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Journal of Computational Science 25 (2018) 50–57

Contents lists available at ScienceDirect

Journal of Computational Science

j ourna l h om epage: www.elsev ier .com/ locate / jocs

path planning method using adaptive polymorphic ant colonylgorithm for smart wheelchairs

huqing Jiao a,∗, Kai Ma b, Yiling Rong c, Peng Wang d, Hongkai Zhang e,∗, Shuihua Wang f,∗

School of Information Science and Engineering, Changzhou University, Changzhou, 213164, ChinaCollege of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, ChinaChangzhou Urban Planning Compilation and Research Centre, Changzhou, 213002, ChinaInstitute of Robots, Changzhou University, Changzhou, 213164, ChinaSchool of Electronic and Information Engineering, Anhui Jianzhu University, Hefei, 230022, ChinaDepartment of Informatics, University of Leicester, Leicester, LE1 7RH, UK

r t i c l e i n f o

rticle history:eceived 7 August 2017eceived in revised form 16 January 2018ccepted 5 February 2018vailable online 7 February 2018

eywords:ath planningolymorphic ant colony algorithmlobal optimummart wheelchairs

a b s t r a c t

In many cases, users of smart wheelchairs have difficulties with daily maneuvering tasks and wouldbenefit from an automated navigation system. With multi-colony division and cooperation mechanism,the polymorphic ant colony algorithm is helpful to solve optimal path planning problems by greatlyimproving search and convergence speed. In this paper, a path planning method for smart wheelchairs isproposed based on the adaptive polymorphic ant colony algorithm. To avoid ant colony from getting intolocal optimum in the process of reaching a solution, the adaptive state transition strategy and the adaptiveinformation updating strategy were employed in the polymorphic ant colony algorithm to guarantee therelative importance of pheromone intensity and desirability. Subsequently, the search ant maintains therandomness for the search of the global optimal solution, and then the deadlock problem is solved bymeans of the direction determination method that improves the global search ability of the algorithm.The target path planning and obstacle path planning are respectively carried out by using the adaptivepolymorphic ant colony algorithm. Experimental results indicate that the proposed method provides

better performance than the improved ant colony algorithm and the polymorphic ant colony algorithm.Furthermore, the efficiency of finding an optimum solution is higher than the average polymorphic antcolony algorithm. The proposed method, which achieves superior performance in path planning for smartwheelchairs, is even racing ahead of other state-of-the-art solutions. In addition, this study reveals thefeasibility of using it as an effective and feasible planning path tool for future healthcare systems.

© 2018 Elsevier B.V. All rights reserved.

. Introduction

Smart wheelchairs give people with disabilities not only mobil-ty but also the necessary help and support to handle daily livingctivities. The smart wheelchair combines a variety of researchelds, such as machine vision [1], robot navigation and posi-

ioning [2], pattern recognition [3], multi-sensor fusion [4] anduman-machine interface [5]. Especially in automatic navigation,ccurate path planning results will greatly improve the perfor-

ance of a smart wheelchair [6]. It is desirable to use reliable

ath planning methods to enhance awareness of the status of con-emporary smart wheelchair technology, and ultimately increase

∗ Corresponding authors.E-mail addresses: jzqtec@163.com (Z. Jiao), zhk@ahjzu.edu.cn (H. Zhang),

huihuawang@ieee.org (S. Wang).

ttps://doi.org/10.1016/j.jocs.2018.02.004877-7503/© 2018 Elsevier B.V. All rights reserved.

the functional mobility and productivity of users. Intelligent opti-mization algorithms, which are simple, efficient and adaptive, havebeen introduced to solve path planning problems, especially ininfrastructures and facilities for healthcare [7–9]. Ant colony opti-mization is an intelligent search algorithm developed by MarcoDorigo’s doctoral thesis from a long-term observation of ant colonyforaging behaviors [10]. Different from other path planning tech-niques, for instance, heuristic search or potential fields, it is aprobabilistic technique for solving computational problems whichcan be reduced to finding good paths through graphs. Hence antcolony algorithm has widely used in transportation, logistics anddistribution, network analysis, pipeline and other fields in recentyears [11,12].

