal deposited on the blades. In addition there is no suggestion in the reference that edge effects be used to generate metal ribbons.
Equally there is no disclosure of the use of appropriate wheel speeds to ensure the specific metal being used is separated into ribbons of the desired size. This is again an important element of the present invention, namely that the wheel speed is selected in dependence on the nozzle size, the gas pressure and the specific metal being converted into ribbons of the desired size. The rotatable wheel is usefully temperature controlled and preferably cooled e. Controlling the temperature of the wheel permits the solidification rate of the molten material to be controlled and this again favors the manufacture of uniform metal strands.
The wheel is expediently made of a metal, for example copper or aluminium, or of a metal alloy or of a ceramic material or of carbon such as graphite. Also layers of one of these materials on a base wheel are possible such as carbon evaporated layers on a copper base wheel. Such materials have good thermal conductivity which again favors the solidification process. If desired the structure of the circumferential surface of the wheel can be made by lithographic technique which can enable sharp structures of small dimensions to be made more easily than by milling or turning.
The wheel is conveniently mounted to rotate within a chamber having an atmosphere at a pressure corresponding to the ambient atmospheric pressure, or to a lower pressure than ambient pressure or to a higher pressure than ambient pressure.
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The atmosphere in the chamber affects the formation of the solidified metal strands and can be used to fine tune the geometry of the metal strands that are produced. For metals which react with the constituents of air it can be favorable to use an inert gas atmosphere in the chamber. Also, under some circumstances a reactive gas atmosphere could be beneficial, for example a nitrogen or carbon containing atmosphere could be used to nitride or carbu- rize suitable steel materials if hardened metal strands are desired. A deflector such as a scraper blade or doctor blade can optionally be provided upstream of the nozzle in the direction of rotation of the wheel to deflect boundary air from the circumferentially extending surface prior to depositing molten metal on the surface via the nozzle.
Such a deflector, which only needs to have a minimum spacing from the circumferential surface of the wheel to avoid damaging the structure thereof and the function of which can also be provided by the nozzle if this is positioned close to the circumferential surface of the wheel , can prevent the boundary air carried along with the wheel from undesirably affecting the flow of molten metal from the nozzle onto the circumferential surface, for example thereby reducing cooling of the metal material prior to it reaching the surface of the wheel.
Generally speaking a gas pressure is applied to the molten metal to force it through the nozzle. The additional gas pressure additional to the weight of the molten metal causes the molten metal to flow through the nozzle. When reference is made here to the pressure applied to the molten metal the pressures recited will be understood to be the amount by which the pressure is higher than the pressure prevailing in the chamber of the apparatus, which is frequently kept below atmospheric pressure, e.
The gas pressure is typically selected in the range from 50mbar to lbar overpressure relative to the pressure external to the nozzle. The gas pressure regulates the deposition rate of molten metal onto the rotating wheel. This parameter controls the dimension of the metal ribbon as well. The nozzle expediently has a rectangular cross-section having a width in the circumferential direction of rotation of the wheel of less than 1 mm. The length direction of the nozzle is oriented perpendicular to the direction of rotation of the circumferential surface of the wheel.
An electric motor is conveniently used to drive the wheel at a frequency up to 95Hz for a wheel having a diameter of mm, i. The circumferential surface of the wheel may have transversely extending features to control the length of the strands produced. Such features could for example comprise a number of transverse, regularly spaced, grooves interrupting the circumferentially extending edges and recesses at the circumferential surface of the wheel. The material of the wheel is selected so that it does not readily bond to the molten metal, for example a wheel of copper can be used for Fe40Ni40B20 alloy, aluminum, or lead.
In the melt spinning process of the invention one applies the metallic melt through the opening of a crucible onto a very quickly rotating metallic wheel. The wheel normally consists of copper and can be well cooled. In particular one can exploit the particularly strong capillary forces of metallic melts for the manufacture of strands of smaller diame- ter. One does not use a smooth spinning wheel but rather a melt spinning wheel, which is structured with elongate circumferentially extending grooves recesses. To a first approximation the lateral dimension of the resulting strand reflects the lateral dimension of the structuring of the wheel.
