SPECIAL ISSUE

Overview of Harmony Search algorithm and its applicationsin Civil Engineering

Do Guen Yoo • Joong Hoon Kim • Zong Woo Geem

Received: 31 July 2013 / Revised: 30 November 2013 / Accepted: 3 December 2013 / Published online: 12 December 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract Harmony Search (HS), a meta-heuristic algo-

rithm, conceptualizes a musical process of searching for a

perfect state of harmony (optimal solution). It allows a

random search without initial values and removes the

necessity for information of derivatives. Since the HS

algorithm was first developed and published in 2001, it has

been applied to various research areas and the world wide

attention on it has rapidly increased. In this paper, appli-

cations of HS algorithm in Civil Engineering (CE) are to be

overviewed. Articles in CE areas including water resour-

ces, structural, geotechnical, environmental, and traffic

engineering are to be reviewed thoroughly. As a results,

variety of application results show that HS can be effec-

tively used as a tool for optimization problems in CE.

Keywords Harmony Search algorithm � Literature

review � Civil Engineering

1 Introduction

Harmony Search (HS) algorithm adapted harmonies of

orchestra developed by Geem et al. [30]. When the orchestra

members first practice, there can be the good and bad har-

monies. While practicing, bad harmonies are removed, and

finally it creates the fantastic harmony (optimal solution).

When the HS algorithm was first developed in 2001, the HS

was initially applied in benchmark optimization, parameter

estimation, the travelling salesman problem, and the optimal

design of Water Distribution Networks (WDNs). In HS

applications of practical problems, however, studies about

water resources and structural engineering hold large majority

in the early stage because the major field of the developer is a

Civil Engineering (CE). In this paper, applications of HS

algorithm to CE are to be overviewed. In Sect. 2, a description

of HS is provided and its rapid growth rate is discussed. Since

2001, it has been applied to various engineering problems, and

the international attention on it has rapidly increased. Sec-

tion 3 summarizes the developing history of HS in CE. The

distribution of the number of papers in each field is presented.

Additionally, historical highlights such as algorithm applica-

tion and improvement aspects are described. In Sect. 4, we

summarize HS applications in CE in detail according to the

results of Sect. 3. Articles in CE areas including structural,

water resources, geotechnical, environmental, and traffic

engineering are to be thoroughly reviewed separately. Sec-

tion 5 is about a few concluding remarks.

2 Harmony Search and its growth

2.1 Harmony Search

A HS algorithm can be conceptualized from a musical

performance process involving searching for a best harmony

[30]. Musical performances seek a fantastic harmony

determined by aesthetic estimation, as the optimization

techniques seek a best state (global optimum) determined by

D. G. Yoo

Research Institute of Engineering and Technology,

Korea University, Seoul 136-713, Korea

J. H. Kim

School of Civil, Environmental and Architectural Engineering,

Korea University, Seoul 136-713, Korea

Z. W. Geem (&)

Department of Energy and Information Technology,

Gachon University, Seongnam 461-701, Korea

e-mail: zwgeem@gmail.com; geem@gachon.ac.kr

123

Evol. Intel. (2014) 7:3–16

DOI 10.1007/s12065-013-0100-4

objective function value. Aesthetic estimation is performed

by the set of the sounds played by musical ensemble, as

objective function value is evaluated by the set of the values

produced by adjusted variables; the better aesthetic sounds

can be improved by constant practice, as the minimization/

maximization of the objective function can mostly be

improved by repeating iteration [30], [48]. Table 1 shows a

brief summary of these two performances and Table 2

shows the brief comparison with other meta-heuristic algo-

rithms in several viewpoints. Among other meta-heuristic

algorithms as shown in Table 2, genetic algorithm (GA),

which is the most widely well-known meta-heuristic algo-

rithm, is a search algorithm based on natural selection and

the mechanisms of population genetics. The theory was

proposed by Holland [35] and further development was

performed by Goldberg [33] and many others researchers.

The HS algorithm uses Harmony Memory (HM), Har-

mony Memory Considering Rate (HMCR), and Pitch

Adjusting Rate (PAR) as optimization parameters. The best

sets of experienced harmony are memorized in HM. Figure 1

shows the structure of the HM. HM stores a group of good

harmonies throughout the practices. The size of HM is fixed.

If a new harmony is better than the worst harmony in HM, the

new harmony replaces the last place in HM. Figure 1 shows

the schematic structure of HM having three musical instru-

ments (saxophone, fiddle, keyboard). The size of HM is 3.

The musical instruments represent decision variables, and

the note of each musical instrument is the value of the

decision variable. The value of objective function corre-

sponds to the harmoniousness. The harmony (C, E, G) in rank

1 has better sound than (C, F, A) and (B, D, G) in rank 2 and 3,

respectively. If a better harmony is discovered, the new

harmony replace the harmony (B, D, G) in rank 3 which is

removed from HM. HMCR is introduced to escape from the

local optima just like the mutation probability used in GA.