At present, a large number of scholars are doing applied researchon the ant colony algorithm. For instance, Xia et al. studied theissues of dynamic nature, instability and multi QoS property restric-tions of Web service in the process of services combinatorial

https://doi.org/10.1016/j.jocs.2018.02.004http://www.sciencedirect.com/science/journal/18777503http://www.elsevier.com/locate/jocshttp://crossmark.crossref.org/dialog/?doi=10.1016/j.jocs.2018.02.004&domain=pdfmailto:jzqtec@163.commailto:zhk@ahjzu.edu.cnmailto:shuihuawang@ieee.orghttps://doi.org/10.1016/j.jocs.2018.02.004

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Z. Jiao et al. / Journal of Comp

ptimization, and proposed a multiple pheromone dynamicallypdated ant colony algorithm [13]. Sheng et al. proposed a cred-

ble service discovery method based on the improved ant colonylgorithm for the service discovery problems in the unstructured2P networks [14]. Luo et al. proposed an improved ant colony algo-ithm based on dynamic node planning for the problem of selectionf optimal measuring points for analog circuit [15]. Shan et al.mployed the ant colony algorithm to the smart wheelchair pathlanning method to solve the problems of local optimal in the pathearch process for the smart wheelchair [16]. Mohamed et al. pro-osed multi-division vehicle routing problems based on the hybridnt colony algorithm by combining local search and basic ant colonylgorithm [17]. Although the ant colony algorithm is widely used,nd reflects good search features during the path optimization, itas shortcomings of likeliness to fall into local optimum and longearch time, etc [18,19].

In traditional ant colony algorithms, the paths are graduallyxplored by ants and the search efficiency of the algorithms is low.o solve this problem, many scholars put forward some improvedethods to cope with such problem. Yao et al. put forward the

daptive parallel ant colony algorithm [20]. With the aid of thisethod, it can determine the optimal combination of parameters

epending on the search stage to avoid stagnation to a certainxtent. Hu et al. applied dynamic calls and the rule of increase ofheromone on the optimal path into the basic ant colony algo-ithm, and proposed the optimal path model with a number ofath quality constraints [21]. Du et al. designed the improved poly-orphic ant colony algorithm based on the secondary annealingechanism according to the advantages of the polymorphic ant

olony algorithm and the simulated annealing algorithm, allowinghe pheromone release to reflect the path quality better than before22]. Li et al. introduced the roulette method to the state transitionule, and classified the search into local search and global search.y doing so, it avoid the algorithm from falling into local optimum23]. Yang et al. proposed the improved ant colony algorithm byombining group intelligence and local search, effectively solvinghe multi-dimensional problem in the traveling salesman problems24].

Containing a variety of ant colonies and pheromones, the poly-orphic ant colony algorithm combines local search and global

earch, allowing the searching speed and convergence speed toe greatly improved [25–27]. In this paper, an adaptive polymor-hic ant colony algorithm is proposed to solve the path planningroblem in smart wheelchairs. The search ant makes state transi-ion according to the pseudo-random rule, and combines the stateransition strategy and the adaptive parallel strategy of the searchnt during the search to get the adaptive state transition strategynd the adaptive information strategy to avoid the algorithm fromalling into local optimum. By employing the direction determin-ng method, the deadlock problem was properly addressed and thencreased efficiency of global search in a complex environment ischieved. The adaptive polymorphic ant colony algorithm proposeds applied separately to the target path and obstacle path planningxperiments, and the experimental results are compared with theesults obtained from the improved ant colony algorithm and theeneral polymorphic ant colony algorithm. The comparison shows,hat the adaptive algorithm in this paper is better to implementhe path planning for smart wheelchairs with fewer iterations andigher search efficiency.

