Multi Attributes Approach for Tourist Trips Design

Transcription

1 Multi Attributes Approach for Tourist Trips Desig Ilaria Baffo 1, Pasquale Caroteuto 2, Atoella Petrillo 3, Fabio De Felice 4 1 Idustrial Egieerig School (DEIM) - Uiversity of Tuscia, Italy ilaria.baffo@uitus.it 2 Istituto per le Applicazioi del Calcolo (IAC) - CNR, Italy p.caroteuto@iac.cr.it 3 Departmet of Egieerig - Uiversity of Naples Partheope, Italy atoella.petrillo@uipartheope.it 4 Departmet of Civil ad Mechaical Egieerig - Uiversity of Cassio ad Souther Lazio, Italy defelice@uicas.it Abstract. The authors propose a Multi Attributes approach to meet the demad of persoalized tourist tours ito cultural cities. Respectig to others works preset ito the literature, i this paper the decisioal process icludes two phases ad a high umber of variables that do t icrease the complexity of the problem. A real applicatio i a Italia city, Florece, is preseted to demostrate the great potetial of this system ito real cotext. The first phase of optimizatio is solved applyig a iovative Geetic Algorithm, the secod oe a Multi Criteria Method, Aalytic Hierarchy Process (AHP). The combiatio of these two approach gives flexibility to the system with respect to umber of variables ad allow to retur a good solutio for tourist i few secod of computatioal time. 1 Itroductio The icreasig use of mobile devices i everyday life has favored the creatio of itelliget applicatios also i field such as tourism, culture ad hobbies. Oe of the most iterestig applicatios provides opportuity to help tourists i choosig the best route give a maximum time of visit. Durig the last years several researchers have faced this problem with the aim to reduce ucertaity ad icrease the persoalizatio of the tourist paths. I the scietific literature, the problem is better kow as Tourist Trip Desig Problem (TTDP). The authors i this work propose a Multi Attributes Decisio Support System (MDSS) to meet the demad of persoalized tourist tours ito cultural cities. As described i the followig may researchers have successfully addressed this problem, but, oly few of these have proposed real applicatios able to cosider several attribute to decisioal process. The Multi Attributes Decisio Support System proposed, facig the TDPP i two steps. Firstly, a Geetic Algorithm (GA) solves i optimal way the Orieteerig Problem (OP) o real istaces comig from Italia historical cities, Florece. The validatio of algorithm is guarateed creatig a A Mathematical Programmig Laguage (AMPL) model able to retur the optimal solutio for small istaces of the same problem. Fially, the optimal solutios are compared o basis of differet attributes havig the features to be added

2 up. The last step has bee coducted with the use of Multi Criteria Aalysis Methods. Thak to this approach, the obtaied solutios ca be evaluated o basis of several attributes like: time of decisio with respect to time of travel, duratio of travel, levels of freedom ito the decisio, degree of additioality of prefereces, umber of decisio-makers, umbers of cultural heritages to visit, etc. Real cases studies are give with the aim to offer developmet ideas for implemetatio of smart applicatios for tourist trips' desig. The proposed methods ca reach importat results where the variables of the problem are umerous ad the optimizatio process too log ad complex. The rest of paper is orgaized as follows: a review of literature is give i sectio 2, the mathematical model ad its resolutio with geetic algorithm is explaied i sectio 3. Sectio 4 presets AHP approach ad its itegratio with optimizatio model is discussed. Applicatio ad results are aalyzed i Sectio 5. Fially, coclusio ad future researches are proposed i sectio 6. 2 Literature Review As well explaied i [5,10] the described route-plaig problem has bee cosidered as a applicatio of the Orieteerig Problem or its variats. I the OP, several locatios with a associated score have to be visited oly oce i order to obtai a total trip score. The objective is to obtai a total trip score as high as possible without violatig a time restrictio. There have bee works o exact methods that have yielded solutios to smaller sized problems. Due to the computatioal limitatios of the exact algorithms, several heuristic were explored to may researchers i the past. The first heuristics were proposed by Tsiligirides (1984) i [9] ad are kow as the S-algorithm ad the D-algorithm. The S-algorithm uses the Mote Carlo method to costruct routes usig probabilities correlated to the ratio betwee ode score ad ode distace from the curret ode. The D-algorithm is built based upo the vehicle schedulig method proposed by Wre ad Holiday (1972) [12]. Others heuristics have bee explored i the years to solve this kid of problems, i [8] a Tabu Search approach has bee used for Multi Costraied Team Orieteerig Problem ad its applicatio i touristic trip plaig. I [7,11] the authors propose to solve the Multi Costrait Team Orieteerig Problem with Multiple Time Widows with kow heuristic like Iterated Local Search (ILS) ad Greedy radomized adaptive search procedure (GRASP). Iterated Local Search is proposed also i [4] to solve real-time Time Depedet Team Orieteerig Problem with Time Widows (TDTOPTW). Durig the last years, may authors have chose to implemet evolutioary algorithm tryig to reduce the computatioal time ad to improve the quality of proposed solutio to tourist. I [2] the authors propose a evolutioary algorithm to solve a multi-objective problem for persoalized tours i street etworks. I this case, the trip is log multiple day ad a Team Orieteerig Problem with Time Widows (TOPTW) is solved with a heuristic approach whose computatioal times are ot clearly declared. The aim of the authors is to give i few secod a optimal solutio of OP ad secodly itroduce more elemets that ca be aalyzed with multi criteria aalysis. I this way, the complexity of the problem is lower ad the computatioal time too, the the approach is more usable for real time digital applicatios. 35