However, a further reduction of the quantity of melt which strikes the wheel per unit of time results in the amalgamation or collection of the quantity of metallic melt at a corner or an edge of the structure on the wheel as a result of the capillary forces that are acting. Thus the melt deposits along a corner such as an edge of a recess of the wheel or along the base of a recess in the wheel.
This makes it possible to obtain very much smaller geometries of the strands than might be expected from the dimensions of the actual structuring of the wheel. Thus, with a lateral structure size of 1mm it is possible to obtain a ribbon of 0. The deposition rate of the metallic melt on the copper wheel and the structuring of the wheel are thus of decisive importance for the invention.
The deposition rate of the metallic melt can be controlled by the speed of rotation of the wheel, by the size of the opening of the crucible and by the pressure with which the melt is pressed through the opening of the crucible. As the length of the nozzle opening transverse to the structured circumferential surface of the wheel extends typically over a plurality of grooves and or lands plural stands can be formed at any one time due to the lateral breaking up of the molten metal on the circum- ferentially structured surface of the wheel.
Reducing the width of the nozzle in the circumferential direction of the wheel reduces the amount of metal forming each strand per unit of time and thus results in the strands becoming finer, i. The structure on the wheel can generally be produced by a technical turning operation such as on a lathe, by milling or by laser ablation. The abrupt solidification of the metallic melt and the high centrifugal forces resulting from the rotation of the wheel lead to the capillary forces becoming unimportant and thus to the wire that is forming being flung away from the wheel, so that it can then be collected in a known collection device.
After the solidification of the melt the metal normally forms no droplets and the wire can now be further processed, e. Thus the melt spinning method can be combined with a method of manufacturing textiles. The web server setting is done as shown in Figure 1. Figure 1. It is based on the directory used to store database taken from JWNL package. Figure 2 shows the snippet. Package provided by JWNL is completed with all the needed files. WordNet retrieving configuration After the configuration is completed, those data are available through functions in the library. Meanwhile the lookupIndexWord function is the main lookup procedure to choose word type: Adjactive, Adverb, Noun and Verb.
The database is consisting of 17 interrelated tables. They are composed of nouns, verbs and adjectives. Figure 3. WordNet database structure In keyword searching, usually noun is referred. As an example, Figure 4 indicates sample of WordNet data from four tables. Tables involved are Word, Sense, Synset and Lexname. Table Word posses the word itself lemma and word number.
It has relationship with Sense table whereby this table list definition for the word. Definition is represented in number. Analyzing the definition from Sense need Synset table. Categories are obtained from Lexname table when a relationship reformed between Synset and Lexname table. Sample WordNet data The relationships of four tables in Wordnet are displayed in Figure 5 in database schema. Those relationships generate categories for certain keyword. Linking between tables to perform relationship will allow in acquiring numerous data from this ontology.
Figure 5. Wordnet database used in the implementation phase In this paper, example of process in finding depth from those data is shown. For the assimilation purpose, 'Java' keyword is used as a sample. WordNet as a lexical ontology is using hypernym-hyponym concept. It acts as a parent-child relationship. Traversing through the hypernyms of word will contribute in depth searching.
To facilitate in illustration, every word, sense and synset is represented with number. Figure 6 shows the route from word to root for 'Java'. Synset in WordNet with hypernyms Word 'Java' has three different meaning called sense. Figure 6 shows the three different routes. For simplicity, only Java programming language depth is calculated. SQL is used over WordNet database and recursive technique is utilized in acquiring its depth.
Figure 7 is the SQL command. The depth value can be used in other applications including similarity measurement between ontologies. The benefit of using this method is the ability in processing complex query. Developers accept it as the strength of SQL. Nevertheless, the technique gives slower results compared to the APIs or libraries.
Web Ontology Language OWL is chosen due to the capability in representing and reuse of domain knowledge. This new concept is capable in sharing information structure among people, machines or applications. Viewing this file in the form of OWL is shown in Figure 8. Furthermore, it is free open source. However, Wordnet. Data from this ontology is accessible in two ways. First is using Jena Inference. It has the ability to do complex query. Although by using inference, results can be obtained in a simplest way, yet, inference engine has not established to provide comprehensive query.