. Polymorphic ant colony algorithm

The multi-colony ant colony is introduced into the polymor-hic ant colony algorithm based on the basic ant colony algorithm,hich includes scouts, search and worker ants. Scouts take the path

nal Science 25 (2018) 50–57 51

node of each wheelchair as the center and leave the investigationelements during the investigation, so that search ants may make achoice when they arrive at the path node. Scouts and search antswork in the polymorphic ant colony and perform tasks as follows:

Scouts: The scouts (quantity: m) are placed separately on thepath nodes of the wheelchairs (quantity: n), and each scout inves-tigates the path nodes of the other wheelchair (quantity: n − 1),taking the path node of the wheelchair as the center, and combinesthe result of the investigation with the existing information to con-stitute the investigation element referred to as s[i][j] and markedon the path from the path node i to the path node j. s[i][j] (i, j = 1, 2,. . ., n − 1, i /= j) is calculated by the following formula:

s[i][j] =

⎧⎨⎩dminij

dij,

path node j is in the selectable

range of the path node i0, otherwise

(1)

where dij the total path of the selected ant; dminij is the minimumdistance to the other n − 1 path nodes when taking the wheelchairpath node i as the center.

Based on this result, the information amount on each path at theinitial time is set firstly as follows:

�ij(0) =

⎧⎨⎩C · s[i][j], s[i][j] /= 0C · dmin

ij

dmaxij

, otherwise(2)

where dmaxij

is the maximum distance to the other n − 1 path nodeswhen taking the path node i as the center. C is the informationamount on each path at the initial time.

Search ant: the adaptive transition probability pkij

(t) of ant k(k = 1, 2, . . ., m) from the path node i to the path node j in the searchprocess is calculated as follows:

pkij(t) =

⎧⎪⎪⎨⎪⎪⎩

�ij(t)˛ · �ij(t)ˇ∑

h/∈tabuk

�ih(t)˛ · �ih(t)ˇ

, j /∈ tabuk and s[i][j] /= 0

0, otherwise

(3)

where �ij(t) is the information amount on the path (i, j) at the timet; �ij(t) is the heuristic function, and its expression is �ij(t) = 1dij ; �is the information heuristic factor, representing the relative impor-tance of the path; ̌ is the desired heuristic factor, representing therelative importance of the visibility; tabuk is the taboo collection,and t is the amount of evolution generation.

After all the ants complete a cycle, the pheromone on each pathis updated as the following formula:

�ij(t + 1) ={� · �ij(t) + (1 − �) · ��ij(t), s[i][j] /= 0� · �ij(t), otherwise

(4)

Where � is the pheromone evaporation factor, 1 − � is thepheromone residual factor; in order to prevent the unlimited accu-mulation of information, the value range of � is P ⊂ [0, 1); ��ij(t)is the amount of information released by all the ants on the path (i,

j) in this cycle, and ��ij(t) =m∑k=1��k

ij(t).

��kij

(t) is the amount of information released by ant k on thepath (i, j) in this cycle, and its formula is as follows:

��kij(t) =

⎧⎨⎩Q · (dmin

ij/dij)

Lk,

ant k goes through(i, j)

and s[i][j] /= 00, otherwise

(5)

5 utational Science 25 (2018) 50–57

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and then moves on in this direction, as shown in the arrow in Fig. 2.The application of this method to solve the deadlock problem

aims at improving the ability of global search of the algorithm,

2 Z. Jiao et al. / Journal of Comp

here Q is a constant, t is the evolution generation, and Lk is theength of the journey traveled by ant k.

. Adaptive polymorphic ant colony algorithm

In the polymorphic ant colony algorithm, search ants may stillall into local optimum in the range determined by the investigationlements, and the pheromone intensity and the desired intensityre ignored in the iterations. Based on polymorphic ant colonylgorithm, the adaptive parallel rule and the pseudo-random pro-ortion rule are introduced in this paper to effectively avoid theroblem of local optimum in the search process. Search ants makes

state transition in accordance with the pseudo-random rule in theearch stage while adopting the adaptive parallel strategy to deter-ine the optimal combination parameters in the state transition

unctions. The state transition rule adopted is as follows:

=

⎧⎨⎩

argj ∈ allowedk

max{

[�ij(t)]˛[�ij(t)]

ˇ}, q < q0

pkij

(t), otherwise(6)

here q is the random number uniformly distributed in [0,1],0 = 1 − e−1/K(K = 1, 2, . . ., N), and N is the iteration number.

