scholarly journals Application of Fuzzy Optimization to the Orienteering Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Madhushi Verma ◽  
K. K. Shukla
Keyword(s):  
Necessary Conditions ◽  
Travelling Salesman Problem ◽  
Fuzzy Optimization ◽  
Orienteering Problem ◽  
Fuzzy Decision ◽  
Travelling Salesman ◽  
Pram Model ◽  
Fuzzy Goals ◽  
Np Hard Problem ◽  
Crew Pram

This paper deals with the orienteering problem (OP) which is a combination of two well-known problems (i.e., travelling salesman problem and the knapsack problem). OP is an NP-hard problem and is useful in appropriately modeling several challenging applications. As the parameters involved in these applications cannot be measured precisely, depicting them using crisp numbers is unrealistic. Further, the decision maker may be satisfied with graded satisfaction levels of solutions, which cannot be formulated using a crisp program. To deal with the above-stated two issues, we formulate thefuzzyorienteering problem (FOP) and provide a method to solve it. Here we state the two necessary conditions of OP of maximizing the total collected score and minimizing the time taken to traverse a path (within the specified time bound) as fuzzy goals and the remaining necessary conditions as crisp constraints. Using the max-min formulation of the fuzzy sets obtained from the fuzzy goals, we calculate the fuzzy decision sets (ZandZ∗) that contain the feasible paths and the desirable paths, respectively, along with the degrees to which they are acceptable. To efficiently solve large instances of FOP, we also present a parallel algorithm on CREW PRAM model.

scholarly journals Penentuan Rute Pengiriman Ice Tube di Kota Malang dengan Algoritma Genetika

2020 ◽  
Vol 11 (1) ◽  
pp. 10
Author(s):  
Nurina Savanti Widya Gotami ◽  
Yane Marita Febrianti ◽  
Robih Dini ◽  
Hamim Fathul Aziz ◽  
San Sayidul Akdam Augusta ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Travelling Salesman Problem ◽  
Combinatorial Problem ◽  
Np Hard ◽  
Travelling Salesman ◽  
Shortest Route ◽  
Reproduction Process ◽  
Delivery Routes ◽  
Np Hard Problem ◽  
Selection Parameter

Abstract. Determining routes for ice tube delivery in Malang is a complex combinatorial problem classified as NP-hard problem. This study aims for optimizing the sales travel routes determination for the delivery to several customers by considering the efficiency of distance traveled. This problem is modeled in the form of Multi Salesman Traveling Problem. Genetic algorithm was used to optimize the determination of ice tube delivery routes that must be taken by each sales. Problems were coded by using permutation representation in which order crossover and swap mutation methods were used for the reproduction process. The process of finding solution was done by using elitism selection. The best genetic algorithm parameters obtained from the test results are the number of iterations of 40 and the population of 40, with the shortest route of 30.3 km. The final solution given by the genetic algorithm is in the form of a travel route that must be taken by each ice tube sales.Keywords: genetic algorithm, mutli travelling salesman problem, optimization, routeAbstrak. Penentuan rute pengiriman ice tube di kota Malang merupakan permasalahan kombinatorial kompleks yang diklasifikasikan sebagai permasalahan NP-hard. Penelitian ini bertujuan untuk melakukan optimasi dalam pembentukan rute perjalanan sales dalam melakukan pengiriman ke beberapa pelanggan dengan mempertimbangkan efisiensi jarak tempuh. Permasalahan ini dimodelkan dalam bentuk Multi Salesman Travelling Problem. Algoritme genetika digunakan untuk mengoptimalkan pembentukan rute pengiriman ice tube yang harus dilalui oleh setiap sales. Permasalahan dikodekan menggunakan representasi permutasi, dengan proses reproduksi menggunakan metode order crossover dan swap mutation. Proses pencarian solusi dilakukan menggunakan elitism selection. Parameter algoritme genetika terbaik yang didapatkan dari hasil pengujian adalah banyaknya iterasi sebesar 40 dan banyaknya populasi sebesar 40, dengan rute terpendek sebesar 30.3 km. Solusi akhir yang diberikan oleh algoritme genetika berupa rute perjalanan yang harus ditempuh oleh setiap sales ice tube.Kata Kunci: algoritme genetika, multi travelling salesman problem, optimasi, rute

scholarly journals A New Approach Based on K-means Clustering and Shuffled Frog Leaping Algorithm to Solve Travelling Salesman Problem

2019 ◽  
Vol 2 (3) ◽  
pp. 446-453
Author(s):  
Murat Karakoyun
Keyword(s):  
Shortest Path ◽  
Travelling Salesman Problem ◽  
Experimental Results ◽  
Hard Problem ◽  
Shuffled Frog Leaping Algorithm ◽  
Travelling Salesman ◽  
New Approach ◽  
Starting Point ◽  
Np Hard Problem ◽  
Shuffled Frog Leaping

