Research Article Decision of Multimodal Transportation Scheme Based on Swarm Intelligence

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1 Hndaw Publshng Corporaton Mathematcal Problems n Engneerng, Artcle ID , 10 pages Research Artcle Decson of Multmodal Transportaton Scheme Based on Swarm Intellgence Ka Le, 1 Xaonng Zhu, 1 Janfe Hou, 2 and Wencheng Huang 1 1 School of Traffc & Transportaton, Bejng Jaotong Unversty, Bejng , Chna 2 Chna Academy of Transportaton Scence, Bejng , Chna Correspondence should be addressed to Xaonng Zhu; leka@bjtu.edu.cn Receved 10 January 2014; Revsed 20 March 2014; Accepted 20 March 2014; Publshed 24 Aprl 2014 Academc Edtor: Ru Mu Copyrght 2014 Ka Le et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. In ths paper, some basc concepts of multmodal transportaton and swarm ntellgence were descrbed and revewed and analyzed related lteratures of multmodal transportaton scheme decson and swarm ntellgence methods applcaton areas. Then, ths paper establshed a multmodal transportaton scheme decson optmzatoathematcal model based on transportaton costs, transportaton tme, and transportaton rsks, explaned relevant parameters and the constrants of the model n detal, and used the weght coeffcent to transform the multobjectve optmzaton problems nto a sngle objectve optmzaton transportaton scheme decson problem. Then, ths paper s proposed by combnng partcle swarm optmzaton algorthm and ant colony algorthm (PSACO) to solve the combnatoral optmzaton problem of multmodal transportaton scheme decson for the frst tme; ths algorthm effectvely combnes the advantages of partcle swarm optmzaton algorthm and ant colony algorthm. The soluton shows that the PSACO algorthm has two algorthms advantages and makes up ther own problems; PSACO algorthm s better than ant colony algorthm n tme effcency and ts accuracy s better than that of the partcle swarm optmzaton algorthm, whch s proved to be an effectve heurstc algorthm to solve the problem about multmodal transportaton scheme decson, and t can provde economcal, reasonable, and safe transportaton plan reference for the transportaton decsoakers. 1. Introducton 1.1. Basc Concepts (1) Swarm Intellgence. Swarm ntellgence refers to the overall ntellgent behavor emergng from nteracton of many smple acts of ndvdual; the swarm ntellgence can produce a number of dfferent ndvdual collectve behavors. Swarm ntellgence s the creatve applcaton and development of thecollectvebehavorsandformsamoreadvancedwhole wsdom. Swarm ntellgence s a hot research topc n artfcal ntellgence researches n recent years, wth no centralzed control, does not provde a global model, and provdes a complex dstrbuted soluton. (2) Multmodal Transportaton. Multmodal transportaton s defned as completng the transportaton process by usng at least two transportaton tools to connect and transport together; t s a knd of transportaton organzaton form whch uses optmum effcency as the goal. There are no new transportaton channels and tools n the multmodal transportaton process; t s a combnaton of modern organzaton means and sngle transportatoode. It has mportant and realstc meanng for savng transportaton costs and transportaton tme and mprovng transportaton servce qualty by researchng the decson of multmodal transportaton scheme n the process of transportaton The Current Analyss Stuaton of the Domestc and Foregn Research (1) Swarm Intellgence. In recent years, the scholars at home andabroadcarredoutalotofresearchworksaboutswarm ntellgence; the swarm ntellgence theory n transportaton related felds has been appled extensvely. Chen and Ma

2 2 Mathematcal Problems n Engneerng [1] gave a new algorthm of glowworm swarm optmzaton algorthm whch was based on swarm ntellgence optmzaton prncple and successfully appled t to the 0-1 knapsack problem; L et al. [2] proposed the Harvard structure and swarm ntellgence optmzaton system based on the CTLS model, whch used swarm ntellgence based on calculaton andsourceofagentnagenttechnologyandthesmulaton based optmzaton theory, and the feasblty and relablty of the modelng optmzatoethod are verfed by smulaton analyss of CTLS half brdge schedulng problem; M [3] proposed an optmzaton algorthm for executon effcency and convergence problems of ntegrated desgn process usng genetc algorthm for task schedulng; the genetc algorthm was mproved and combned wth the partcle swarm algorthm by consderng the effect of couplng relatonshp between tasks to the task executon results. It s verfed wth an example; the results showed that the algorthm has a fast convergence speed and stable result; L et al. [4] establshed automated warehouse sngle pock horzontally rotatng storage shelf system mathematcal model and used the ant colony optmzaton algorthm to solve