An Improved Routing Optimization Algorithm Based on Travelling Salesman Problem for Social Networks

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1 sustainability Article An Improved Routing Optimization Algorithm Based on Travelling Salesman Problem for Social Networks Naixue Xiong 1,2, Wenliang Wu 1 and Chunxue Wu 1, * 1 School Optical-Electrical and Computer Engineering, University Shanghai for Science and Technology, Military Road, No. 516, Shanghai , China; xiongnaixue@gmail.com (N.X.); wwl@st.usst.edu.cn (W.W.) 2 Department Mamatics and Computer Science, Norastern State University Address: 611 N, Grand Ave, Tahlequah, OK 74464, USA * Correspondence: wcx@usst.edu.cn Received: 5 April 2017; Accepted: 6 June 2017; Published: 8 June 2017 Abstract: A social network is a social structure, which is organized by relationships or interactions between individuals or groups. Humans link physical network with social network, and services in social world are based on data and analysis, which directly influence decision making in physical network. In this paper, we focus on a routing optimization algorithm, which solves a well-known and popular problem. Ant colony algorithm is proposed solve this problem effectively, but random selection strategy traditional algorithm causes evolution speed be slow. Meanwhile, positive feedback and distributed computing model make algorithm quickly converge. Therefore, how improve convergence speed and search ability algorithm is focus current research. The paper proposes improved scheme. Considering difficulty about searching for next better city, new parameters are introduced improve probability selection, and delay convergence speed algorithm. To avoid shortest being submerged, and improve sensitive speed finding shortest, it updates pheromone regulation formula. The results show that improved algorithm effectively improve convergence speed and search ability for achieving higher accuracy and optimal results. Keywords: ant colony algorithm; positive feedback; pheromone; convergence speed 1. Introduction A social network is a social structure, which is organized by relationships or interactions between individuals or groups. Humans link physical network with social network, and services in social world are based on data and analysis, which directly influence decision making in physical network. In this paper, we focus on Travelling Salesman Problem (TSP), which is introduced by a company [1] in United States solve problem using linear programming, and it is a very well-known problem in computer science field at present. TSP is a special case travelling purchaser problem and vehicle routing problem. In recent years, with continuous development economy and road traffic, travelling around country has become leisure time for many workers. How select best route travelling and not miss every scenery has become a problem that needs be considered. This common example exactly reflects well-known problems in field Mamatics TSP problem [2], where a businessman visits n cities and n returns back starting city, with premise is that a city only be visited once determine shortest [3,4]. TSP problem as a combinarial optimization problem is attracting great concern humanity [5]. At present, re are many solutions this problem, such as dynamic programming, genetic algorithm, simulated annealing algorithm and so on, but implementation se algorithms is more complex. At this point, ant colony algorithm (ACO) came in being, which is Sustainability 2017, 9, 985; doi: /su

2 Sustainability 2017, 9, a new ant colony intelligent behavior optimization algorithm that was first proposed by Italian scholar Dorigo [6] at beginning 1990s. Ant colony algorithm [7], an optimization algorithm find optimal, is used solve combinarial optimization problem, which is based on cooperative behavior ant foraging. It has also been widely used in many fields, such as travelling sales, distribution scheduling and dynamic routing [8]. The algorithm simulates foraging process ants, where ants secrete pheromones during food search process record ir, and or ants perceive density pheromones choose a shorter find food. The more ants on, more pheromones are secreted, and will be chosen by more ants. On contrary, fewer ants on, less pheromone are secreted, fewer ants will choose, so most ants will choose pheromone concentration find food. This shows that algorithm has good distributed collaboration and robustness, which is why it is widely used in logistics and distribution, network optimization and optimization problem, is one algorithms solve combinarial optimization problems [9 11]. The remainder this paper is organized as follows. In Section 2, we introduce related works. The research ant colony algorithm is described in detail in Section 3. Then, improvement algorithm is introduced in Section 4. Next, in Section 5, experiments our method and compared methods on two parameters demonstrate effectiveness and improved performance improved method, and application scenario analysis Applied Improved Ant Colony Algorithm. After that, we interpret our results in this section. Finally, we conclude this paper and discuss future works in Section Related Works Convergence rates that are o fast or o slow are not good for ant colony algorithm. In Zao and Wang [12], convergence ant colony optimization algorithm is discussed. In Wang and Li [13], a game ory quantum ant colony algorithm is proposed solve problem that TSP is easy fall in local optimization and slow converge. This algorithm uses game model generate game sequence that makes most effective benefit, which effectively solves convergence rate and stability ant colony algorithm. In Sun [14], improve search ability and convergence speed ant colony algorithm, an efficient pheromone updating and selection mechanism is adopted speed up global convergence speed and expand search ability. In Zhang et al. [15], aiming at problem optimization, we propose a kind competition way change updating mechanism pheromone, which makes search result algorithm better and more accurate. The fuzzy set concept is introduced in Jiang [16], and fuzzy evaluation in ant searching was carried out by membership degree. The pheromone is updated according evaluation result, so that convergence speed algorithm is accelerated and algorithm performance is improved. In Sun et al. [17], a hybrid algorithm is proposed, which combines particle swarm optimization and ant colony optimization optimize parameters ant colony system, and introduces pheromone swapping operation make it better than or algorithms on TSP. In Hu and Huang [18], for sake solving problem that convergence rate TSP clustering becomes slow, a new ant colony algorithm is proposed. The TSP problem is decomposed in several sub problems from data domain, which is solved separately improve convergence speed algorithm, in Chen and Jiang [19], overcome shortcomings large scale TSP problem, such as it is easy fall in local optimum, process crossing and mutation, vaccination and immune selection are added make it strong global optimization ability and better search convergence in Ant Colony Optimization and Particle Swarm Optimization (ACO-PSO) hybrid algorithm. In Kai et al. [20], based on artificial fish swarm algorithm, linear recursive inertia weighting strategy particle swarm algorithm is introduced in artificial fish swarm algorithm; artificial fish is processed and visual field artificial fish is dynamically changed form a new particle group fish swarm algorithm (PSO-AFSA), which makes global convergence better and faster. In Zhang et al. [21], an adaptive ant colony optimization method is proposed:

