The Robust Cold Standby Redundancy Allocation in Series-Parallel Systems With Budgeted Uncertainty

Abstract

This paper studies a redundancy allocation problem (RAP) with cold standby strategy in non-repairable series-parallel systems. We assume that the components' reliabilities are uncertain values in a budgeted uncertainty set, with unknown probability distributions. Because the system reliability is a nonlinear function of the components' reliabilities, classical robust optimization approaches cannot be directly applied to construct the robust counterpart of this problem. Therefore, this paper for the first time proposes linear mixed integer programming (MIP) and binary equivalent models for the cold standby RAP; and by exploiting the problem structure, robust counterparts are developed to deal with budgeted uncertainty in this problem. Then, two exact solution methods are proposed: one of them solves a MIP model iteratively in a Benders' decomposition framework, and the other one solves a single binary linear model. The validity and the performance of the proposed approach are tested through a Monte Carlo simulation, and computational results.Index Terms-Budgeted uncertainty, cold standby redundancy allocation, mixed integer nonlinear programming, robust optimization, series-parallel system.

Integer Encoding Genetic Algorithm for Optimizing Redundancy Allocation of Series-parallel Systems

“…This scheme was computationally efficient but did not involve active redundancy. Feizollahi [14] studied RAP in series-parallel systems with a cold standby strategy. The linear mixedinteger programming and binary-equivalent models for the cold standby RAPs were proposed for the first time.…”

Robust quadratic assignment problem with budgeted uncertain flows

“…In practice, for an uncertain mixed integer programming (MIP) problem with interval data, solving robust counterparts for budgeted uncertainty sets is much easier than finding the minmax regret solution. For example, in redundancy allocation problems, this difference is obvious by comparing the results in [48][49][50][51], respectively. In addition, former method can find solutions with different levels of conservativeness, while the latter approach outputs only one conservative solution.…”

A hybrid Jaya algorithm for reliability–redundancy allocation problems

“…Artificial Bee Colony (ABC) (Yeh and Hsieh 2011), a hybrid algorithm of space partitioning and tabu-genetic (SP/TG) (Ouzineb, Nourelfath, and Gendreau 2011) for non-homogeneous RRAP, Honey Bee Mating Optimization (HBMO) (Sadjadi and Soltani 2012), a new mixed strategy which uses cold-standby and active strategies with a proposed GA for reliability optimization of series-parallel systems (Ardakan and Hamadani 2014b), compromise programming (Soltani, Sadjadi, and Tavakkoli-Moghaddam 2015), binary equivalent models and Mixed Integer Nonlinear Programming (MINLP) for the cold standby RRAP (Feizollahi, Soltani, and Feyzollahi 2015), Immune Algorithm (IA) (Chen and You 2005;Chen 2006), a multi-objective multi-stage reliability growth planning strategy (Li, Mobin, and Keyser 2016) using a modified non-dominated sorting GA (NSGA-II) in the early product-development stage and also multi-objective reliability optimization using GA proposed by (Ardakan, Hamadani, and Alinaghian 2015), Improved Bat Algorithm (IBA) (Liu 2016), neighbourhood search heuristic method with nonlinear programming (Chatwattanasiri, Coit, and Wattanapongsakorn 2016), and a Penalty Jaya algorithm (Rao 2016) is a new simple and efficient algorithm. Similar to the other algorithms, it only has the common parameters that will be determined by the user like population number and iterations of algorithm without need of any specific control parameters that would be determined by the user.…”