{'fraction_non_alphanumeric': 0.02759084791386272, 'fraction_numerical': 0.0, 'mean_word_length': 5.608888888888889, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Bi-objective Optimization of Network Reliability by Genetic Algorithm

In the real world, many infrastructures, for example, the internet, power/water supply and traffics, are network systems where high reliability is required. Independently, these systems may need costs for the construction or maintenance of components. In this study, we consider a bi-objective network with objectives of maximizing all-terminal reliabilities and minimizing costs. In general, there is trade-off relation between reliability and cost, and these objectives cannot be optimized simultaneously. Therefore, solving the problem is to find the set of Pareto solutions. However, evaluating all-terminal reliability of a given network is computationally intractable, which means that this bi-objective problem is also computationally intractable Therefore, previous study provided a Genetic Algorithm (GA) obtaining a set of quasi-Pareto solutions. However, this algorithm needed much computing time when the number of nodes was large. In this study, we improve the previous GA algorithm. Proposed algorithm reconsiders parents selection such that all non-dominated solutions and good solutions are included as parents candidates in each generation. In addition, we analyze the GA process, and the properties and distributions of non-dominated solutions are reflected in crossover process. And then, numerical experiments evaluate superiority of proposed algorithm based on comparison with other algorithms.