Reliability-redundancy Optimization Problem with Interval Valued Reliabilities of Components via Genetic Algorithm

This paper deals with the reliability-redundancy optimization problem considering the reliability of each component as an interval valued number that involves the selection of components with multiple choices and redundancy levels which maximize the overall system reliability subject to the given resource constraints arise on cost, volume and weight. Most of the classical mathematical methods have failed in solving the reliability-redundancy optimization problems because the objective functions as well as constraints are non-convex in nature. As an alternative to the classical mathematical methods, heuristic methods have been given much more attention by the researchers due to their easier applicability and ability to find the global optimal solutions. One of these heuristics is genetic algorithm (GA). GA is a computerized stochastic search method of global optimization based on evolutionary theory of Darwin: "The survival of the fittest" and natural genetics. Here we present GA based approach for solving interval valued mixed integer programming in reliability-redundancy optimization problem with advanced genetic operators. Finally, a numerical example has been solved and also to study the effects of changes of different GA parameters, sensitivity analyses have been carried out graphically.

[1]  Kaisa Miettinen,et al.  Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms , 2003, J. Glob. Optim..

[2]  Way Kuo,et al.  Recent Advances in Optimal Reliability Allocation , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[3]  K. I. M. McKinnon,et al.  A convexification method for a class of global optimization problems with applications to reliability optimization , 2001, J. Glob. Optim..

[4]  Masatoshi Sakawa,et al.  Genetic Algorithms and Fuzzy Multiobjective Optimization , 2001 .

[5]  Mitsuo Gen,et al.  Soft computing approach for reliability optimization: State-of-the-art survey , 2006, Reliab. Eng. Syst. Saf..

[6]  Duan Li,et al.  Optimality Condition and Branch and Bound Algorithm for Constrained Redundancy Optimization in Series Systems , 2002 .

[7]  Asoke Kumar Bhunia,et al.  Genetic algorithm based multi-objective reliability optimization in interval environment , 2012, Comput. Ind. Eng..

[8]  Lev V. Utkin,et al.  New Reliability Models Based on Imprecise Probabilities , 2000 .

[9]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[10]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[11]  Way Kuo,et al.  Reliability redundancy allocation: An improved realization for nonconvex nonlinear programming problems , 2006, Eur. J. Oper. Res..

[12]  Leandro dos Santos Coelho,et al.  An efficient particle swarm approach for mixed-integer programming in reliability-redundancy optimization applications , 2009, Reliab. Eng. Syst. Saf..

[13]  J. Onishi,et al.  Solving the Redundancy Allocation Problem With a Mix of Components Using the Improved Surrogate Constraint Method , 2007, IEEE Transactions on Reliability.

[14]  David W. Coit,et al.  Optimization of system reliability in the presence of common cause failures , 2007, Reliab. Eng. Syst. Saf..

[15]  Luca Podofillini,et al.  Optimal design of reliable network systems in presence of uncertainty , 2005, IEEE Transactions on Reliability.

[16]  Hans-Jürgen Zimmermann,et al.  Fuzzy global optimization of complex system reliability , 2000, IEEE Trans. Fuzzy Syst..

[17]  Way Kuo,et al.  An annotated overview of system-reliability optimization , 2000, IEEE Trans. Reliab..

[18]  Asoke Kumar Bhunia,et al.  Interval oriented multi-section techniques for global optimization , 2009 .

[19]  Alice E. Smith,et al.  An ant colony optimization algorithm for the redundancy allocation problem (RAP) , 2004, IEEE Transactions on Reliability.

[20]  Way Kuo,et al.  Multi-path heuristic for redundancy allocation: the tree heuristic , 2006, IEEE Transactions on Reliability.

[21]  Lev V. Utkin,et al.  Imprecise Reliability of General Structures , 2013, Knowledge and Information Systems.

[22]  A. Saidane,et al.  Optimal Reliability Design: Fundamentals and Applications , 2001 .

[23]  Elias P. Zafiropoulos,et al.  Reliability and cost optimization of electronic devices considering the component failure rate uncertainty , 2004, Reliab. Eng. Syst. Saf..

[24]  Lirong Cui,et al.  Reliability for Sparsely Connected Consecutive-$k$ Systems , 2007, IEEE Transactions on Reliability.

[25]  Sanat Kumar Mahato,et al.  Interval-Arithmetic-Oriented Interval Computing Technique for Global Optimization , 2006 .

[26]  Laura Painton,et al.  Genetic algorithms in optimization of system reliability. , 1995 .

[27]  Tongdan Jin,et al.  System optimization with component reliability estimation uncertainty: a multi-criteria approach , 2004, IEEE Transactions on Reliability.

[28]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[29]  Dilip Roy,et al.  Reliability stochastic optimization for a series system with interval component reliability via genetic algorithm , 2010, Appl. Math. Comput..

[30]  Sung Chang Sup,et al.  Branch-and-bound redundancy optimization for a series system with multiple-choice constraints , 1999 .

[31]  David W. Coit,et al.  Redundancy allocation for series-parallel systems using a max-min approach , 2004 .

[32]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[33]  Lirong Cui,et al.  Optimal allocation of minimal & perfect repairs under resource constraints , 2004, IEEE Transactions on Reliability.

[34]  R. K. Gupta,et al.  A GA based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components , 2009, J. Comput. Appl. Math..

[35]  Manju Agarwal,et al.  Penalty function approach in heuristic algorithms for constrained redundancy reliability optimization , 2005, IEEE Transactions on Reliability.

[36]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[37]  Zbigniew Michalewicz,et al.  Genetic algorithms + data structures = evolution programs (3rd ed.) , 1996 .