Allocation and sequencing in 1-out-of-N heterogeneous cold-standby systems: Multi-objective harmony search with dynamic parameters tuning

doi:10.1016/j.ress.2016.08.022

Reliability Engineering & System Safety

Volume 157, January 2017, Pages 78-86

https://doi.org/10.1016/j.ress.2016.08.022 Get rights and content

Highlights

•
This paper considers a redundancy allocation and standby element sequencing problem.
•
To solve this problem, a multi-objective harmony search algorithm is proposed.
•
Dynamic parameters tuning method is applied to improved the algorithm.
•
With this method, sensitivity of the algorithm to initial parameters is reduced.

Abstract

A redundancy allocation is a famous problem in reliability sciences. A lot of researcher investigated about this problem, but a few of them focus on heterogeneous 1-out-of-N: G cold-standby redundancy in each subsystem. This paper considers a redundancy allocation problem (RAP) and standby element sequencing problem (SESP) for 1-out-of-N: G heterogeneous cold-standby system, simultaneously. Moreover, here, maximizing reliability of cold-standby allocation and minimizing cost of buying and time-independent elements are considered as two conflict objectives. This problem is NP-Hard and consequently, devizing a metaheuristic to solve this problem, especially for large-sized instances, is highly desirable. In this paper, we propose a multi-objective harmony search. Based on Taguchi experimental design, we, also, present a new parameters tuning method to improve the proposed algorithm.

Graphical abstract

Example of solution encoding

Introduction

The system reliability optimization is very important in the real world applications. Many designers are devoted to improving the reliability of manufacturing systems or product elements to be more competitive in the market [1]. The importance of reliability in systems conceptions has been growing with advances on technologies in order to avoid failures. Reliability can be defined as the probability for a system does not fail during an interval of time in which the system must be working [2].

Since in systems, there are human errors, poor maintenance and else, failure in each subsystem is unavoidable [3] and we must reduce the probability of failure. In this regards, mainly, there are two techniques for improving the system reliability:

1.
Improving reliability of each element: this way can increase reliability of elements, but this technique is not well for all times, because improving the reliability of elements needs much time to redesign them and sometimes, this way becomes extremely costly and cannot provide desirable reliability of system [4].
2.
Use of structural standby redundancy: in general, there are three groups of redundancy strategies; hot, cold and warm standby strategies. In the first strategy (hot standby), the redundant units start to operate simultaneously with the primary online unit. This standby technique is generally used for applications. The second strategy (cold-standby) technique is commonly used and in which the standby elements do not operate until the primary element failed and standby element replace with defective element. The last redundancy strategy is warm standby that compromizes the hot and cold. Examples of the warm standby systems are redundant hard disks used to replace the failed disks in a storage system. Other examples of warm standby are in power plant and wireless sensors network [7].

The main aim of this paper is to consider the cold-standby allocation and sequencing problems that includes redundancy allocation and standby element sequencing with 1-out-of-N: G heterogeneous cold-standby systems as a multi-objective optimization problem. The sequencing of cold standby element is important and the restoration cost for standby elements is related to the time of remaining in standby condition and all of the elements have time-dependent cost, so in this study, we consider two objectives cold-standby system reliability and the sum of buying and time-independent costs. Since this problem is NP-hard [6], use of a metaheuristic algorithm can be appropriate and in this paper as well as a multi-objective metaheuristic, a new dynamic parameters tuning is also proposed to improve the metaheuristic algorithm.

The organization of this paper is given as follows. In Section 2, problem definition, the problem modeling, assumptions, notations and mathematical model are explained. In Section 3 the harmony search algorithm as a solving methodology are introduced. Moreover, in this section, solution encoding and interpretation of the dynamic tuning of the algorithm's parameters are explained. Section 4, presents the experimental design related to compare of the dynamic parameters tuning against the static parameters tuning and finally, Section 5 states our conclusions and further researches.

Section snippets

Literature review

Since 1960s, researchers have tried to solve the serial-parallel redundancy allocation problem [8]. One of the first papers that investigated on the redundancy allocation problem is Fyffe et al. [9]. The redundancy allocation problem is NP-hard; consequently, in the literature different metaheuristics have been proposed. Liang and Chen [10] used a variable neighborhood search algorithm for redundancy allocation of series-parallel systems. Safari [11] used a type of Non-dominated Sorting Genetic

Assumptions

Since different constraints and assumptions can result in different problems, we introduce the following characters which are considered in this paper.