the path plannng problem based on the goods selecton. Ths method s capable of rotatng storage rack system for rapd selecton of goods and fnds the optmal goods pckng path n the global, hgh qualty soluton and short calculaton tme; Wu and Sh [5] establshed ant colony algorthm based on the mproved meetng algorthm and proposed ant colony algorthm ant tourng qualty, meetng algorthm, and a parallel algorthm whch s combned wth the proposed strategy; the expermental results show that ths algorthm has better effectveness; Xao et al. [6] proposed the mathematcal model of concurrent tolerance optmzaton desgn and then mapped nto a specal travelng salesman problem order multple travelng salesman problem; so as to reduce the dffculty of problem solvng, they proposed a hybrd swarm ntellgence algorthm for concurrent tolerance optmzaton desgn problem. Through calculaton examples, the effcency would be hybrd swarm ntellgence algorthm wth genetc algorthm and smulated annealng algorthm has better search ablty and hgher. Ma et al. [7] mnmzed the energy consumpton and delay tme, mproved the evolutonary algorthms for solvng the travelng salesman problem based on artfcal neural network algorthm, and establshed the swarm ntellgence analyss model and used t to analyze the lnes plannng for publc travel. The expermental results showed that, the mproved hybrd ntellgent computng method was smple and effectve and helped to overcome the blndness of algorthm selecton, to further expand the research drecton of computatonal ntellgence. From the above research lteratures, t s not dffcult to see that the swarm ntellgence has not only attracted much attenton n recent years but also has a lot of space n the feld of transportaton applcatons. Ths paper was proposed by combnng partcle swarm optmzaton algorthm and ant colony algorthm (PSACO) to solve the combnatoral optmzaton problem of multmodal transportaton scheme decson for the frst tme whch caake up shortcomngs of ther own at the same tme. (2) Decson of Multmodal Transportaton Scheme. Inrecent years, scholars at home and abroad dd a lot of research works on how to choose the proper transportatoode n the multmodal transportaton access. Among them, Lozano and Storch s [8] research was about the problem of shortest feasble path n the multmodal transportaton and used the sequental algorthm to solve the problem; Calvete et al. [9] studed the VRP wth soft tme wndow vehcles path problem and used the goal programmng method to solve the problem. L and Zhao [10] usedthemnmumtotalcostasthe optmzaton objectve, whch ncluded transportaton cost, transfer cost and penalty cost; the goods delvery tme and transportaton capacty were used as constrant condtons; they bult mxed nteger lnear programmng model and desgned the nteger codng genetc algorthm. Wang et al. [11] studed and establshed the multmodal transportaton 0-1 nteger programmng model under the tme and capacty constrants, desgned the natural number codng genetc algorthm based on the characterstcs of the model, and fnallytestedvaldtyofthemodelandthealgorthmwth examples. Feng and Zhang [12] consdered the envronmental polluton, energy consumpton, and safety factors nto multmodal transportaton sustanable development and then ntroduced the concept of total socety cost of multmodal transportaton, used ths mnmum cost value as a whole object, and bult a multmodal transportaton collaboratve optmzatoodel. Tong and Ne [13] transformed ntermodal path optmzaton problem nto a generalzed shortest path problem, used tme and cost as optmzaton objectve, establshed multmodal transportatoathematcal model for the optmzaton of path changes n volume, and solved and verfed actual problem by usng ant colony algorthm. Zhang [14] deeply studed the whole contaner multmodal transportaton network, expounded the key elements and the operatoechansm of multmodal contaner transportaton network n the whole system, and, n accordance wth the exstng problems, put forward the basc countermeasures ratonalzaton. L and Zeng [15]mprovedpathshortesttme model under the multmodal transportaton n the fourth party logstcs, gave the transportaton cost model based on satsfactory tme path under the condton of multmodal transportaton, and mproved genetc algorthm to solve the problem. Wen [16]usedmultmodalcontanertransportaton optmzaton as the research object and dscussed the optmzaton method of contaner multmodal transportaton routes, transportaton, and tme constrants modes. L [17] dscussed the development of transportatoode choce as well as the man transportatoode selectoethod and then put forward the concept of generalzed transportaton cost. Wang [18], n order to acheve tme delvery, reduced the cost, accordng to the actual stuaton of the key problem of logstcs dstrbuton n the process of transportaton and traffc network of multmodal transportaton wth tme wndow of mnmum cost problem. Zhang [19]analyzed Chnese ralway contaner transportaton features and operaton process, used the transportaton path selecton as the goal to mprove the effcency of contaner transport and shorten the contaner transport cycle, and reduced transportaton costs for the purpose; then he used the optmzaton theory and