HMCR is the ratio indicating whether a new harmony is

formed from the harmonies stored in HM or should be ran-

domly generated. In Fig. 1, the harmony (B, D, G) is in rank 3

which is the worst harmony in HM. Based on HMCR, a new

harmony can be developed using (E, F, D) or (C, D, E, F, G,

A, B) if the new harmony has to be formed from the har-

monies in HM or has to be randomly generated, respectively.

PAR is adopted for improving solution by searching adjacent

region, thus helping not be trapped in local optima. HS

preserves the history of past vectors (HM) and is able to vary

the adaptation rate (HMCR) from the beginning to the end of

computation. Also HS manages several vectors simulta-

neously similar to simple GA, but HS is different from simple

GA in that (1) HS works with the parameters themselves, not

en-/de-coding of the parameter set, (2) HS considers each

parameters independently when it generates a new harmony,

and (3) HS makes a new harmony from all the existing har-

mony. And these features help HS have greater flexibility

and produce better solutions. In addition, (4) HS may over-

come the drawback of GA’s building block theory which

works well only if the relationship among variables in a

chromosome is considered. If neighbor variables in a chro-

mosome have weak relationship than remote variables,

building block theory may not work well because of cross-

over operation. However, HS explicitly considers the rela-

tionship using HMCR operation.

Figure 2 shows the flowchart and Table 3 is pseudo

code of the HS algorithm. The steps in the procedure of HS

are as follows.

• Step 1. Initialize a HM.

• Step 2. Improvise a new harmony from HM.

Table 1 Comparison between musical performance and optimization

Musical performance process Optimization process

Aesthetic standard Objective function

Fantastic Harmony Global optimum

Pitches of instruments Values of variables

Musical instruments Variables

Each practice Each iteration

Solution vector Harmony

Table 2 Comparison with other meta-heuristic algorithms

Meta-heuristics Population-based versus

single point search

Using memory Generating initial

solution

Number of

neighbor

solutions

Genetic algorithm Population-based Memory less Random One neighbor

Ant colony optimization Population/single based Using memory to store

amount of pheromones

Random/local

search

n Neighbor

solutions

Simulated annealing Single based Memory less Random search One neighbor

Tabu search Single based Short term (Tabu lists),

midterm, and long

term memory

Local search n Neighbor

solutions

Harmony search Population-based algorithm

(Harmony Memory)

Using memory Random search One neighbor

4 Evol. Intel. (2014) 7:3–16

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• Step 3. If the new harmony is better than worst

harmony in HM, include the new harmony in HM, and

exclude the worst harmony from HM.

• Step 4. If stopping criteria are not satisfied, go to Step

2.

First, in Step 1, algorithm parameters are specified such

as the number of musical instruments (the number of

decision variables), the pitch range of each instrument (the

value range of each variable), the size of HM [the number

of harmonies (vectors) in HM], HMCR and Stopping Cri-

teria (for example, maximum number of iterations). Next,

harmonies (vectors) are generated randomly to fill in the

HM and sorted by aesthetic estimation (objective function

value). In Step 2, a new harmony is generated from the

HM. For instance, the pitch of the first instrument in the

new harmony (the value of the first variable in the new

vector) is one out of the stuffed pitches in HM. The pitches

of other instruments can be chosen in the same manner. On

the other hand, in smaller possibility, an instrument pitch

can be chosen from all possible ranges. An algorithm

parameter, HMCR (ranges from 0 to 1), is used for the

above procedure. For example, a HMCR of 0.95 means that

the algorithm chooses a variable value for each parameter

at each iteration from HM with 95 % probability and from

within all the possible ranges with 5 % probability. The

reason why the HMCR value of 1.00 is not recommended

is that there are some chances for the solution to be

improved with the values from outside the HM. This is the

same reason why GAs use the mutant ratio in the selection

process. In Step 3, if the new harmony is better than the

minimum harmony in HM, the new harmony is included in

HM, and the existing minimum harmony is excluded from

HM. After that, the HM is sorted by aesthetic estimation.

Finally, in Step 4, the computation is terminated when the

stopping criteria is satisfied. If not, the computation con-

tinues from Step 2.

2.2 Growth of algorithm

Since the HS algorithm was first developed in 2001, it

has been applied to various research areas including

fuzzy logic, robotics, and so on and the international

attention on it has rapidly increased as shown in Fig. 3.

In the early stage, there were attempts to modify the

optimization parameters, called the modified HS,

revised HS, and improved HS. Recently, self-adaptive

and/or parameter setting free versions of HS were

developed in an effort to avoid the providing initial

values of decision variables as well as changing the

parameter values manually in the course of the search.

Also, recent trends with the HS are multi-objective

application and developing hybrid models. Hybrid

models aim to take advantage of merits in different

types of algorithm leading to a better performance.

