A Comprehensive Survey on the Multiple Travelling Salesman Problem: Applications, Approaches and Taxonomy

Real Life ◽

Travelling Salesman ◽

Comprehensive Survey ◽

The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc.Although the importance of this optimization problem, there is no survey dedicated to reviewing recent MTSP contributions. In this paper, we aim to fill this gap by providing a comprehensive review of existing studies on MTSP. In this survey, we focus on MTSP’s recent contributions to both classical vehicles/robots and unmanned aerial vehicles. We highlight the approaches applied to solve the MTSP as well as its application domains. We analyze the MTSP variants and propose a taxonomy and a classification of recent studies.

A Comprehensive Survey on the Multiple Travelling Salesman Problem: Applications, Approaches and Taxonomy

10.36227/techrxiv.14124350 ◽

2021 ◽

Author(s):

omar cheikhrouhou

Keyword(s):

Unmanned Aerial Vehicles ◽

Optimization Problem ◽

Optimization Problems ◽

Real Life ◽

Travelling Salesman ◽

Comprehensive Survey ◽

An efficient genetic algorithm for solving open multiple travelling salesman problem with load balancing constraint

Decision Science Letters ◽

10.5267/j.dsl.2021.5.003 ◽

2021 ◽

Vol 10 (4) ◽

pp. 525-534 ◽

Cited By ~ 1

Author(s):

Purusotham Singamsetty ◽

Jayanth Kumar Thenepalle

Keyword(s):

Genetic Algorithm ◽

Load Balancing ◽

Optimization Problems ◽

Limited Attention ◽

Travelling Salesman ◽

Practical Applications ◽

Comparative Results ◽

The multiple travelling salesman problem (MTSP) is one of the widely studied combinatorial optimization problems with various theoretical and practical applications. However, most of the studies intended to deal with classical MTSP, very limited attention has been given to an open multiple travelling salesman problem and its variants. In this paper, an open multiple travelling salesman problem with load balancing constraint (OMTSPLB) is addressed. The OMTSPLB differs from the conventional MTSP, in which all the salesmen start from the central depot and need not come back to it after visiting the given number of cities by accomplishing the load balance constraint, which helps in fairly distributing the task among all salesmen. The problem aims to minimize the overall traversal distance/cost for operating open tours subject to the load balancing constraint. A zero-one integer linear programming (0-1 ILP) model and an efficient metaheuristic genetic algorithm (GA), is established for the OMTSPLB. Since no existing study on OMTSPLB, the proposed GA is tested on the relaxed version of the present model, comparative results are reported. The comparative results show that the proposed GA is competent over the existing algorithms. Furthermore, extensive experiments are carried out on OMTSPLB and the results show that proposed GA can find the global solution effectively.

Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem

Mathematical Problems in Engineering ◽

10.1155/2020/3431420 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Maha Ata Al-Furhud ◽

Zakir Hussain Ahmed

Keyword(s):

Genetic Algorithm ◽

Heuristic Algorithms ◽

Optimization Problems ◽

Hybrid Genetic Algorithm ◽

Travelling Salesman ◽

Complex Optimization ◽

Problem Instances ◽

Search Approach ◽

The multiple travelling salesman problem (MTSP), an extension of the well-known travelling salesman problem (TSP), is studied here. In MTSP, starting from a depot, multiple salesmen require to visit all cities so that each city is required to be visited only once by one salesman only. It is NP-hard and is more complex than the usual TSP. So, exact optimal solutions can be obtained for smaller sized problem instances only. For large-sized problem instances, it is essential to apply heuristic algorithms, and amongst them, genetic algorithm is identified to be successfully deal with such complex optimization problems. So, we propose a hybrid genetic algorithm (HGA) that uses sequential constructive crossover, a local search approach along with an immigration technique to find high-quality solution to the MTSP. Then our proposed HGA is compared against some state-of-the-art algorithms by solving some TSPLIB symmetric instances of several sizes with various number of salesmen. Our experimental investigation demonstrates that the HGA is one of the best algorithms.

Quantum Inspired General Variable Neighborhood Search (qGVNS) for Dynamic Garbage Collection

10.20944/preprints201711.0128.v1 ◽

2017 ◽

Author(s):

Christos Papalitsas ◽

Panayiotis Karakostas ◽

Theodore Andronikos ◽

Spyros Sioutas ◽

Konstantinos Giannakis

Keyword(s):

Variable Neighborhood Search ◽

Optimization Problems ◽

Real Life ◽

Neighborhood Search ◽

Np Hard ◽

Np Hard Problem ◽

Gps System ◽

Tools And Techniques

General Variable Neighborhood Search (GVNS) is a well known and widely used metaheuristic for efficiently solving many NP-hard combinatorial optimization problems. Quantum General Variable Neighborhood Search (qGVNS) is a novel, quantum inspired extension of the conventional GVNS. Its quantum nature derives from the fact that it takes advantage and incorporates tools and techniques from the field of quantum computation. Travelling Salesman Problem (TSP) is a well known NP-Hard problem which has broadly been used for modelling many real life routing cases. As a consequence, TSP can be used as a basis for modelling and finding routes for Geographical Systems (GPS). In this paper, we examine the potential use of this method for the GPS system of garbage trucks. Specifically, we provide a thorough presentation of our method accompanied with extensive computational results. The experimental data accumulated on a plethora of symmetric TSP instances (symmetric in order to faithfully simulate GPS problems), which are shown in a series of figures and tables, allow us to conclude that the novel qGVNS algorithm can provide an efficient solution for this type of geographical problems.

