Solving the Redundancy Allocation Problem using Tabu Search

Solving the Redundancy Allocation fuss victimization verboten SearchEfficiently Solving the Redundancy Allocation Problem victimisation prohibited SearchAbstractThe redundancy allocation chore is a common and extensively studied program involving outline design, reliableness engineering and operations re look for. There is an ever increasing need to invite good etymons to this reliability optimisation caper beca office many telecommunications (and other) agreements atomic number 18 befitting more(prenominal) heterogeneous while the development schedules ar limited. To provide solutions to this, a proscribed search meta-heuristic has been developed and no-hitly. Tabu search is a sinless solution to this paradox as it has a lot of advantages compared to alternative regularitys. Tabu search nookie be utilize for more confused conundrum domain compared to the mathematical programming methods. Tabu search is more businesslike than the macrocosm based search methodologies such as genetic algorithmic rules. In this paper, Tabu search is employ on tierce diametric problems in comparison to the integer programming and genetic algorithm solutions and the results show that tabu search has more benefits while solving these problems.INTRODUCTION of ArticlesRedundancy allocation problem(RAP) is a popular and a complex reliability design problem. The problem has been solved development different optimization approaches. Tabu search(TS) has more advantages eitherplace the other approaches but has non 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 alike have high reliability requirements. Solutions to the RAP problem has the optimal faction of component selections. Mathematical programming techniques have proven to be successful in breaking 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. transmittable Algorithms have proven to be a better alternative to the mathematical programming technique and has provided excellent results. Despite this, genetic algorithms is a community 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 dewy-eyed solution technique that event by dint of 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 efficienc y of the method.The well-nigh unremarkably studied design configuration for RAP is the series parallel problem. The representative of the design is shown below.NomenclatureR(t, x) = system reliability at time t, depending on xxij = quantity of the jth available component usedin subsystem imi = chip of available components for subsystemis = number of subsystemsnmax,i = ni nmax,iiC(x) = system salute as a utilisation of xW(x) = system weight as a function of xC, W, R = system-level constraint limits for cost,weight,and reliabilityk = minimum number of operating components inevitable for subsystemij = parameter for exponential distribution,fij(t) = ij exp(ijt)Fj = operable solutions contained on the tabu dispositionTj = summation number of solutions on the tabu listj = feasibleness ratio, j = Fj/Tj .Explanation of the work presented in journal articlesThe RAP function can be formulated with system reliability as the purpose function or in the constraint set. Problem(p1) maxi mizes the system reliability and problem(p2) maximizes the system cost.The TS requires nameination of a tabu list of unavailable moves as it successively proceeds from one criterion to another. For the series parallel system, the encoding is a substitute code of size i=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 jump step involves generating a feasible random sign 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 manageable 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 eccentric by adding or subtracting one. The TSRAP that does not allow component mixing involves ever-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 shell 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 with in the tabu list.The fourthly and the final step is checking for the stopping criterion. It is the maximum number of iterations without finding an advance 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 punishment method has been developed for problems solved by TS as they prove to sustain better solutions. The objective function for the infeasible solution is penalized by using subtractive or additive penalization function. A light penalty is imposed on the infeasible solutions within the NFT piece( Near Feasible Treshold) and heavily penalized beyond it. The penalized objective function is based on the unpenalized objective function, the compass point of infeasibility and information from the TS short-term and massive-term memory. The objective function is for problem 1Rp(tox) is the penalized objective function. The un penalized system reliability of the bes t 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 tightly fitting 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 isCp(x) is the penalized objective function. Call is the unpenalized (feasible or infeasible) system cost of the bestsolution found so far, and Cfeas is the system cost of thebest feasible solution found so far.Discussion of ContributionsThe most important contribution is that as a result of this paper it is straightway 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, co mplex 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 virtually 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 ImprovementsAlthough an unexploited approach to find the optimal solution has been tried and tested to be efficient, there is probable 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 effic iency by considering the access of these features to the TS devisedhere.SummaryTS has previously been demonstrated to be a successfuloptimization 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.ReferencesBellman, R.E. and Dreyfus, E. (1962) Applied Dynamic Programming,Princeton University Press, Princeton, NJ.Bland, J.A. (1998a) Memory-bas ed technique for optimal geomorphologic design.Engineering Applications of Artificial Intelligence, 11(3), 319-325.Bland, J.A. 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