Hierarchical optimization: an introduction
Annals of Operations Research - Special issue on hierarchical optimization
Reliability Importance and Invariant Optimal Allocation
Journal of Heuristics
Multi-level redundancy optimization in series systems
Computers and Industrial Engineering - Special issue: Selected papers from the 27th international conference on computers & industrial engineering
Optimal multilevel redundancy allocation in series and series-parallel systems
Computers and Industrial Engineering
Genetic algorithm based multi-objective reliability optimization in interval environment
Computers and Industrial Engineering
A tutorial for competent memetic algorithms: model, taxonomy, and design issues
IEEE Transactions on Evolutionary Computation
Recent Advances in Optimal Reliability Allocation
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
On the computational complexity of reliability redundancy allocation in a series system
Operations Research Letters
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With the popularity of multilevel design in large scale systems, reliability redundancy allocation on multilevel systems is becoming attractive to researchers. Multilevel redundancy allocation problem (MLRAP) is not only NP-hard, but also qualifies as hierarchy optimization problem. Exact method could not tackle MLRAP very well, so heuristic and meta-heuristic methods are often used to solve it. To improve the effectiveness of current algorithms on MLRAP, this paper proposes a hybrid genetic algorithm (HGA) based on the two dimensional redundancy encoding mechanism. Instead of hierarchical genotype representation, a two dimensional array is used to represent the solutions to MLRAP. Each row of the array contains the redundancy information of a certain unit in the system and each element in one row stands for the redundancy value of one element of that unit. The number of rows of this array is fixed and equals to the number of distinct units in the system. Each row of the array is an unfixed-length vector whose length depends on the redundancy of all elements of its parent unit. On top of this two dimensional arrays, a local search operator employing simulated annealing strategy is used to generate new population for the next generation instead of the traditional genetic operators. Experimental results have shown that our two dimensional arrays based HGA outperforms the state-of-the-art approaches using two kinds of multilevel system structure.