The Travelling Salesman Problem (TSP), which is a combinatorial NP-hard problem, aims to find the shortest possible path while visiting all cities (only once) in a given list and returns to the starting point. In this paper, an approach, which is based on k-means clustering and Shuffled Frog Leaping Algorithm (SFLA), is used to solve the TSP. The proposed approach consists of three parts: separate the cities into k clusters, find the shortest path for each cluster and merge the clusters. Experimental results have shown that the algorithm get better results as the number of cluster increase for problems that have a large number of cities.

Recombination Operators in Permutation-Based Evolutionary Algorithms for the Travelling Salesman Problem

2012 ◽  
pp. 268-285
Author(s):  
Camelia Chira ◽  
Anca Gog
Keyword(s):  
Genetic Algorithms ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Genetic Material ◽  
Hard Problem ◽  
Travelling Salesman ◽  
Routing And Scheduling ◽  
Np Hard Problem ◽  
Account Information ◽  
Ant Colony Systems

The Travelling Salesman Problem (TSP) is one of the most widely studied optimization problems due to its many applications in domains such as logistics, planning, routing, and scheduling. Approximation algorithms to address this NP-hard problem include genetic algorithms, ant colony systems, and simulated annealing. This chapter concentrates on the evolutionary approaches to TSP based on permutation encoded individuals. A comparative analysis of several recombination operators is presented based on computational experiments for TSP instances and a generalized version of TSP. Numerical results emphasize a good performance of two proposed crossover schemes: best-worst recombination and best order recombination which take into account information from the global best and/or worst individuals besides the genetic material from parents.

ON THE VERTEX-CONNECTIVITY PROBLEM FOR GRAPHS WITH SHARPENED TRIANGLE INEQUALITY

2004 ◽  
Vol 15 (05) ◽  
pp. 701-715
Author(s):  
ALESSANDRO FERRANTE ◽  
MIMMO PARENTE
Keyword(s):  
Triangle Inequality ◽  
Travelling Salesman Problem ◽  
Minimum Cost ◽  
Time Algorithm ◽  
Performance Ratio ◽  
Travelling Salesman ◽  
Vertex Connectivity ◽  
Worst Case ◽  
Spanning Subgraph ◽  
Np Hard Problem

Given a graph with the edge costs satisfying the β-sharpened triangle inequality: cost(u,v)≤β(cost(u,x)+cost(x,v)), for l/2≤β<1, we study the NP-hard problem of finding a minimum cost spanning subgraph which is k-vertex-connected, k≥2. We analyze an approximation quadratic-time algorithm whose performance ratio is [Formula: see text]. The main motivation of this study is to provide an algorithm with a good performance ratio and a practical worst case running time for significative subclasses of the metric Travelling Salesman Problem and the naturally related to it connectivity problems.

scholarly journals Tourist Route Optimization in the Context of Covid-19 Pandemic

2021 ◽  
Vol 13 (10) ◽  
pp. 5492
Author(s):  
Cristina Maria Păcurar ◽  
Ruxandra-Gabriela Albu ◽  
Victor Dan Păcurar
Keyword(s):  
Travelling Salesman Problem ◽  
Route Planning ◽  
Route Optimization ◽  
Travelling Salesman ◽  
Social Distancing ◽  
Tourist Destinations ◽  
Innovative Method ◽  
The Social ◽  
Immediate Response

The paper presents an innovative method for tourist route planning inside a destination. The necessity of reorganizing the tourist routes within a destination comes as an immediate response to the Covid-19 crisis. The implementation of the method inside tourist destinations can bring an important advantage in transforming a destination into a safer one in times of Covid-19 and post-Covid-19. The existing trend of shortening the tourist stay length has been accelerated while the epidemic became a pandemic. Moreover, the wariness for future pandemics has brought into spotlight the issue of overcrowded attractions inside a destination at certain moments. The method presented in this paper proposes a backtracking algorithm, more precisely an adaptation of the travelling salesman problem. The method presented is aimed to facilitate the navigation inside a destination and to revive certain less-visited sightseeing spots inside a destination while facilitating conformation with the social distancing measures imposed for Covid-19 control.

A column-and-row generation approach for the flying sidekick travelling salesman problem

2021 ◽  
Vol 124 ◽  
pp. 102913
Author(s):  
Maurizio Boccia ◽  
Adriano Masone ◽  
Antonio Sforza ◽  
Claudio Sterle
Keyword(s):  
Travelling Salesman Problem ◽  
Travelling Salesman
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