3 Mathematcal Problems n Engneerng 3 operatons research theory to establsh the ralway contaner transportaton route choce model. There are some shortcomngs exstng n the domestc and foregn documents all above about the multmodal transportatoodes selecton; the man problem s that the mpact of transportaton cost and tme selecton on multmodal transportatoodes was consdered n the past; only a sngle target stuaton for multmodal transportaton mode optmal selecton faled to consder other factors n the problems. But, n the actual decson process selecton ultmodal transportatoodes, n order to ensure the contnuty and safety, we need to consder transportaton safety and transportaton rsk factors comprehensvely; only n ths way we caeet the actual needs of transportaton. Multmodal transportaton s a knd of holstc and ntegrated operaton process about the mutual coordnaton and cooperaton betweeultmodal transportaton network nodes, node enterprses lnes, socal economc condtons, and natural envronment factors. Rsk factors exsted n several aspects of the multmodal transportaton network, ncludng multmodal transportaton enterprses, transportaton channels, external economc, socal envronment, and natural factors; these rsk factors are not only the necessary condtons for the formaton of multmodal transportaton network rsk but also aportant prerequste for the exstence of multmodal transportaton network rsk. The transportaton rsk s one of the mportant factors of the multmodal transportaton selecton n ths paper, but tcanbefoundfromthedomestcandforegndocuments researches that few scholars consdered transportaton rsk as the mportant factor, when they conducted researches n the choce of transportatoode and multmodal transportaton problems; so the present researches cannot be well adapted to the actual stuaton of multmodal transportaton modes selecton; t s also dffcult to gve correct gudance to practce and reference. 2. Establshment of the Optmzaton Model 2.1. Problem Descrpton. We suppose that a company has a batch of goods to transport from orgn pont O to destnaton pont D through a multmodal transportaton network; a pluralty of hub nodes composed the multmodal transportaton network; several transportatoodes can be chosen between two arbtrary adjacent nodes; each node s a transt hub for dfferent transportatoodes; when we swtched the goods from one mode to another mode, we need to spend some tme and cost, but total transportaton tme cannot exceed the scope of delvery tme. We hoped to delver the goods safely, economcally, and convenently through the proper choce of the transportatoodes durng the agreed perod Makng the Assumpton (1)Wehaveknownandfxedalltherelevantconstants; (2) there s one transportatoode exstent at least on any secton of known delvery path; (3) the same batch of goods cannot be separated durng the transport process; that s to say, we can only choose one transportatoode n the known arbtrary secton path when delverng one batch of goods; (4) the goods are transted at hub nodes, and the transt for each batch of goods n each hub node occurs one tme at most. (5) when choosng the transportatoodel, just consder the nfluence of the transportaton operaton rsk, not ncludng the others Descrpton of the Model Parameters C k,+1 s the per unt cost of the selected k transportaton mode from the node to the node +1. d k,l stheunttransfercostfromthetransportaton mode k to transportatoode l n the node. t k,+1 s transportaton tme of the selected k transportaton mode from the node to the node +1. f k,l s transfer tme from the transportatoode k to transportatoode l n the node. RT s the rsk factors of the delvery goods. RC k,+1 s the transportaton rsk factor of the selected k transportatoode from the node to the node +1. s the transfer rsk factor from the transportaton mode k to transportatoode l n the node. RF k,l A k,+1 s the transportaton ablty of the selected k transportatoode from the node to the node +1. Consder x k,+1 = 1, select k transportatoode from the node to the node +1 0, otherwse, = 1, from the transportatoode k to transportatoode l n the node 0, otherwse. (1) T s the actual goods delvery tme, w s the earlest goods delvery tme, and V s the latest goods delvery tme, V T w>0. I a s each unt goods warehousng cost when delvery advanced and V d s each unt goods penalty cost when delvery s late.