2. Four types of problem

Combinatorics: A Very Short Introduction ◽

10.1093/actrade/9780198723493.003.0002 ◽

2016 ◽

pp. 7-27

Author(s):

Robin Wilson

Keyword(s):

Optimization Problem ◽

Optimization Problems ◽

Travelling Salesman ◽

Counting Problems ◽

Problem Construction ◽

Colour Problem ◽

Efficiency Of Algorithms ◽

Enumeration Problems ◽

Knight’S Tour

‘Four types of problem’ explains that combinatorics is concerned with four types of problem: existence problems (does x exist?); construction problems (if x exists, how can we construct it?); enumeration problems (how many x are there?); and optimization problems (which x is best?). Existence problems discussed include tilings, placing dominoes on a chess board, the knight’s tour problem, the Königsberg bridges problem, the Gas–Water–Electricity problem, and the map-colour problem. Construction problems include solving mazes, and the two types of enumeration problems considered are counting problems and listing problems. Examples of an optimization problem include the minimum connector problem and the travelling salesman problem. The efficiency of algorithms is also explained.

Seed based plant propagation algorithm for multiple travelling salesman problem

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i2.33.14823 ◽

2018 ◽

Vol 7 (3.3) ◽

pp. 515

Author(s):

S Kalaiarasi ◽

P Sriramya

Keyword(s):

Optimization Problems ◽

Routing Algorithm ◽

Complex Problem ◽

Travelling Salesman ◽

Biologically Inspired ◽

Plant Propagation ◽

Propagation Algorithm ◽

Biologically Inspired Algorithms ◽

Multiple Travelling Salesman Problem is a complex problem in which route for a salesman is assigned to visit a city that has various hurdles such as congested road, damaged road, etc. In recent years biologically inspired algorithms are most widely used to solve many optimization problems. Here seed based plant propagation algorithm is applied for the multiple travelling salesman problem that is also a optimization problem, and the result is compared with a short-cut routing algorithm. The result shows that Seed based Propagation Algorithm is easy to implement since it has few parameters to be utilized and also time complexity is reduced when implemented in multiple travelling salesman problem.

Representasi Matriks untuk Proses Crossover Pada Algoritma Genetika untuk Optimasi Travelling Salesman Problem

Matematika ◽

10.29313/jmtm.v16i1.4050 ◽

2017 ◽

Vol 16 (1) ◽

Cited By ~ 2

Author(s):

Ismi Fadhillah ◽

Yurika Permanasari ◽

Erwin Harahap

Keyword(s):

Genetic Algorithm ◽

Genetic Algorithms ◽

Optimization Problems ◽

Matrix Representation ◽

Optimal Number ◽

Travelling Salesman ◽

Fitness Value ◽

The City

Abstrak. Travelling Salesman Problem (TSP) merupakan salah satu permasalahan optimasi kombinatorial yang biasa terjadi dalam kehidupan sehari-hari. Permasalahan TSP yaitu mengenai seseorang yang harus mengunjungi semua kota tepat satu kali dan kembali ke kota awal dengan jarak tempuh minimal. TSP dapat diselesaikan dengan menggunakan metode Algoritma Genetika. Dalam Algoritma Genetika, representasi matriks merupakan representasi kromosom yang menunjukan sebuah perjalanan. Jika dalam perjalanan tersebut melewati n kota maka akan dibentuk matriks n x n. Matriks elemen Mij dengan baris i dan kolom j dimana entry M(i,j) akan bernilai 1 jika dan hanya jika kota i dikunjungi sebelum kota j dalam satu perjalanan tersebut, selain itu M(i,j)=0. Crossover adalah mekanisme yang dimiliki algoritma genetika dengan menggabungkan dua kromosom sehingga menghasilkan anak kromosom yang mewarisi ciri-ciri dasar dari parent. Algoritma Genetika selain melibatkan populasi awal dalam proses optimasi juga membangkitkan populasi baru melalui proses crossover, sehingga dapat memberikan daftar variabel yang optimal bukan hanya solusi tunggal. Dari hasil proses crossover dalam contoh kasus TSP melewati 6 kota, terdapat 2 kromosom anak terbaik dengan nilai finess yang sama yaitu 0.014. Algoritma Genetika dapat berhenti pada generasi II karena berturut-turut mendapat nilai fitness tertinggi yang tidak berubahKata kunci : Travelling Salesman Program (TSP), Algoritma Genetika, Representasi Matriks, Proses Crossover Abstract. Travelling Salesman Problem (TSP) is one of combinatorial optimization problems in everyday life. TSP is about someone who had to visit all the cities exactly once and return to the initial city with minimal distances. TSP can be solved using Genetic Algorithms. In a Genetic Algorithm, a matrix representation represents chromosomes which indicates a journey. If in the course of the past n number of city will set up a matrix n x n. The matrix element Mij with row i and column j where entry M (i, j) will be equal to 1 if and only if the city i before the city j visited in one trip. In addition to the M (i, j) = 0. Crossover is a mechanism that is owned by the Genetic Algorithm to combine the two chromosomes to produce offspring inherited basic characteristics of the parent. Genetic Algorithms in addition to involve the population early in the optimization process will also generate new populations through the crossover process, so as to provide optimal number of variables is not just a single solution. From the results of the crossover process in the case of TSP passing through six cities, there are two the best offspring with the same finess value which is 0.014. Genetic Algorithms can be stopped on the second generation due to successive received the highest fitness value unchanged.Keywords: Travelling Salesman Program (TSP), Genetic Algorithm, Matrix Representation, Crossover Process

