Stadium Tour Planning and Management using Genetic Algorithm and Dynamic Programming

Stadium Tour Planning and Management using Genetic Algorithm and Dynamic Programming

Kriti Chapagain

School Of Computer Science and Engineering Vellore Institute of Technology, Vellore

India

Mitanshi Kshatriya

School of Computer Science and Engineering Vellore Institute of Technology, Vellore India

AbstractThe happening to web and emwering of dwnlding musi, the musi business is nfrnting rerius derese in D sales which used membership-based revenue stream f musi industry. The sales have endured to greet extent beuse of illicit dwnlds and membership-based musi dministrtins like Stify, Gnn nd s n. resently, the rimry wellsring f slry f musi industry is turing. Beuse f r lgistis, blunder nd r rute deisins numerus ren visits neglet t rdue benefit. This tsk mkes ren visiting ging gret redure nd s rtil s uld resnbly be exeted. The mnent f finding the mst brief wy will h dwn the suerfluus st tht re used in trnsrting the stge equis just s the turing singer,bnd individuls, bk u rtists, reinfrement rtists, fundtin vlists nd ther required stffs. This rjet hs vrius mdules tht will hel in betterment f lgistis side f the tur. T generte shrtest ssible rute nsisting ll required ities Geneti lgrithm nd dynmi rgrmming rh is used. This rblem nentrtes n trvelling slesmn rblem.

Keywords Traveling Salesman Problem, Genetic Algorithm, Dynamic Programming, Logistics, NP-hard

1. INTRODUCTION

   This section is aimed at introducing the traveling salesman problem which we have used later to address and tackle the issues faced by the music industry in tour planning. We have also briefly introduced the two approaches that we have used for finding the optimal route. These approaches are genetic algorithms and dynamic programming. We have elaborated on the algorithm in the proposed methodology section.

   1. Traveling Salesman Problem

      TSP (Travelling Salesman Problem) is a classical NP-hard problem in the field of computer science and operations research and combinatorial optimization, The problem is to find the shortest path among the given cities, such that all cities are covered once in the path and return to the starting city. This problem can be applied to solve many real-world problems. Taking the instance of a courier company, they have to deliver a number of packages throughout the city, they can use TSP problem to find most optimal route thus saving time and fuel. Also while planning a route for drone flight, choosing an optimal route through the specified way-points can not only reduce time but may also extend the area that could be covered in every single flight. There can be other parameters needing optimization in each of those problems, but at the core, each can be viewed as solving a modification of TSP. It's an NP- hard problem in computational optimization important in

      research and theoretical technology. The amount of time required to solve this problem grows exponentially with the number of cities or inputs being increased. TSP is expressed as follows:

      Let 1, 2, up to n be the marks of the n urban communities and C = [ca,b] be an n x n cost lattice where each entry of the matrix represents the expense of heading out from the city a to b.

      In TSP, we need to find an optimal route such that each city is visited only once and the last city visited should be the originating city.

      The absolute cost of a route is given by: A(n)= (i=1 to n-1) a,a+1 + 1, (1)

      This paper introduces two ways to solve TSP-based on genetic algorithm and dynamic programming approach.

   2. Genetic Algorithm

      Geneti lgrithms, resented by J. Hllnd (1975), re mtivted frm the Drwin dvnement hythesis: in the ule develment, the best ele, whih re mre djusted t their nditin, n utlst fr quite while, n the ther hnd, the ele, whih re nt fits t their nditin, vnish with the entry f ges. In this wy, its hrmsme nd rer wellness ity t be hrterized t ssess ele de every ersn. Initilly, G mrises t rbitrrily rete intrdutry ule, t tht int, geneti ertrs (seletin, rssver, muttin), inside determined rbbilities, re lied t deliver nther genertin tht nsidered best thn its revius versins.

      The traveling salesman problem is considered as an optimization problem. It can be solved using a genetic algorithm since genetic algorithm is used for solving optimization problems.

