05-Chena TC_ You PS - Immune algorithms-based approach for redundant reliability problems with multiple component choices (1158526), страница 4
Текст из файла (страница 4)
4.In the figure, three lines illustrates this observation ofcomparisons, whereR RNMR RCS; L2 ¼1 RNM1 RCSR RHsiehL3 ¼1 RHsiehL1 ¼andThe definition of the lines as above indicates themaximum possible improvement (MPI) which is thefraction that the best feasible solution achieved of themaximum possible improvement, considering thatreliability 1 [5]. Herein, R is the reliability by theproposed IAs approach, RN&M the reliability by Nakagawa and Miyazaki [4], RC&S the reliability by Coitand Smith [5] and RHsieh the reliability by Hsieh [7].203According to the comparison of numerical results inTable 3 and Fig. 3, it shows that the proposed IAsapproach performs better in those test problems withlarger values of W. In general, the immune algorithmsbased approach find better solutions for 24 test problems (W = 160, 162, 169 and 171–191), and tie thewell-known best solutions found by other methods inthe above three literatures.Although the immune algorithm found bettersolutions of 24 out of 33 test problems, theimprovement was extremely tiny, for instance: in testproblem 32 where the difference is on the order of105.
The differences are probably insignificant giventhe possible lack of precision in the constraintparameters such as in test problems 24 and 25.However, in all 33 problems, then, one could say thatimmune algorithms did find solutions of qualitycomparable to those previously published in theliterature. Above all, compared with the solutionsfound by Nakagawa and Miyazaki [4] and Hsieh [7],the solutions found by proposed method are with moresignificant improvement. Nevertheless, the solutioncomparison between the proposed method and geneticapproach [5] shows the improvement is small (lessthan 5%). It has to be emphasized that even very smallimprovements in reliability are often hard to beobtained in high reliability applications.
Moreover,besides the solutions found by the proposed approach,no any of the other three approaches can dominate anyother two methods.RRCSRRHsiehNMFig. 4. The comparison of numerical results for 33 test problems. L1 ¼ RR1RNM (symbol ^), L2 ¼ 1RCS (symbol *) and L3 ¼ 1RHsieh(symbol ~).204T.-C. Chen, P.-S. You / Computers in Industry 56 (2005) 195–205It seems that GAs and IAs are very similar, butthere are an essential difference in the memoryadopting system and the production system of variousantibodies.
It allows the global optimum to beacquired by using this algorithms form manyoptimization problems. The main reason is that theIA’s diversity characteristic in memory makes theproposed approach with more probability search theglobal optimal solution. However, the above merit ofthe IAs may become its disadvantage while the CPUtime is taken into account. Compared with GAs, thememory-adopting process in IAs will take slightlylonger CPU time for each iteration. Although moreCPU time will be taken in IAs than in GAs, it is stillworth to do so since obtaining a system design withhigher reliability is very difficult and important in thereal-world applications.According to above observation, it can beconcluded that the performance of the proposedapproach are superior than the other three methodswhen used to find the maximum reliability for theseredundant reliability problems with multiple component choices (CPU time is ignored).5.
ConclusionsThe IA-based approach to the series–parallelredundant reliability subject to multiple separablelinear constraints is proposed. Unlike genetic algorithms, immune algorithms based approach preservesdiversity so that it is able to discover new optima overtime. Therefore, the convergence of immune algorithms-based approach is never completed and thisdiversity acts like a preventive measure.
This notion ofviability of enabling further adaptations is preciselywhat genetic algorithms were lacking and this maybecome the reason why immune algorithms-basedapproach provides superior solution than geneticalgorithms-based approaches do. The IAs-basedapproach has been applied to solve the combinatoryoptimization engineering problems but the problemsolved in this research is different than thoseseparated in the literature, since the type of componentand the component redundant levels are to bedecided simultaneously for the system optimizationproblem.
To deal with this difficulty, a solutionrepresentation and special solution procedures areproposed. Based on our limited experience, it suggeststhat the IAs-based approach finds solutions whichare of a quality and are comparable to that ofother heuristic algorithms while the CPU time isignored. The proposed method achieves the globalsolution or finds a near-global solution for eachproblem tested.AcknowledgmentsThe research is supported by grants from NationalScience Council, Taiwan, under contract NSC 932213-E-150-012. The authors also thank a number ofanonymous referees for their valuable comments anduseful suggestions.References[1] K.B. Misra, J.
Sharma, A new geometric programming formulation for a reliability problem, International Journal Control 18 (1973) 497–503.[2] W. Kuo, V. Rajendra Prasad, An annotated overview of systemreliability optimization, IEEE Transaction on Reliability 49 (2)(2000) 176–187.[3] F.S. Hiller, G.J. Lieberman, An Introduction to OperationsResearch, McGraw-Hill, New York, 1995.[4] Y.