Optimal recombination in genetic algorithms for combinatorial optimization problems: Part II

Yugoslav journal of operations research ◽

10.2298/yjor131030041e ◽

2014 ◽

Vol 24 (2) ◽

pp. 165-186 ◽

Cited By ~ 14

Author(s):

Anton Eremeev ◽

Julia Kovalenko

Keyword(s):

Genetic Algorithm ◽

Genetic Algorithms ◽

Computational Complexity ◽

Optimization Problems ◽

Makespan Minimization ◽

Travelling Salesman ◽

Hamilton Path ◽

Optimal Recombination

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. In Part II, we consider the computational complexity of ORPs arising in genetic algorithms for problems on permutations: the Travelling Salesman Problem, the Shortest Hamilton Path Problem and the Makespan Minimization on Single Machine and some other related problems. The analysis indicates that the corresponding ORPs are NP-hard, but solvable by faster algorithms, compared to the problems they are derived from.

Application of genetic algorithm in solving the travelling Salesman problem

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/1208/1/012032 ◽

2021 ◽

Vol 1208 (1) ◽

pp. 012032

Author(s):

Fatka Kulenović ◽

Azra Hošić

Keyword(s):

Genetic Algorithm ◽

Optimization Problems ◽

Path Selection ◽

Exact Methods ◽

Travelling Salesman ◽

Mutation Operators ◽

Complete Problems ◽

The Given

Abstract The Travelling Salesman Problem is categorized as NP-complete problems called combinatorial optimization problems. For the growing number of cities it is unsolvable with the use of exact methods in a reasonable time. Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions, however they give good approximation usually in time. Studies have shown that the proposed genetic algorithm can find a shorter route in real time, compared with the existing manipulator model of path selection. The genetic algorithm depends on the selection criteria, crosses, and mutation operators described in detail in this paper. Possible settings of the genetic algorithm are listed and described, as well as the influence of mutation and crossing operators on the efficiency of the genetic algorithm. The optimization results are presented graphically in the MATLAB software package for different cases, after which a comparison of the efficiency of the genetic algorithm with respect to the given parameters is performed.

Solving the University course timetabling problem using bat inspired algorithm

Tanzania Journal of Science ◽

10.4314/tjs.v47i2.23 ◽

2021 ◽

Vol 47 (2) ◽

pp. 674-685

Author(s):

Ushindi Limota ◽

Egbert Mujuni ◽

Allen Mushi

Keyword(s):

Combinatorial Optimization ◽

Optimization Problem ◽

Optimization Problems ◽

Real Life ◽

Bat Algorithm ◽

Discrete Version ◽

Timetabling Problem ◽

University Course Timetabling ◽

Metaheuristic Methods

Many mathematical optimization problems from real-life applications are NP-hard, and hence no algorithm that solves them to optimality within a reasonable time is known. For this reason, metaheuristic methods are mostly preferred when their size is big. Many meta-heuristic methods have been proposed to solve various combinatorial optimization problems. One of the newly introduced metaheuristic methods is a bat-inspired algorithm, which is based on the echolocation behaviour of microbats. Bat algorithm (BA) and its variants have been used successfully to solve several optimization problems. However, from the No-free Lunch Theorem, it is known that there is no universal metaheuristic method that can solve efficiently all optimization problems. Thus, this study work focused on investigating the usefulness of BA in solving an optimization problem called Course Teaching Problem (CTP). Since BA was originally designed to solve continuous problems, and CTP is a combinatorial optimization problem, a discrete version of BA for CPT has been proposed and tested using real-life data from the Dar es Salaam University College of Education (DUCE). The algorithm has produced promising results, as in each execution test, it generated a timetable in which all hard constraints were met and soft constraints were significantly satisfied within a few iterations. Keywords: Combinatorial optimization, Timetabling problem, Metaheuristic algorithms, Bat algorithm.