Unmanned combat aerial vehicles (UCAVs) have been of great interest to military organizations throughout the world due to their outstanding capabilities to operate in dangerous or hazardous environments. UCAV path planning aims to obtain an optimal flight route with the threats and constraints in the combat field well considered. In this work, a novel artificial bee colony (ABC) algorithm improved by a balanceevolution strategy (BES) is applied in this optimization scheme. In this new algorithm, convergence information during the iteration is fully utilized to manipulate the exploration/exploitation accuracy and to pursue a balance between local exploitation and global exploration capabilities. Simulation results confirm that BEABC algorithm is more competent for the UCAV path planning scheme than the conventional ABC algorithm and two other stateoftheart modified ABC algorithms.
Developments in automated and unmanned flight technologies have become an irresistible trend in many countries. As a matter of fact, unmanned combat aerial vehicles (UCAVs) have been of great importance to many military organizations throughout the world due to their capabilities to work in remote and hazardous environments [
For the UCAV path planning scheme, an optimal solution corresponds to one path that minimizes the flight route, average altitude, fuel consumption, exposure to radar or artillery, and so forth [
Like most realworld optimization problems, finding the global optimum is enormously difficult. To avoid enumerating for the global optimums, evolutionary algorithms (EAs) have been well investigated and developed as a primary branch of the heuristic algorithms, such as genetic algorithm (GA) [
ABC algorithm is a swarm intelligence algorithm motivated by the foraging behaviors of bee swarms. In this algorithm, the bee swarm mainly consists of three components: the employed bees, the onlooker bees, and the scout bees [
Applications of ABC algorithm span the areas of image processing [
Viewing improvements ever made for ABC algorithm, attentions have seldom been paid to fully utilizing the convergence messages hiding in the iteration system [
In this paper, a novel ABC algorithm modified by a balanceevolution strategy is applied for this path planning scheme. In this new algorithm (which is named BEABC), convergence status in the iteration will be fully utilized so as to manipulate the exploration/exploitation accuracy and to make a tradeoff between local exploitation and global exploration. Besides, the rule guiding the scout bees is modified according to an overall degradation procedure. This work intends for some intensive research to evaluate the performance of BEABC algorithm in this UCAV path planning scheme, in comparison with two recent stateoftheart modifications of ABC.
The remainder of this paper is organized as follows. In Section
There are some threatening installations in the combat field, for instance, missiles, radars, and antiaircraft artilleries. The effects of such installations are presented by circles in the combat field of different radiuses and threat weights [
Schematic diagram of combat field modeling.
To make this problem more concrete, let us draw a segment
To accelerate the processing speed, it is encouraged to take the
Regarding the evaluation of one candidate flight path, the threat cost
To simplify the integral operations, the flight cost from the point along
Schematic diagram of flight cost computation.
If the flight path shown above falls into a threat region, the threat cost is calculated as follows:
The preceding section holds a description of combat field model. The optimal vector
In ABC, three kinds of bees cooperate to search for the optimal nectar sources in the space, namely, the employed bees, the onlooker bees, and the scout bees [
Let
At first, all the
In each cycle of the iterations, an employed bee executes a crossover and mutation process to share information with one randomly chosen companion and search in the new position
In this equation, the
After such crossover and mutation process for the employed bees, the greedy selection strategy will be implemented. If
Afterwards, an index named
Each of the onlooker bees needs an employed bee to follow. In this case, if
In this equation, the
During the iteration, once an employed bee searches globally but finds no better position, or once an onlooker bee exploits around an employed bee without finding a better position, the invalid trail time
IABC algorithm was proposed by Li et al. in 2012 [
Equation (
IFABC algorithm mainly differs from the conventional ABC algorithm in the utilization of
Before the iteration process, as many as
In each cycle of iteration, an employed bee executes a crossover and mutation procedure to share information with its one (randomly selected) companion. This procedure is expressed in (
Afterwards, onlooker bees take over the searching process. In the IFABC algorithm, each of the employed bees is given a chance to be followed by an onlooker regardless they are “qualified” or not, pursuing to bring about more chances (i.e., more dynamics and diversity) for evolution and to fight against premature convergence. However, qualifications of the employed bees should be taken into account after all. IFABC algorithm seeks a new way to evaluate the searching performance.
Now that the roulette selection strategy is discarded in IFABC, the onlookers will directly choose their corresponding employed bees to search locally using (
For each of the employed bees together with the corresponding onlookers, the parameter
Since
To briefly conclude, the variable
BEABC algorithm mainly differs from IFABC algorithm in two aspects. One is the utilization of the parameter
Regarding the exploration procedure, a convergence factor is added in the crossover and mutation equation to manipulate the exploration accuracy. Besides, the number of elements involved in the crossover and mutation process is designed to be adaptable.
In detail, the
After such crossover and mutation process for the employed bees, the greedy selection strategy will be implemented. If
Regarding the onlooker bees, only one element in the solutions will be changed at one time using (
In each cycle of iteration, after the exploration and the exploitation procedures, any
In detail,
The pseudocode of BEABC for numerical optimization is given in Pseudocode
(1) initialize solution population using (
(2) set
(3)
(4)
(5) crossover and mutate using (
elements for the
(6) adopt greedy selection
(7)
(8)
(9)
(10)
(11)
(12)
(13) calculate each
(14) set
(15)
(16) crossover and mutate using (
(17) adopt greedy selection
(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26) set
(27)
(28)
(29) reinitialize randomly selected 90% employed bees using (
(30)
(31) memorize current best solution
(32)
(33) output global optimum
In order to investigate the efficiency and robustness of these ABC relevant algorithms, three simulation cases have been investigated. All the contrast experiments involved in this section were implemented with MATLAB R2010a and each kind of experiment was repeated 50 times with different random seeds. It is constantly set that
In the first case, the starting point is set to
Information of threat installations in combat field.
Case number  Threat center location  Threat radius  Threat grade 

