Integer encoding genetic algorithm for optimizing redundancy allocation of series-parallel systems

Abstract

Reliability redundancy allocation is a combinatorial optimization problem, and numerous intelligent evolutionary algorithms (e.g., genetic algorithm and ant colony optimization) have been proposed to solve it. However, various shortcomings, such as problem specificity and high complexity, hinder their applications. An integer encoding genetic algorithm, namely, integer matrix chromosome encoding scheme, was proposed to improve the effectiveness and computational efficiency of redundancy allocation for series-parallel systems and represent the component mixing in subsystems with integers. The related crossover with a binary window and mutation using a matrix with random float numbers was developed to perform combinatorial evolution. The adjusting operator was designed to guarantee the feasibility of chromosomes, combined with the non-dominated sorting genetic algorithm (NSGA-II) in which a constraint Pareto dominance was introduced to handle design constraints without external coefficients. Numerical and engineering examples of an agricultural Internet of Things for greenhouse planting were provided to illustrate the effectiveness of the proposed algorithm. Results show that the proposed novel algorithm can solve a typical model for reliability redundancy allocation, i.e., a non-maintained bi-state series-parallel system with active redundancy and component mixing strategy. The constraint Pareto dominance is introduced on the basis of the traditional NSGA-II to avoid the complexity and instability of penalty function approaches. The constructed three-objective redundancy allocation problem model can measure the trade-off relationship among three objectives, namely, system reliability, cost, and weight. The improved NSGA-II has the best stability when the optimized value for crossover probability is 0.98 and the mutation probability is set to a small value. Advantages of the presented model and method include its convenience and suitability for different genetic evolutionary platforms.