   3. Dynamic Programming

   Dynamic rgrmming is useful computer programming method as well as a mthemtil for solving optimization problems. It can be used to determine an optimal sequene f interrelted deisins. The main idea followed in this methds lication is dividing f ress int several stages fter whih n optimal result is chosen fr every stge. Dynamic programming is applied to problems recursive in nature. To save the computation cost of repeating recursive calls, the recursive calls are stored. If the recursive calls value is in store

   that value can be used right away. There re tw fundmentl rhes fr solving TS: reise nd estimted. reise utlks re generlly funded n Brnh nd Bund, Dynmi rgrmming, Integer Alied Mthemtis. All of them can give optimal solutions for TSP.

   However, the methods above give exponential time complexity i.e. the time taken by the methods increases exponentially with increasing time. The time complexity for the Dynmi rgrmming method is calculated to be (n^2

   .2^n). Thus, while solving TSP with Dynamic Programming, it can at best handle 40-60 cities or data points using branch and bound strategy. It might be able to fathom up to 200 cities or data points.

2. LITERATURE REVIEW

   In the literature, researchers the joining of Genetic calculations (GAs) with hierarchical data sets to take care of the combinatorial issue in asset enhancement and the board.

   1. The authors of the paper have proposed using two levels of knowledge – procedural and declarative. It will help in addressing the issues of combinational optimization as well as numerical functions. [2] The authors of this paper showed Genetic Algorithms can be integrated in any form of DSS or decision support system to ensure economical use of resources. TS is detiled s disvering hnge f n urbn res, whih hs the bse exense. This issue is widely knwn as an N- hrd problem [2, 4, 5]. Numerus lultins hve been rsed t tkle this issue [2, 3, 4, 5, 7, 10, 11, 12, 14, 15, 17]. There re tw fundmentl methdlgies fr ddressing TS: ext nd rximte. Definite methdlgies re tyilly funded n Dynmi rgrmming, Brnh nd Bund, Whle number Liner rgrmming nd ll gve the idel nswers fr TS. However, it must be noted that the lultins which are using these methdlgies hve remrkble running time s M. Held nd R. M. Kr [2] inted ut in their research work. Dynmi rgrmming tkes (n^2.2^n) running time. Thus, while solving TSP with Dynamic Programming, it can at best handle 40-60 cities or data points using branch and bound strategy. It might be able to fathom up to 200 cities or data points.

      .[3] The authors of this paper have used tree decomposition with dynamic programming to further optimize the solution for TSP. Let there be trveling slesmn rblem (TS), the solution for it is tur H i grh G. An operation k-mve will remve k-edges frm H nd then proceed to dd k-edges f G s as to form new tur namely H. The well known k-T heuristi fr TS uses the k-moves method. It firstly finds ll minima by strting frm n rbitrry tur H nd subsequently imrving it using sequene f k-mves.

      Vrius muttinl Testing shwed tht new G hrmsme rh result in smller serh se, furthermre, muh f the time, delivers referble rrngements ver st redures.[4] The MTS is similr problem t the popular NP-hard trveling slesersn rblem (TS) with the dded onstraint tht eh city can be visited by ny ne from the sles team. revius studies investigted slving the MTS with geneti lgrithms (Gs) using

      stndrd TS hrmsmes nd ertrs. The above paper presents a new chromosome for GA and then proceeds to compare its performance in accordance with time and space complexities.

3. PROPOSED METHODOLOGY

Stadium Tour Management framework is an attempt to defeat the logistics issue confronted while leading an arena visit. It will decrease the odds of scattering of any stage hardware as a database can be utilized to cross-check if each gear is available or not. Our venture would be a great guide to the tour manager as he/she will have all the data pretty much every one of the necessities of the visit. All the data can be seen by the administrator.

The Stadium Tour Management framework has 4 modules:

1. Stadium

2. Staff

3. Equipment

4. Merchandise

All the modules have all common features of what is expected in a database management system like – create, read, update and delete along with some additional features.

1. Database

   1. Stadium Database

      Fig. 1. Stadium Database

   2. Equipment Database

      Fig. 2. Equipment Database

   3. Staff Database

      Fig. 3. Staff Database

   4. Merchandise Database

   5. Distance Matrix Table

      Fig. 4. Distance Matrix Table

2. Algorithms used

• Generating the shortest route covering all cities is equivalent to traveling salesman problem. For this two approaches have been used-

• 1. Genetic algorithm

• 2. Dynamic programming

• The distance matrix is generated with the help of a table containing the distance of one city to other. Distance is zero for the same city.