According to Google scholar, the paper that was

Saxophone Fiddle Keyboard

Rank1

Rank2

Rank3

C

C

B

E

F

D

G

A

G

Excellent

Good

Fair

Harmony Memory

Evaluation

Fig. 1 Structure of harmony memory

Fig. 2 Flowchart of harmony search

Table 3 Pseudocode of Harmony Search

Pseudo Code of HS

begin

Objective function f(x), x=(x1,x

2, …,x

d)

T

Generate initial harmonies (real number arrays) Define pitch adjusting rate (r

par), pitch limits and bandwidth

Define harmony memory considering rate (rhmcr

)

while ( t<Max number of iterations ) Generate new harmonies by considering existing harmonies Adjust pitch to get new harmonies (solutions) if (rand<r

hmcr), choose an existing harmony randomly

if (rand<rpar

), adjust the pitch within limits

end if else generate a new harmony via randomization end if Accept the new harmonies (solutions) if better end while Find the current best solutionsEnd

Evol. Intel. (2014) 7:3–16 5

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announced about HS for the first time, has been cited

1,143 times. In particular, the number of citation in

major literature is 343 times in Web of science [Science

Citation Index Expanded (SCIE), Social Science Cita-

tion Index (SSCI), Arts & Humanities Citation Index

(A&HCI)]. The number of citation has been sharply

increased up to July 2013 as shown in Fig. 4.

3 Developing history of HS in Civil Engineering

The number of citation in each field among 69 publications

is presented in Fig. 5 and Table 4. Application of the

structural engineering accounts for more than half and

water resources engineering occupies about 28 %. Ingram

and Zhang [36] also described that the main application

Fig. 3 Various applications and algorithm development of harmony search

Fig. 4 Citation growth in major literature (SCI(E), SSCI, and A&HCI) of harmony search

6 Evol. Intel. (2014) 7:3–16

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areas of HS are these two parts. Other fields such as geo-

technical, environmental, and traffic engineering accounts

for less than 10 %, separately. Even though the number of

publications can be changed somewhat because of sub-

jective judgment, it is a fact that the applications of HS

have been rarely performed relatively in these three areas.

The chronology of developments and applications of the

HS in each field are shown from Figs. 6, 7, 8, 9, 10. The upside

part in each figure indicated the history of applications and

downside part is the chronology of algorithm improvement.

Applications and development area of HS in water

resources engineering can be divided into three parts—

hydrological, WDNs, and groundwater management prob-

lems. In case of structural engineering, the application parts

are very varied. The number of application problem of geo-

technical, environmental, and traffic engineering is very few

because the number of publications is few themselves.

Especially, most of studies about HS applications are related

to slope stability analysis. In case of traffic engineering,

optimal design of urban road network, lot-sizing, and traffic

reconfiguration problems are applied coupled with HS.

Likewise other meta-heuristic algorithm, algorithm

improvement is performed commonly. After the application

of original HS in each field, modified or improved versions of

HS are developed. And then, some hybrid or multi-objectiveFig. 5 Proportion of the number of papers in each field of Civil

Engineering

Table 4 Distribution of the number of papers in each field of Civil Engineering

Division ’01 ’02 ’03 ’04 ’05 ’06 ’07 ’08 ’09 ’10 ’11 ’12 ’13 Sum

Water resources 2 2 1 1 3 2 4 2 2 19

Structural 1 1 1 2 6 7 8 10 3 39

Traffic 2 2 4

Geotechnical 1 1 4 6

Environmental 1 1

Sum 2 0 0 1 3 1 3 3 9 9 16 14 8 69

Fig. 6 Chronology of developments and applications of the HS in water resources engineering

Evol. Intel. (2014) 7:3–16 7

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HS are developed. Especially, these changes show remark-

ably in structural engineering. The detailed description of the

application in each field will be shown in Sect. 4.

4 Applications of HS in Civil Engineering

In Sect. 4, we summarize HS applications in CE. Articles

in CE areas including structural, water resources,

geotechnical, environmental, and traffic engineering are to

be thoroughly reviewed respectively.

4.1 Water resources engineering applications

The initial publications of the HS were applied in water

resources engineering in 2001. The performance of the

algorithm is illustrated with a least-cost pipe network

design problem [30] and the parameter estimation problem

Fig. 7 Chronology of developments and applications of the HS in structural engineering

Fig. 8 Chronology of developments and applications of the HS in geotechnical engineering

8 Evol. Intel. (2014) 7:3–16

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of the nonlinear Muskingum model [48]. Since then,

applications and development area of HS in water resour-

ces engineering can be divided into three parts—hydro-

logical, WDNs, and groundwater management problems.