The SSE is developed using user profiling and domain ontology concept by utilizing semantic similarity measurement discussed in . Table II shows the characteristics of the search engines. Slurp and bingbot as crawler SSE User profiling and domain ontology Google is an internet-related services and products. Search engine is one of its popular invented products using PageRank technology. Meanwhile Yahoo! Previously, Yahoo!
Slurp and the latest crawler is Bingbot. Google and Yahoo! Search have been giving ultimate benefits to internet searchers since and respectively. However, distinct features in SSE have advantages in terms of ontological concept, categorization and user profiling. It is capable to give categorized and personalized results.
Google is giving millions of results when 'Java' keyword is entered as shown in Error! Reference source not found. Results from Google using keyword 'Java' Figure Results from Yahoo! Additionally, these results are mixed up in different categories. Therefore, SSE is proposed in this paper. Three categories are listed they are Object-oriented programming language, Beverage and Island.
The categories are based on the keyword entered. Each chosen category will produce results on the right side of the application related to the keyword and category. Approximattely, search engines e give ten t 10 linkss or web pagees per page. Figure These data are coompared with h other searchh engine. In this stage, G Google and Yahoo!
Y are used as comparison. Thhis is based onn first f links givven. Google only gives 84 links l out of links whille Yahoo givees Figurre Results for Programming P Langguage category forr three different seearch engines. Tablee III listed nu umber of weeb pages provvided by the three search engines. SSE E gives maxiimum number n which is ten 10 links l for everyy pages whilee Google and Yahoo give lless than that.
For exam mple, Googlee uses Page P Rank allgorithm that listed popularr web pages oon the higher list of resultss. Java Prograamming Langguage is i highly seleected by inteernet users thhat make it popular p basedd on that algoorithm.zq-dev.quadmetrics.com/3548.php
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Thereefore, Googlee and Yahoo! Y are still s giving much m number of links for this categoryy. However Beverage caategory of Jaava in Figure F 14 shoows significannt reduction in i results acquuisition. Gooogle only givees six 6 resuults out of first web w pages whhile Yahoo! Resuults for Beverage ccategory for three different d search enngine Table IV shows resultts from Java category Beeverage for eaach page.
SS SE gives bettter results whhen it comes c towardds personalization using user u profiling.. Various techniques can be done in manipulating the data. The attempts can assist in addressing issues in handling over increasing data and internet users. SSE is one of the alternative search engines for better information retrieval and managing information when it comes towards personalization using user profiling.
The future work for this research is to test our SSE on the Cloud for its response time and usage as well as its relevant results. Internet World Stats. Introduction to information retrieval Vol. Cambridge: Cambridge University Press. Introduction to semantic search engine. In Electrical Engineering and Informatics, International Conference on Vol. The effect of user characteristics on search effectiveness in information retrieval. Toward the semantic search by using ontologies. CCE Baaldeeb gmail. Norita usim. IWD is a recent metaheuristic population- based algorithm belongs to swarm intelligent category which simulate river system.
Examination timetabling is a combinatorial optimization problem that concerns with allocating exams to timeslots efficiently. As an initial study, the IWD Algorithm is tailored to solve uncapacitated examination timetabling problem by using carter dataset and is able to produce acceptable results, though they were not better than those already reported in the literature. Some examination timetabling heuristic methods such as Saturation degree concepts have been embedded in IWD to ensure the feasibility, while the IWD operators have been trigged to iteratively improve the results.
Index Terms— Scheduling, Uncapacitated Examination Timetabling problem, intelligent water drops algorithm. As the process requires an intricate detail with extensive efforts, the construction of a timetable can be an extremely complex task for managers and administrators. Hence, resolving the examination timetabling issues lead to a quality based timetable that give a significant impact on the quality of the associated institutions .
The examination timetabling problem is essentially defined as allocating the exams into a limited number of timeslots, while fulfilling the maximum number of constraints which differ greatly from institution to institution. Thus examination timetabling problems are differed in their size, complexity and constraints . In the timetabling literature, there are two categories of constraints: Hard constraints and soft constraints, as per following explanation: [15, 13].
