乌鸦搜索算法及其对应原文

A novel metaheuristic method for solving constrained engineering

optimization problems: Crow search algorithm

Alireza Askarzadeh

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Department of Energy Management and Optimization, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology,

Kerman, Iran

article info

Article history:

Received 27 September 2015

This paper proposes a novel metaheuristic optimizer, named crow search algorithm (CSA), based on the

intelligent behavior of crows. CSA is a population-based technique which works based on this idea that

crows store their excess food in hiding places and retrieve it when the food is needed. CSA is applied to

optimize six constrained engineering design problems which have different natures of objective func-

tions, constraints and decision variables. The results obtained by CSA are compared with the results of

various algorithms. Simulation results reveal that using CSA may lead to finding promising results com-

pared to the other algorithms.

Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Engineering design is defined as a decision making process to

solutions.

Conventional search methods have long been applied to solve

engineering design problems. Although these methods find

promising results in many real problems, they may fail in more

complex design problems. In real design problems, the number

of decision variables can be very large and their effect on the objec-

tive function can be very complicated. The objective function may

have many local optima, whereas the designer is interested in the

global optimum. Such problems cannot be handled by conven-

tional methods that only find local optima. In these cases, efficient

but there is no guarantee that optimal solutions can be reached. It

is hoped that these algorithms work most of the time, but not all

the time. Metaheuristic algorithms could be suitable for global

optimization [2]. Based on Glover’s convention, all the modern

nature-inspired methods are called metaheuristics [3].

Current trend is to utilize nature-inspired metaheuristic algo-

rithms to tackle difficult problems and it has been shown that

metaheuristics are surprisingly very efficient [1,2]. For this reason,

the literature of metaheuristics has expanded tremendously in the

last two decades [4,5]. Some of the well-known metaheuristic algo-

[10], group search optimizer (GSO) based on animal searching

behavior [11], firefly algorithm (FA) based on the flashing light pat-

terns of tropic fireflies [12], etc. To date, researchers have only used

a very limited characteristics inspired by nature and there is room

for development of more algorithms. One of the main motivations

of this paper is to develop a user-friendly (simple concept and easy

implementation) metaheuristic technique by which we may obtain

promising results when solving optimization problems.

Crows are widely distributed genus of birds which are now con-

sidered to be among the world’s most intelligent animals [13,14].

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Tel./fax: +98 342 6233176.

E-mail addresses: a.askarzadeh@kgut.ac.ir, askarzadeh_a@yahoo.com

Computers and Structures 169 (2016) 1–12

ði ¼ 1; 2; ...; N;

Þ where x

¼ x

; x

; ...; x

. This is the best position that crow i has obtained so far.

The memory of each crow is initialized. Since at the initial iter-

ation, the crows have no experiences, it is assumed that they have

hidden their foods at their initial positions.

Step 3: Evaluate fitness (objective) function

For each crow, the quality of its position is computed by insert-

ing the decision variable values into the objective function.

Step 4: Generate new position

Crows generate new position in the search space as follows: sup-

pose crow i wants to generate a new position. For this aim, this

crow randomly selects one of the flock crows (for example crow

Fig. 1. Flowchart of state 1 in CSA (a) fl < 1 and (b) fl > 1. Crow i can go to every position on the dash line.

Fig. 2. Pseudo code of the proposed CSA.

3

r

Table 2 represents the best solution obtained by CSA for three-

bar truss design problem over 50 independent runs. Table 3 shows

the comparison of the statistical results obtained by CSA and those

of the best index, CSA produces better results than SC and MBA. In

this case, the results produced by CSA are same as the results