3 Sustainability 2017, 9, Sustainability 2017, 9, threshold selection parameter in threshold receiving algorithm is used change choice ant colony and chance random selection. The ant colony algorithm is prevented from falling threshold receiving algorithm is used change choice ant colony and chance random in local optimum and search space is better. selection. The ant colony algorithm is prevented from falling in local optimum and search space is better. As a typical Non-deterministic Polynomial (NP) problem, TSP problem is used test and compare performance As a typical Non-deterministic algorithm, which Polynomial has become (NP) problem, research TSP problem object is used algorithm test and [22,23]. Based compare on search performance ability and convergence algorithm, speed which has ant become colony algorithm, research this object paper puts algorithm forward method [22,23]. Based improving on search antability colonyand algorithm convergence and updating speed ant method colony algorithm, pheromone this according paper puts defects forward such as method characteristics improving and shortcomings ant colony algorithm existing and updating algorithms. method The new pheromone parameters are according introduced defects changesuch as probability characteristics selectionand mode shortcomings delay convergence existing algorithms. rate. At The same time, new parameters new update are introduced mechanism ischange used improve probability search selection efficiency mode and delay result convergence algorithm inrate. At pheromone same time, update process. new update mechanism is used improve search efficiency and result algorithm in pheromone update process. 3. Introduction Ant Colony Algorithm 3. Introduction Ant Colony Algorithm 3.1. Working Principle Ant Colony Algorithm 3.1. Working Principle Ant Colony Algorithm Ant colony algorithm as a heuristic algorithm, whose working method is simulate foraging process Ant colony ants: ants algorithm will search as a for heuristic food based algorithm, on pheromones whose working left bymethod or ants; is y simulate will choose ir foraging process take; and ants: ants probability will search for food selected based on pheromones is proportional left by or ants; concentration y will pheromones choose ir on. take; Therefore, and probability collective behavior selected many is proportional ants constitutes a positive concentration feedback phenomenon pheromones [6] on information. Therefore, learning: more collective ants onbehavior a will increase many ants probability constitutes ants a positive choosing that feedback. phenomenon Ants communicate [6] information with each or learning: through more ants information on a will increase find probability shortest ants food. choosing Positive that feedback. Ants phenomenon communicate is shown with each in Figure or through 1: when antsinformation have just started find feeding, it shortest is assumed that food. initial Positive pheromone feedback is phenomenon same in each is, shown so in 40 Figure ants set 1: when out from ants have A node just look started for feeding, food (D it nodes) is assumed with that same initial probability. pheromone They is find same that re in each are, two so s 40 ants set D out node, from A node look for food (D nodes) with same probability. They find that re are two and number ants in A B D and A C D are 20. Because A B D and A C D s D node, and number ants in A B D and A C D are 20. Because distances are 20 m and 30 m, respectively, number ant trips through A B D is greater A B D and A C D distances are 20 m and 30 m, respectively, number ant trips through than number A C D in unit time; thus, more pheromone is left on this, and A B D is greater than number A C D in unit time; thus, more pheromone is left probability that will be selected by later ants increases. After a period time, as shown in on this, and probability that will be selected by later ants increases. After a period Figure time, 2, as shown ants on in Figure A B D 2, ants increased on A B D 30, and on increased A C D 30, and reduced on A C D 10. It be seen reduced that 10. continued It be seen role that positive continued feedback role phenomenon positive feedback ants will phenomenon continue ants increase will number continue ants increase on A B D number. ants Finally, on A B D ants will. find Finally, best ants waywill food, find which best shows way that food, feedback which shows mechanism that teedback algorithm mechanism in optimal algorithm solutionin convergence optimal solution probability convergence is increased signifitly probability is [24,25]. increased signifitly [24,25]. Figure 1. The ants start find food, with equal probability choose eir. Figure 1. The ants start find food, with equal probability choose eir.

