Evolving Combinatorial Problem Instances That Are Difficult to Solve

2006 ◽  
Vol 14 (4) ◽  
pp. 433-462 ◽  
Author(s):  
Jano I. van Hemert
Keyword(s):  
Evolutionary Computation ◽  
Structural Properties ◽  
Constraint Satisfaction ◽  
Travelling Salesman Problem ◽  
Combinatorial Problem ◽  
Boolean Satisfiability ◽  
Combinatorial Optimisation ◽  
Travelling Salesman ◽  
Binary Constraint ◽  
Problem Instances

This paper demonstrates how evolutionary computation can be used to acquire difficult to solve combinatorial problem instances. As a result of this technique, the corresponding algorithms used to solve these instances are stress-tested. The technique is applied in three important domains of combinatorial optimisation, binary constraint satisfaction, Boolean satisfiability, and the travelling salesman problem. The problem instances acquired through this technique are more difficult than the ones found in popular benchmarks. In this paper, these evolved instances are analysed with the aim to explain their difficulty in terms of structural properties, thereby exposing the weaknesses of corresponding algorithms.

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

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Maha Ata Al-Furhud ◽  
Zakir Hussain Ahmed
Keyword(s):  
Genetic Algorithm ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Hybrid Genetic Algorithm ◽  
Travelling Salesman ◽  
Complex Optimization ◽  
Problem Instances ◽  
Search Approach ◽  
Multiple Travelling Salesman Problem

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.

The Travelling Salesman Problem (A Guided Tour of Combinatorial Optimisation

1986 ◽  
Vol 70 (454) ◽  
pp. 327
Author(s):  
Mike Worboys ◽  
E. L. Lawler ◽  
J. K. Lenstra ◽  
A. H. G. Rinnooy Kan ◽  
D. B. Shmoys
Keyword(s):  
Travelling Salesman Problem ◽  
Combinatorial Optimisation ◽  
Travelling Salesman ◽  
Guided Tour

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

Slope-to-optimal-solution-based evaluation of the hardness of travelling salesman problem instances

2020 ◽  
Vol 28 (1) ◽  
pp. 45-57 ◽  
Author(s):  
Miguel Cárdenas-Montes
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Random Walk ◽  
Random Forests ◽  
Fitness Landscape ◽  
Travelling Salesman Problem ◽  
Optimal Solution ◽  
Travelling Salesman ◽  
Two Cities ◽  
Problem Instances

Abstract The travelling salesman problem is one of the most popular problems in combinatorial optimization. It has been frequently used as a benchmark of the performance of evolutionary algorithms. For this reason, nowadays practitioners request new and more difficult instances of this problem. This leads to investigate how to evaluate the intrinsic difficulty of the instances and how to separate ease and difficult instances. By developing methodologies for separating easy- from difficult-to-solve instances, researchers can fairly test the performance of their combinatorial optimizers. In this work, a methodology for evaluating the difficulty of instances of the travelling salesman problem near the optimal solution is proposed. The question is if the fitness landscape near the optimal solution encodes enough information to separate instances in function of their intrinsic difficulty. This methodology is based on the use of a random walk to explore the closeness of the optimal solution. The optimal solution is modified by altering one connection between two cities at each step, at the same time that the fitness of the altered solution is evaluated. This permits evaluating the slope of the fitness landscape. Later, and using the previous information, the difficulty of the instance is evaluated with random forests and artificial neural networks. In this work, this methodology is confronted with a wide set of instances. As a consequence, a methodology to separate the instances of the travelling salesman problem by their degree of difficulty is proposed and evaluated.

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