It common to not find feasible solution that compliments the as they are differed from one institution to another, in its significance and types. At times, soft constraints conflict with each other. For example: o Exams which are conflicting are best to be split throughout the examination session in avoiding consecutive timeslots of the exams or two exams on the same day. A solution to and examination timetabling which do not discredit the Hard constraint is termed as feasible timetable. Therefore, they are omitted in the objective function [3, 9].
In computing terms, examination timetabling is a hard combinatorial optimization problem which originates from an NP-hard class for most of its variations. This problem usually incorporates a huge and rugged search space with substantial local optimal solutions . This makes it hard to lend itself to be tackled using classical methods .
Uncapacitated Examination timetabling Problem is emphasized in this paper. Over the last five decades, a wide variety of approximation techniques to resolve Uncapacitated Examination timetabling Problem have been established by the Artificial Intelligence and Operational Research communities. An extensive and exhaustive summary of these techniques has been provided by . Prior establishment were based on graph coloring heuristic methods that assigned exams to timeslots, one by one, based on the level of difficulty.
As a recovery approach to timetable with unscheduled exams, a backtracking method is often used with these techniques. Carter initiated the main research of Uncapacitated Examination timetabling Problem was initiated by incorporating several graph coloring heuristic methods to Uncapacitated Examination timetabling Problem .
Other studies incorporating graph coloring heuristic methods for Uncapacitated Examination timetabling Problem are also involved [6, 11]. Several meta-heuristic approaches have been established for solving UETP , classified into two main types, single- based approaches e. Surveys and overview have been conducted by Burke et al. Many researchers have shown interest on single-based approaches due to the ability of these approaches to utilize the search space in a short time, although these approaches are reported with limitations include it being easy to get stuck in local optima .
Based on the algorithms, population-based approaches can be divided into either Evolutionary Algorithms or Swarm Intelligence [1, 19] depending on the nature of the phenomenon simulated by the algorithm. The usual Evolutionary Algorithms have been applied for timetabling problems can be found in the following literature [8, 14, 17, 26]. In Shah Hosseini looked into establishing algorithms that model the natural phenomena of a swarm of water drops with the soil onto the river bed .
IWD is a population based technique inspired by nature optimization algorithm that replicates certain natural phenomena of a swarm of water drops with the soil onto the river bed. Over the course of five years, it was investigated that the utilization of IWD theory has shown tremendous success in various discrete optimization problems [5, 16, 20, 21, 29, 28] and machine learning tasks  leading to its application in continuous optimization problems . This is partly due to the fundamental benefit of IWD compared to other conventional optimization techniques [29, 31].
It incorporates a less complex although wholesome mathematical model. It is easily applicable to numerous optimization problems which is in conjunction to both discrete and continuous problems, instantly converging it to the optimal solution. It functions in constructing the solution of population based on the obtained data based on the familiarity iteration of the search instead of taking into account the refinement of the present population.
Hence, IWD is catered successfully to a variety optimization problem such as feature selection, TSP, Knapsack, however, based on its sophistication nature of optimization problems. The method has also been altered and hybridized to increase performance. However, it also need to be noted that the theoretical analysis of the behavior of IWD still under research . In this paper, the main aim is to investigate the applicability of IWDs algorithm for examination timetabling as an initial exploration of this method in scheduling domain.
Although the results not reached the state-of-the-art methods, possible improvement can be adopted in the future research to tweak the IWD operators, thus, producing more successful results. Water drops are observed to flow naturally in rivers forming huge moving swarms in which the water drops created the path of the movement. This is greatly influenced by the environment that result in the paths of the water drops being altered gradually and continuously so in the future.
Huge moving swarms formed by the following water drops are naturally observed in rivers. This can be exemplified in the case of hard soils environment resisting more than the soft soils. Therefore, the occurrence of the natural river phenomenon is based on the constant rivalry of the water drops in a swarm and the resistance of its surrounding water drops environment . Most of the rivers observed follow a twisted path with various turns which naturally guide the water drops to its destination, usually a lake or sea.
Having no obstacles along its paths, the water drops influenced by its environment is forced to gravitate to its surrounding matters in a straight line via the shortest path leading to the center of the earth . Velocity is the key characteristic to the water drop flow. By assuming that every water drop carries a proportion of soil, it is transferred from one place to another usually from the fast path to the slow path.