4 Sustainability 2017, 9, Sustainability 2017, 9, Figure2. 2. Aftera a period time, number ants ants on on two two s s is different. is different Path Probability Selection According According ant ant foraging foraging process, process, solution solution TSP TSP problem problem be effectively be effectively helped. helped. In TSP problem, ants are randomly divided in nodes, because each node only be In TSP problem, ants are randomly divided in nodes, because each node only be accessed accessed once, probability ant k (k = 1, 2, 3, m) access next j node in i node is: once, probability ant k (k = 1, 2, 3..., m) access next j node in i node is: [ ( )] [ ( )] p (t) = [ j allowed [ ( )] [ ( )] (1) τij (t) ] [ α β η 0else ij (t)] p k In Formula (1), p ij (t) is (t) = probability s allowedk that [τant is (t)] k will α [η is be (t)] transferred β j allowed k (1) from city i target city j at time t; τ represents pheromone concentration 0on else(i, j); α and β are, respectively, y information elicitation facr and expected heuristic facr, both which reflect relative influence In Formula (1), information p k ij (t) is content probability and that expected ant k will value; be transferred η = 1/d from represents city i a target heuristic city j at time information t; τ ij represents from node i pheromone node j (where concentration d represents on (i, j); distance α and βbetween are, respectively, node i yand information node elicitation j); and allowed facr represents and expected a collection heuristic all facr, nodes both is not accessed. which reflect It be seen relative that influence under this information formula, content access probability and expected is determined value; by η ij = 1/d pheromone ij represents concentration a heuristic information τ and heuristic from node i information node j (where η. d ij represents distance between node i and node j); and allowed k represents a collection all nodes is not accessed. It be seen that under this formula, access probability is determined 3.3. Pheromone byupdate pheromone concentration τ ij and heuristic information η ij. When ants release pheromone on during process accessing node, avoid 3.3. Pheromone Update re being o residual pheromone is, which leads heuristic information being hidden, it is necessary When update ants release pheromone after on an ant finishes during its visit process a node or accessing complete node, access avoid re all being nodes. otherefore, residual pheromone update formula is, which leads pheromone heuristic τ on information (i, j) is: being hidden, it is necessary update pheromone after an ant τ (t) finishes = (1 ρ)τ its visit (t 1) a + τ node or complete access all (2) nodes. Therefore, update formula pheromone τ ij on (i, j) is: τ = τ (3) τ ij (t) = (1 Q ρ)τ ij (t 1) + τ ij (2) τ (i, j) L = L (4) 0else m k Therefore, Formulas (2) (4) are combined: τ ij = τ ij (3) k=1 τ ij k = { Q L c (i, j) L k 0 else (4) Therefore, Formulas (2) (4) are combined:

5 Sustainability 2017, 9, τ ij (t) = (1 ρ)τ ij (t 1) + m τ k ij (i, j) L k k=1 (1 ρ)τ ij (t 1) else (5) where ρ represents attenuation coefficient pheromone, its range is 0 < ρ < 1; τ ij (t 1) represents last pheromone after search (i, j); τ ij represents pheromone increment on search ; L k represents search ant k; and Q L c represents pheromone increment ant k on (i, j) (Q represents incremental coefficient pheromone and L c represents optimal solution this search, which is related L k ) Algorithm Flow The general steps ant colony algorithm for solving TSP problems are as follows: (1) First, required parameters are initialized by algorithm. Set cycle times Nc = 0, maximum number iterations Nc Max, and Path initialization information τ ij (t) (where τ ij (t) = C, C is constant, τ ij (0) = 0). (2) m ants will be placed in n cities, and each ant accesses next node j by route choice probability p k ij, where j belongs allowed k. (3) The length each ant is calculated, and optimal solution current search is recorded. (4) Modify pheromone according update formula. (5) On pheromone increment τ ij and Nc cycles were set for τ ij = 0, Nc = Nc + 1. (6) If Nc Max > Nc, n jump Step (2). (7) If condition is satisfied, current optimal solution will be output. The process algorithm is show in Algorithm 1: where FinishALC( ) represents completion about cycle algorithm, calculate( ) represents calculated each nodes length, currentops is current optimal solution, and havefinisheditenum( ) represents wher it reaches numbers iterations. Algorithm 1. Ant Colony Algorithm Based on TSP Problems. 1: Parameters Initialization 2: Ants visit next node via selection probability 3: The number cycles increased 4: Taboo index number increased 5: F i = FinishALC( ) 6: do { 7: Path length is determined by ants 8: C i = Calculate(length) 9: R i = Record(currentOPS) 10: Pheromones are secreted 11: U i = Update(pheromones) 12: } 13: while(!havefinisheditenum( )) 14: O i = Output(currentOPS) 15: Tabu_list is empty 16: End