3 3 Problem Descriptio I this work the authors face the sigle day Tourist Trip Desig Problem (TTDP) modellig a Orieteerig Problem (OP). I the OP, a set of N locatio, also called Poit of Iterest (PoIs), correspodig with odes i is give, each with a score S i. The startig poit ad the ed poit are fixed. The time t ij eeded to travel from vertex i to j is kow for all vertices. The problem became more complex because ot all the vertices ca be visited sice a give threshold T max limits the available time. The goal of the OP is to determie a path, limited by T max that visits some of the vertices, i order to maximize the total collected score. Other works propose to optimize the problem maximizig the umber of PoIs visited, the problems coicide if we suppose each poit s score equal to 1. The scores are assumed to be etirely additive ad each vertex ca be visited at most oce. I this algorithm the maximum time available to visit the PoIs is cosidered as costrai of the problem. At the same time, all solutios are defied by a set of PoIs visited, a time of visit for each poit ad a time of walkig from oe poit to aother poit. The OP ca be formulated as follows: S i 0 is the score associated to ode i, c ij is the cost associated to path betwee ode i ad ode j. Usually odes are cosidered i the Euclidea plae. Sice the distace ad travel time betwee odes are determied by the geographical measure, distace is used as the represetative of path s cost. Geerally, the mathematical model of the OP is formulated as follows: S i i=1 Subject to j=1 x ij x 1j = x i =1 j= i=1 x ik = x kj 1 i=2 j=2 c ij x ij T max i 1 j 1 2 ui ui uj x ij k=2,,-1 i, j 1,, i 1,, i,j 1,, (7) x ij 0,1 i,j 1,, Where (1) represets the problem s Objective Fuctio to maximize the total collected score S. Costrait (2) guaratee that the path starts i vertex 1 ad eds i vertex N. Costrait (3) esures the coectivity of the path ad guaratee that every vertex is visited at most oce. Costrait (4) esures the limited time budget T. 36 (1) (2) (3) (4) (5) (6)

4 Costraits (5) ad (6) are ecessary to prevet sub-tours. Costraits (7) requires that the variables are biary. The decisioal variable x ij is equal to 1 if the ode j to i are coected, 0 else. This formulatio guaratees as result a tour able to: Visit as may PoIs as possible; Visit PoIs at most oce; Visit PoIs that maximize the Total Score (Objective Fuctio); Visit PoIs coected amog them; ad Visit PoIs respectig the limitatio time. The set of solutios comig from the geetic algorithm represet the iputs for multi criteria approach with AHP. 4 Multi criteria approach: Aalytic Hierarchy Process. The AHP breaks dow a decisio-makig problem ito several levels i such a way that they form a hierarchy with uidirectioal hierarchical relatioships betwee levels [3]. The AHP for decisio makig uses objective mathematics to process the iescapably subjective ad persoal prefereces of a idividual or a group i makig a decisio. With the AHP, oe costructs hierarchies or feedback etworks, the makes judgmets or performs measuremets o pairs of elemets with respect to a cotrollig elemet to derive ratio scales that are the sythesized throughout the structure to select the best alterative. The top level of the hierarchy is the mai goal of the decisio problem. The lower levels are the tagible ad/or itagible criteria that cotribute to the goal. The bottom level is formed by the alteratives to evaluate i terms of the criteria. The modelig process requires a pairwise comparisos of the elemets i each level usig a scale of 1-9, as suggested by Saaty [6]. The result of the compariso is the so-called domiace coefficiet a ij that represets the relative importace of the compoet o row (i) over the compoet o colum (j), i.e., a ij =w i /w j. The pairwise comparisos ca be represeted i the form of a matrix. After all pairwise compariso is completed, the priority weight vector (w) is computed as the uique solutio of Aw=λ maxw, where λ max is the largest eigevalue of matrix A. Fially, cosistecy idex CI is estimated. CI could the be calculated by: CI=(λ max )/ 1. I geeral, if CI is less tha 0.10, satisfactio of judgmets may be derived. For this applicatio the AHP takes as iput the results of optimizatio process ad evaluates these uder several criteria better explaied i the ext paragraph. As first activity, the mathematical model is supposed to model the capacitated orieteerig problem, as secod phase we solve the formulatio implemeted a meta-heuristic kow as Geetic Algorithm (GA). The, we applied a multi-criteria aalysis (AHP model) to algorithm s results to order the fouded solutios respect to the followig objectives: Time L-path, Visited places, Ticket cost. 5 Problem Resolutio The authors propose a optimizatio approach that draw ispiratio o Geetic Algorithm (GA) as developed by Hollad (1975) ad the described by Goldberg (1989). GA starts iitializig a First Populatio composed by a pre-determiate umber of idividuals. Each idividual represets a solutio for the faced problem ad it is characterized by several elemets such a chromosome ad a fitess value. 37