According to this rule, whenever the ants select which pathode to move to, a random number is generated in [0,1], and thenhe transition direction is determined based on the state transitionule. The adaptive transition probability pk

ij(t) can be calculated as

ollows:

kij(t) =

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

�ij(t)4˛tN

+ 1 · �ij(t)2ˇtN

+ 1

∑h/∈tabuk

�ih(t)4˛tN

+ 1 · �ih(t)2ˇtN

+ 1,

j /∈ tabuk

and s[i][j] /= 0

0, otherwise

(7)

here �ij(t) is the information amount on the path (i, j) at the time t;

ij(t) is the heuristic function, and its expression is �ij(t) = 1dij ; a ishe information heuristic factor, representing the relative impor-ance of the path; ̌ is the desired heuristic factor, representinghe relative importance of the visibility; tabuk is the taboo collec-ion, t is the evolution generation, and N is the maximum evolutioneneration.

In the polymorphic ant colony algorithm, the search ant willeave the pheromone in a possible optimal solution path whilegnoring the other paths, which may lead to a final solution which

ay not be the best one. To avoid this, this paper introduces thedaptive information update strategy, and the adaptive informa-ion amount is determined by the following formula:

�kij(t) =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎛⎜⎜⎜⎜⎜⎝

[Q · (dminij/dij)]

l∑k=1dLk

· 1Lbest

⎞⎟⎟⎟⎟⎟⎠

2tN

+ 1

,k goes through(i, j)

and s[i][j] /= 0

0, otherwise(8

here Q is a constant, t is the evolution generation, N is the maxi-um evolution generation, Lbest is the current optimal path length,

is the optimal path among the first l paths, and dLk

is the unsorted

ath length.

Adaptively updating the amount of information in the searchrocess avoids the ignorance of the paths because less pheromonere left on them, and also prevents the pheromone from decreasing

Fig. 1. The smart wheelchair falls into deadlock.

with the increase of the number of iterations [28,29]. However, theant colony may fall into a deadlock when encountering a complexenvironment during the path search. With the grid length set as 1 m,the algorithm falls into the deadlock state if the smart wheelchaircannot move to the other positions around when it continues totravel at point A and point B in the direction of the arrow in Fig. 1.

In order to solve the deadlock problem, Wang et al. adopted EarlyDeath method [30]. The main idea of their method is to make theant in the deadlock dead, so it stops updating the pheromone of thepath already traveled. When lots of ants are in the deadlock state,this method is not conducive to the global optimum search and italso reduces the diversity of path solutions. Hong et al. solved theproblem by Fallback method [31,32]. When an ant is in deadlock,do not make it die but allow it to take a step back and continue thesearch.

In this paper, the direction determination method is a tool todeal with deadlock, in which the taboo table is updated when theant is in deadlock, and the pheromone on the edge of deadlock ispunished so that the ant may adjust the forward direction in theoriginal position and find a direction where there is no obstruction,

Fig. 2. The intelligent wheelchair searches the direction without obstacles.

utational Science 25 (2018) 50–57 53

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Table 1Application effects of TSP-based algorithms.

Algorithm Optimal path length/m Number of Iterations

OACA 4.1725 60IACA 4.1725 20GPACA 4.1585 15APACA 4.1585 6

Z. Jiao et al. / Journal of Comp

nd effectively reducing the possibility of the other ants to fall intoeadlock in the same position. Its pheromone penalty function is:

rs = (1 − �)�rs (9)

here (1 − �) is the corresponding penalty coefficient.The specific steps of the adaptive polymorphic ant colony path

lanning method are as follows:Step 1 Environmental modeling is made using the grid method,

nd constant Q, amount of information C, and the maximumvolution generation N and the wheelchair starting position arenitialized;

Step 2 The m (quantity) scouts are placed separately in the nquantity) path nodes, and each scout investigates the nodes of thether (n − 1) paths with the path node as the center; the investi-ated elements are calculated as Eq. (1), and the results are put inhe S[i][j];

Step 3 The amount of information on each path at the initialoment is set according to Formula (2), and the initial value of the

volution generation NC is set as 0;Step 4 The initial position of each search ant is randomly selected

nd placed in its corresponding tabu table;Step 5 The position where search ant k will be transferred is

alculated according to Eq. (6), and is set as j; the previous positions set as i, and j is placed into the corresponding tabu table of theearch ant k until each search ant completes a cycle to obtain aolution; if ant k falls into deadlock in the path search, the directionetermining method will be employed to deal with the deadlock;

