Solving the Redundancy Allocation Problem using Tabu Search

Solving the Redundancy Allocation Problem using Tabu Search Efficiently Solving the Redundancy Allocation Problem using Tabu Search Abstract The redundancy allocation problem is a common and extensively studied program involving system design, reliability engineering and operations research. There is an ever increasing need to find efficient solutions to this reliability optimization problem because many telecommunications (and other) systems are becoming more complex while the development schedules are limited. To provide solutions to this, a tabu search meta-heuristic has been developed and successfully. Tabu search is a perfect solution to this problem as it has a lot of advantages compared to alternative methods. Tabu search can be used for more complex problem domain compared to the mathematical programming methods. Tabu search is more efficient than the population based search methodologies such as genetic algorithms. In this paper, Tabu search is used on three different problems in comparison to the integer programming and genetic algorithm solutions and the results show that tabu search has more benefits while sol ving these problems. INTRODUCTION of Articles Redundancy allocation problem(RAP) is a popular and a complex reliability design problem. The problem has been solved using different optimization approaches. Tabu search(TS) has more advantages over the other approaches but has not been tested for its effectiveness. In this paper a TS is used to solve a problem, called TSRAP, and the results are compared to the other approaches. The RAP is used for designs that have large assemblies and are manufactured using off-the shelf components and also have high reliability requirements. Solutions to the RAP problem has the optimal combination of component selections. Mathematical programming techniques have proven to be successful in finding solutions to these problems. Unfortunately, these problems have some constraints which are necessary for the optimization process but not for the actual engineering design process. Genetic Algorithms have proven to be a better alternative to the mathematical programming technique and has provided excellent results. Despite this, genetic algorithms is a population based search requiring the evaluation of multiple prospective solutions because of which a more efficient approach to this problem is desired. TS is an alternative to these optimization methods that has been optimized by GA. Its a simple solution technique that proceeds through successive iterations by considering neighboring moves. In this paper the TS method is used on three different problems and the results are compared with the alternate optimization methods. TS is not like GA, which is population based, instead it successively moves from solution to solution. This helps increase the efficiency of the method. The most commonly studied design configuration for RAP is the series parallel problem. The example of the design is shown below. Nomenclature R(t, x) = system reliability at time t, depending on x; xij = quantity of the jth available component used in subsystem i; mi = number of available components for subsystem i; s = number of subsystems; nmax,i = ni à ¢Ã¢â‚¬ °Ã‚ ¤ nmax,ià ¢Ã‹â€ Ã¢â€š ¬i; C(x) = system cost as a function of x; W(x) = system weight as a function of x; C, W, R = system-level constraint limits for cost,weight, and reliability; k = minimum number of operating components required for subsystem; ÃŽÂ »ij = parameter for exponential distribution, fij(t) = ÃŽÂ »ij exp(à ¢Ã‹â€ Ã¢â‚¬â„¢ÃƒÅ½Ã‚ »ijt); Fj = feasible solutions contained on the tabu list; Tj = total number of solutions on the tabu list; à Ã‚ j = feasibility ratio, à Ã‚ j = Fj/Tj . Explanation of the work presented in journal articles The RAP function can be formulated with system reliability as the objective function or in the constraint set. Problem(p1) maximizes the system reliability and problem(p2) maximizes the system cost. The TS requires determination of a tabu list of unavailable moves as it successively proceeds from one step to another. For the series parallel system, the encoding is a permutation code of size à ¢Ã‹â€ Ã¢â‚¬Ëœi=1 s nmax, I representing the list of components in each subsystem including nonused components. The tabu list length is reset every 20 iterations to an integer value distributed uniformly between [s, 3s] and [14s,18s] for Problems (P1) (s = 14) and (P2) (s = 2), respectively. TSRAP is done through four steps. The first step involves generating a feasible random initial solution. S integers are chosen from the discrete uniform distribution, representing the number of components in parallel for each subsystem. Using this procedure, a solution is produced with an average number of components per subsystem. It becomes the initial solution if feasible, else the whole process is repeated. The second step checks for possible defined moves for each subsystem in the neighborhood. The TSRAP that allows component mixing within the subsystem allows for its first move to change the number of a particular component type by adding or subtracting one. The TSRAP that does not allow component mixing involves changing the number of components by adding or subtracting one for all individual subsystems. These