6 Sustainability 2017, 9, Improvement Ant Colony Algorithm 4.1. Shortcomings Ant Colony Algorithm Through continuous research many scholars, ant colony algorithm is ten insufficient in solving TSP problem for following reasons: (1) due lack global search ability in algorithm, it is easy produce local optimal solution when search found almost same solution; (2) longer search time; (3) calculation time is long, and phenomenon stagnation is easy occur; (4) pheromone left by ant colony in first cycle is not necessarily optimal direction ; (5) effect positive feedback leads enhancement information on non-optimal and hindrance global optimal solution; and (6) traditional ant colony algorithm updates pheromones on all search s, which will reduce efficiency searching optimal The Improved Ant Colony Algorithm From previous formula, ant colony algorithm is based on pheromone left by ants on each enhance search optimal solution. In or words, ant will preferentially select with high pheromone concentration. However, when frequency optimal solution is constantly updated, many ants gar on fewer ant colony, so that phenomenon stagnation and prematureness occurs, which leads local optimal solution. Based on algorithm in optimization process search and speed convergence, selection probability and pheromone are updated avoid above phenomena improve convergence speed and accuracy algorithm The Improvement Path Selection Probability In traditional ant colony algorithm, probability selecting each ant is mainly determined by pheromone concentration τ ij and heuristic information η ij, which is generated by current node i access next node j. To some extent, this will mislead ant choose best probability, so that it fall in dilemma local optimal solution. To avoid production above situation, paper improves selection probability formula based on literature [26]. The probability that an ant will visit next node j from node i is: when q is greater than q 0, formula is: when q is less than or equal q 0, formula is α p k ij (t) = b pk ij (t) j allowed k (6) p k ij (t) = b pk ij (t) j allowed k (7) α where b is equal (1+q 0 ), β b is equal (1+q) β, q 0 is a given parameter value with range (0, 1), q is a random number between 0 and 1, and β α parameter indicates ratio information heuristic expected heuristic. The probability algorithm is affected delay convergence rate algorithm by parameter introduction. When q > q 0, it will use q 0 search method; orwise, it will use q search method maintain probability selection in a reasonable range. The selection q 0 adjusts balance between random search and deterministic search, and size q 0 determines merits algorithm. If value q 0 is very large, it will cause algorithm fall in local optimal solution; if value q 0 is o small, it will affect degree search algorithm, so that convergence rate algorithm is o slow Improved Pheromone Update In traditional ant colony algorithm, updating pheromone is relatively simple, which results in algorithm not taking full advantage shortest resulted from last

7 Sustainability 2017, 9, cycle, thus affecting accuracy search algorithm. To improve situation, pheromone formula is improved, which prevent premature ants through same resulting in local optimal solution, and its pheromone adjustment formula is: τ ij (t) = τ ij(t) + ρ 1 ρ τ ij (i, j) / L k (8) τ ij = { Q L (i, j) ɛ L t 0 else (9) where represents tal length current search. L t represents a collection longest search. Pheromone adjustment formula avoids reducing convergence speed algorithm, and improves sensitivity ant colony shortest, and n quickly searches for a new shortest from neighborhood. Thus, improved algorithm illustrates this process in Algorithm 2. Algorithm 2. The Improved Algorithm Based on TSP Problems. 1: Parameters Initialization 2: do { 3: Nc = Nc + 1 4: do { 5: visit next city via new selection probability 6: Tabu_list = Modify( ) 7: } while (! IsTableFull( )) 8: Path length is determined by ants 9: C i = Calculate(length ) 10: R i = Record(currentOPS) 11: New pheromones update Formula is proposed 12: U i = Update(pheromones) 13: RR i = AgainRecord(currentOPS) 14: Tabu_list is empty 15: }while(!havefinishediteratenum( )) 16: O i = Output(currentOPS) 17: End 5. Performance Evaluation 5.1. Simulation Environment In this paper, experimental environment this paper is based on simulation stware platform win7 system, and ant colony algorithm is used solve TSP problem, improved algorithm proposed in this paper is compared with ant colony algorithm performance, and n performance improved algorithm is analyzed. In this paper, we will take Berlin52TSP and Rat99TSP as examples illustrate feasibility algorithm, and all data will come TSP standard database [27,28]. Thus, its simulation parameters are set n = 52 or 99 (where n represents number cities), m = 30, α = 1, β = 4, ρ = 0.4, Q = 100, q = 0.5 and so on. The two algorithms are compared with each or, and number iterations is 200 times Comparison Simulation Results In environment simulation stware platform, this paper selects shortest and average facrs compare performance improved algorithm and ant colony algorithm. The Berlin52TSP problem simulation results are shown in Figures 3 and 4.