Step 6 The objective function value Lk (k = 1, 2, . . ., m) is cal-ulated for each search ant, and the current optimal solution isecorded;

Step 7 If the specified evolution generation has been reachedr the obtained solution has no significant improvement in the

ast several generations, execute Step 9; otherwise, modify theheromone concentration of each path according to Eq. (8);

Step 8 Set ��ij as 0, clear the tabu table; update the evolutioneneration from NC + 1 to NC, and return to Step 4;

Step 9 Output the optimal solution.

. Experimental results

The traveling salesman problem (TSP) asks for an optimal tourhrough a specified set of points [33]. To solve a particular instancef the problem, it is necessary to find a shortest tour and verifyhat no better tour exists. Some techniques can be employed inhe Concorde code for the TSP, focusing on the difficult verificationask [34]. A typical one is to select a path for the wheelchair to visitvery point exactly once and return to the initial position. Lots ofrevious work has touched the quite old scenario and many solu-ions are available, such as ant colony algorithm and its derivativelgorithms.

The simulated coordinates (in m) of 20 points are (0.5, 0.5),1, 0.7), (0.7, 0.5), (0.2, 0.9), (0, 1), (0.1, 0.6), (1, 0.2), (0.6, 0.7),0.9, 0.2), (0.8, 0.3), (0.3, 0.8), (0.7, 0.3), (0, 0.2), (0.3, 0.4), (0.8,.8), (0.5, 0.9), (1, 0.9), (0.1, 0.4), (0.2, 0.9) and (0.9, 0.7), respec-ively. The application effects of the adaptive polymorphic antolony algorithm (APACA) are compared with those of other TSP-ased methods, including original ant colony algorithm (OACA),

mproved ant colony algorithm (IACA), general polymorphic antolony algorithm (GPACA), and adaptive polymorphic ant colonylgorithm (APACA). The essential parameters are set as follows:

he number of ants m = 120, the number of iterations N = 200, thenformation heuristic factor � = 1, the desired heuristic factor ̌ = 5,he pheromone evaporation coefficient � = 0.9, the constant Q = 100,he information amount on each path at the initial time C = 3. The

Fig. 3. The evolution curve of path distance by IACA.

optimal path lengths and the numbers of iterations by above fourTSP-based algorithms are shown in Table 1, respectively.

Evidently, APACA provides the shortest optimal path length andthe least number of iterations. It is superior to OACA, a very fun-damental TSP-based method, and the other two solutions evolvedfrom OACA. Not only that, the focus of this paper lies in solvingoptimal path planning problems of automated navigation systemsfor smart wheelchairs. In formal experiment, we set up 15 itemsand each item represents a point. A person in the smart wheelchairpicks up each item starting from one point, and the ultimate tar-get is to find the shortest path for the wheelchair to pick up all theitems. The position coordinates (in m) of the fifteen items are A (2,8), B (0, 4), C (1, 6), D (3, 5), E (4, 2), F (6,2), G (3, 0), H (10, 4), I (4, 3), J(2, 1), K (7, 0), L (9, 4), M (11, 3), N (13, 2), and O (5, 1), respectively.

The application effects of the adaptive polymorphic ant colonyalgorithm are compared with those of the other typical path plan-ning methods. Experimental parameters are set as follows: thenumber of ants m = 120, the number of iterations N = 200, the infor-mation heuristic factor � = 1, the desired heuristic factor ̌ = 5, thepheromone evaporation coefficient � = 0.9, the constant Q = 100, theinformation amount on each path at the initial time C = 3. The evolu-tion curves of distance paths by IACA, GPACA and APACA are shownin Figs. 3–5, respectively. In addition, the performance comparisonof IACA, GPACA, and APACA is shown in Table 2.