4 4 Mathematcal Problems n Engneerng J a s all goods warehousng cost when delvery advanced; J a = max[0, (w T)I a ]. S d s all goods penalty cost when delvery s late; S d = max[0, (T V)V d ]; M sasuffcentlylargepenaltyfactor Establshment of the Model (1) Objectve 1: the least transportaton cost for the decson of multmodal transportaton scheme s as follows: Mn Z= C k m,+1 Xk,+1 + =1 k=1 d k,l =1 k=1 l=1 + max [0, (w T) I a ]+max [0, (T V) V d ]. (2) (2) Objectve 2: the least transportaton tme for the decson of multmodal transportaton scheme s as follows: Mn T= t k m,+1 xk,+1 + =1 k=1 f k,l =1 k=1 l=1. (3) (3) Objectve 3: the lowest transportaton rsk for the decson of multmodal transportaton scheme s as follows: Mn R = RT Constrants of the Model =1 k=1 x k,+1 RCk,+1 m RF k,l. =1 k=1 l=1 (4) (1) We can only choose one transportatoode between two nodes. Consder m x k,+1 k=1 =1, n. (5) (2) Only transportatoodes can be changed n a node. Consder m m k=1l=1 =1, n. (6) (3) Ensure contnuty durng the transportaton process. Consder x k 1, +xl,+1 2yk,l, n, k m, l m. (7) (4) Goods transportaton tme should meet the actual tme range allowed. Consder w t k,+1 xk,+1 =1 k=1 + m f k,l =1 k=1 l=1 V, V >w>0. (8) (5) Cargo weght should not exceed the transportaton capacty. Consder Qx k,+1 Ak,+1, n, k m, l m. (9) (6)Thedecsonvarables0or1.Consder x k,+1 0, 1}, n, k m, l m, 0, 1}, n, k m, l m. (7) Nonnegatve constrants of varables. Consder t k,+1 0, n, k m, l m, f k,l 0, n, k m, l m. (10) (11) 2.6. Model Processng. Multobjectve programmng model s dffcult to solve because of the ncoordnaton of the target vectors and the exstence of constrants; n ths paper, the objectve functon was smplfed nto a sngle objectve functon; usually we use the lnear weghted method drectly and sum multple objectve functons nto a sngle objectve functon, but ths method s only applcable to the transformaton of the dmensonless objectve functon or unform dmenson objectve functon; t must be dmensonless or a dmensonally unfed treatment for the multobjectve problem whose dmenson s not unform. We should change the orgnal objectve functons (2), (3), and (4) ntothe followng: Max Z =Z max Max T =T max C k,+1 Xk,+1 =1 k=1 m d k,l =1 k=1 l=1 J a S d, t k,+1 xk,+1 =1 k=1 m f k,l, =1 k=1 l=1 Max R =R max RT m =1 k=1 l=1 =1 k=1 RF k,l. x k,+1 RCk,+1 (12)

5 Mathematcal Problems n Engneerng 5 Accordng to the evaluaton functoethod of multple objectve functon optmzatoethod, referrng to the weght degree of each target weght, we gave, respectvely, the transportaton cost, transportaton tme, and transportaton rsk weght as α, β,andδ and α+β+δ=1, α, β, δ [0,1]. Atthesametme,nordertosolvethedmensonal consstency problem of the objectve functon, we need to transform the target functon (12): Max Z =(Z max C k,+1 Xk,+1 =1 k=1 m d k,l =1 k=1 l=1 J a S d ) brds predaton. The algorthm s ntally rules by brds cluster actvtes of the enlghtenment, usng swarm ntellgence to establsh a smplfed model. Partcle swarm optmzaton algorthm s based on the observaton of anmal collectve behavor; because of nformaton sharng, the whole populaton movement from dsorderly to orderly evoluton process n the problem space by the ndvdual n the group, then, obtaned the optmal soluton. PSO s smlar to genetc algorthm; t s an optmzaton algorthm based on teraton. The system s ntalzed wth a set of random solutons, searchng for the optmal value through the teratve, but t has no genetc algorthm wth the crossover and mutaton; the partcles search n the soluton space to follow the optmal partcle; PSO s smple and easy to realze and there s no need to adjust many parameters. (Z max ) 1, Max T =(T max t k,+1 xk,+1 =1k=1 m f k,l ) =1 k=1 l=1 (T max ) 1, Max R =(R max RT =1 k=1 x k,+1 RCk,+1 (13) 3.2. The Advantages of PSO Algorthm (1) The algorthm s smple, wth less adjustable parameters, and easy to mplement. (2) The random ntalzaton populaton has strong global searchng ablty, whch s smlar to genetc algorthm. (3) It uses the evaluaton functon to measure the ndvdual searchng speed. (4) It has strong scalablty. m RF k,l ) =1 k=1 l=1 (R max ) 1. In the objectve functon (13), Z, T,andR are the goal functon after dmensonless treatment, the range for the three s [0, 1). Among them, Z max, T max,andr max are the respectve maxma of target functons (2), (3), and (4) n each generaton of the genetc algorthm; so, n ths paper, we establshed the comprehensve objectve functon: f(z, T, R) =α Z +β T +δ R. (14) The states and effects of the three ndexes weghts n the comprehensve evaluaton results are not the same n the comprehensve objectve functon (14); t s so mportant for the model soluton when choosng the weght values. Generally speakng, n the decson of ntermodal transportaton scheme, the selected weght values mostly depend on the type ofgoodsandthedecsonpreference. 