moves are advantageous as they do not require re-calculation of the entire system reliability. The best among the two types of moves that are performed independently are selected. The selected move is the best move available, hence it is called best move. If the solution is TABU and the solution is not better than the best so far solution then it is disallowed and step 1 is repeated, else it is accepted. The third step involves updating the Tabu list. To check for the feasibility of an entry in the Tabu list, the system cost and weight are stored with the subsystem structure involved in the move within the tabu list. The fourth and the final step is checking for the stopping criterion. It is the maximum number of iterations without finding an improvement in the best feasible so far. When reached at a solution, the search is completed and the best feasible so far is the is the TSRAP recommended solution. An adaptive penalty method has been developed for problems solved by TS as they prove to give better solutions. The objective function for the infeasible solution is penalized by using subtractive or additive penalty function. A light penalty is imposed on the infeasible solutions within the NFT region( Near Feasible Treshold) and heavily penalized beyond it. The penalized objective function is based on the unpenalized objective function, the degree of infeasibility and information from the TS short-term and long-term memory. The objective function is for problem 1: Rp(to;x) is the penalized objective function. The un penalized system reliability of the best solution so far is represented by Rall and Rfeas represents the system reliability of the best feasible solution found so far. If Rall and Rfeas are equal or close to each other in value then the search continues, else if Rall is greater then Rfeas, there is a difficulty in finding the feasible solutions and the penalty is made larger to filter the search into the feasible region. Similarly, the objective function for problem 2 is: Cp(x) is the penalized objective function. Call is the unpenalized (feasible or infeasible) system cost of the best solution found so far, and Cfeas is the system cost of the best feasible solution found so far. Discussion of Contributions The most important contribution is that as a result of this paper it is now proved that the Tabu search is a more efficient method that the mathematical programming technique and the genetic algorithms. The penalization method was used which proved to give better results too. As a result of this paper, complex problem domains can now be optimized better using the Tabu search. As a result of this paper, weve come to realize that TSRAP is better in performance and results in greater efficiency than GA although they are almost similar in procedures. Due to the short schedules to find the optimal solution for complex redundancy allocation problems, Tabu search is found to be the most efficient approach. Discussion of Dificiency and Potential Improvements Although an unexploited approach to find the optimal solution has been tried and tested to be efficient, there is potential for future scope. In this paper , the TS approach used is rather simple in a way that few factors that could have been were not incorporated. Features that are normally used such as candidate lists and long term memory strategies which prove to be more effective were not used. The use of these features can prove to be more efficient in complex problems. There are opportunities for improved effectiveness and efficiency by considering the addition of these features to the TS devised  here. Summary TS has previously been demonstrated to be a successful optimization approach for many diverse problem domains. So, TS approach , as a result of this paper has been tried and tested to be more efficient approach to the complex problems domain of the redundancy allocation problem. The use of penalty function in this research has promoted the search in the infeasible region by changing the NFT. In this paper, TS has been tested in three different problems and has provided more efficient results than the other alternative methods. When compared, the TS produces better results than the genetic algorithm method. In spite of this, the use of features such as candidate lists and long term memory strategies could have been to be more effective in complex problem domains. References Bellman, R.E. and Dreyfus, E. (1962) Applied Dynamic Programming,  Princeton University Press, Princeton, NJ. Bland, J.A. (1998a) Memory-based technique for optimal structural design.  Engineering Applications of Artificial Intelligence, 11(3), 319-  325. Bland, J.A. (1998b) Structural design optimization with reliability constraints  using tabu search. Engineering Optimization, 30(1), 55-74. Brooks, R.R., Iyengar, S.S. and Rai, S. (1997) Minimizing cost of redundant  sensor-systems with non-monotone and monotone search  algorithms, in Proceedings of the Annual Reliability and Maintainability  Symposium, IEEE, New York, pp. 307-313. Bulfin, R.L. and Liu, C.Y. (1985) Optimal allocation of redundant components  for large systems. IEEE Transactions on Reliability, 34, 241-247. Chern, M.S. (1992) On the computational complexity of reliability redundancy  allocation in a series system. Operations Research Letters,11, 309-315.  

