Bi-objective redundancy allocation problem in systems with mixed strategy: NSGA-II with a novel initialization

The redundancy allocation problem (RAP) aims to maximize system availability while minimizing costs, subject to weight constraints. The solution to the bi-objective RAP is represented by a Pareto front, comprising non-dominated system configurations. Previous studies have focuses on refining processes such as dominance relationship determination, selection, crossover, and mutation. This paper enhances the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) by introducing a novel approach for generating the initial population. While genetic algorithms traditionally rely on random population generation, this work proposes Scaled Binomial Initialization (SBI), which adjusts the probability of generating binary numbers for subsequent individuals in the initial population. SBI improves the diversity of chromosomes encoding component allocation priorities within subsystems, resulting in greater solution dispersion in the search space and enhanced exploration of regions with extreme objective function values. SBI is specifically designed for indirect chromosome encoding, ensuring feasible solutions across the population in all generations, thereby eliminating the need for a penalty function. A continuous-time Markov chain was developed to estimate the availability of k-out-of-n subsystems with a mixed redundancy strategy. The proposed method was evaluated on four benchmarks: a series system, a series-parallel system, a complex bridge system, and a large-scale system. For small-scale systems, NSGA-II with both random initialization and SBI achieved comparable levels of effectiveness and diversity in the Pareto front. However, for large-scale systems, NSGA-II with SBI demonstrated significant advantages, as reflected in the performance metrics of the approximated Pareto front.