3. Partcle Swarm Optmzaton (PSO) 3.1. Introducton of the Algorthm. Partcle swarm optmzaton s an evolutonary computaton technque, proposed n 1995 by Dr. Eberhart and Dr. Kennedy, from the behavor of 3.3. The Dsadvantages of PSO Algorthm (1) The algorthm cannot make full use of the feedback nformaton n the system. (2) Its ablty to solve combnatoral optmzaton problems s not strong. (3) Its ablty to solve the optmzaton problem s not very well. (4) It s easy for ths algorthm to obtan local optmal soluton The Basc Prncple of the Algorthm. The algorthm s descrbed as follows: hypothess n a D dmenson target searchng space, N partcle to form a communty, the partcle vector to represent a D dmenson, and the poston vector. Consder X =(x 1,x 2,...,x D ), =1,2,...,N. (15) The velocty of vector partcle s also a D dmenson, the velocty vector V = (V 1, V 2,...,V D ), =1,2,...,N. (16)

6 6 Mathematcal Problems n Engneerng The partcle s the searched best poston called ndvdual extreme value by far and s denoted as P best =(p 1,p 2,...,p D ), =1,2,...,N. (17) The optmal poston of the whole partcle swarm searched so far s called global extreme and s denoted as g best =(p g1,p g2,...,p gd ). (18) After fndng out these two optmal values, partcles updated therveloctyandpostonaccordngtothefollowngformulas: V d =w V d +c 1 r 1 (p d x d ) +c 2 r 2 (p gd x d ), (19) x d =x d + V d. (20) Among them, w s the nerta factor; c 1 and c 2 are the learnng factors, and r 1 and r 2 are the ranges of [0, 1] for the unform random numbers. The formula (19) s composed of three parts on the rght: the frst part reflects the movement of partcles and represents partcles whch have mantaned ther prevous velocty trend; the second part reflects memory partcles on the hstorcal experence and represents partcles whch are close to the optmal poston of ts hstorcal trend; the thrd part reflects the cooperaton and knowledge, sharng group hstory experence synergy between partcles. 4. Ant Colony Algorthm (ACO) 4.1. Introducton of the Algorthm. Ant colony algorthm (ACO)sanewntellgentoptmzatonalgorthmproposed by Italan scholars M. Dorgo, V. Manezzo, and A. Colorn n the twenteth century and early 90s; t has been appled to the TSP, secondary dstrbuton and quadratc assgnment problems, graph colorng problem, and many classcal combnaton optmzaton problems and ganed very good results The Advantages of ACO Algorthm (1) It uses a knd of postve feedback mechansm and gets converges to the optmal path on the objectve through the pheromone update ceaselessly. (2) It s a knd of optmzatoethod of dstrbuton; t s easy to mply n parallel. (3) It s a knd of method for global optmzaton, used not only for the sngle objectve optmzaton problems, but also for solvng the multobjectve optmzaton problems. (4) It s sutable to solve the dscretzaton problems. (5) It has strong robustness The Dsadvantages of ACO Algorthm (1) The solvng speed s slow because of the shortage n the ntal stage of nformaton algorthm. (2) The algorthm based on the dscrete problem cannot drectly solve contnuous optmzaton problems. (3) Ths algorthm lacks strong searchng ablty The Basc Prncple of the Algorthm. The basc prncple of the algorthm s usng K ants jontly to construct a feasble soluton; each ant s an ndependent one for the constructon process of soluton; the ants between each other exchange nformaton through nformaton value and constantly optmze the cooperatve soluton and at the same tme gve the ants dstrbuton lst (recorded the vsted pont of ths ant); ntroduce the other one ant to follow the frst ant s behavor; contnue to search n the remanng ponts. The ant s task s under many constrants; look for communcatng nodes one by one, and leave the pheromone n the connected node arc. Use arc pheromone and heurstc nformaton to determne assgnment order