1 

10  2 

10  10  

8  1  

12  2  

9  3  

7  5  

10  2  

10  4  


2 

90  7 

90  7  

20  5  

20  5  

20  5  

20  6  

20  5  

20  6  

20  5  


3 

10  5 

21  5  

10  5  

17  5  

27  5  

10  5  

20  5  

11  5 
The mean and standard deviations of cost function values.
Case number  MCN 

ABC  IABC  IFABC  BEABC  

Mean  S.D.  Mean  S.D.  Mean  S.D.  Mean  S.D.  
1  500  20  49.8813  0.5976  54.3889  3.6656  49.7975  0.6393 


500  30  52.9887  1.4259  60.4591  3.2883  51.9396  1.3434 



500  50  59.9722  2.9133  80.1747  7.7575  59.9569 


2.2310  


2  1000  20  161.7459  2.5523  171.6983  2.1826  160.1839 


1.5195 
1000  30  154.9276  2.5123  185.7927  3.7547  153.5837 


0.5549  
1000  50  157.2044  3.6031  164.9908  2.8118  157.8147  1.9058 





3  1000  20  73.5090  0.2486  73.7209  0.4729  73.0254  0.1079 


1000  30  73.9346  1.0134  74.8452  0.8904  73.6928 


0.4634  
1000  50  78.8720  3.1422  81.8885  2.7718  77.4828  2.0989 


Those bold values denote the best solutions (mean or S.D.) among four algorithms in every single case.
Comparative path planning results optimized by different ABC relevant algorithms in Case 1 (
Comparative path planning results optimized by different ABC relevant algorithms in Case 1 (
Comparative convergence curves of ABC, IABC, IFABC, and BEABC in Case 1 (
Comparative convergence curves of ABC, IABC, IFABC, and BEABC in Case 1 (
Comparative path planning results optimized by different ABC relevant algorithms in Case 2 (
Comparative convergence curves of ABC, IABC, IFABC, and BEABC in Case 2 (
Comparative path planning results optimized by different ABC relevant algorithms in Case 3 (
Comparative convergence curves of ABC, IABC, IFABC, and BEABC in Case 3 (
Regarding the paths plotted in Figures
Viewing the results in Table
In the meantime, in some early cycles of iteration, the convergence speed of BEABC tends to be roughly the same with that of the conventional ABC. Such phenomenon may be due to the fact that, during the early cycles of iteration, it is relatively easy to evolve for each of the employed bees; that is,
In this paper, BEABC algorithm is applied for the UCAV path planning optimization problem. Simulation results clearly indicate that BEABC shows more stability and efficiency in this twodimensional flight path planning optimization scheme than ABC, IABC, and IFABC.
BEABC algorithm intends to fully utilize the convergence status within the iteration system so as to manipulate the searching accuracy and also to strike a balance between the local exploitation with global exploration. Previous studies concerning the improvements of ABC always focused on the remedies from the outside world, neglecting the true convergence status hiding in the internal iteration process. In this sense, this work can be regarded as publicity for such idea. Our future work will cover some further comparisons with more stateoftheart intelligent algorithms.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported in part by the School of Advanced Engineering (SAE) in Beihang University and sponsored by the 5th and 6th National College Students’ Innovation and Entrepreneurial Training Programs in China.