Why many travelling salesman problem instances are easier than you think

2020 ◽  
Author(s):  
Swetha Varadarajan ◽  
Darrell Whitley ◽  
Gabriela Ochoa
Keyword(s):  
Travelling Salesman Problem ◽  
Travelling Salesman ◽  
Problem Instances

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.

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.

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.

A NEURO-ETHOLOGICAL APPROACH FOR THE TSP: CHANGING METAPHORS IN CONNECTIONIST MODELS

1994 ◽  
Vol 02 (03) ◽  
pp. 357-366 ◽  
Author(s):  
O. MIGLINO ◽  
F. MENCZER ◽  
P. BOVET
Keyword(s):  
Travelling Salesman Problem ◽  
Living Systems ◽  
Neural Systems ◽  
Connectionist Models ◽  
Travelling Salesman ◽  
Motor Systems ◽  
Simulated Environments ◽  
Sensory Motor ◽  
Problem Instances ◽  
Time And Space Complexity

Biological systems often offer solutions to difficult problems which are not only original but also efficient. Connectionist models have been inspired by neural systems and successfully applied to the formulation of algorithms for solving complex problems such as the travelling salesman problem. In this paper we extend the connectionist metaphor to include an ethological account of how problems similar to the travelling salesman problem are solved by real living systems. A model is presented in which a population of neural networks with simple sensory-motor systems evolve genetically in simulated environments which represent the problem instances to be solved. Preliminary results are discussed, showing how the ethological metaphor allows to overcome some shortcomings of other connectionist models, such as their time and space complexity.

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