In Fig. 3, the optimal solution obtained by IACA iterated to about30 times, and in Fig. 4, the optimal solution obtained by GPACAiterated to about 10 times while the optimal solution obtained byAPACA iterated to about 5 times in Fig. 5. In Table 2, the optimalpath distance for the smart wheelchair obtained by IACA and GPACAis 37.2991 m, and the optimal path distance obtained by APACAis 36.9428 m. The optimal path obtained using the algorithm pre-sented in this paper is optimized by 0.3563 m compared to theshortest path obtained using the previous two algorithms, espe-cially the worst solution and the average solution of the optimal

path are better than IACA.

Regarding to the solving efficiency of the optimal solution,the optimal solution was obtained after about 5 iterations using

54 Z. Jiao et al. / Journal of Computational Science 25 (2018) 50–57

Table 2Performance comparison of IACA, GPACA and APACA in path planning.

Algorithm Optimaldistance/m

Average distanceworst solution/m

Average distanceoptimal solution/m

Optimal path

IACA 37.2991 70.0112 43.3014 H → L → F → O → E → I → D → A → C → B → J → G → K → N → MGPACA 37.2991 46.9854 42.2154 L → H → M → N → K → G → J → B → C → A → D → I → E → O → FAPACA 36.9428 47.1254 42.8912 L → H → M → N → K → O → G → J → B → C → A → D → I → E → F

Fig. 4. The evolution curve of distance by GPACA.

toruti

dapeTmtem

Fig. 6. The shortest path searched by IACA.

IACA. According to the convergence curves in Figs. 12–14, APACA

Fig. 5. The evolution curve of distance by APACA.

he algorithm in this paper. However, the optimal solutions werebtained using IACA and GPACA after about 30 and 10 iterationsespectively, resulting in the optimal solution and the efficiencysing the algorithm in this paper are better than IACA. Accordingly,he shortest paths obtained from the above algorithms are shownn Figs. 6–8, respectively.

TPS mainly focuses on optimal path choice, while the problemescribed in this paper includes not only optimal path choice, butlso obstacle avoidance problem of smart wheelchairs. The com-arison of the performance of IACA, GPACA, and APACA has beenxecuted in the obstacle path planning for the smart wheelchair.he experimental parameters are as follows: the number of ants

= 50, the number of iterations N = 100, the information heuris-

ic factor � = 1, the desired heuristic factor ̌ = 5, the pheromonevaporation coefficient � = 0.8, the constant Q = 1, and the infor-ation amount on each path at the initial time C = 3. The obstacle

Fig. 7. The shortest path searched by GPACA.

path optimization curves of IACA, GPACA, and APACA are shown inFigs. 9–11, respectively.

In Figs. 9–11, the optimal path distances obtained from the threealgorithms are respectively 30.38 m, 29.21 m and 28.038 m. Thepath distance obtained from APACA is better than IACA and GPACA.It is evident that APACA dose plays an important role in finding anoptimal path for the smart wheelchair. The corresponding conver-gence curves of IACA, GPACA, and APACA are shown in Figs. 12–14,respectively. The results of obstacle path planning for the smartwheelchair using the three algorithms are shown in Table 3.

According to Figs. 12–14, APACA and GPACA achieve optimalvalue after about 40 times, so its iteration effect is better than

proposed in this paper obtains the optimal path distance with theleast amount of iterations. According to the data in Table 3, theoptimal path length of IACA and GPACA is much longer than the

Z. Jiao et al. / Journal of Computational Science 25 (2018) 50–57 55

Table 3Results of obstacle path planning using IACA, GPACA and APACA.

No.IACA GPACA APACA

The optimal length/m Iterations 40 28.321 4 46 36.45 26 >40 29.36 8 8 29.782 9 47 30.47 15 10 29.21 14 14 30.442 25 98 41.31 25 >40 38.02 26 >40 29.361 11 69 36.43 12 >40 29.45 2 2 28.291 8 810 43.13 22 >40 36.24 7 >40 29.571 21 11

Fig. 8. The shortest path searched by APACA.

iaatpcit

Fig. 10. GPACA path optimization curve.