Mother and Daughter, a Heavenly Relationship Failed Essay

Daughter and mother relationship is an endless topic for many writers. They are meant to share the bond of love and care for each other. In the real world, however, their relationship is not as successful as it ought to be. The stories â€Å"How to Talk to Your Mother† and â€Å"I Stand Here Ironing† are the examples of this conflict. Lorrie Moore is distinguished for the clever wordplay, irony and sardonic humor of her fiction. â€Å"How to Talk to Your mother† is a short story in her collection Self-Help. It is about a failed relationship of a daughter and her mother over time. Similarly, Tillie Olsen’s â€Å"I Stand Here Ironing† portrays powerfully the economic and domestic burdens a poor woman faced, as well as the responsibility and powerlessness she feels over her child’s life. Both stories have the same theme, but each has different technique, and the conflicts from the characters are opposite. Poor communication over time is the theme both stories share. In â€Å"How to Talk to Your Mother,† Ginny, the author, faded the relationship with her mother as time goes and things changed from 1939 to 1982. In 1952, Ginny started to break away by slamming the door and say â€Å"Don’t I know it† (Moore 105) when her mother asks about her crush in junior high. Then, she becomes a young adult with a new life and would not come home for holidays. However, it is not until her mother called her by her sister’s name that makes she feels uncomfortable. â€Å"Learn that you have a way of knowing each other which somehow slips out and beyond the ways you have of not knowing each other at all† (Moore 103). The simply â€Å"How to† title belies the complexities of broken communication between mother and daughter. Ginny attempts to communicate with her mother throughout decades, but it never works. In â€Å"I Stand Here Ironing,† the mother faced the same problem with poor communication. Readers feel deeply sorry for the mother as she is economically alone, lonely, overworked and tired. The mother is always busy and preoccupied with other children. â€Å"I was working, there were four smaller ones now, there was not time for her† (Olsen 191). She has little or no time to talk to Emily, the daughter. The only time they met each other is at night, when Emily is struggle over books and the mother be ironing, or do other house chores. In both stories, the mothers and daughters have really  poor communication. Each character has her own life and stared to ignore their love ones. Ginny lives her wild life with romance. On the other hand, the mother in â€Å"I Stand Here Ironing† is so busy with her low-class life. As a result, their relationship failed as time rolls. Although both stories share similarity, each story was written with different styles, point-of-views, and languages. Lorrie Moore presents â€Å"How to Talk to Your Mother† in reverse chronological order, from latest to earliest. This technique supports her main idea by illustrating the broken communication pattern existing since the narrator’s childhood. With this style, readers find it amusing as they can read forward or backward. Moreover, this kind of writing is very rare in literature. Tillie Olsen’s â€Å"I Stand Here Ironing† was written in a traditional flashback. It started with the mother blaming herself for Emily’s outturn. Then, she remembered all the life events that result in bad decisions she made for Emily. Both stories also have different point-of-view. â€Å"How to Talk to Your Mother† is told in second-person, using â€Å"you,† instead of â€Å"I.† The second-person narration distances the narrator from the pa in inflicted by her mother, father, and lovers. This is Moore’s clever choice. Readers can relate and sympathize with Ginny. On the other hand, â€Å"I Stand Here Ironing† is told in first-person. The mother is telling readers about her faults and her attempts to help Emily through difficult years. Readers can see the hardship the mother faced and understand her situation. Nevertheless, Moore writes the story like one would write in her diary, very informal. The full title is â€Å"How to Talk to Your Mother (Notes),† and the language is not very aesthetic. On the contrast, Olsen writes her story in formal, literature language. In response to her story, Helen Pike Bauer writes: â€Å"Olsen’s story is a dialogue between circumstances and desire, constraint and love, absence and presence, silence and speech, power and helplessness.† The conflicts of each character are opposite. The primary conflict in â€Å"How to Talk to Your Mother† is between Ginny and herself. She feels like she has her own life and her mother becomes annoying. In 1971, she wrote: â€Å"Go for long walks to get away from her. Walk through wooded area; there is a life you have forgotten† (Moore 103). Throughout the story, readers can see the  broken relationship is resulted from the external events of her life. She has three abortions and involving many relationships with men that she don’t even like. â€Å"Sometimes you confuse her with the first man you ever love, who ever loved you †¦Ã¢â‚¬  (Moore 102). Ginny almost blamed herself for their relationship. Her mom is always there, in her house since 1967. A year before death, her mother tells her: â€Å"Is that any way to talk to your mother (Moore 101)?