5 The idividual s chromosome is composed by several gee that ca assume biary or iteger value, the combiatio of these gees usually represets the problem s solutio thaks to a correspodece betwee the gee s value ad the problem s variables value. The idividual s fitess value correspods to solutio objective fuctio s value, ad it s basic ito determiate the idividual s probability to survive at evolutio process, so that bad idividuals are destied to ot have a log life ito populatio. The differece betwee the old ad the ew populatio i the evolutioary process is guarateed by the presece of two importat operatios called Mutatio ad Crossover. After several geeratios, the best solutio coverges, ad it hopefully represets the optimum or suboptimum solutio to the problem at had. GA are successfully applied to differet cotexts i order to solve a very large umber of problems, for this purpose various ad origial geetic operators are developed, that revisit the origial cocept of mutatio ad crossover. I this applicatio the authors adopt a circular represetatio of chromosome ad several heuristic techiques to improve the evolutioary process through mutatio ad crossover operatios. I our GA the chromosome is composed of all odes that the tourist wat visit, without the start ode ad the ed ode that ca be added at the ed of optimizatio process. This codig of chromosome with respect to problem s solutio represetig by a sigle tour, allows to have oly admissible solutios better or worst o basis of Total score reached by visitig more or more better PoIs. The Fig. 1 shows like each chromosome represets a sequece of visitig PoIs, i.e. a tour, i.e. a solutio for the OP. The Closed loop Structure of Chromosome code allows a wider ad faster research of solutios. Fig. 1: Ecodig ad Decodig process As previously described the GA structure is based o costitutio of a populatio at each iteratio. This populatio step by step evolves ad the algorithm foud better solutios for the faced problem. Followig a sythetic descriptio of the implemeted GA pseudocode is reported. Parameters Settig Iitializatio Geerate a feasible solutio radomly as idividual 38

6 Save them ito the populatio Pop (i) Loop util the populatio s size S is reached Calculate Fitess to defie the Best Idividual BI(i) of P(i) While the umber of iteratios is t reached do Set iteratio i = 0 Selectio: Roulette fuctio for selectig two idividual as paret Crossover (Sigle, PMX) Evaluate Fitess Update the Best idividual whe offsprig is better tha actual Best Idividual BI(i) Mutatio (Smart Swap) Evaluate Fitess Update the best idividual whe offsprig is better tha actual Best Idividual BI(i) Build Build ew Populatio Pop (i+1) as collectio of idividuals geerated with Crossover ad Mutatios Operatios Next i Ed - Retur the best idividual cotaiig the best tour More details are give ito a previous publicatio of authors i [1]. The solutios give by optimizatio process costitute iputs for Multi Criteria Aalysis Approach. Fially, the Multi Attributes Approach for Tourist Trips Desig Problem (MATTDP) gives as output a solutio that takes ito accout a lot of variables, some of these are cosidered ito optimizatio process ad others ito Multi Criteria Aalysis Process. 5.1 Real Applicatio I this paragraph, we propose the results obtaied for the sigle-day Tourist Trip Desig Problem (TTDP) i the city of Florece. We cosider 24 PoIs, all icluded ito urba areas of the city. We fix the PoIs of departures ad of arrival ad the maximum time that the tourist has to visit the city, variable from 390 miutes to 930 miutes. We calculated the distace matrix ad set the algorithm parameters (umbers of idividuals, populatio ad Best Solutio Cotaiers s (BSC) size, Frequecy rate of geetic operators) o the basis of prelimiary tests that have give the best cofiguratio of algorithm. For each PoI, we suppose that the tourist assigs a differet score o the basis of your preferece. The Total time of tourist path is calculated as summarize betwee the time to reach the PoI ad the time to visit it that it is supposed to be equal to 30 mi for each oe. The Table 2 presets the results comig from the optimizatio process; the authors foud 5 solutios/tours (called 1, 2, 3, 4, 5) for 5 differet time each oe startig from PoI 1 ad edig to PoI 24. Each PoI is represeted by a umber from 1 to 24 ad each Tour ca be cosidered as a sequece of visited PoIs. As showed i Table 1 for each solutio a Real time of tour, a total time of tour, a total score of tour ad the umber of visited PoIs are give. T max real is expressed i miutes like Time for visit the PoIs ad the relative Total Time. T max is expressed i a covetioal measure used ito the algorithm, Total Score ad Visited PoIs have o uits of measure. For summarizig, each solutio comig from optimizatio process is characterized by a umber or a sequece of visited PoIs, ad a Total time eeded for completig the tour as sum of time to reach all PoIs of tour ad time to visit them. 39

