A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems

•Propose a math model to optimize redundancy-availability of a mega-systems.•Considering the multi-state components with minor or major failure.•A vendor selection is added to the redundancy-reliability optimization problem.•Considering Tec-and-Org activities to increase the components’ reliability.•Adopting the Multi-Objective evolutionary algorithms to solve the model. This paper presents a multi-objective availability-redundancy allocation optimization model for a hyper-system. The hyper-system consists of B systems with shared resources. The structure of the systems is series-parallel subsystems consisting of multi-failure and multi-state components. The components may be purchased from different suppliers based on their price and discounts. It is assumed that technical and organizational activities continuously affect the components' failure rates and the subsystems' working conditions before starting the system's mission horizon. The model aims to find the optimal number and the type of the subsystems' components for all systems from each supplier and the level of the technical and organizational activities. The problem is classified as an NP-hard class of problems; thus, four multi-objective meta-heuristics are adapted to solve the proposed model. These four meta-heuristics are non-dominated sorting genetic algorithm type II (NSGA-II) and type III (NSGA-III), non-dominated ranking genetic algorithm (NRGA), and multi-objective evolutionary algorithm based on decomposition (MOEA/D). The parameters of all algorithms are calibrated using response surface methodology. Moreover, a method based on a sequential combination of multi-objective evolutionary algorithms and data clustering is used on the Pareto solutions to yield a smaller and more manageable set of prospective solutions. The results showed the superiority of the NSGA-III and the MOEA/D algorithms to solve the presented model.