Efficient local search with search space smoothing: a case study of the traveling salesman problem (TSP)

1994 ◽  
Vol 24 (5) ◽  
pp. 728-735 ◽  
Author(s):  
Jun Gu ◽  
Xiaofei Huang
Keyword(s):  
Local Search ◽  
Traveling Salesman Problem ◽  
Search Space ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

Solution Attractor of Local Search System: A Method to Reduce Computational Complexity of the Traveling Salesman Problem

2020 ◽  
Author(s):  
Weiqi Li
Keyword(s):  
Computational Complexity ◽  
Local Search ◽  
Traveling Salesman Problem ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Solution Space ◽  
Search Space ◽  
Traveling Salesman ◽  
Search System ◽  
The Traveling Salesman Problem

The traveling salesman problem (TSP) is presumably difficult to solve exactly using local search algorithms. It can be exactly solved by only one algorithm—the enumerative search algorithm. However, the scanning of all possible solutions requires exponential computing time. Do we need exploring all the possibilities to find the optimal solution? How can we narrow down the search space effectively and efficiently for an exhausted search? This chapter attempts to answer these questions. A local search algorithm is a discrete dynamical system, in which a search trajectory searches a part of the solution space and stops at a locally optimal point. A solution attractor of a local search system for the TSP is defined as a subset of the solution space that contains all locally optimal tours. The solution attractor concept gives us great insight into the computational complexity of the TSP. If we know where the solution attractor is located in the solution space, we simply completely search the solution attractor, rather than the entire solution space, to find the globally optimal tour. This chapter describes the solution attractor of local search system for the TSP and then presents a novel search system—the attractor-based search system—that can solve the TSP much efficiently with global optimality guarantee.

A Two Stage Method for the Multiple Traveling Salesman Problem

2020 ◽  
Vol 11 (3) ◽  
pp. 79-91
Author(s):  
Azcarie Manuel Cabrera Cuevas ◽  
Jania Astrid Saucedo Martínez ◽  
José Antonio Marmolejo Saucedo
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Difficulty Level ◽  
Median Problem ◽  
Two Stage ◽  
Multiple Traveling Salesman Problem ◽  
Solution Methods ◽  
The Many ◽  
The Traveling Salesman Problem

The variation of the traveling salesman problem (TSP) with multiple salesmen (m-TSP) has been studied for many years resulting in diverse solution methods, both exact and heuristic. However, the high difficulty level on finding optimal (or acceptable) solutions has opposed the many efforts of doing so. The proposed method regards a two stage procedure which implies a modified version of the p-Median Problem (PMP) alongside the TSP, making a partition of the nodes into subsets that will be assigned to each salesman, solving it with Branch & Cut (B&C), in the first stage. This is followed by the routing, applying an Ant Colony Optimization (ACO) metaheuristic algorithm to solve a TSP for each subset of nodes. A case study was reviewed, detailing the positioning of five vehicles in strategic places in the Mexican Republic.

Application of an Improved Genetic Algorithm with the Search Space Compression in TSP

2013 ◽  
Vol 765-767 ◽  
pp. 687-689
Author(s):  
Yi Song ◽  
Ni Ni Wei
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Random Search ◽  
Search Space ◽  
Traveling Salesman ◽  
Improved Genetic Algorithm ◽  
Space Compression ◽  
Accelerate Convergence ◽  
The Traveling Salesman Problem ◽  
Exponential Relation

The Traveling Salesman Problem is a combinatorial optimization problem, the problem has been shown to belong to the NPC problem, the possible solution of Traveling Salesman Problem and the scale of the cities have the exponential relation, so the more bigger of the scale. In this paper, improve the search process of the genetic algorithm by introducing the idea is to compress the search space. The simulation results show that for solving the TSP, the algorithm can quickly obtain multiple high-quality solutions. It can reduce the blindness of random search and accelerate convergence of the algorithm.

scholarly journals Solve traveling salesman problem using EMF-CE algorithm

2020 ◽  
Author(s):  
Meng Luo ◽  
Shiliang Gu
Keyword(s):  
Local Search ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
Search Algorithm ◽  
Feedback Regulation ◽  
Critical Value ◽  
Traveling Salesman ◽  
Online Library ◽  
The Traveling Salesman Problem ◽  
Algorithm Implementation

<p>In this paper, a novel search algorithm that based on the Contraction-Expansion algorithm and integrated three operators Exchange, Move, and Flip (EMF-CE) is proposed for the traveling salesman problem (TSP). EMF-CE uses a negative exponent function to generate critical value as the feedback regulation of algorithm implementation. Also, combined Exchange Step, Move step with Flip step and constitute of more than twenty combinatorial optimizations of program elements. It has been shown that the integration of local search operators can significantly improve the performance of EMF-CE for TSPs. We test small and medium scale (51-1000 cities) TSPs were taken from the TSPLIB online library. The experimental results show the efficiency of the proposed EMF-CE for addressing TSPs compared to other state-of-the-art algorithms.</p>

Sign in / Sign up

Export Citation Format

Share Document