Fig. 9. IACA path optimization curve.

mproved adaptive polymorphic ant colony algorithm. In the oper-tion of 10 times, the first two algorithms have respectively 5 timesnd 6 times less than 35 m or less, while the third algorithm has 10imes of the calculations, results less than 35 m and the optimalath length of 28.038 m was found. The experimental results indi-

ate that in terms of the optimal path, the convergence and theterative effect, the obstacle path planning results obtained usinghe adaptive polymorphic ant colony algorithm in this paper are

Fig. 11. APACA path optimization curve.

better than those from improved ant colony algorithm and thegenerally polymorphic ant colony algorithm.

Obviously, the path planning results using adaptive polymor-phic ant colony algorithm is better than the results with other

similar algorithms. Moreover, the proposed method can help smartwheelchairs to proactively identify the best path classify the cur-rent situation where a user is standing on as sidewalk, roadway and

56 Z. Jiao et al. / Journal of Computatio

Fig. 12. IACA convergence curve.

Fig. 13. GPACA convergence curve.

Fig. 14. APACA convergence curve.[

[

nal Science 25 (2018) 50–57

traffic intersection, which prevents the collisions of vehicle at thetraffic intersection.

5. Conclusions

In this paper, the adaptive polymorphic ant colony algorithmis proposed as a path planning method for smart wheelchairs. Thesearch ant can determine the optimal combination parameters inaccordance with actual situation and make the state transition inthe search process to effectively prevent the search ant from fallinginto local optimum to a certain extent. The direction determiningmethod also employed to accelerate convergence, improving theefficiency of the algorithm in searching the global optimal solution.The improved polymorphic ant colony algorithm is applied sepa-rately to the target path planning and obstacle path planning, andis compared with the improved ant colony algorithm and the gen-erally polymorphic ant colony algorithm, respectively. Our methodachieves superior performance in this challenging problem, whichis even racing ahead of the recently developed state-of-the-art solu-tions. Additionally, this study reveals the feasibility of using it asan effective and feasible planning path tool for future healthcaresystems.

It is noteworthy that in a point to point path planning, the smartwheelchair is just regarded as an idealized point rather than a prac-tical model in our experiment. There are lots of existing modelsregarding wheelchair or similar. Actually, safe mission planningtypically seeks to construct a route from origin to destination thatminimizes the risk imposed; nevertheless, the robot has limitationin making rotation during automatic drive. In the future study, wewill consider some practical models for the smart wheelchair inpath planning.

Acknowledgements

The authors would like to thank the reviewers and the editors fortheir valuable comments and suggestions on improving this paper.This work is supported by the University Natural Science ResearchProgram of Jiangsu Province (No. 17KJB510003).

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Shuihua Wang is currently an Assistant Professor at theDepartment of Informatics, University of Leicester, UK.She received her Ph.D. from Nanjing University, in 2016.Her research interest is biomedical image processing andcomputer aided diagnosis.

Z. Jiao et al. / Journal of Comp

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12] Changman Son, Intelligent rule-based sequence planning algorithm withfuzzy optimization for robot manipulation tasks in partially dynamicenvironments, Inform. Sci. 342 (2016) 209–221.

13] Yamei Xia, Bo Cheng, Junlian Chen, Xiangwu Meng, Dong Liu, Optimizingservices composition based on improved ant colony algorithm, Chin. J.Comput. 35 (2) (2012) 270–280.

14] Guojun Sheng, Tao Wen, Quan Guo, Xiaoying Song, Trustworthy servicediscovery based on a modified ant colony algorithm, J. Commun. 34 (10)(2013) 37–48.

15] Hui Luo, Xingliang Jian, Wei Lu, Optimal test node selection based on dynamicant colony algorithm for analog circuit, Chin. J. Sci. Instrum. 35 (10) (2014)2231–2237.

16] Baoming Shan, Dexiang Zhang, Path planning of robot based on ant colonyoptimization algorithm, Appl. Mech. Mater. 614 (2014) 199–202.

17] Mohamed Abdulkader, Yuvraj Gajpal, Tarek Y. ElMekkawy, Hybridized antcolony algorithm for the multi compartment vehicle routing problem, Appl.Soft Comput. 37 (C) (2015) 196–203.

18] Yogita Gigras, Kusum Gupta, Ant colony based path planning algorithm forautonomous robotic vehicles, J. Artif. Intell. Appl. 3 (6) (2012) 31–38.

