scholarly journals Can the Agent with Limited Information Solve Travelling Salesman Problem?

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Tomoko Sakiyama ◽  
Ikuo Arizono
Keyword(s):  
Heuristic Algorithm ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
The Other ◽  
Time Dependent ◽  
Critical Properties ◽  
Limited Information ◽  
Travelling Salesman ◽  
Benchmark Data ◽  
Benchmark Datasets

Here, we develop new heuristic algorithm for solving TSP (Travelling Salesman Problem). In our proposed algorithm, the agent cannot estimate tour lengths but detect only a few neighbor sites. Under the circumstances, the agent occasionally ignores the NN method (choosing the nearest site from current site) and chooses the other site far from current site. It is dependent on relative distances between the nearest site and the other site. Our algorithm performs well in symmetric TSP and asymmetric TSP (time-dependent TSP) conditions compared with the NN algorithm using some TSP benchmark datasets from the TSPLIB. Here, symmetric TSP means common TSP, where costs between sites are symmetric and time-homogeneous. On the other hand, asymmetric TSP means TSP where costs between sites are time-inhomogeneous. Furthermore, the agent exhibits critical properties in some benchmark data. These results suggest that the agent performs adaptive travel using limited information. Our results might be applicable to nonclairvoyant optimization problems.

scholarly journals Coordination of Pheromone Deposition Might Solve Time-Constrained Travelling Salesman Problem

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Tomoko Sakiyama ◽  
Ikuo Arizono
Keyword(s):  
Ant Colony Optimization ◽  
Travelling Salesman Problem ◽  
Ant Colony ◽  
The Other ◽  
Critical Properties ◽  
Ant System ◽  
Travelling Salesman ◽  
Time Limits ◽  
System Models ◽  
Benchmark Datasets

In this study, we develop two Ant Colony Optimization (ACO) models as new metaheuristic models for solving the time-constrained Travelling Salesman Problem (TSP). Here, the time-constrained TSP means a TSP in which several cities have constraints that the agents have to visit within prescribed time limits. In our ACO models, only agents that achieved tour under certain conditions defined in respective ACO models are allowed to modulate pheromone deposition. The agents in one model are allowed to deposit pheromone only if they achieve a tour satisfying strictly the above purpose. The agents in the other model is allowed to deposit pheromone not only if they achieve a tour satisfying strictly the above purpose, but also if they achieve a tour satisfying the above purpose in some degree. We compare performance of two developed ACO models by focusing on pheromone deposition. We confirm that the later model performs well to some TSP benchmark datasets from TSPLIB in comparison to the former and the traditional AS (Ant System) models. Furthermore, the agent exhibits critical properties; i.e., the system exhibits complex behaviors. These results suggest that the agents perform adaptive travels by coordinating some complex pheromone depositions.

scholarly journals Ants Colony Optimisation of a Measuring Path of Prismatic Parts on a CMM

2016 ◽  
Vol 23 (1) ◽  
pp. 119-132 ◽  
Author(s):  
Slavenko M. Stojadinovic ◽  
Vidosav D. Majstorovic ◽  
Numan M. Durakbasa ◽  
Tatjana V. Sibalija
Keyword(s):  
Travelling Salesman Problem ◽  
Ant Colony ◽  
The Other ◽  
Ant Colony Optimisation ◽  
Travelling Salesman ◽  
Prismatic Parts ◽  
On Line ◽  
Optimisation Model ◽  
Set Of Points ◽  
The Mathematical Model

AbstractThis paper presents optimisation of a measuring probe path in inspecting the prismatic parts on a CMM. The optimisation model is based on: (i) the mathematical model that establishes an initial collision-free path presented by a set of points, and (ii) the solution of Travelling Salesman Problem (TSP) obtained with Ant Colony Optimisation (ACO). In order to solve TSP, an ACO algorithm that aims to find the shortest path of ant colony movement (i.e. the optimised path) is applied. Then, the optimised path is compared with the measuring path obtained with online programming on CMM ZEISS UMM500 and with the measuring path obtained in the CMM inspection module of Pro/ENGINEER®software. The results of comparing the optimised path with the other two generated paths show that the optimised path is at least 20% shorter than the path obtained by on-line programming on CMM ZEISS UMM500, and at least 10% shorter than the path obtained by using the CMM module in Pro/ENGINEER®.

Heuristic algorithm for the Split-Demand One-Commodity Pickup-and-Delivery Travelling Salesman Problem

2018 ◽  
Vol 97 ◽  
pp. 1-17 ◽  
Author(s):  
Hipólito Hernández-Pérez ◽  
Juan José Salazar-González ◽  
Beatriz Santos-Hernández
Keyword(s):  
Heuristic Algorithm ◽  
Travelling Salesman Problem ◽  
Pickup And Delivery ◽  
Travelling Salesman

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.