Nakagawa, S. Miyazaki, Surrogate constraints algorithm forreliability optimization problems with two constraints, IEEETransaction on Reliability R-30 (1981) 175–180.[5] D.W. Coit, A.E. Smith, Reliability optimization of series–parallel systems using a genetic algorithm, IEEE Transactionon Reliability 45 (1996) 254–260.[6] D.W. Coit, A.E. Smith, Penalty guided genetic search forreliability design optimization, Computers and Industrial Engineering 30 (1996) 895–904.[7] Y.C.
Hsieh, A linear approximation for redundant reliabilityproblems with multiple component choices, Computers andIndustrial Engineering 44 (2003) 91–103.[8] W. Kuo, C.L. Hwang, F.A. Tillman, A note on heuristicmethods in optimal system reliability, IEEE Transaction onReliability R-27 (1978) 320–324.[9] Z.
Xu, W. Kuo, H.H. Lin, Optimization limits in improvingsystem reliability, IEEE Transaction on Reliability R-39(1990) 51–60.[10] Y.C. Hsieh, T.-C. Chen, D.L. Bricker, Genetic algorithms forreliability design problems, Microelectronics Reliability 38(1998) 1599–1605.[11] M.S. Chern, On the computational complexity of reliabilityredundancy allocation in a series system, Operations ResearchLetters 11 (1992) 309–315.T.-C.
Chen, P.-S. You / Computers in Industry 56 (2005) 195–205[12] K.B. Misra, U. Sharma, An efficient algorithm to solve integerprogramming problems arising in system-reliability design,IEEE Transaction on Reliability 40 (1) (1991) 81–91.[13] W. Kuo, H. Lin, Z. Xu, W. Zhang, Reliability optimization withthe Lagrange multiplier and branch-and-bound technique,IEEE Transaction on Reliability R-36 (1987) 624–630.[14] R.E. Bellman, E.
Dreyfus, Dynamic programming and reliability of multicomponent devices, Operations Research 6(1958) 200–206.[15] D.E. Fyffe, W.W. Hines, N.K. Lee, System reliability allocation and a computational algorithm, Operations Research 17(1968) 64–69.[16] J. Sharma, K.V. Venkateswaran, A direct method for maximizing the system reliability, IEEE Transaction on ReliabilityR-20 (1) (1971) 256–259.[17] P.M. Ghare, R.E. Taylor, Optimal redundancy for reliability inseries system, ORSA 17 (1969) 838–847.[18] L. Painton, J. Campbell, Genetic algorithms in optimization ofsystem reliability, IEEE Transaction on Reliability 44 (1995)172–178.[19] N.K. Jerne, The immune system, Scientific America 229 (1)(1973) 52–60.[20] N.K.
Jerne, Clonal selection in lymphocyte network, in: G.M.Edelman (Ed.), Cellular Selection and Regulation in theImmune Response, Raven Press, New York, 1974.[21] J.D. Farmer, N.H. Packard, A.S. Perelson, The immune system, adaptation, and machine learning, Physica D 22 (1986)187–204.[22] L.N. De Castro, J. Timmis, Artificial Immune Systems: A newComputational Intelligence Approach, Springer, New York,2002.[23] S.J.
Huang, Enhancement of thermal unit commitment usingimmune algorithms based optimization approaches, ElectricalPower and Energy Systems 21 (1999) 245–252.205[24] I.L. Weissman, M.D. Cooper, How the immune system develops, Scientific American 269 (3) (1993) 33–40.[25] S.J.
Huang, An immune-based optimization method to capacitor placement in a radial distribution system, IEEE Transaction on Power Delivery 15 (2) (2000) 744–749.[26] L.N. De Castro, F.J. Von Zuben, The clonal selection algorithmwith engineering applications, in: Workshop Proceedings ofthe GECCO 2000, #####, 2000, pp. 36–37.[27] Z. Michalewicz, Genetic algorithm + Data structures = Evolution Programs, Springer-Verlag, Berlin, 1994.[28] T.-C. Chen, G.W.
Fischer, A GA-based method for the tolerance allocation problem, Artificial Intelligence in Engineering14 (2000) 133–141.Ta-Cheng Chen is currently an Associate Professor in the Department of Information Management at National FormosaUniversity, Taiwan. He received his Ph.D.in industrial engineering from the University of Iowa in 1997. His researchinterests include AI approaches appliedin optimization problems, data miningand applied operations research.Peng-Sheng You is an Associate Professor at the Graduate Institute of Transportation and Logistics in the National ChiaYi University.
He received his Ph.D. inmanagement science and engineeringfrom University of Tsukuba. His researchinterests include yield management,inventory management and system reliability..
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