8 Sustainability Sustainability 2017, 2017, 9, 985 9, Sustainability 2017, 9, 985 Ant Colony Algorithm Improved ant colony algorithm Optimal /meters Optimal /meters Ant Colony Algorithm Improved ant colony algorithm The number iterations Figure Figure Chart The number Chart iterations shortest shortest pat. pat. Figure 3. Chart shortest pat. In Figure In Figure 3, both 3, both improved algorithm and original algorithm obtain good solutions with fewer fewer cycles cycles In when Figure when 3, both program improved is is just algorithm running. and However, original with algorithm continuous obtain good solutions implementation with fewer cycles when program is just running. in However, with 10 continuous implementation program, stagnation phenomenon appears in cycle 10 times in original algorithm, algorithm program, does stagnation not sp phenomenon convergence appears continue cycle search 10 times in until original 137 times. algorithm, The improved algorithm does not sp convergence continue search until 137 times. The improved algorithm algorithm does not sp convergence continue search until 137 times. The improved shows algorithm a shows a strong search capability ate 18 times, and constantly finds its shortest. The algorithm strong search shows a capability strong search ate capability 18 times, ate and 18 times, constantly and constantly finds finds its shortest its shortest.. The The optimal solution optimal is found solution when is found program when runs program aboutruns 119 times, about 119 andtimes, shortest and shortest is is However, optimal solution is found when program about 119 and shortest is original However, However, algorithm original original finds algorithm algorithm shortest finds finds shortest shortest in cycle 138, in and in cycle cycle its 138, shortest 138, and and its shortest its shortest is is In is summary, In summary, with improved algorithm still maintains a with In continuous summary, with running continuous program, running program, improved algorithm improved algorithm still maintains still maintains a strong a strong strong search capability when original algorithm stagnates. The The optimal optimal is found is found in in search capability when original algorithm stagnates. The optimal is found in case case case fewer fewer cycles. Figure 4 is shortest road road map. map. fewer cycles. Figure 4 is shortest road map Figure Route 600 map shortest Figure 4. Route map shortest. Figure Figure 5 represents 5 represents search search Figure 4. Route average map distance shortest between. original original algorithm algorithm and and improved improved algorithm. algorithm. It is obvious It is obvious that that original algorithm and improved algorithm find find at same speed between 0 and 10 cycles. When algorithm is cycled 18 times, at Figure same 5 represents speed between search 0 and 10 cycles. average When distance algorithm between is cycled original 18 times, algorithm average and s improved two algorithm. are different; It is it obvious bethat seen that original search algorithm and speed improved two algorithms find is different in this at time, same andspeed speed between improved 0 and 10 algorithm cycles. When is faster algorithm than original is cycled algorithm 18 times, from average. After 200 cycles, average original algorithm is , and improved algorithm is The average reduced by 3%, which obviously indicates that improved

9 Sustainability 2017, 9, Sustainability 2017, 9, average s two are different; it be seen that search speed two algorithms average is different s in this two time, are and different; speed it be improved seen that algorithm search is faster speed than original two algorithms is from different average in this. time, After and 200 cycles, speed improved average algorithm is original faster than algorithm original is , algorithm and Sustainability 2017, 9, from improved average algorithm. After is cycles, The average average reduced by original 3%, which algorithm obviously is , indicates and that improved algorithm is is superior The average original reduced algorithm by 3%, on which average obviously. indicates The reason that is that improved improving algorithm pheromone is superior update and original probability algorithm selection make average. algorithm The reason search is ability that algorithm is superior original algorithm on average. The reason is that improving improving continue enhance pheromone update for facilitating and probability search selection algorithm make search algorithm city search faster, ability reby pheromone update and probability selection make algorithm search ability continue enhance continue reducing average enhance. The performance facilitating improved search algorithm search be improved city faster, by this reby method, for facilitating search algorithm search city faster, reby reducing average. reducing and average reliability. and The validity performance algorithm improved is proven. algorithm be improved by this method, The and performance reliability and improved validity algorithm algorithm is be proven. improved by this method, and reliability and validity algorithm is proven. 10,600 Ant Colony Algorithm 10,600 10,400 Ant Colony Improved Algorithm Algorithm 10,400 Improved Algorithm 10,200 Average /meters Average /meters 10,200 10,000 10, The number 100 iterations The number iterations Figure 5. Chart average. Figure Figure Chart Chart average average.. To furr demonstrate performance this algorithm, in this paper, we take Rat99TSP To problem furr To furr as demonstrate an example, as shown performance in Figure 6. this algorithm, in in this this paper, paper, we we take take Rat99TSP Rat99TSP problem problem as an as an example, as as shown in in Figure 6. Optimal /meters Optimal /meters Ant Colony Algorithm Ant Colony Improved Algorithm Ant Colony Algorithm Improved Ant Colony Algorithm The number iterations The number iterations Figure 6. Chart shortest. Figure 6. Chart shortest. Figure 6. Chart shortest. In Figure 6, when program has just started, improved algorithm in jitter level aspect is much better than original algorithm, and it shows that improved algorithm has a large search space. With continuous operation program, original algorithm has been caught in a stagnant state after 22 cycles in algorithm, and improved algorithm has maintained a steady downward continuous search. At final stage program, optimal improved algorithm is , which is signifitly better than original algorithm (1364.9). In general, due introduction parameters and pheromone update, improved algorithm takes more time