and use local optmzaton of pheromone to update; after all, the k ants are constructed completng the applcaton, then apply to the global pheromone update. τ j (t) stated at the t moment n the node, j connecton nformaton; α s the mportance degree of resdual nformaton n ant path, j; η j s the heurstc nformaton, the expected degree of ants from node to node j; nths paper, η j = 1/d j (d j s the dstance between node and node j); β s the mportance degree of the heurstc nformaton. The ntal tme of nodes, each ant was placed on the random selecton path constructon accordng to the transton probabltes; the K ant s transfer probablty of node to node j at t tme s P k j,whchsfeasblentheant K sentnel node set. Consder 0, otherwse, p k j (t) = [τ j (t)] α [η j ] β, j N k [τ j (t)] α [η j ] β Nk. (21) Accordng to the rules and update tme determned by dfferent update quantty of nformaton, all the ants of each group after the completon of travel n the set the pheromone should be adjusted; the ant densty model was used n ths paper; that s to say, ants moved from node to node j and updated pheromone of the path j.amongthem,δτ k j shows the number of unt length of messages of ant K n the path from to j; γ s evaporaton coeffcent of pheromone; constant Q s ants leavng tracks number. Consder Q, ant k transfers from node to Δτ k j (t, t + 1) = node j at the t tme to t+1tme, 0, otherwse. (22)

7 Mathematcal Problems n Engneerng 7 Updaterulescorrespondngnformatonsasfollows: τ j (t+1) = (1 γ) τ j (t) +Δτ j (t, t + 1), (23) O 2 7 D Δτ j (t, t + 1) = m Δτ k j k=1 (t, t + 1). (24) Partcle Swarm and Ant Colony Algorthm (PSACO) 5.1. Introducton of the Algorthm. In ths paper, PSACO algorthm whch combnes the partcle swarm algorthm and ant colony algorthm s proposed, combnng the advantages of two knds of algorthms and make up for the dsadvantages of the two algorthms. Partcle swarm algorthm s more sutable for solvng contnuous optmzaton problems and s slghtly nferor n solvng combnatoral optmzaton problems, but, due to the random dstrbuton of the ntal partcle, we use t to solve the combnatoral optmzaton problems; the algorthm has better global search ablty and fast soluton speed; the ant colony algorthm s better n solvng combnatoral optmzaton problems than the partcle swarm optmzaton algorthm, because the ntal dstrbuton s unform, whch makes the ant colony algorthm wth blndness at the begnnng of the algorthm, so t does not converge very quckly. PSACO algorthm combnes partcle swarm algorthm and ant colony algorthm, absorbs the advantages of the two algorthms, and overcomes the shortcomngs; the advantage s complementary and better than that of ant colony algorthm n tme effcency and the partcle swarm algorthm n accuracy and effcency The Basc Ideas and Steps of PSACO Algorthm. The PSACO algorthm combnes advantages of partcle swarm algorthm and ant colony algorthm, and ts basc dea s as follows: n the frst stage, the PSACO algorthm makes full use of random, rapd, global features of the partcle swarm optmzaton algorthm, and, after a certan number of teratons, fnds out the suboptmal soluton of the problem and adjusts the ntal dstrbuton; n the second stage of the algorthm, PSACO algorthm uses nformaton dstrbuton n the frst stage, makes full use of parallelsm, postve feedback, and hgh accuracy advantages of ant colony algorthm, and completes the entre problem solvng progress. Specfcally, accordng to the characterstcs of the soluton problem, combnng two groups of algorthms s effectve to solve the combnatoral optmzaton problem of multmodal transportaton choce mode. The PSACO algorthm s dvded nto two parts; frstly, partcle swarm algorthm generates transportaton connectvty nodes from node start to node fnsh and then uses the ant colony algorthm to fnd the optmal combnaton of the sequence nodes of the transportatoode; the basc steps are as follows. Fgure 1: Schematc dagram of a multmodal transportaton network. Step 1. Partcle swarm algorthm parameters and varables are ntalzed. Step 2. Set the ant colony algorthm parameters ntalzaton and each ant s poston as follows: (1) accordng to the selecton probablty formula (21) and the roulette wheel method, choose the path for each ant; (2) when structural path, each ant updates pheromone locally at the same tme accordng to the formula (23); (3) execute (1), (2), and(3) crcularly untl every ant generates a complete path; (4) record and calculate the objectve functon value of each ant accordng to the tabu lst and gve the optmal and worst ant; (5) update global pheromone for the best ant and worst ant accordng to formula (23); (6) execute (2) (6) untl they meet the end condton. Step 3. Call the ant colony algorthm to get each partcle s ftness and update the hstorcal optmum partcle poston vector and global optmum partcle poston vector. Step 4. Updatethepartcleveloctyvectorandtheposton vector accordng to the formula (19)and(20). Step 5. Execute Steps 2 4 to satsfy the end condtons and use the ant colony algorthm to get the optmal soluton. Step 6. End. 6. Example For example, a transportaton enterprse needs to transport 100 tons of goods from cty O to cty D; each passng secton has four knds of transportatoodes to select. Fgure 1 shows the schematc dagram of a multmodal transportaton network. Table 1 shows the transportatoodes that we can choose between two adjacent cty nodes, the transportaton costs, transportaton tme, and rsk values about dfferent transportatoodes. Table 2 shows the unt transfer cost, unt transt tme, and transfer rsk about dfferent transportatonmodes.thecargodelverytmentervalwas[130h,165h]

8 8 Mathematcal Problems n Engneerng Table 1: Transportaton costs/transportaton tme/transportaton rsk/transportaton capacty of dfferent transportatoodes. Start node Termnal node Transportaton mode Transportaton costs/yuan Transportaton tme/hour Transportaton rsk Transportaton capacty O 1 Ralway O 1 Road O 1 Waterway O 1 Avaton O 2 Ralway O 2 Road O 2 Waterway O 2 Avaton O 3 Ralway O 3 Road O 3 Waterway O 3 Avaton Ralway Road Waterway Avaton Ralway Road Waterway Avaton Ralway Road Waterway Avaton Ralway Road Waterway Avaton Ralway Road Waterway Avaton Ralway Road Waterway Avaton Ralway Road Waterway Avaton Ralway Road Waterway Avaton Ralway Road Waterway

9 Mathematcal Problems n Engneerng 9 Start node Termnal node Transportaton mode Table 1: Contnued. Transportaton costs/yuan Transportaton tme/hour Transportaton rsk Transportaton capacty 5 7 Avaton Ralway Road Waterway Avaton D Ralway D Road D Waterway D Avaton Ralway Road Waterway Avaton Ralway Road Waterway Avaton D Ralway D Road D Waterway D Avaton Table 2: Unt transfer costs (yuan)/unt transt tme (second)/transfer rsk of dfferent transportatoodes. Ralway Road Waterway Avaton Ralway 0/0/0 2/2/2 3/4/3 4/4/3 Road 2/2/2 0/0/0 3/4/4 4/3/4 Waterway 3/4/3 3/4/4 0/0/0 4/3/3 Avaton 4/4/3 4/3/4 4/3/3 0/0/0 n the contract; the goods penalty cost coeffcent was 6 yuan/hour, when delvery advanced, and 10 yuan/hour, when delvery s late, the rsk factor to send the goods was 3. How to choose the multmodal transportaton path and let the transportaton enterprse fnd the optmal scheme to save transportaton costs, reduce the total transportaton tme, andreducethetotalrsk. Accordng to the example, by combnng decsoakers multmodal transportaton needs, the weghts of transportaton costs, transportaton tme, and transportaton rsk value weresetto0.6,0.1,and0.3(dfferentdecsonswllleadtodfferent weghts settng); ths paper adopted MATLAB to verfy the effectveness of the proposed algorthm; frst the 20 teratons of partcle swarm algorthm were the ntal soluton of the problem; then we used the results of the ntal soluton by ant colony algorthm for dstrbuton. γ = 0.02 n ant colony algorthm; the number of ants was equal to the multmodal transportaton cty node number; α=2and β=5; Table 3 shows the comparson of PSACO algorthm and basc ant colony algorthm n solvng ablty and effcency. ItcanbeseenfromthesmulatonresultsthatthePSACO algorthmscomparedwththebascacoalgorthm;t has not only better results than the ant colony algorthm, but also hgher computaton effcency; that s, because, after the partcle swarm algorthm, ntal pheromone dstrbuton was mproved, avodng the basc ACO algorthm for blnd ntal pheromone dstrbuton searchng; thus, t s helpful for ant colony algorthm to get more accurate searches. Table 4 shows the optmal transport scheme. 7. Concluson Thspapersaboutthedecsonproblemofmultmodal transportaton scheme; t searched and analyzed relevant research lteratures at home and abroad, combned them wth the dverse needs of transportaton scheme decson, and proposed and establshed combnatoral optmzatoathematcal model of ntermodal transportaton plan decson based on transportaton tme and transportaton cost and rsk; at the same tme, t used heurstc algorthm whch combned partcle swarm optmzaton algorthm and ant colony algorthm to solve the model and got the transportaton scheme optmzaton. The experments showed that the algorthm has acheved very good results n tme performance and optmzaton performance; t was a feasble algorthm. The content of ths paper enrched and perfected