(I)
Elements have two states: completely healthy or completely destroyed.
(II)
The time-to-failure distribution of the elements are pre-determined.
(III)
The mission time is fixed.
(IV)
The heterogeneous 1-out-of-N: G cold standby redundancy strategy with non-identical elements is used for increasing reliability of the subsystem.
(V)
It is possible the fault detection and

Solving methodology: harmony search

Harmony search (HS) algorithm, proposed by Geem et al. [27], a nature-inspired algorithm that mimickes the improvization of musician's notes [25]. Three advantages of harmony search algorithm are easy understanding of their concepts, sampling in execution and few in parameters [28]. The pseudo code of HS is shown in the Fig. 3.

The improving process takes place in the different steps, i.e., after generating a initial solution, based on the random numbers, one/two operator(s) of the HA is/are

Performance evaluation

In this section, accuracy of the proposed method to obtain the cold standby system reliability with dynamic parameters tuning is examined. In this regards, Coit [26] proposed an exact method for evaluating the reliability of a system with 14 subsystems, but he/she only considered Erlang distribution for each time-to-failure distribution of elements. His/her result of optimal solution was 0.9863 and answer of the numerical analysis method was 0.98502 (the mission time is divided into 200 parts);

Conclusion and future works

For the first time, this paper considered a redundancy allocation problem (RAP) and standby element sequencing problem for 1-out-of-N G heterogeneous cold-standby systems, simultaneously. RAP is a famous problem in reliability engineering, but if the cold-standby strategy is used in subsystem, calculating the reliability of system will be difficult. Since, initial sequence of the system's elements has a significant effect on expected costs e.g., restoration costs, holding costs, in this paper,

References (33)

T.-C. Chen
IAs based approach for reliability redundancy allocation problems
Appl Math Comput
(2006)
L.D. Afonso et al.
Modified imperialist competitive algorithm based on attraction and repulsion concepts for reliability-redundancy optimization
Expert Syst Appl
(2013)
H. Garg et al.
Multi-objective reliability-redundancy allocation problem using particle swarm optimization
Comput Ind Eng
(2013)
M.-S. Chern
On the computational complexity of reliability redundancy allocation in a series system
Oper Res Lett
(1992)
G. Levitin et al.
Optimal sequencing of warm standby elements
Comput Ind Eng
(2013)
S.J. Sadjadi et al.
Alternative design redundancy allocation using an efficient heuristic and a honey bee mating algorithm
Expert Syst Appl
(2012)
Y.-C. Liang et al.
Redundancy allocation of series-parallel systems using a variable neighborhood search algorithm
Reliab Eng Syst Saf
(2007)
J. Safari
Multi-objective reliability optimization of series-parallel systems with a choice of redundancy strategies
Reliab Eng Syst Saf
(2012)
A. Najafi
Two metaheuristics for solving the reliability redundancy allocation problem to maximize mean time to failure of a series–parallel system
Sci Iran
(2013)
G. Levitin et al.
Cold-standby sequencing optimization considering mission cost
Reliab Eng Syst Saf
(2013)

E. Zhang et al.

A practical approach for solving multi-objective reliability redundancy allocation problems using extended bare-bones particle swarm optimization

Reliab Eng Syst Saf

(2014)

Y.-K. Lin et al.

Evaluate the system reliability for a manufacturing network with reworking actions

Reliab Eng Syst Saf

(2012)

J. Sadeghi et al.

A hybrid vendor managed inventory and redundancy allocation optimization problem in supply chain management: an NSGA-II with tuned parameters

Comput Oper Res

(2014)

G. Levitin et al.

Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems

Eur J Oper Res

(2014)

C. Wang et al.

A fast approximation method for reliability analysis of cold-standby systems

Reliab Eng Syst Saf

(2012)

S. Sivasubramani et al.

Multi-objective harmony search algorithm for optimal power flow problem

Int J Electr Power Energy Syst

(2011)

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In the case of RAPs, however, several studies considered the heterogeneous cases [26]. Valaei and Behnamian [27] considered a heterogeneous RAP and solved the problem using a harmony search algorithm. In heterogeneous systems, the sequence of components comes into play if the standby strategy is implemented.
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Allocation and sequencing in 1-out-of-N heterogeneous cold-standby systems: Multi-objective harmony search with dynamic parameters tuning

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Literature review

Assumptions

Solving methodology: harmony search

Performance evaluation

Conclusion and future works

Appl Math Comput

Expert Syst Appl

Comput Ind Eng

Oper Res Lett

Comput Ind Eng

Expert Syst Appl

Reliab Eng Syst Saf

Reliab Eng Syst Saf

Sci Iran

Reliab Eng Syst Saf

Reliab Eng Syst Saf

Reliab Eng Syst Saf

Comput Oper Res

Eur J Oper Res

Reliab Eng Syst Saf

Int J Electr Power Energy Syst