10 much better than original algorithm, and it shows that improved algorithm has a large search space. With continuous operation program, original algorithm has been caught in a stagnant state after 22 cycles in algorithm, and improved algorithm has maintained a steady downward continuous search. At final stage program, optimal Sustainability improved 2017, algorithm 9, 985 is , which is signifitly better than original algorithm (1364.9). 10 In 15 general, due introduction parameters and pheromone update, improved algorithm takes more time secrete pheromone in optimal, which increases searching ability secrete algorithm pheromone and inreduces its convergence optimal speed,, which which makes increases it faster and searching more stable, ability and algorithm result is and optimal. reduces Figure its convergence 7 is shortest speed, which road makes map. it faster and more stable, and result is optimal. Figure 7 is shortest road map Figure 7. Route map shortest. Figure 7. Route map shortest. In Figure 8, when program has run, average two algorithms is about same. With In program Figure 8, running when continuously, program has run, average average change two algorithms two algorithms is about issame. obvious: average With program algorithm running is continuously, less than original average algorithm, change and two experimental algorithms is results obvious: show average algorithm is less than original algorithm, and experimental results show that that average algorithm is , while average original algorithm is average algorithm is , while average original algorithm is When When number iterations is about 8, average two algorithms starts be different. number iterations is about 8, average two algorithms starts be different. After After eight iterations, average improved algorithm is obviously lower than that eight iterations, average improved algorithm is obviously lower than that common common algorithm algorithm because because algorithm algorithm will select optimal according according probability probability formula formula used used select select position next city. However, algorithmis used is used update update probability probability selection formula and and update pheromone, which leads algorithm be stronger be stronger than than general general algorithm and and always chooses optimal reach destination. It It be be seen seen that that performance improved algorithm is greatly improved compared with with general general Sustainability 2017, 9, algorithm, algorithm, which which furr furr shows that that improved algorithm is is better Ant Colony Algorithm Improved Ant Colony Algorithm 1750 Average /meters The number iterations Figure Figure Chart average Application Analysis Applied Improved Ant Colony Algorithm We apply improved ant colony algorithm clustering algorithm wireless sensor networks. As we all know, traditional clustering algorithm has some shortcomings in number nodes surviving, packet communication and average energy consumption nodes. Therefore, Applied Improved Ant Colony Algorithm we proposed aims optimize energy consumption in

11 Sustainability 2017, 9, Application Analysis Applied Improved Ant Colony Algorithm We apply improved ant colony algorithm clustering algorithm wireless sensor networks. As we all know, traditional clustering algorithm has some shortcomings in number nodes surviving, packet communication and average energy consumption nodes. Therefore, Applied Improved Ant Colony Algorithm we proposed aims optimize energy consumption in network extend life cycle. Low Energy Adaptive Clustering Hierarchy (LEACH) algorithm [29], a so-called low-power adaptive hierarchical routing algorithm, works by repeatedly randomly selecting cluster-heads, and n average energy will be distributed in networks each sensor node, enabling networks reduce energy consumption, and increase survival time. In low-power adaptive hierarchical routing algorithm, each node exists in different clusters and is free organize, and each cluster has only one cluster-head. In addition, all data sent by non-cluster-heads node are received by cluster-heads because concern about transmission same data. To reduce transmission data redundancy, cluster-heads have be sent back base station receive data fusion. On or hand, each non-cluster-head node cluster knows header information, and smaller routing tables be maintained by cluster-heads. However, each node has act as cluster-head prevent excessive energy consumption cluster-heads. Compared with LEACH algorithm, according setting parameters in [30], simulation environment is described as follows: node number entire networks is 200, range is 200 m 200 m and initial energy nodes is 0.5 J. The energy consumed by node send and receive data is E TX = E RX = 50 nj/bit, E fs = 10 pj/bit/m 2, E mp = pj/bit/m 4, and E DA = 5 pj/bit/signal.. The experimental results follow. Figure 9 is node average residual energy map Applied Improved Ant Colony Algorithm in clustering algorithm and LEACH clustering algorithm. We compare 200-cycle experimental data. First, from slope two curves in graph, we obviously see that Applied Improved Ant Colony Algorithm curve slope is greater than LEACH clustering algorithm, and use Applied Improved Ant Colony Algorithm node residual energy degradation rate is signifitly slower than LEACH algorithm. From specific data, when network runs 100 rounds, residual energy LEACH algorithm is about 0.42 J. At this time, residual energy node using Applied Improved Ant Colony Algorithm is 0.45 J. However, when network runs 160 rounds, residual energy node using Applied Improved Ant Colony Algorithm is reduced 0.42 Sustainability J, which2017, 9, show 985 that utilization rate residual energy node using Applied Improved Ant Colony Algorithm is much higher than that LEACH algorithm LEACH Applied Improved Ant Colony Algorithm Remaining Energy Each Node Round Number Figure 9. Average residual energy. Figure 9. Average residual energy. Figure 10 is a comparison two algorithms transmitting packets from cluster-heads sink. The use Applied Improved Ant Colony Algorithm nodes for transmitting average data packets is 13 bit, while ordinary LEACH clustering algorithm transmit average data packets is about 9.45 bit, whose packets throughput using Applied Improved Ant Colony Algorithm is