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As the removed soils taken out from the fast path, it creates a deeper indent which attract more water to be formed in that area. This lead to the removed soil carried by the water drops being disposed in the slower beds of the river. This assumption incorporates the natural flow of the water drop from one destination in the river to the next one with three considerable changes throughout the transition: a.
Increased velocity of the water drop. Increased soil of the water drop. The first two mentioned properties may differ during the lifetime of IWD. Throughout the course of its journey, it flows from the environment in which it removes some soil resulting in acceleration. Theoretically, it will flow in discrete steps from its present point to the next with an increase velocity by non-linearly proportional to the inverse of the soil between the two points. Hence, the lesser soil path allows the IWD to be faster than the one that has more soil .
Throughout the course of its journey, an IWD collects the Soil in the environment and remove it from the path connecting its two points. The quantity of the Soil added to the IWD is non-linearly proportional to the inverse of the time needed for the IWD to flow from its present point to the next. According to the laws of physics for linear motion, the time interval is calculated as proportional to the velocity of the IWD and inversely proportional to the distance between the two points.
Moreover, the portion of the environment that uses more IWDs will have fewersoil. It can be deduced that the soil is the source for the data obtained as the environment and water drops are both interrelated to the soil . In addition, based on the study conducted by Shah-Hosseini , it reveals that an IWD requires a mechanism to choose the path of its next point. Due to this nature, the IWD naturally prefers the paths with less soil rather than more soil. This characteristic of path selection is applied by imposing a uniform random distribution on the soils of the available paths resulting in the probability of the next path to be chosen is inversely proportional to the soils of the available paths.
Therefore, identifying the paths with less soil has an increased chance to be chosen by the IWD. Problem definition The Uncapacitated Examination timetabling Problem variation in this study emphasized on assigning a set of exams, each taken by a set of students, to a set of timeslots with determined hard H1 and soft constraint S1. H1: Conflicting exams whereby students cannot sit for two exams at the same time. S1: Exams spread out whereby the exams taken by the same student should be spread out across a timetable.
In Uncapacitated Examination timetabling Problem, the aim is to minimise the proximity cost function of soft constraint violation in a feasible timetable. The proximity cost function divides the penalty of soft constraint violations by the total number of students.
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This function will be described formally in the next section . Problem formulation Table 1 shows the notation for Uncapacitated Examination timetabling Problem formulation. This provides the quality of a solution in terms of how well the exams are spread. P The number of timeslots.
M The number of students. In graph coloring, the examination timetabling solution is represented as a graph of N nodes and the edge between the adjacent nodes represent the existence of sharing resource between the two exams . For example, Figure 1 shows a timetabling solution of 5 exams. In IWD, each node is exam, and the graph refers to a complete and feasible solution in examination timetabling.
For each IWD moving from node i to node j, update its velocity. Compute the soil. Update the soil. Number of IWD, which equal to the number of timetabling solutions. Initial Soil placed on the edges of the graph. Initial velocity that is prevalent for each water drop timetabling solution. Maximum number of iterations. Using this presentation via the graph, each IWD initiates its movement on the nodes exams of the graph along the edges neighboring exams between these nodes and constructing its own solution.
A complete iteration of the algorithm is based upon the completion of all IWDs. The iteration-best solution is established at the end of each iteration and it is applied to update the global best solution. The amount of Soil on the edges of is updated in regards to the quality of the solution. This is followed by a new iteration with new IWDs but with the same soils on the edges of the graph. When the algorithm reaches the maximum number of iterations itermax or reaches the expected quality it must stop.
Static parameters are the unchanged parameters during the search using IWD algorithm such as number of iterations, number of solutions and soil and velocity parameters whereas Dynamic parameters are interchangeable and they are reinitialized after each iteration of the IWD algorithm such as local best solution , global best solution , velocity, soil. In UETP the means that the best timetabling solution in the population which has the minimum penalty. The maximum number of iterations NI is specified by the user. The iteration counter NI is set to zero. The number of water drops number of timetabling solutions is set to a positive integer value.
Indeed  suggested to set the water drop equal the number of nodes Nc of the graph for example, if the number of exams is , the IWDs algorithm suggested to set the initial population size to However, in timetabling, the numbers of exams are normally large and to set the number of solution equal to number of exams might be affect the performance. Both parameters InitSoil and InitVel are user selected and they should be tuned experimentally for the application. Step 2: Initialization of dynamic parameters.