In case of hydrological fields, Paik et al. [63] proposed

automatic parameter calibration method of tank model. In

that study, three optimization algorithms were tested for

automatic calibration: the first one is nonlinear pro-

gramming algorithm (Powell’s method) and the others

are a GA and HS. In applications, Modified HS, which

changed the PAR and HMCR, is adopted. The results

showed that the success of the powerful heuristic opti-

mization algorithms enables researchers to focus on other

aspects of the tank model rather than parameter calibra-

tion. The PSF-HS also adopted in hydrological problem

[27]. Geem [27] applied to the parameter estimation of

the nonlinear Muskingum model, which is an optimiza-

tion problem with continuous decision variables. Results

show that the proposed technique found good model

parameter values while outperforming a classical HS

algorithm with fixed algorithm parameter values. Kougias

and Theodossiou [49] presented classic dam scheduling

problem. This application concerned the optimum oper-

ation of a four-reservoir system over 24 h. The water

released from each dam was used for hydropower gen-

eration and irrigation. The objective was to maximize the

daily benefits gained from the reservoir system over 12

(2-h) time steps. The results showed the potential of HS

and prove its efficiency to optimize complex optimization

problems successfully.

In case of WDNs problem, the study was about cost

minimization model for the design of water distribution

pipes [24] to satisfy the minimum nodal pressure and/or

proper velocity of the pipe [29]. In addition, HS was

applied to optimal water pump switching problems in serial

water pumping system [23], [25] to minimize the energy

cost, which is vulnerable to the pump suction and discharge

pressures, and to optimize calibration using simulated and

observed data [62]. Geem [26] proposed a modified HS

algorithm with incorporating particle swarm concept. This

algorithm was applied to the design of four bench-mark

networks (two-loop, Hanoi, Balerma, and New York City

Fig. 9 Chronology of developments and applications of the HS in environmental engineering

Fig. 10 Chronology of developments and applications of the HS in traffic engineering

Evol. Intel. (2014) 7:3–16 9

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networks), with good results. Baek et al. [7] developed a

new hydraulic simulation model which can be operated

with a hydraulic simulator and an upgraded version of

Revised HS algorithm with a customized searching scheme

in WDNs, called HSPDA. The suggested model is applied

to two water distribution systems having different size each

other under abnormal operating conditions, and its results

are comparatively better than the previous hydraulic sim-

ulation model. Yoo et al. [74] optimized the nodal water

demands to satisfy the nodal pressure requirement under

the abnormal condition using revised HS. The total water

supply is optimized and defined as the effective supply,

which is the maximum water supply while maintaining the

nodal pressure requirements to guarantee the customer’s

convenience. In 2011, Geem and Cho [28] proposed a

novel parameter-setting-free technique for two major

algorithm parameters (HMCR and PAR) and combined it

with the HS algorithm, called PSF-HS. When this model

was applied to the optimal design of a popular benchmark

water networks, it reached the global optimum with good

results the global standard of optimum. Thus, PSF-HS was

expected to be used in the real-world design process under

the more user-friendly environment. The latest application

in water supply system is a multi-objective problem.

Kougias and Theodossiou [50] adjusted HS Algorithm

(HSA) in order to deal with multi-criteria water manage-

ment problems successfully. This adjustment resulted in

the creation of Multi-Objective HSA (MO-HSA). In addi-

tion, they designed the multi-objective variant Polyphonic-

HSA (Poly-HSA), which is inspired by the independent

development of different voices in music and borrows

elements from Swarm Intelligence and the single-objective

variant Global-Best HSA. MO-HSA and Poly-HSA was

introduced towards the optimization of a pump scheduling

problem. The objectives considered are water supply,

pumping cost, electric power peak demand and pump

maintenance cost. Both methods converged to non-domi-

nated fronts and provided excellent results, indicating that

these methods can be effectively used in multi-objective

water management problems.

The HS first introduced in aquifer modeling [3] in 2007.