DIMMA

2010 ◽  
Vol 1 (4) ◽  
pp. 57-74 ◽  
Author(s):  
Masoud Yaghini ◽  
Rahim Akhavan
Keyword(s):  
Tabu Search ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Metaheuristic Algorithms ◽  
Standard Process ◽  
Travelling Salesman ◽  
Design And Implementation ◽  
The Future ◽  
Implementation Methodology

Metaheuristic algorithms will gain more and more popularity in the future as optimization problems are increasing in size and complexity. In order to record experiences and allow project to be replicated, a standard process as a methodology for designing and implementing metaheuristic algorithms is necessary. To the best of the authors’ knowledge, no methodology has been proposed in literature for this purpose. This paper presents a Design and Implementation Methodology for Metaheuristic Algorithms, named DIMMA. The proposed methodology consists of three main phases and each phase has several steps in which activities that must be carried out are clearly defined in this paper. In addition, design and implementation of tabu search metaheuristic for travelling salesman problem is done as a case study to illustrate applicability of DIMMA.

Analysis and Branch-and-Cut Algorithm for the Time-Dependent Travelling Salesman Problem

2014 ◽  
Vol 48 (1) ◽  
pp. 46-58 ◽  
Author(s):  
Jean-François Cordeau ◽  
Gianpaolo Ghiani ◽  
Emanuela Guerriero
Keyword(s):  
Travelling Salesman Problem ◽  
Branch And Cut ◽  
Time Dependent ◽  
Travelling Salesman

scholarly journals Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

2021 ◽  
Vol 8 ◽  
Author(s):  
Tilo Strutz
Keyword(s):  
Computational Complexity ◽  
Optimization Problems ◽  
State Of The Art ◽  
Travelling Salesman Problem ◽  
Limited Time ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Major Difficulty ◽  
Travelling Salesman ◽  
New Approach

Finding the shortest tour visiting all given points at least ones belongs to the most famous optimization problems until today [travelling salesman problem (TSP)]. Optimal solutions exist for many problems up to several ten thousand points. The major difficulty in solving larger problems is the required computational complexity. This shifts the research from finding the optimum with no time limitation to approaches that find good but sub-optimal solutions in pre-defined limited time. This paper proposes a new approach for two-dimensional symmetric problems with more than a million coordinates that is able to create good initial tours within few minutes. It is based on a hierarchical clustering strategy and supports parallel processing. In addition, a method is proposed that can correct unfavorable paths with moderate computational complexity. The new approach is superior to state-of-the-art methods when applied to TSP instances with non-uniformly distributed coordinates.

DIMMA

2012 ◽  
pp. 583-601
Author(s):  
Masoud Yaghini ◽  
Mohammad Rahim Akhavan Kazemzadeh
Keyword(s):  
Tabu Search ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Metaheuristic Algorithms ◽  
Standard Process ◽  
Travelling Salesman ◽  
Design And Implementation ◽  
The Future ◽  
Implementation Methodology

Metaheuristic algorithms will gain more and more popularity in the future as optimization problems are increasing in size and complexity. In order to record experiences and allow project to be replicated, a standard process as a methodology for designing and implementing metaheuristic algorithms is necessary. To the best of the authors’ knowledge, no methodology has been proposed in literature for this purpose. This paper presents a Design and Implementation Methodology for Metaheuristic Algorithms, named DIMMA. The proposed methodology consists of three main phases and each phase has several steps in which activities that must be carried out are clearly defined in this paper. In addition, design and implementation of tabu search metaheuristic for travelling salesman problem is done as a case study to illustrate applicability of DIMMA.

DIMMA

2012 ◽  
pp. 90-108
Author(s):  
Masoud Yaghini ◽  
Mohammad Rahim Akhavan Kazemzadeh
Keyword(s):  
Tabu Search ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Metaheuristic Algorithms ◽  
Standard Process ◽  
Travelling Salesman ◽  
Design And Implementation ◽  
The Future ◽  
Implementation Methodology

Metaheuristic algorithms will gain more and more popularity in the future as optimization problems are increasing in size and complexity. In order to record experiences and allow project to be replicated, a standard process as a methodology for designing and implementing metaheuristic algorithms is necessary. To the best of the authors’ knowledge, no methodology has been proposed in literature for this purpose. This paper presents a Design and Implementation Methodology for Metaheuristic Algorithms, named DIMMA. The proposed methodology consists of three main phases and each phase has several steps in which activities that must be carried out are clearly defined in this paper. In addition, design and implementation of tabu search metaheuristic for travelling salesman problem is done as a case study to illustrate applicability of DIMMA.

2. Four types of problem

2016 ◽  
pp. 7-27
Author(s):  
Robin Wilson
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Travelling Salesman ◽  
Counting Problems ◽  
Problem Construction ◽  
Colour Problem ◽  
Efficiency Of Algorithms ◽  
Enumeration Problems ◽  
Knight’S Tour

‘Four types of problem’ explains that combinatorics is concerned with four types of problem: existence problems (does x exist?); construction problems (if x exists, how can we construct it?); enumeration problems (how many x are there?); and optimization problems (which x is best?). Existence problems discussed include tilings, placing dominoes on a chess board, the knight’s tour problem, the Königsberg bridges problem, the Gas–Water–Electricity problem, and the map-colour problem. Construction problems include solving mazes, and the two types of enumeration problems considered are counting problems and listing problems. Examples of an optimization problem include the minimum connector problem and the travelling salesman problem. The efficiency of algorithms is also explained.

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