19] Adem Tuncer, Mehmet Yildirim, Dynamic path planning of mobile robots withimproved genetic algorithm, Comput. Electr. Eng. 38 (6) (2012) 1564–1572.

20] Baozhen Yao, Adaptive parallel ant colony optimization algorithm, PatternRecognit. Artif. Intell. 20 (4) (2007) 458–461.

21] Yaomin Hu, Weiming Liu, Solving of optimal path problem based onimproved ant colony algorithm, J. South China Univ. Technol. (Nat. Sci. Ed.) 38(10) (2010) 105–109.

22] Zhenxin Du, Zhaoqing Wang, Zhinan Wang, Wei Qin, Yuntao Duan, Improvedpolymorphic ant colony algorithm with double simulated annealing, J. Cent.South Univ. (Sci. Technol.) 42 (10) (2011) 3112–3118.

23] Chengbing Li, Ruixue Guo, Min Li, Application of improved ant colonyalgorithm in traveling salesman problem, J. Comput. Appl. 34 (S1) (2014)131–132, 165.

24] Jianyi Yang, Ruifeng Ding, Yuan Zhang, Maoqin Cong, Fei Wang, Guoan Tang,An improved ant colony optimization method for the quasi travelingsalesman problem, Int. J. Geograph. Inform. Sci. 29 (9) (2015) 1534–1551.

25] Chen Qing, Yong Zhong, Liuming Xiang, Cloud database dynamic routescheduling based on polymorphic ant colony optimization algorithm,Comput. Modell. New Technol. 18 (2) (2014) 161–165.

26] Wenli Lei, Fubao Wang, Research on an improved ant colony optimizationalgorithm for solving traveling salesmen problem, Int. J. Database TheoryAppl. 9 (9) (2016) 25–36.

27] Fanghong Guo, Changyun Wen, Jianfeng Mao, Guoqi Li, Yong-Duan Song, Adistributed hierarchical algorithm for multi-cluster constrained optimization,Automatica 77 (2017) 230–238.

28] Yudong Zhang, Xueyan Wu, Siyuan Lu, Hainan Wang, Preetha Phillips,Shuihua Wang, Smart detection on abnormal breasts in digitalmammography based on contrast-limited adaptive histogram equalizationand chaotic adaptive real-coded biogeography-based optimization,Simulation 92 (9) (2016) 873–885.

29] Yudong Zhang, Bo Peng, Shuihua Wang, Yuxiang Liang, Jiquan Yang, Kwok-FaiSo, Ti-Fei Yuan, Image processing methods to elucidate spatial characteristicsof retinal microglia after optic nerve transaction, Sci. Rep. 6 (2016) 21816.

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34] Andrey V. Savkin, Hailong Huang, Optimal aircraft planar navigation in staticthreat environments, IEEE Trans. Aerosp. Electron. Syst. 53 (5) (2017)2413–2426.

Zhuqing Jiao is presently an Associate Professor at

the School of Information Science and Engineering,Changzhou University, China. He received his Ph.D. inJiangnan University, Wuxi, in 2011. His current projectsare in the areas of intelligent computing and healthcaresystem, etc.

nal Science 25 (2018) 50–57 57

Kai Ma is a Doctor’s Degree candidate at the College ofComputer Science and Technology, Nanjing University ofAeronautics and Astronautics, China. He received his Mas-ter’s Degree in Changzhou University, Changzhou, in 2017.His research interests encompass intelligent computingand complex networks.

Yiling Rong is presently a National Registered UrbanPlanner at Changzhou Urban Planning Compilation andResearch Centre, China. She received her Master’s Degreein Southeast University, Nanjing, in 2011. Her researchinterests include overall plan and path plan.

Peng Wang is a Master’s Degree candidate at the Insti-tute of Robotics, Changzhou University, China. He receivedhis BS in Changzhou University, Changzhou, in 2015. Hisresearch interest is robot control system.

Hongkai Zhang is presently an Assistant Professor atthe School of Electronic and Information Engineering,Anhui Jianzhu University, China. He received his Master’sDegree in Jiangnan University, Changzhou, in 2007. Hiscurrent research focuses on artificial intelligence and pat-tern recognition technologies.

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