Accepted Manuscript

Title: An efficient memory-based electromagnetism-like mechanism for the redundancy allocation problem

Author: Arash Zaretalab Mohammad Teimouri S.T.A. Niaki

Mani Sharifi

PII: S1568-4946(15)00615-8

DOI: http://dx.doi.org/doi:10.1016/j.asoc.2015.09.043

Reference: ASOC 3229

To appear in: Applied Soft Computing

Received date: 21-1-2014

Revised date: 6-7-2015

Accepted date: 30-9-2015

Please cite this article as: A. Zaretalab, M. Teimouri, S.T.A. Niaki, M.

Sharifi, An efficient memory-based electromagnetism-like mechanism for the redundancy allocation problem, Applied Soft Computing Journal (2015), http://dx.doi.org/10.1016/j.asoc.2015.09.043

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Page 1 of 39

Ac ce pte d M an us cri pt 2

InitializationSet parameters and best solution = [ ] i=1

Generate ith particle randomly i=i+1

No

If i=popsize?

Yes No

Update memory matrix and ith particle= new particle

Counter = LSITER - 1

Counter = counter + 1

Yes

No

YesIs the new particle better than ith particle?

Yes i=1 and counter =1

New particle = ith particle and selecting subsystems j=1 ≤ ROM?

No

Yes

No

Change subsystem using memory matrix

Are all of the elements in jth row of memory matrix zero?

Change subsystem using neighborhood structures j=j+1

Is j = number of selected subsystem?

No i=i+1

Yes

No <

If i= popsize?

Local Search

Force Calculation

Yes

Yes

If i= popsize? i=1 Calculate Fi i=i+1

No

Move

Yes i=1

Is i = popsize?

Move the ith particle i=i+1

No

Update the best solution

Output the best solution and stop

No

Yes

Terminal condition?

Page 2 of 39

Ac ce pte d M an us cri pt 3

Highlights An efficient MBEM is proposed to solve the redundancy allocation problem MBEM employs a memory matrix in local search to save the features of good solutions Various test problems and benchmarks are used to evaluate the performance of MBEM Experimental results show that optimal solutions of all benchmark instances are obtained The computer execution times of the algorithm on all large-scale instances are reasonable

Page 3 of 39

Ac ce pte d M an us cri pt 4

An efficient memory-based electromagnetism-like mechanism for the redundancy allocation problem

Arash Zaretalaba, Mohammad Teimourib, S.T.A. Niakic, Mani Sharifib a

Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Avenue, Tehran, Iran

Emails: arash_zaretalab@yahoo.com b

Faculty of Industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Emails: m66.teimouri@gmail.com, m.sharifi@qiau.ac.ir c Department of Industrial Engineering, Sharif University of Technology, P.O. Box 11155-9414 Azadi Ave., Tehran 1458889694, Iran

Email: Niaki@Sharif.edu

Abstract

Meta-heuristic algorithms have been successfully applied to solve the redundancy allocation problem in recent years. Among these algorithms, the electromagnetism-like mechanism (EM) is a powerful population-based algorithm designed for continuous decision spaces. This paper presents an efficient memory-based electromagnetism-like mechanism called MBEM to solve the redundancy allocation problem. The proposed algorithm employs a memory matrix in local search to save the features of good solutions and feed it back to the algorithm. This would make the search process more efficient. To verify the good performance of MBEM, various test problems, especially the 33 well-known benchmark instances in the literature, are examined. The experimental results show that not only optimal solutions of all benchmark instances are obtained within a reasonable computer execution time, but also MBEM outperforms EM in terms of the quality of the solutions obtained, even for large-size problems.

Keywords: Redundancy allocation problem; electromagnetism-like mechanism; Local search; Memory-based algorithms

Page 4 of 39

Ac ce pte d M an us cri pt 5 1. Introduction

Optimization of system reliability is a widely surveyed subject in the field of reliability, where various types of models have been introduced so far. There are two general strategies to maximize system reliability namely, (1) increasing the reliability of system components, and (2) finding the optimal number of redundant components used in the system. The latter that introduces the so-called redundancy allocation problem (RAP) involves a combinatorial optimization problem, in which the aim is to find optimal number of proper components [1-3]. The models proposed for RAP are applicable to design highly reliable systems that are assembled and manufactured using off-the-shelf components. Some realworld applications include transportation system design [3], telecommunication design [4], and electrical power system design [5].

Depending on system configuration, the structure of a system in the literature of RAP is categorized as series, parallel, series–parallel [6], k-out-of-n [7], and hierarchical series–parallel or complex. Among these, the series-parallel is a common structure that is used in many designs due to its wide applications and in this research; the RAP is addressed for this system structure. A series-parallel system includes a total of s independent subsystems arranged in series, in which the ith subsystem has up to nmax functionally equivalent components arranged in parallel. Each component potentially differs in reliability, weight, cost, and other features. A subsystem can work efficiently if at least one of its components is operational. Besides, the number of components in the ith subsystem, ni, can be selected from Ti available component types where multiple copies of each type can be chosen. The schematic view of a typical series-parallel system is depicted in Fig. 1.