7 Table 1: Data of solutios Solutios Tmax Real Tmax Time of visit Total time Total score Visited PoIs The outputs of optimizatio process as before described are give as iputs of AHP model built as i Fig. 2. I the preset paper AHP Absolute model is applied as i [3]. Table 2: Solutios of optimizatio Solutios Tour AHP Absolute model is based o paired comparisos amog the elemets of a set with respect to a commo attribute. Experts team developed pairwise compariso matrices to determie the weights of criteria. Cosistecy idex has bee estimated (CI 0.018). Results show that the most importat criteria is C1. Time L path with a score of 56%, followed by C3. Ticket cost with a score of 32%, ad fially is the criteria C2. N Visited places with a score of 12%. I AHP Absolute model criteria are further subdivided ito a level for itesities. The scores of these itesities are each weighted by the priority of its criterio ad summed to derive a total ratio scale score for the alterative. Each criterio has ratigs listed uder it. Tab. 3 shows the fial rakig of the AHP Model. Fig. 2. AHP Absolute Model Priorities C1 Time Lpath C2 N* Place Visited C3 Ticket cost km km km km km Tab. 3. Fial Rakig 40

8 6 Coclusios ad Future Researches I this work the authors preset a Multi Attributes Approach for solvig sigle-day Tourist Trips Desig Problem (MATTDP). The proposed System is applied to a real case ito the Italia city of Florece. Thaks to two phases of this approach it is possible to iclude several variables ito the decisioal process without icrease the complexity of the problem. For future researches, the authors wat to implemet the system i a big istace of the problem cosiderig also time widows costraits for visitig PoIs. The ext step could be to implemet a mobile applicatio for smartphoe ad tablet i order to test the real usability of this system i real cotext. Refereces 1. Baffo, I., Caroteuto, P., Storchi, G., A geetic algorithm to desig touristic routes i a bike sharig system, 14th iteratioal coferece o modelig ad applied simulatio, At Bergeggi (Liguria) Italy, (2015). 2. De Falco, I., Scafuri, U., & Taratio, E. A multiobjective evolutioary algorithm for persoalized tours i street etworks. I Europea Coferece o the Applicatios of Evolutioary Computatio. Spriger Iteratioal Publishig. (2015) De Felice F., Petrillo A., Absolute measuremet with aalytic hierarchy process: A case study for Italia racecourse. Iteratioal Joural of Applied Decisio Scieces. Volume 6, Issue 3, 2013, (2013) Garcia, A., Arbelaitz, O., Liaza, M. T., Vasteewege, P., & Souffriau, W. Persoalized tourist route geeratio. I Iteratioal Coferece o Web Egieerig. Spriger Berli Heidelberg. (2010) Gavalas, D., Kostatopoulos, C., Mastakas, K., & Patziou, G. A survey o algorithmic approaches for solvig tourist trip desig problems. Joural of Heuristics, 20(3), (2014) Saaty, T.L., (1977. A scalig method for priorities i hierarchical structures. Joural of Mathematical Psychology 15, Souffriau, W., Vasteewege, P., Vade Berghe, G., & Va Oudheusde, D. The multicostrait team orieteerig problem with multiple time widows. Trasportatio Sciece, 47(1), (2013), Sylejmai, K., Dor, J., & Musliu, N. A tabu search approach for multi costraied team orieteerig problem ad its applicatio i touristic trip plaig. I Hybrid Itelliget Systems (HIS), 12th Iteratioal Coferece o IEEE. (2012) Tsiligirides, T., Heuristic Methods Applied to Orieteerig. Joural of Operatioal Research Society, vol. 35, o. 9, (1984) Vasteewege, P., Souffriau, W., & Va Oudheusde, D. The orieteerig problem: A survey. Europea Joural of Operatioal Research, 209(1), (2011) Vasteewege, P., Souffriau, W., Berghe, G. V., & Va Oudheusde, D. Metaheuristics for tourist trip plaig. I Metaheuristics i the Service Idustry. Spriger Berli Heidelberg. (2009) Wre A., Holiday A., Computer Schedulig of Vehicles from Oe or More Depots to a Number of Delivery Poits. Operatios Research Quarterly, vol. 23, (1972)