Vol.:(0123456789) 1 3 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2019) 41:293 https://doi.org/10.1007/s40430-019-1792-x TECHNICAL PAPER A swarm intelligence‑based approach for reliability–redundancy allocation problems Najeh Ben Guedria 1,2  · Hichem Hassine 1,3 Received: 17 October 2017 / Accepted: 10 June 2019 © The Brazilian Society of Mechanical Sciences and Engineering 2019 Abstract This paper presents a new algorithm belonging to the class of swarm intelligence methods, called the adaptive simpli- fed PSO (ASPSO)-based algorithm, for solving reliability–redundancy allocation problems. In this constrained nonlinear mixed-integer problem, both the number of redundant components and their reliability in each subsystem are to be decided simultaneously so as to maximize the reliability of the system. The proposed ASPSO operates with a new updating model to adjust the position of particles, without dealing with velocity. In addition, a randomization technique, based on the dispersion of particle bests through the search space, is used to speed up the convergence of the proposed approach and prevent it from being trapped within the local optimum. Moreover, to control the balance between exploration and exploitation, during the search process, two adaptive functions are utilized. The simulation results of four diferent benchmarks for the reliability– redundancy allocation problem are reported and compared. Accordingly, the solutions given by the new presented approach are all superior to those best known solutions provided by several methods in the literature. Keywords Reliability optimization · Redundancy allocation · Particle swarm optimization · Particles dispersion · Adaptive function 1 Introduction The main challenge for industries is to produce high-quality products at minimum cost. This goal is directly related to the reliability, maintainability and availability of the dif- ferent components of production systems. However, with the technological development and industrial revolution, manufacturing systems are more and more complex. These systems should be operational and available over the produc- tion time. Nevertheless, their failure is inevitable. Therefore, in the recent years, improving system/product reliability has become an important issue to reach satisfactory perfor- mances in real-world engineering systems. Reliability can be defned as the probability that a component, device, system or process will perform its intended function without failure for a given time when operated correctly under specifed environmental conditions. Hence, reliability studies aim to predict and estimate the probability of failure in order to optimize the operational management related to the provi- sion of failure in maintenance policies. The redundancy strategy is a helpful approach to assist the operational system design for reliability. Using redun- dant components is much more afordable to improve the system reliability instead of costing too much to enhance the component reliability. This approach has been applied in several engineering felds [1–3]. The optimal site of sys- tem parts is addressed as the redundancy allocation prob- lem (RAP). System reliability can be maximized by adding suitable redundant parts to each subsystem, while fulfll- ing particular system-level constraints such as cost, weight and volume. Thus, the main goal of the RAP is to choose Technical Editor: Fernando Antonio Forcellini, Dr. * Najeh Ben Guedria najeh.benguedria@istls.rnu.tn Hichem Hassine hassinehichem@yahoo.fr 1 Higher Institute of Transport and Logistics of Sousse, University of Sousse, Cité Erriadh Sousse BP 247, 4023 Sousse, Tunisia 2 Mechanical Laboratory of Sousse (LMS), National school of Engineering of Sousse, BP 264 Sousse Erriadh, 4023 Sousse, Tunisia 3 Mechanics, Modelling and Manufacturing Laboratory (LA2MP), National School of Engineers of Sfax, BP 1173, 3038 Sfax, Tunisia