10 10 Mathematcal Problems n Engneerng Algorthm The comprehensve evaluaton value Table 3: The results and comparson of PSACO algorthm. Transportaton tme/hour Transportaton costs/yuan Transportaton rsks Operate tme/second PSACO algorthm ACO algorthm Transportaton route Transportatoode Table 4: The optmal transport scheme. The optmal transport scheme O D Ralway-road-waterway-ralway-avaton the theores and methods of the hot ssues n the study of ntermodal transportaton scheme decson, and the results provded the references and reasonable arrangements for the transportaton process and transportaton project decson makng. Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. References [1] K. Chen and L. Ma, Glowworm swarm optmzaton algorthm for 0-1 knapsack problem, Applcaton Research of Computers, vol. 4, no. 30, pp , [2] B. L, X. Q. Yan, and J. X. Hu, Model of contaner termnal logstcs optmzaton system based on the Harvard structure and swarm ntellgence, JournalofJangsuUnverstyofScence and Technology,vol.3,no.25,pp ,2011. [3] J. M, Improved swarm ntellgence optmzaton algorthm used n the task sortng, Bejng Informaton Scence and Technology Unversty,vol.3,no.25,pp.13 18,2010. [4] H. L, X. Chen, and M. Zhang, The path plannng problem based on swarm ntellgence algorthm, Tsnghua Unversty,vol.3,pp ,2007. [5] B.WuandZ.Z.Sh, AkndofTSPproblembasedonantcolony algorthm partton algorthm, Computers,vol.12,pp , [6] R.-B. Xao, Z.-W. Tao, and H.-F. Zou, Concurrent tolerance optmzaton desgn based on hybrd swarm ntellgence algorthm, Computer Integrated Manufacturng Systems, vol. 13, no. 4, pp , [7]Q.L.Ma,W.N.Lu,D.H.Sun,andY.F.Dan, Travelroute plannng model based on fuson of mult ntellgent algorthm, Computer Scence,vol.10,pp ,2010. [8] A. Lozano and G. Storch, Shortest vable path algorthm n multmodal networks, Transportaton Research A: Polcy and Practce,vol.35,no.3,pp ,2001. [9] H. I. Calvete, C. Galé, M.-J. Olveros, and B. Sánchez-Valverde, A goal programmng approach to vehcle routng problems wth soft tme wndows, European Operatonal Research,vol.177,no.3,pp ,2007. [10] Y. L and J. Zhao, Choce of multmodal transportatoodal wth fxed freght, Southwest Jaotong Unversty,vol. 47, no. 5, pp , [11] X. Wang, Z. B. Ch, and X. L. Ge, Whole vehcle multmodal transportatoodel research and analyss wth tme wndows, Computer Research and Applcaton,vol.28,no.2,pp , [12] F. L. Feng and Q. Y. Zhang, Organzaton collaboratve optmzaton model of multmodal transportaton based on envronment, Ralway Scence and Engneerng, vol. 9, no. 6, pp , [13] L. Tong and L. Ne, Multmodal transportaton path optmzaton model and method research, Logstcs Technology,vol.29, no.5,pp.57 60,2010. [14] J. W. Zhang, Multmodal contaner transportaton network path ratonalzaton process, Bejng Jaotong Unversty, [15] L. L and Y. C. Zeng, Multmodal transportatoodel and algorthm n logstcs transportaton, Statstcs and Decson Makng,vol.20,pp.27 29,2009. [16] J. Wen, Optmzatoodel to control the cost of contaner multmodal transportaton, Changsha Scence and Technology Unversty,2010. [17] L. L, Multmodal transportatoodes generalzed cost optmal choce under condtons, Bejng Jaotong Unversty,2006. [18] X. X. Wang, The multmodal transportatonmum cost problem wth tme wndow, Bejng Posts and Telecommuncatons Unversty,2009. [19] J. Zhang, Ralway contaner transportaton network model and algorthm, Central South Unversty,2007. [20] Z. J. Ja, The rsks analyss and control of the goods multmodal transportaton, Chongqng Jaotong Unversty,2009. [21] F. Lu, The contaner multmodal transportaton corrdor plannng and transportatoodes selecton, Southwest Jaotong Unversty, [22] X. K. Luo, Optmzaton algorthm research of logstcs and multmodal transportaton, Shangha Jaotong Unversty,2004.

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