This study proposed an inverse solution algorithm through

which both the aquifer parameters and the zone structure of

these parameters could be determined based on a given set

of observations on piezometric heads. In the zone structure

identification problem Fuzzy C-Means clustering method

was used. The association of the zone structure with the

transmissivity distribution was accomplished through an

optimization model. The HS was used as an optimization

technique. After that, HS was widely applied in ground-

water resources management models [4, 5, 6, 58]. Ayvaz

[4, 5] proposed a groundwater resources management

model in which the solution was performed through a

combined simulation–optimization model. The Modular

three-dimensional finite difference groundwater flow

model, MODFLOW and MT3DMS were used as the sim-

ulation models. These models were then combined with a

HS. The performance of the proposed HS based manage-

ment model was tested on three separate groundwater

management problems. The results showed that HS yields

nearly same or better solutions than the previous solution

methods. Afshari et al. [1] compared the performance of

the Improved HS algorithm to that of the HS, PSO (Particle

Swarm Optimization), SA (Simulated Annealing) and GA

in well placement optimization problems. A streamline

based simulator has been used as the objective function

evaluator to speed up the optimization procedure. These

algorithms have been compared in solving well placement

optimization problem of four study cases. In all of the

cases, Improved HS algorithm outperformed other algo-

rithms and produced better solutions. Luo et al. [58] pro-

posed a new multi-objective optimization methodology,

whereby a Multi-Objective Fast HS (MOFHS) was coupled

with a groundwater flow and transport model to search for

optimal design of groundwater remediation systems under

general hydrogeological conditions. The MOFHS incor-

porated the niche technique into the previously improved

fast HS and was enhanced by adding the Pareto solution set

filter and an elite individual preservation strategy to guar-

antee uniformity and integrity of the Pareto front of multi-

objective optimization problems. Also, the operation

library of individual fitness was introduced to improve

calculation speed. Moreover, the MOFHS was coupled

with the commonly used flow and transport codes MOD-

FLOW and MT3DMS, to search for optimal design of

pump-and-treat systems, aiming at minimization of the

remediation cost and minimization of the mass remaining

in aquifers. Compared with three existing multi-objective

optimization methods, including the Improved Niched

Pareto Genetic Algorithm, the Non-dominated Sorting

Genetic Algorithm II, and the MOHS, the proposed

methodology then demonstrated its applicability and effi-

ciency through a two-dimensional hypothetical test prob-

lem and a three-dimensional field problem in Indiana.

Ayvaz and Elci [6] developed a linked simulation–opti-

mization model to search alternative well field locations

with minimum cost of pumping. The proposed model

integrated MODFLOW-2000 with HS-Solver which was a

recently proposed global–local hybrid optimization algo-

rithm that integrates heuristic HS algorithm with the

spreadsheet solver add-in. Using the proposed model, a

pumping cost minimization problem was solved for dif-

ferent number of wells by considering the pumping rates as

well as the locations of additional new wells as the decision

variables. The performance of the proposed model was

evaluated on the groundwater flow model of the Tahtali

10 Evol. Intel. (2014) 7:3–16

123

watershed (Izmir-Turkey), an urban watershed which was a

key component of Izmir’s water supply system. Also, a

sensitivity analysis was performed to evaluate the model

results for different sets of HS solution parameters. Results

indicate that the proposed simulation–optimization model

was found to be efficient in identifying the optimal num-

bers, locations, and pumping rates of the pumping wells for

satisfying the given constraints. Results also showed that

the model was not only capable of obtaining just any

mathematically plausible solution but a realistic one that

could be confirmed by repetitive runs of the model.

4.2 Structural engineering applications

Structural engineering is a field of engineering dealing with

the analysis and design of structures that support or resist

loads. Structural engineering is usually considered within

CE, but it can also be studied in its own right. Saka and

Geem [68] already performed an extensive review for

mathematical and meta-heuristic applications in design

optimization of steel frame structures including HS appli-

cation. However, wide structural applications for utilizing

HS will be reviewed in this paper.

Lee and Geem [54] first described a structural optimi-

zation method based on the HS meta-heuristic algorithm.

The results indicated that the HS was a powerful search and

optimization method for solving structural engineering

problems compared to conventional mathematical methods

or GA-based approaches. In addition, discrete search

strategy using the HS algorithm was presented in detail

with its effectiveness and robustness, as compared to cur-

rent discrete optimization methods, demonstrated through

several standard truss examples in [55] and [73]. The

optimum geometry design of single layer geodesic domes

was performed in [65]. It treated the height of the crown as

design variable in addition to the cross-sectional designa-

tions of members. The design examples had shown that HS

algorithm obtained the optimum height and sectional des-

ignations for members in relatively less number of sear-

ches. HS was also applied to optimum design of steel

frames and bars in [16, 17, 19, 20, 66, 70]. Among these

studies, the objective of the design algorithm in [16] was to

obtain minimum weight frames by selecting suitable sec-

tions from a standard set of steel sections such as American

Institute of Steel Construction (AISC) wide-flange

(W) shapes. Strength constraints of AISC load and resis-

tance factor design specification and displacement con-

straints were imposed on frames. The effectiveness and

robustness of HS algorithm, in comparison with GA and

ACO, were verified using three steel frames. The com-

parisons showed that the HS algorithm yielded lighter

designs. HS based optimum design method was also pre-

sented for the grillage systems in [67]. The design

algorithm considered the serviceability and ultimate

strength constraints which were implemented from Load

and Resistance Factor Design-American Institute of Steel

Construction (LRFD-AISC). It selected the appropriate

W-sections for the transverse and longitudinal beams of the

grillage system out of 272 discrete W-section designations

given in LRFD-AISC. This selection was carried out such

that the design limitations described in LRFD-AISC were

satisfied and the weight of the system was the minimum.

Besides, HS was utilized to find optimum parameters of

Tuned Mass Damper in [8], optimum design of slab-

formwork in [38], cost optimization of a composite floor

system in [37], cost optimization of a reinforced concrete

one-way joist floor system in [39], mass optimization on

shape and sizing in [21], and the optimum design of a

monopod offshore tower [72]. Recently, HS applied in

optimum design of real-world structures [51]. The pro-

posed methodology was applied to an overhead crane

structure using different finite element simulations corre-

sponding to a solid discretization as well as mixed dis-

cretization with shell-solid and beam-solid elements. In

case of other issues, task of positioning temporary facilities

on a construction site was solved using HS in [31]. This

paper solved the problem of assigning a set of predeter-

mined facilities to a set of pre-allocated locations within a

construction site. Also, HS utilized in convenient design of

High-Performance Concrete mixtures [52] and [53]. Suh

et al. [71] proposed method for determining the material

parameters of a fatigue cracking model based on Acceler-

ated Pavement Testing.

