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https://doi.org/10.1007/s10489-021-02862-w
A hybrid salp swarm algorithm based on TLBO for reliability
redundancy allocation problems
Tanmay Kundu1·Deepmala1·Pramod K. Jain2
Accepted: 17 September 2021/ Published online: 10 February 2022
©The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022
Abstract
A novel optimization algorithm called hybrid salp swarm algorithm with teaching-learning based optimization (HSSATLBO)
is proposed in this paper to solve reliability redundancy allocation problems (RRAP) with nonlinear resource constraints.
Salp swarm algorithm (SSA) is one of the newest meta-heuristic algorithms which mimic the swarming behaviour of salps.
It is an efficient swarm optimization technique that has been used to solve various kinds of complex optimization problems.
However, SSA suffers a slow convergence rate due to its poor exploitation ability. In view of this inadequacy and resulting
in a better balance between exploration and exploitation, the proposed hybrid method HSSATLBO has been developed
where the searching procedures of SSA are renovated based on the TLBO algorithm. The good global search ability of SSA
and fast convergence of TLBO help to maximize the system reliability through the choices of redundancy and component
reliability. The performance of the proposed HSSATLBO algorithm has been demonstrated by seven well-known benchmark
problems related to reliability optimization that includes series system, complex (bridge) system, series-parallel system,
overspeed protection system, convex system, mixed series-parallel system, and large-scale system with dimensions 36, 38,
40, 42 and 50. After illustration, the outcomes of the proposed HSSATLBO are compared with several recently developed
competitive meta-heuristic algorithms and also with three improved variants of SSA. Additionally, the HSSATLBO results
are statistically investigated with the wilcoxon sign-rank test and multiple comparison test to show the significance of the
results. The experimental results suggest that HSSATLBO significantly outperforms other algorithms and has become a
remarkable and promising tool for solving RRAP.
Keywords Salp swarm algorithm ·TLBO ·Reliability redundancy allocation problem ·Constrained optimization
1 Introduction
Since 1950, reliability optimization plays a progressively
decisive role because of its critical requirements on sev-
eral engineering and industrial applications, and has become
a hot research topic in the engineering field. To be more
competitive in daily life, the basic goal of a reliability
engineer is always to improve the reliability of product com-
ponents or manufacturing systems. Obviously, an excellent
reliability design facilitates a system to run more safely
and reliably. In general, reliability optimization problems
Deepmala
dmrai23@gmail.com
Extended author information available on the last page of the article.
can be classified into two classes: integer reliability prob-
lems (IRP) and mixed-integer reliability problems (MIRP).
In IRP, the components reliability of the system is known
and the main task is only to allocate the redundant com-
ponents number. In case of MIRP, both the component
reliability and the redundancy allocation of the system are
to be designed simultaneously. This kind of problem in
which the reliability of the system is maximized through
the choices of redundancy and component reliability is
also known as the reliability-redundancy allocation prob-
lem (RRAP). To optimize a RRAP, redundancy levels and
component reliabilities of the system are considered as inte-
ger values and continuous values lies between zero and
one respectively. Several researchers works on this field to
solve RRAP with the objective of maximizing system reli-
ability under constraints such as the system cost, volume,
and weight etc., [44–48,66,76]. RRAP has been consid-
ered to be an NP-hard combinatorial optimization problem
because of its complexity and it has been considered as
Applied Intelligence (2022) 52:12630–12667
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