All IWDs are set to have zero amount of Soil. Step 3: Spread the IWDs randomly on the nodes of the graph as their first visited nodes; Restate, in UETP that we assign randomly timeslot from the timeslots range to the first exam for each candidate solution. Step 4: Update the visited node list of each IWD to include the nodes just visited. In UETP we updated the visited node exams that assigned by timeslots by assigned timeslot value to it and assigned -1 for all unvisited nodes exams.
We initiate -1 for all solutions as an initial value for all exams. Step 5: Repeat Steps 5. It is worthy to note that in UETP, the next exam i. In SD, the exam of the least number of available timeslots must be timetabled first . Step 7: Update the Soils on the paths form the current iteration-best solution by: 7 Update the global best solution by the current iteration-best solution using: 8 In UETP the global best solution is the solution that it has the lowest penalty on all iteration while the local best solution is the best solution in each iteration, it means that we will find the global best solution from all the solutions found by the IWDs solutions by comparing the value of local best solution by the value of global best solution then we will assign the value of local best solution to the if it was better than the old value for global best solution.
Step 8: Increment the iteration number by: 9 It was found that the IWD has displayed to have the property of convergence in value , enabling it to find the optimal solution if the number of iterations are adequately large. Of these, the most widely used are those given by Carter  for the uncapacitated exam timetabling problem. The characteristics of Carter dataset are shown in Table 3, in this research we implemented IWDs algorithm to all 12 datasets. The objective function adds a penalty for a timetable whenever a student must sit two examinations within a timeslots of each other as in Eq.
Based on the table, graph density is calculated as the ratio of the number of exams that clash with each other to the square of the total number of exams. Results for these problems are reported as average penalty per student. Andrew's Junior High School, Toronto 13 0. It is also worth noting that these parameters have been decided based on an intensive trial and error cases. The results of IWD have been recorded in Table 6. These results display the best and worst penalty value of ten different runs for each Carter dataset.
The proposed Intelligent Water Drops IWD Algorithm is compared with some published methods using the Carter datasets, known and available for the authors. The key of the comparative methods are summarized in Table 4. The numbers in bold show the best solution obtained for that Carter dataset lowest is best. The numbers in italic fonts indicate that a different dataset version was used.
Note that the results obtained by the proposed method are recorded in column 1 of the comparative table. In the IWDs Algorithm, the results unable to supersede those produced by heuristic, hyper-heuristic, local-search based, population-search based and memetic methods in 23 out of 12 Carter datasets shown in Table 5. It is due to this matter the heuristic and hyper-heuristic methods have not met the standard results obtained by the Metaheuristic -based methods in terms of solution quality.
Nevertheless, this study can be considered as an initial exploration to show the validity of using IWD in the scheduling domain despite the incompetent result. In the meantime, this study provides numerous possibilities of future improvements with high potential of being successful in the future.
Abdullah et al. Qu and Burke Caramia et al. Asmuni et al. Merlot et al. Eley Carter et al. Burke et al. Di Gaspero Qu et al. Table 6 shows that the results of the implementation of IWDs algorithm being initially reasonable and acceptable with no modification on the algorithm. An improvement on this method will hopefully provide high quality results and will expectably compete with the results of the other techniques that used to solve university exam timetabling problem.
The adaptation is initially conducted within IWD operators where the Saturation degree concepts have been incorporated. The researchers tried to implement the original IWD operators in this study to reveal its strengths and weaknesses in dealing with examination timetabling domain. Based on the initial results obtained by IWD, it is found that the algorithm is capable of solving university examination timetabling problem. Although the results produced in this research are presently not at par with the previously reported literature, an improvement using local search-based algorithm is required and is presently in progress to enhance its performance possibly superseding the methods used previously.
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We recommend that the Sn Unable to display preview. Download preview PDF. Skip to main content. Advertisement Hide. Original Paper First Online: 11 April This is a preview of subscription content, log in to check access. Acta Metall Sin — Google Scholar. Shalaby RM Effect of rapid solidification on mechanical properties of a lead free Sn