From 2009, some modified and hybrid versions of HS

were developed. Improvement or modification of HS was

conducted by [2, 9, 40, 46, 59, 61]. Improved HS was

utilized to find optimal locations for structural dampers in

[2], the effectiveness and robustness of the dome design

optimization in [9], optimal design of steel frames under

seismic loading in [46], cost optimization of the reinforced

concrete cantilever soil retaining wall of a given height

satisfying some structural and geotechnical design con-

straints in [40], solution of multimodal structural optimi-

zation in [59], and the time-domain visco-elastic function

of hot-mix asphalt (HMA) concrete materials in [61]. In

case of hybrid HS, Zou et al. [75] proposed an Effective

Global HS (EGHS) to solve the complex bridge system

optimization problem. The EGHS combined HS with

concepts from the swarm intelligence of PSO to solve

optimization problems. The EGHS changed the structure of

HS, which makes it simpler. In addition, it excluded two

operations of HS, and they are harmony memory consid-

eration and pitch adjustment, respectively. Instead, it

introduced a new operation, and it was called location

updating. The results had demonstrated that the EGHS had

strong convergence and capacity of space exploration on

Evol. Intel. (2014) 7:3–16 11

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solving optimization problem. Kaveh and Ahangaran [42]

developed social HS model for cost optimization of com-

posite floors and Gholizadeh and Barzegar [32] proposed

an efficient HS-based algorithm for solving the shape

optimization problem of pin-jointed structures subject to

multiple natural frequency constraints. In the proposed

algorithm, an enhanced version of HS was employed in the

framework of the sequential unconstrained minimization

technique. The efficiency of the presented Sequential HS

algorithm was illustrated through several benchmark opti-

mization examples and the results were compared to those

of different optimization techniques. And a hybrid heuristic

method was developed using the HS and Charged System

Search (CSS), called HS-CSS in [43]. In this algorithm the

use of HS improved the exploitation property of the stan-

dard CSS. An energy formulation of the force method was

developed and the analysis, design and optimization are

performed simultaneously using the standard CSS and HS-

CSS. The minimum weight design of truss structures was

formulated using the CSS and HS-CSS algorithms and

applied to some benchmark problems from literature. In

addition, a Heuristic Particle Swarm Optimizer (HPSO)

algorithm for truss structures with discrete variables was

presented based on the standard PSO and the HS scheme in

[57]. The HPSO was tested on several truss structures with

discrete variables and was compared with the PSO and the

PSO with Passive Congregation (PSOPC), respectively.

The results showed that the HPSO was able to accelerate

the convergence rate effectively and had the fastest con-

vergence rate among these three algorithms. The research

showed the proposed HPSO could be effectively used to

solve optimization problems for steel structures with dis-

crete variables. In addition, a Heuristic Particle Swarm Ant

Colony Optimization (HPSACO) was also presented for

optimum design of trusses in [45]. The algorithm was

based on the PSO with PSOPC, ACO and HS scheme.

HPSACO applied PSOPC to global optimization and the

ant colony approach was used to update positions of par-

ticles to attain the feasible solution space. HPSACO han-

dled the problem-specific constraints using a fly-back

mechanism, and HS scheme deals with variable con-

straints. Results demonstrate the efficiency and robustness

of HPSACO, which performed better than the other PSO-

based algorithms having higher converges rate than PSO

and PSOPC. After that, HPSACO also applied in discrete

optimization of reinforced concrete planar frames subject

to combinations of gravity and lateral loads based on ACI

318-08 code [44].

The multi-objective HS was applied to design of low-

emission cost-effective residential buildings in [22]. In this

study, building envelope parameters were considered as

design variables and the objectives were reducing life cycle

cost and carbon dioxide emissions.

In case of self-adaptive algorithm, Hasancebi et al. [34]

presented an adaptive HS algorithm for solving structural

optimization problems. The HMCR and PAR were con-

ceived as the two main parameters of the technique for

generating new solution vectors. The adaptive HS algo-

rithm proposed here incorporates a new approach for

adjusting these parameters automatically during the search

for the most efficient optimization process. The efficiency

of the proposed algorithm is numerically investigated using

two large-scale steel frameworks that were designed for

minimum weight according to the provisions of ASD-AISC

specification. Likewise, Degertekin [18] developed two

improved HS algorithms called Efficient HS algorithm and

Self Adaptive HS algorithm, applying for sizing optimi-

zation of truss structures. Kaveh et al. [41] presented an

adapted HS algorithm was also developed for solving

facility layout optimization problems.