12 0.34 Round Number Figure 9. Average residual energy. Sustainability 2017, 9, Figure 10 is a comparison two algorithms transmitting packets from cluster-heads sink. Figure The use 10 is a Applied comparison Improved Ant two algorithms Colony Algorithm transmitting nodes packets for transmitting from cluster-heads average data packets sink. The is 13 use bit, while Applied ordinary Improved LEACH Ant clustering Colony algorithm Algorithm transmit nodes for average transmitting data packets average is about data packets 9.45 bit, is whose 13 bit, while packets ordinary throughput LEACH clustering using algorithm Applied transmit Improved average Ant Colony data packets Algorithm is about is 9.45 improved bit, whose because, packets when throughput cluster-heads using transmits Applied Improved data Ant sink Colony node, Algorithm node is improved using because, Applied when Improved cluster-heads Ant Colony transmits Algorithm data will route sink according node, node using length Applied next Improved hop for Ant selecting Colony Algorithm optimal will route transmit according packets, and length traditional next LEACH hop for selecting clustering algorithm optimal only transmit transmit packets, data packets and traditional according LEACH established clustering method. algorithm It only be seen transmit that data packets optimization according effectively established help method. node It find be seen most that suitable optimization routing way effectively effectively help transmit node packets find most sink suitable node, routing which way improves effectively node s transmit work efficiently. packets It really sink plays node, a which particularly improves critical node s role in work continuous efficiently. development It really plays a wireless particularly sensor critical network. role in continuous development wireless sensor network. 14 Deliver Packets from Cluster Heads Sink LEACH Applied Improved Ant Colony Algorithm Round Number Figure 10. The packets from cluster-heads sink. Figure 10. The packets from cluster-heads sink. The network running node will cause death, so we take cluster-heads average energy consumption as a comparison parameter when running network before first 100 rounds, as shown in Figure 11. It be seen in figure that average energy consumption level cluster-heads using Applied Improved Ant Colony Algorithm is lower than that LEACH algorithm, and maximum energy consumption is about J and minimum energy consumption is J. LEACH algorithm cluster-heads average energy consumption is about J, and minimum is about J. The average cluster-heads energy consumption optimized cluster algorithm is about J after number rounds network operation. The average cluster-heads energy consumption LEACH clustering algorithm is about J. Energy consumption increased by nearly 55.85%. It is also clear from figure that data fluctuation using Applied Improved Ant Colony Algorithm is gentler than LEACH clustering algorithm, which shows that network balance is stable and once again validates that Applied Improved Ant Colony Algorithm reduce node energy consumption and extend node s life cycle.

13 Energy consumption increased by nearly 55.85%. It is also clear from figure that data fluctuation using Applied Improved Ant Colony Algorithm is gentler than LEACH clustering algorithm, which shows that network balance is stable and once again validates that Applied Improved Ant Colony Algorithm reduce node energy consumption and extend node s life cycle. Sustainability 2017, 9, Average Energy Consumption Cluster Heads 10 x LEACH Applied Improved Ant Colony Algorithm Round Number Figure 11. Average energy consumption cluster-heads. Figure 11. Average energy consumption cluster-heads. 6. Conclusions and Future Works 6. Conclusions and Future Works A social network is a social structure, which is organized by relationships or interactions between A social individuals network oris groups. a social Humans structure, linkwhich physical is organized network by with relationships social network, interactions and services between inindividuals social world groups. are based Humans on data link and analysis, physical which network directly with influence social network, decision making and in services physical in social network. world Within are based wireless on data network, and analysis, as a social which network, directly how influence extend decision network making life in cycle physical and reduce network. energy Within consumption wireless network, is an issue as that a social we must network, consider. how Meanwhile, extend network studylife energy cycle and consumption reduce energy has aconsumption useful reference is an forissue futurethat sustainability we must consider. and it will Meanwhile, help future sustainable study development energy consumption energy. has Ina this useful paper, reference method for future selecting sustainability formula and it will andhelp pheromone future sustainable updating is development adopted improve energy. In this convergence paper, speed method and selecting search ability formula ant and colony. pheromone Considering updating convergence is adopted speed improve and searching convergence abilityspeed and existing search algorithms, ability ant deficiency colony. Considering ant colony algorithm convergence is not speed fullyand considered. searching This paper ability proposes existing an improved algorithms, algorithm for deficiency problem ant colony algorithm, is which not fully is mainly considered. embodied This paper in proposes choice an accessing improved probability algorithm and for pheromone problem update. ant colony First, based algorithm, on traditional which is ant mainly colony embodied algorithm, in search choice for accessing next better probability city is difficult and because pheromone update. choicefirst, based based on on probability traditional selection ant colony formula algorithm, ant, search so newfor parameters next better are introduced city is difficult improve because probability choice based selection, probability and convergence selection formula speed algorithm ant, so new is delayed. parameters Second, are introduced avoid improve shortest probability be submerged, selection, and and improve convergence sensitivity speed shortest find shortest, it updates pheromone regulation formula improve search ability ant colony. Simulation results show that improved algorithm effectively improve convergence speed and search ability algorithm, and achieve goal higher accuracy and best results. The research this algorithm has certain reference significe for future improvement ant colony algorithm, and provides some methods for future research TSP problem, and we apply algorithm clustering algorithm, which reduce network energy consumption and extend life cycle network. It also promotes role for social networks, and it is conducive our future study social networks energy consumption provide some related services. In this paper, we improve routing formula and pheromone update mechanism, but re are still some deficiencies. In future works, research includes following aspects: a. Ant colony algorithm is a probabilistic algorithm, which learn from or mature intelligent optimization algorithm. It is conducive birth a new type ant colony algorithm from a mamatical point view furr analysis.