† While Ginny experienced the external conflict of her life, the mother in â€Å"I Stand Here Ironing† faced an internal conflict involving Emily. She makes a very meaningful statement at the end of story: help Emily to know that â€Å"she is more than this dress on the ironing board, helpless before the iron† (Olsen 193). The mother constantly referred to the bad decisions she had made for Emily during her childhood. She sent Emily to live with her relatives as a toddler and came back with â€Å"all baby loveliness gone† (Olsen 188). Then, she sent her off again to a convalescent home. These decisions caused the mother to constantly nag at her internal self. Emily turned to a comedic teen is the result of the mother’s ignorant and poor relationship, which makes the mother blaming herself. She feels like the conflict is caused by her and Emily deserved a better life. Thackeray says, â€Å"God cannot be everywhere and therefore he made mother.† Parents are the caretaker of their children. From their experiences, they know what is best and they would never mean ill for them. â€Å"How to Talk to Your Mother† and â€Å"I Stand Here Ironing† are short stories that remind readers to cherish their relationships with parents. Both stories have the same theme of communication, but each has different technique, and the conflicts from the characters are opposite. Their situations are very difficult: poverty, low-class, and early motherhood. Lorrie Moore writes â€Å"How to Talk to Your Mother† to mock the popular â€Å"How-to† style. She marks off each stage of the plot by repeated works and ideas of heart, babies, containers, and unsuccessful talks between mother and daughter. Tillie Olsen writes â€Å"I Stand Here Ironing† with many symbolisms. For example, the iron is the torment, outside pressures. The dress is her problem, or Emily. The mother is ironing out the problem from inside her heart. Both stories carry the same message of mother and daughter relationship that most people faced the same path. In the society right now, there are many children experienced  child abuses. As for many parents, they could not get their kids to listen to them. The heavenly relationship failed as lives go on.

Criticism and Reflection of the Color Purple by Alice Walker

Criticism and Reflection of the Color Purple by Alice Walker Criticized as a novel containing graphic violence, sexuality, sexism, and racism, The Color Purple was banned in several schools across the United States. Crude language and explicit detail chronicle the life of Celie, a young black woman subjected to society’s cruelties. Although immoral, the events and issues discussed in Alice Walker’s The Color Purple are prominent in today’s society, and must be public and conversed rather than unknown and silenced. If each person is given the right to raise her voice, express herself, and tell her tale, who holds the authority to brand a book unfit for society? Literature encompasses the details of life thus, enabling the†¦show more content†¦Itemized by fathers and husbands before meeting her friend Shug, Celie was unable to love and feared expressing herself. Open and uncompetitive, Celie and Shug’s relationship nurtures each character’s livelihood. Together the two express themselves simply by enjoying the other’s opinion and company â€Å"Us lay with our arms round each other. Sometimes Shug read the paper out loud. The news always sound crazy. People fussing and fighting †¦never even looking for no peace. People insane, say Shug. Yeah, I say but some things pleasant† (Walker 217). Sharing both physical and emotional love, the two characters explore each other’s emotions and develop feelings for one another. However, the current society fails to recognize the growth the characters undergo because they fail to accept that each character feels love for someone of the same gender. Lacking possessive qualities common to relationships with men, each woman pursues creativity. Enlivened by sense of self Shug awakens, Celie defies the time period’s restraints on gender by crafting pants anybody can wear â€Å"in every color and size under the sun.† (Walker 218) while it is said â€Å"only men spose to wear the pants.