4.3 Geotechnical engineering applications

Geotechnical engineering is the branch of CE concerned

with the engineering behavior of earth materials. Geo-

technical engineering is important in CE, but is also used

by military, mining, petroleum, or any other engineering

concerned with construction on or in the ground. Geo-

technical engineering uses principles of soil mechanics and

rock mechanics to investigate subsurface conditions and

materials; determine the relevant physical/mechanical and

chemical properties of these materials; evaluate stability of

natural slopes and man-made soil deposits; assess risks

posed by site conditions; design earthworks and structure

foundations; and monitor site conditions, earthwork and

foundation construction. In case of geotechnical engineer-

ing, most of studies about HS applications are related to

slope stability analysis. HS was introduced in geotechnical

engineering for the first time in 2007. Cheng et al. [13]

applied six heuristic optimization algorithms including HS

to some simple and complicated slopes. The effectiveness

and efficiency of these algorithms under different cases

were evaluated, and it was found that no single method

could outperform all the other methods under all cases, as

different method had different behavior in different types

of problems. In conclusion, authors insisted that the PSO

appeared to be effective and efficient over various condi-

tions for normal cases, and this method is recommended to

be used. For special cases where the objective function was

highly discontinuous, the SA method appears to be a more

stable solution. Unlike the other applications, Kayhan et al.

[47] proposed to obtain input ground motion datasets

compatible with given design spectra based on HS algo-

rithm. The utility of the solution model was demonstrated

by generating ground motion datasets matching the Euro-

code-8 design spectra for different soil types out of an

12 Evol. Intel. (2014) 7:3–16

123

extensive database of recorded motions. A total of 352

records were selected from the Pacific Earthquake Engi-

neering Center Strong Motion Database based on magni-

tude, distance, and site conditions to form the original

ground motion domain. Then, the proposed HS based

solution algorithm is applied on the pre-selected 352 time-

series to obtain the ground motion record sets compatible

with design spectra. The results demonstrated that the

proposed HS based solution model provides an efficient

way to develop input ground motion record sets that were

consistent with code-based design spectra.

After that, an improved HS algorithm [15] was proposed

which is found to be more efficient than the original HS

algorithm for slope stability analysis. The effectiveness of

the proposed algorithm was examined by considering

several published cases. The improved HS method was

applied to slope stability problems with five types of pro-

cedure for generating trial slip surfaces. It is demonstrated

that the improved HS algorithm is efficient and effective

for the minimization of factors of safety for various diffi-

cult problems. In 2011, two hybrid HS and one improved

HS algorithms were proposed in [12, 14, 56]. Cheng et al.

[12] determined the factor of safety for a prescribed slip

surface from an equivalent lower bound method, which

could satisfy all equilibrium conditions without an inter-

slice force function. This approach gave an overall factor

of safety close to that of the classical methods for normal

problems, while the thrust line, the local factor of safety for

individual slice/block and the progressive yielding phe-

nomenon could be estimated, which would be useful for

some special cases. The force and moment equilibrium of

every slice would be satisfied, while the location of the

thrust line would always be acceptable in the proposed

formulation. To solve the difficult optimization problem,

an innovative coupled PSO and HS algorithm was pro-

posed, and a practical engineering problem for which the

factor of safety was close to 1.0 was used to illustrate the

consideration of the residual strength in the limit equilib-

rium slope stability analysis. Li et al. [56] proposed hybrid

algorithm that two new parameters simulating the HS

strategy could be adopted instead of the three parameters

which were required in the original PSO algorithm to

update the positions of all the particles. The improved PSO

was used in the location of the critical slip surface of soil

slope, and it was found that the improved PSO algorithm

was insensitive to the two parameters while the original

PSO algorithm could be sensitive to its three parameters.

Cheng et al. [14] tried to demonstrate that the variation

principle could be replaced by the use of modern artificial

intelligence based HS which can be applied to much more

complicated problems. Two different improved HS algo-

rithms are proposed in this paper. The new algorithms

differ from the original algorithm in that: (1) The

harmonies are rearranged into several pairs and the better

pairs are used to develop several new harmonies; (2) dif-

ferent probabilities are assigned to different harmonies.

The robustness of the proposed methods is demonstrated by

using three difficult examples in geotechnical problems,

and the sensitivities of the related optimization parameters

are investigated through statistical orthogonal analysis.

4.4 Environmental engineering applications

In general, environmental engineering is the integration of

science and engineering principles to improve the natural

environment (air, water, and/or land resources), to provide

healthy water, air, and land for human habitation and for

other organisms, and to remediate pollution sites. Fur-

thermore it is concerned with finding plausible solutions in

the field of public health, such arthropod-borne diseases,

implementing law which promotes adequate sanitation in

urban, rural and recreational areas. It involves waste water

management and air pollution control, recycling, waste

disposal, radiation protection, industrial hygiene, environ-

mental sustainability, and public health issues as well as

knowledge of environmental engineering law. At many

universities, environmental engineering programs follow

either the department of CE or the department of chemical

engineering at engineering faculties. Environmental ‘civil’

engineers focus on hydrology, water resources manage-

ment, bioremediation, and water treatment plant design. In

this paper, application of hydrology and water resources

management is excluded in environmental engineering. In

case of environmental engineering field, therefore, only

one paper has been published in major literature. Even

though the number of publications can be changed some-

what because of subjective judgment, it is a fact that the

applications of HS have been rarely performed in envi-

ronmental engineering area. Chang et al. [11] proposed a

novel Quantum HS (QHS) algorithm-based Discounted

Mean Square Forecast Error (DMSFE) combination model.

