A novel global harmony search algorithm for reliability problems (2010)(Impact Factor: 1.516; 5-Year Impact Factor:2.028)

Student: Jing-Feng DengAdvisor: Wei-Chang YehReport Date:11/29/2013

Outline• Introduction• The HS algorithm• A novel global harmony search algorithm• Experimental results and analysis• Conclusion• Some interesting applications• Books on harmony search• Reference• Q&A

Introduction• Harmony Search (HS) was proposed by

Zong Woo Geem in 2001• A novel global harmony search algorithm (NGHS) is proposed

to solve reliability allocation problem (RAP)• The proposed algorithm includes two important operators:• Position updating : to make the worst harmony of harmony

memory move to the global best harmony in each iteration• Genetic mutation: to overcome premature convergence of the

NGHS• The proposed algorithm has demonstrated stronger capacity

of space exploration than most other approaches on solving reliability problems

• Large number of experiments were done in this paper

The HS algorithm (1/3)• The HS algorithm is based on natural musical performance

processes that occur when a musician searches for a better state of harmony.

• Some Mappings• Global solution => Perfect state / Harmony• Aesthetics => Fitness function• Practice => Iteration• Experience => Harmony memory matrix• Pitch => A decision variable• Pitch range => Value range of a variable

The HS algorithm (2/3)• Step 1: Initialize the problem and algorithm parameters• Harmony memory size (HMS): the number of solution vectors in

the harmony memory• Harmony memory considering rate (HMCR)• Bandwidth (bw)• Pitch adjusting rate (PAR)• Number of improvisations (K): a stopping criterion

• Step 2: Initialize the harmony memory

The HS algorithm (3/3)• Step 3: Improvise a new harmony

• Step 4: Update harmony memory• If improvised harmony vector is better than the worst harmony,

replace the worst harmony in the HM• Step 5: Check the stopping criterion• If stopping criterion is satisfied, computation is terminated.• Otherwise, repeat step 3

A novel global harmony search algorithm (1/2)• NGHS modifies the improvisation step of the HS such that the

new harmony can mimic the global best harmony in the HM.• The NGHS and the HS are different in 3 aspects as follows:• (1) In Step 1,

• harmony memory considering rate (HMCR) and pitch adjusting rate (PAR) are excluded form the NGHS

• Genetic mutation probability (pm) is included in the NGHS

• (2) In Step 3,

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A novel global harmony search algorithm (2/2)• (3) In Step 4, the NGHS replaces the worst harmony xworst in

HM with the new harmony x’ even if x’ is worse than xworst

(Source: http://scialert.net/fulltext/?doi=jas.2010.2998.3006&org=11)

Experimental results and analysis (1/8)• 3 famous benchmark

problems are calculated• P1: A Complex (bridge)

system (Coelho, 2009)

Experimental results and analysis (2/8)• P2: A Overspeed protection system for a gas turbine (Coelho,

2009)

Experimental results and analysis (3/8)• P3: a large-scale system reliability problem (n=50)(Prasad and

Kuo, 2000; Gen and Yun, 2006)

Experimental results and analysis (4/8)

Experimental results and analysis (5/8)

Experimental results and analysis (6/8)

Experimental results and analysis (7/8)

Experimental results and analysis (8/8)

Conclusion• The optimization performance of the NGHS algorithm on

solving reliability problems has been extensively investigated by using a large number of experimental studies

• NGHS has demonstrated better convergence than the other approaches in recent literature

• NGHS has higher exploration capability of solution space through the whole iteration due to the utilization of genetic mutation

Some interesting applications

• Generalized Orienteering Problem (OP)

Sudoku Puzzle

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Timetabling Problem

Books on harmony search

Reference• http://en.wikipedia.org/wiki/Harmony_search• http://harmonysearch.info• Geem Z.W., Kim J.-H., Loganathan GV, “A new heuristic

optimization algorithm: harmony search,” Simulation 76(2), pp. 60-68, 2001.

• MATLAB• http://www.mathworks.com/matlabcentral/fileexchange/41158-

harmony-search-algorithm• C++• https://code.google.com/p/nll/

• Python• https://pypi.python.org/pypi/pyHarmonySearch

Q & A• Thanks for your listening