†(Walker 218) Merely a feature of female friendship estranged to current society, the characters’ physical love is compassionate but unaccepted by most of society. Among the many arguments in favor of banning Alice Walker’s The Color Purple, the most contended is the novel’s brutalShow MoreRelatedAlice Malsenior6001 Words   |  25 PagesAlice Walker: Peeling an Essence As an African- American novelist, short–story writer, essayist, poet, critic, and editor, Alice Walker’s plethora of literary works examines many aspects of African American life as well as historical issues that are further developed by Walker’s unique point of view. Writers like Alice Walker make it possible to bring words and emotions to voices and events that are often silenced. Far from the traditional image of the artist, she has sought what amounts to aRead Moreâ€Å"Alice Walker’s Depiction of Female Characters in ‘the Color Purple’ Is Intended to Act as a Stark Contrast to How Many Female Characters Have Been Portrayed Throughout Literature† Discuss This Statement with Reference1780 Words   |  8 Pagesâ€Å"Alice Walker’s depiction of female characters in ‘The Color Purple’ is intended to act as a stark contrast to how many female characters have been portrayed throughout literature† Discuss this statement with reference to the critical anthology Throughout literature there has been an array of female portrayals, most prominently those in 19th century fiction, who didn’t work unless driven to it by necessity. Instead, the focus of interest was on the heroine’s choice of marriage partner, which wouldRead MoreAnalysis Of Barbara Bushs Speech2033 Words   |  9 Pagestrue colors.† Her purpose was to impart wisdom onto her audience. Barbara Bush’s speech was an inspiration to the Wellesley Class of 1990 and continues to serve as a beacon of light for their daughters. Like any great speech by a political figure, there was controversy surrounding the arrival of Bush to Wellesley. Prior to inviting a commencement speaker, the senior class voted on their top choices. Barbara Bush came in second and was asked after first choice Alice Walker, author of The Color PurpleRead MoreStephen P. Robbins Timothy A. Judge (2011) Organizational Behaviour 15th Edition New Jersey: Prentice Hall393164 Words   |  1573 PagesCulture 525 Creating a Positive Organizational Culture 527 Spirituality and Organizational Culture 529 What Is Spirituality? 529 †¢ Why Spirituality Now? 530 †¢ Characteristics of a Spiritual Organization 530 †¢ Achieving a Spiritual Organization 531 †¢ Criticisms of Spirituality 531 Global Implications 532 Summary and Implications for Managers 533 S A L Self-Assessment Library What’s the Right Organizational Culture for Me? 512 glOBalization! Face Culture, Dignity Culture, and Organizational Culture

Should Entertainment Education Be Taught - 1423 Words

Our world today is filled with new advanced technologies. Children as young as the age of two are able to learn how to use these electronics. Watching television, using the computer, playing with the tablet or an Iphone are few items that interest and keep the children entertained. When no source of entertainment is presented, children will find something that does attract them.Students are more engaged in a learning environment when some sort of entertainment is presented. Starting off a discussion and displaying a question or some sort of hook, whether it relates to the topic or not, will initiate the students and force them to think and make connections. Education in previous generations compared to now has differed. Before,†¦show more content†¦In reality, this is not the case. When the students do not receive the grade they believe they have earned, they are quick to complain and talk to a superior to get the grade they â€Å"deserve†. The students then spread r umors about the teachers who fail them and once a negative rumor is spread, students do not want any association with that teacher. If the teacher does not have a certain amount of students to teach a class, the teacher loses their money and to a certain extent, may also be fired. To avoid the issue, teachers make their grading policies easier to gain attention of the students. According to the text, â€Å"One of the ways we’ve tried to stay attractive is by loosening up. We grade much more softly than our colleagues†¦.and not challenge -the students† (Edmundson 396). Taking â€Å"easier† classes is another route students choose to take. When the students decide in taking easier classes, they limit themselves in majoring is specific courses.This is the way of the current education creating flaws in students curriculum. RSA Animate:Changing Education Paradigms† by Ken Robinson is another author who shares his input on the necessary changes in the curre nt education system and how the current system is affected the children. Throughout the video, he mentions the struggles the millennials go through in a classroom. While watching the video, Robinson claims, â€Å"We are getting our children through education byShow MoreRelatedAmusing Ourselves For Death By Neil Postman1475 Words   |  6 Pagesto Death, the author examines the medium of education in order to exhibit how it has affected and fashioned modern public discourse. Postman uses a two-part argument on the topic of the influence that television has over education. In order to properly demonstrate the authors view and evidence on this subject of discourse, as well as my own, I will explore how television presents education as well as how exactly television has managed to alter education when it is faced outside of television. PostmanRead More The Production of Video Games Taught At School1436 Words   |  