In the DMSFE combination forecasting model, almost all

investigations assign the discounting factor (b) arbitrarily

since b varied between 0 and 1 and adopt one value for all

individual models and forecasting periods. The original

method did not consider the influences of the individual

model and the forecasting period. This work contributed by

changing b from one value to a matrix taking the different

model and the forecasting period into consideration and

presenting a way of searching for the optimal b values by

using the QHS algorithm through optimizing the Mean

Absolute Percent Error (MAPE) objective function. The

QHS algorithm-based optimization DMSFE combination

forecasting model was established and tested by forecast-

ing CO2 emission of the World top-5 CO2 emitters. The

evaluation indexes such as MAPE, Root Mean Squared

Evol. Intel. (2014) 7:3–16 13

123

Error and Mean Absolute Error were employed to test the

performance of the approach. In conclusion, it is a note-

worthy fact that application HS algorithms in environ-

mental engineering are new and fresh even if few papers

have been published.

5 Traffic engineering applications

Traffic engineering is a branch of CE that uses engineering

techniques to achieve the safe and efficient movement of

people and goods on roadways. It focuses mainly on research

for safe and efficient traffic flow, such as road geometry,

sidewalks and crosswalks, segregated cycle facilities, shared

lane marking, traffic signs, road surface markings and traffic

lights. Traffic engineering deals with the functional part of

transportation system, except the infrastructures provided. In

case of traffic engineering, HS applied in urban road, traffic

and dynamic lot size design problem [10, 60, 64, 69]. Mi-

andoabchi et al. [60] investigated bimodal discrete urban

road network design problem with bus and car modes. The

problem consisted of decision making for lane addition to the

existing streets, new street constructions, converting some

two-way streets to one-way streets, lane allocation for two-

way streets, and the allocation of some street lanes for

exclusive bus lanes. Two objectives were considered in the

problem: maximization of consumer surplus, and maximi-

zation of the demand share of the bus mode. The interaction

of automobile and bus flows were explicitly taken into

account and a modal-split/assignment model was used to

obtain the automobile and bus flows in the deterministic user

equilibrium state. The main contribution of this paper is in

proposing a new network design problem that combined the

road network design decisions with the decision making for

bus networks. The problem was formulated as a mathemat-

ical program with equilibrium constraints. A hybrid of GA

and SA, a hybrid of PSO and SA, and a hybrid of HS and SA

were proposed to solve the problem. Piperagkas et al. [64]

solved the dynamic lot-size problem under stochastic and

non-stationary demand over the planning horizon. The

problem was tackled by using three popular heuristic meth-

ods from the fields of evolutionary computation and swarm

intelligence, namely particle swarm optimization, differen-

tial evolution and HS. The algorithms are properly manip-

ulated to fit the requirements of the problem. Their

performance, in terms of run-time and solution accuracy, is

investigated on test cases previously used in relevant works.

Salcedo-Sanz et al. [69] focused on the reconfiguration of

one-way roads in a city after the occurrence of a major

problem (e.g. a long-term road cut) in order to provide

alternative routes that guarantee the mobility of citizens. In

this manuscript a novel definition of this problem was for-

mulated, for whose efficient resolution a two-objective

approach based on the HS algorithm was proposed. The

effectiveness of this proposal was tested in several synthetic

instances, along with a real scenario in a city near Madrid,

Spain. Extensive simulation results had been analyzed to

verify that our proposal obtains excellent results in all the

considered scenarios.

6 Conclusions

In this paper, articles in CE areas including structural, water

resources, geotechnical, environmental, and traffic engi-

neering are thoroughly reviewed. From the results of over-

view, we can conclude some remarks. Since the development

of HS, the most applications of HS in CE are focused on

water resources and structural engineering. However, the

applications in environmental and traffic engineering are

fresh and new even though few papers were published lately.

There have been some attempts to enhance the quality of

optimization results in CE areas. In the early stage, some

papers attempted to modify the parameters called the

modified HS, revised HS, and improved HS. In these days,

self-adaptive or parameter setting free versions of HS have

been developed in an effort to avoid the providing initial

values of decision variables as well as changing the

parameter values manually in the course of the search.

Also, recent trends with the HS are multi-objective appli-

cation and developing hybrid models.

In applications aspects, the HS was initially applied in

benchmark and simple engineering problems to verify the

applicability of the algorithm itself. Recently, however, it

has been used and utilized in the real-world problems. The

application results show that HS can be effectively used as

tool for optimization problems in CE. Therefore, it can be

recommended as the world-wide optimization techniques,

and it also can be used in wide range of CE.

Acknowledgments This work was supported by the Gachon Uni-

versity research fund of 2013 (GCU-2013-R390).

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