Муравьиный алгоритм (1158534), страница 4
Текст из файла (страница 4)
In addition, therandomly selection of a subsystem in Algorithms 2 and 3 has beenyielded better performance (the purposefully selections have beenyielded an increase in the CPU time without any significantimprovement in the objective function). Then, the best performance of ACS has been obtained with Max iter ¼ 2000; Antsize ¼ 20, q0 = 0.9, b = 1, q = q0 = 0.1 and z = S/2.To evaluate the given cases, each of the problem instances hasbeen tested for 10 trials. The summarized results of examples 1–5 are, respectively, shown in Tables 2–6, which give comparisonsbetween the eight different cases.
The time representing the average computational time is in seconds. As seen, the performances ofIn this paper, an ant colony approach is presented for reliabilityoptimization of a series system with multiple-choice and budgetconstraints. Each artificial ant constructs a solution by iterativelyapplying a pseudo-random transition rule based on both the heuristic information and the pheromone trails.
The heuristic information is calculated based on an aggregation of two fuzzy sets. Thegenerated solution may be infeasible; in other words, the total costof the chosen technologies may be greater than the available budget. An infeasible solution is replaced by a feasible one using aneighborhood search procedure which randomly searches andfinds a feasible solution with nearly highest reliability. The solutionis then improved by an efficient local search method.
Finally, theant changes the pheromone intensity on each edge related to itschosen technologies using the local updating rule. Once all antshave built their solutions, the pheromone trails are globally modified in order to make the search more directed. To evaluate the performance of the developed approach, it has been compared withthe only available algorithm. Our algorithm has effectively beenable to obtain optimal or near optimal solutions for large problems.Computational experiments are given to show the superiority ofthe proposed ant colony approach.Table 7Performance comparison.Example1234ACSASMinimumAverageStd. dev.MaximumMinimumAverageStd. dev.Maximum0.8570540.9150420.9651340.8654390.8570540.9150420.9651340.86543900000.8570540.9150420.9651340.8654390.857050.915040.964060.864650.857050.915040.964390.86491000.000500.000380.857050.915040.965130.865433646F. Ahmadizar, H.
Soltanpanah / Expert Systems with Applications 38 (2011) 3640–3646ReferencesAit-Kadi, D., & Nourelfath, M. (2001). Availability optimization of fault-tolerantsystems. In International conference on industrial engineering and productionmanagement (IEPM’2001), Quebec.Chen, T. C. (2006). IAs based approach for reliability redundancy allocationproblems.
Applied Mathematics and Computation, 182, 1556–1567.Coit, D., & Smith, A. (1996). Reliability optimization of series–parallel systems usinga genetic algorithm. IEEE Transactions on Reliability, 45(2), 254–260.Dorigo, M. (1992). Optimization, learning and natural algorithm. PhD thesis, DEI,Politecnico di Milano, Itally (in Italian).Dorigo, M., & Gambardella, L.
M. (1997a). Ant colonies for the traveling salesmanproblem. BioSys, 43, 73–81.Dorigo, M., & Gambardella, L. M. (1997b). Ant colony system: A cooperative learningapproach to the traveling salesman problem. IEEE Transactions on EvolutionaryComputation, 1, 53–66.Dorigo, M., Maniezzo, V., & Colorni, A. (1996). The ant system: Optimization by acolony of cooperating agents.
IEEE Transactions on Systems man and Cybernetics– Part B, 26, 29–41.Dorigo, M., & Stutzle, T. (2003). The ant colony optimization metaheuristic:algorithms, applications and advances. In F. Glover & G. Kochenberger (Eds.),Handbook of metaheuristics (pp. 251–285). Norwell, MA: Kluwer AcademicPublishers.Garey, M. R., & Johnson, D. S. (1979).
Computers and intractability. San Francisco:Freeman.Hsieh, Y. C. (2003). A linear approximation for redundant reliability problems withmultiple component choices. Computers & Industrial Engineering, 44, 91–103.Nahas, N., & Nourelfath, M. (2005). Ant system for reliability optimization of a seriessystem with multiple-choice and budget constraints. Reliability Engineering &System Safety, 87, 1–12.Nauss, R. M. (1978).
The 0–1 knapsack problem with multiple choice constraints.European Journal of Operational Research, 2(2), 121–131.Nourelfath, M., & Nahas, N. (2003). Quantized Hopfield networks for reliabilityoptimization. Reliability Engineering & System Safety, 81, 191–196.Ramirez-Marquez, J. E., & Coit, D. W. (2004). A heuristic for solving the redundancyallocation problem for multi-state series–parallel systems.
ReliabilityEngineering & System Safety, 83, 341–349.Ruan, N., & Sun, X. (2006). An exact algorithm for cost minimization in seriesreliability systems with multiple component choices. Applied Mathematics andComputation, 181, 732–741.Sinha, P., & Zoltners, A. A. (1979). The multiple choice knapsack problem.
OperationsResearch, 27(3), 503–515.Sung, C. S., & Cho, Y. K. (2000). Reliability optimization of a series system withmultiple-choice and budget constraints. European Journal of OperationalResearch, 127, 159–171.Sung, C. S., & Lee, H. K. (1994). A branch-and-bound approach for spare unitallocation in a series system. European Journal of Operational Research, 75(1),217–232.Tan, Z. (2003).
Minimal cut sets of s–t networks with k-out-of-n nodes. ReliabilityEngineering & System Safety, 82, 49–54.Tavakkoli-Moghaddam, R., Safari, J., & Sassani, F. (2008). Reliability optimization ofseries–parallel systems with a choice of redundancy strategies using a geneticalgorithm. Reliability Engineering & System Safety, 93, 550–556.Yeh, W. C. (2004). A simple algorithm for evaluating the k-out-of-n networkreliability. Reliability Engineering & System Safety, 83, 93–101.Yeh, W. C. (2006).
A new algorithm for generating minimal cut sets in k-out-of-nnetworks. Reliability Engineering & System Safety, 91, 36–43.Yeh, W. C. (2009). A two-stage discrete particle swarm optimization for the problemof multiple multi-level redundancy allocation in series systems. Expert Systemswith Applications, 36, 9192–9200.You, P. S., & Chen, T. C. (2005). An efficient heuristic for series–parallel redundantreliability problems. Computers & Operations Research, 32, 2117–2127.Zhao, R., & Liu, B. (2004).
Redundancy optimization problems with uncertainty ofcombining randomness and fuzziness. European Journal of Operational Research,157, 716–735.Zhao, J. H., Liu, Z., & Dao, M. T. (2007). Reliability optimization using multiobjectiveant colony system approaches. Reliability Engineering & System Safety, 92,109–120..
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