6 Pageswithin school are addicted to video games, therefore the school system should provide a career pathway on how to create and program video games because it will allow these gaming students to participate in school while having entertainment. Having video game development as a career pathway in school would allow students to get more interactive in school, have another field that they can decide to major in, and develop entertainment, but still be focused within school. Around the world there are videoRead MoreConformity in Fahrenheit 451827 Words   |  4 Pagesleisure, and fright. The children in the society are never actually taught during school hours. Captain Beatty, another firefighter, tells Montag that the schools Cram them full of non-combustible data, chock them so damned full of â€Å"facts† they feel stuffed, but absolutely â€Å"brilliant† with information† (61). The â€Å"teachers† (actually film) stuff the students with â€Å"knowledge†, making them feel smart, but they are never taught to question any of the information or form their own opinion on mattersRead MoreThe Process Of Learning Process Essay1266 Words   |  6 Pagesentirely possible to incorporate education with education without compromising content. Buckingham and Scanlon (2000) refer to this as â€Å"Edu-tainment†, which is dependent on visual material, narrative or game-like formats, and on less formal and didactic styles of address as those used in HeLa, Hamilton and, ‘Thug notes.’ All these three examples aim at educating while entertaining. They will form part an integral part of this discussion on education and entertainment. Firstly, learning is an integralRead MoreThe Taliban Of The Swat Valley1092 Words   |  5 Pagesthe Swat Valley, so citizens would succumb to their way of life. This affected people’s jobs, education and their health. The Swat Valley was just one of the many places that were occupied by the Taliban. The Taliban ruined thousands of lives of those in Pakistan and Afghanistan. Using violence, the Taliban controlled and affected the lives of people in terms of their careers, mental states and education. To begin, the Taliban restricted the lives of people in relation to their careers. To exemplifyRead MoreIncrease in the Legal Drinking Age870 Words   |  3 Pagescentury youth about alcohol misuse are ineffective and impractical. Alcohol educations programs are mainly about scaring teens out of any type of alcohol consumption (McCardell), which in reality makes drinking attractive to them because of the mystery involved (Minimum Drinking Age). As a result, the programs intended to prevent underage drinking actually have the opposite effect (Ogilvie); instead, alcohol education should be based on the reality of the bingeing environments teens and young adultsRead MoreLiterature : The Definition Of Literature1302 Words   |  6 Pagesthose many years. It has also been debated over if literature has any value and if it is necessary to the world in which we live in. Another question arises when talking about literature is, if it does have any value at all, then how and why should it be taught in schools and to younger and future generations. What is literature? It is a question that has been debated and discussed over for years and it will probably still be for years to come. Many people have been tried making a definition for literatureRead MoreThe History of Childresn Literature Essay1599 Words   |  7 Pagesthe hand of his true love. They were told to both children and adults alike, because children and adults were all treated similarly during this time. In the early years of the fifth century through the fifteenth century this was the avenue for entertainment and to teach many of the lessons that they needed. Children would listen to the stories that the adults would listen to. These stories were often kept or preserved by the means of carving them into the wall of a cave, or putting them onto clayRead MoreTechnology For More Knowledge?1017 Words   |  5 PagesTechnology for More Knowledge As a child we watched T.V. shows for entertainment and today we use technologies like tablets and phones for entertainment purposes. When we watch T.V. or play on our phone elderly might have told you, â€Å"Stop staring at a screen and get some actual book!† or if you are Asian like me you might have heard, â€Å"Get off the T.V., put your phone down, and Study, Study!† Technology and T.V. were always viewed as a distraction in student’s educational life. However watching T.VRead MoreThe Stigma Of Mental Disorders921 Words   |  4 Pagesas schizophrenia, psychosis, autism, and many more, is heavily wide spread through the world. Those who are misinformed about what these mental disorders are like are given their information through the media whether it is through articles or entertainment based media. (Theurer) First though it must be understood what a mental disorder is. According to the Merriam-Webster dictionary a mental disorder or illness is, â€Å"a mental or bodily condition marked primarily by sufficient disorganization of personality