190 research outputs found
Traveling Salesman Problem
This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering
Traveling Salesman Problem
The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance
On the Traveling Salesman Problem in Nautical Environments: an Evolutionary Computing Approach to Optimization of Tourist Route Paths in Medulin, Croatia
The Traveling salesman problem (TSP) defines the problem of finding the optimal path between multiple points, connected by paths of a certain cost. This paper applies that problem formulation in the maritime environment, specifically a path planning problem for a tour boat visiting popular tourist locations in Medulin, Croatia. The problem is solved using two evolutionary computing methods ā the genetic algorithm (GA) and the simulated annealing (SA) - and comparing the results (are compared) by an extensive search of the solution space. The results show that evolutionary computing algorithms provide comparable results to an extensive search in a shorter amount of time, with SA providing better results of the two
How Good Is Neural Combinatorial Optimization?
Traditional solvers for tackling combinatorial optimization (CO) problems are
usually designed by human experts. Recently, there has been a surge of interest
in utilizing Deep Learning, especially Deep Reinforcement Learning, to
automatically learn effective solvers for CO. The resultant new paradigm is
termed Neural Combinatorial Optimization (NCO). However, the advantages and
disadvantages of NCO over other approaches have not been well studied
empirically or theoretically. In this work, we present a comprehensive
comparative study of NCO solvers and alternative solvers. Specifically, taking
the Traveling Salesman Problem as the testbed problem, we assess the
performance of the solvers in terms of five aspects, i.e., effectiveness,
efficiency, stability, scalability and generalization ability. Our results show
that in general the solvers learned by NCO approaches still fall short of
traditional solvers in nearly all these aspects. A potential benefit of the
former would be their superior time and energy efficiency on small-size problem
instances when sufficient training instances are available. We hope this work
would help better understand the strengths and weakness of NCO, and provide a
comprehensive evaluation protocol for further benchmarking NCO approaches
against other approaches
An Edge-Aware Graph Autoencoder Trained on Scale-Imbalanced Data for Travelling Salesman Problems
Recent years have witnessed a surge in research on machine learning for
combinatorial optimization since learning-based approaches can outperform
traditional heuristics and approximate exact solvers at a lower computation
cost. However, most existing work on supervised neural combinatorial
optimization focuses on TSP instances with a fixed number of cities and
requires large amounts of training samples to achieve a good performance,
making them less practical to be applied to realistic optimization scenarios.
This work aims to develop a data-driven graph representation learning method
for solving travelling salesman problems (TSPs) with various numbers of cities.
To this end, we propose an edge-aware graph autoencoder (EdgeGAE) model that
can learn to solve TSPs after being trained on solution data of various sizes
with an imbalanced distribution. We formulate the TSP as a link prediction task
on sparse connected graphs. A residual gated encoder is trained to learn latent
edge embeddings, followed by an edge-centered decoder to output link
predictions in an end-to-end manner. To improve the model's generalization
capability of solving large-scale problems, we introduce an active sampling
strategy into the training process. In addition, we generate a benchmark
dataset containing 50,000 TSP instances with a size from 50 to 500 cities,
following an extremely scale-imbalanced distribution, making it ideal for
investigating the model's performance for practical applications. We conduct
experiments using different amounts of training data with various scales, and
the experimental results demonstrate that the proposed data-driven approach
achieves a highly competitive performance among state-of-the-art learning-based
methods for solving TSPs.Comment: 35 pages, 7 figure
Attention, Learn to Solve Routing Problems!
The recently presented idea to learn heuristics for combinatorial
optimization problems is promising as it can save costly development. However,
to push this idea towards practical implementation, we need better models and
better ways of training. We contribute in both directions: we propose a model
based on attention layers with benefits over the Pointer Network and we show
how to train this model using REINFORCE with a simple baseline based on a
deterministic greedy rollout, which we find is more efficient than using a
value function. We significantly improve over recent learned heuristics for the
Travelling Salesman Problem (TSP), getting close to optimal results for
problems up to 100 nodes. With the same hyperparameters, we learn strong
heuristics for two variants of the Vehicle Routing Problem (VRP), the
Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting
TSP (PCTSP), outperforming a wide range of baselines and getting results close
to highly optimized and specialized algorithms.Comment: Accepted at ICLR 2019. 25 pages, 7 figure
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