14 Sustainability 2017, 9, b. Most m are aimed at improving convergence ant colony algorithm. There are some limitations on innovation algorithm itself. c. The application depth ant colony algorithm is not enough because most simulation experiments are carried out under specific experimental conditions, while actual situation is dynamic. Thus, relevant issues have yet be furr expanded. d. Compared with or algorithms, ant colony algorithm has characteristics such as good distributed computing mechanism and strong robustness, so it be combined with or algorithms put forward a more powerful algorithm. Acknowledgments: The authors would like appreciate all anonymous reviewers for ir insightful comments and constructive suggestions polish this paper in high quality. This research was supported by Shanghai Science and Technology Innovation Action Plan Project ( ) and Shanghai key lab modern optical system. Author Contributions: All authors have contributed conception and development this manuscript. Naixue Xiong, Wenliang Wu and Chunxue Wu conceived and designed experiment. Wenliang Wu wrote paper. Conflicts Interest: The authors declare no conflict interest. References 1. Dorigo, M. Optimization, Learning and Natural Algorithms. Ph.D. Thesis, Politecnico Di Milano, Milan, Italy, Chen, H.; Li, J. Review outlier detection. Da Zhong Ke Ji 2005, 9, Zhu, X.; Li, F. Several intelligent algorithms for solving traveling salesman problem. Comput. Digit. Eng. 2010, 38, Lin, D.; Wang, D.; Li, Y. Two-level degradation hybrid algorithm for multiple traveling salesman problem. Appl. Res. Comput. 2011, 28, Wang, Z.; Bai, Y.; Yue, L. An Improved Ant Colony Algorithm for Solving TSP Problems. Math. Pract. Theory 2012, 42, Dorigo, M.; Maniezzo, V.; Colorni, A. Ant system: Optimization by a colony cooperating agents. IEEE Trans. Syst. Man Cybern Part B 1996, 26, [CrossRef] [PubMed] 7. Wang, H.; Tong, Y.; Tan, S. Research progress on outlier mining. CAAI Trans. Intell. Syst. 2006, 1, Li, Y.; Li, H.; Qian, X. A Review and Analysis Outlier Detection Algorithms. Comput. Eng. 2002, 28, Cagnina, L.C.; Susana, C.E.; Carlos, A.C.C. Solving constrained optimization problems with a hybrid particle swarm optimization algorithm. Eng. Optim. 2011, 43, [CrossRef] 10. Duan, H. The Principle and Application Ant Colony Algorithm; Science Press: Beijing, China, Xu, J.; Cao, X.; Wang, X. Polymorphic Ant Colony Algorithm. J. Univ. Sci. Technol. China 2005, 35, Zao, B.; Wang, L. The analysis convergence ant colony optimization algorithm. Front. Electr. Electron. Eng. 2007, 2, Wang, Q.; Li, W. Study TSP Problem Solving Based on Improved Quantum Ant Colony Algorithm. Microprocessors 2015, 3, Sun, J. Research on Ant Colony Algorithm for Solving Traveling Salesman Problem; Wuhan University Technology: Wuhan, China, Zhang, K.; Zhang, Y.; Wan, S. Application an Improved Competitive Ant Colony Algorithm in TSP. Comput. Digit. Eng. 2016, 44, Jiang, Y. The Application an Improved Ant Colony Optimization for TSP; South-central University for Nationalitie: Wuhan, China, Sun, K.; Wu, H.; Wang, H. Hybrid ant colony and particle swarm algorithm for solving TSP. Comput. Eng. Appl. 2012, 48, Hu, X.; Huang, X. Solving TSP with Characteristic Clustering by Ant Colony Algorithm. J. Syst. Simul. 2004, 16, Chen, W.; Jiang, Y. Improving ant colony algorithm and particle swarm algorithm solve TSP problem. Inf. Technol. 2016, 2016,

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