Genetic algorithm:

1. Creating distance matrix It is a2D array where the entry at i, j represents the distance from the ith city to the jth city.

2. Creating population Population is a collection of possible routes.

3. Determining the fitness of the population-

4. Select the mating pool

5. Breed/ordered crossover

6. Mutate

7. Repeat the above process until the required number of iterations is reached. We are using 2000, 4000, 5000 iterations.

Dynamic programming:

1. Cost ({1}, 1) = 0

1. for s = 2 to n do

   1. for all subsets S [1, 2, 3, , n] of size s and containing 1

      2.1.1 C (S, 1) =

   2. for all j S and j 1

      2.2.1 Cost(S, j) = min [Cost (S {j}, i) + d(i, j) for i

      S and i j]

2. Return min j Cost ({1, 2, 3, , n}, j) + d(j, i)

1. TESTING AND RESULTS

   We used D nd G ntrst t rete minimum snning th. The lultins were lied f distne mtrix f eight ities. Geneti lgrithm seem t disver gret nswers fr the Trveling Slesmn rblem, nywy it lys rtiulrly n hw it is ended nd whih rssver nd muttin strtegies re utilized. Likewise, it des not hve ne timl slutin. Hwever, it rvides with best ssible slutin. Dynmi rgrmming rh is reltively simle t de yet it requires sme investment when the munt f dt inrements

   .dditinlly, beginning ity must be indited in its de. It is exensive fr memry s well s time. The qulity f slutin deends n the de.

   Comparison of algorithms used –

   Algorithm	Time Taken	Result(cos t)	Time Complexit y	Advantage	Disadvant age
   Genetic	77.041	1355.0	O(Kmn)	Best	No
   Algorithm				possible	optimal
   				solution is	solution is
   				generated	reached
   Dynamic	0.2513	1355.0	O(n2 *2n)	Generates	Expensive
   programm				an	for
   ing				optimal	memory as
   				solution	well as
   					time
   				Easy to
   				code	Quality of
   					solution
   					depends
   					on the
   					code

   Algorithm	Time Taken	Result(cos t)	Time Complexit y	Advantage	Disadvant age
   Genetic	77.041	1355.0	O(Kmn)	Best	No
   Algorithm				possible	optimal
   				solution is	solution is
   				generated	reached
   Dynamic	0.2513	1355.0	O(n2 *2n)	Generates	Expensive
   programm				an	for
   ing				optimal	memory as
   				solution	well as
   					time
   				Easy to
   				code	Quality of
   					solution
   					depends
   					on the
   					code

   TABLE I. RESULTS

   Fig. 5. Time taken by GA and DP approaches with various amount of data

   The accompanying chart shows that with less amount of data dynamic programming give a lot quicker outcome than the hereditary calculation for tackling traveling salesman problem. However, as the size of information begins to expand the time taken by powerful programming builds exponentially when contrasted with that of genetic calculation.

   The exhibitions of the two calculations are unequivocally influenced by their parameters just as their applications. GA is skilled at looking for ideal arrangements in low input cases. Now and again, for example, with various input greater than 100, the presentation of GA is better than that of DP. In any case, for a lower amount of data GA takes additional time than DP.( DP has a decent presentation in acquiring steady and top- notch solutions, even in looking through huge search space. Be that as it may, because of its exhaustive enumerating nature, it costs n abundance of time in a huge amount of data cases.

   As of late, touring has become the significant wellspring of salary for the music industry. Arena visits the executives' framework makes the logistics part of touring

   simpler and increasingly practical. It will decrease any utilization of paper in keeping up information about visits.

2. CONCLUSION

In sum up, this research contains a function for generating the shortest-path spanning all the cities. This will help in covering all cities in a much smaller total distance. Anyway, this venture doesn't mull over a few things like the different levies forced while traveling interstate or the accessibility of arenas on required dates, and so on. With everything taken into account whole undertaking may come convenient for touring chiefs.

Tools used: The project is implemented using python 3 and sqlite3 packages for the database.

REFERENCES

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