1,901 research outputs found
Computational Numerical Solution for Traveling Salesman Problem
This paper examined and analysed the desire of Traveling Salesman Problem (TSP) to find the cheapest way of visiting all given set of cities and returning to the starting point. We presented a unique decomposition approach model for TSP in which the requirements and features of practical application in communication network, road transportation and supply chains are put into consideration. We used a Mathematical Modeling solution with the application of Ant Colony Search Algorithm (ACSA) approach for result computation. In our approach, different Agents were created for difference purposes. Information agent gathered information about best tour and detected the solution agent that arrived at a given point with information message containing details of where the solution agent has come from as well as best tour cost. The place ant performs local pheromone decay on the relevant links. This help to avoid random visit to irrelevant edges and allows the place ant to calculate the cost of tour of all place ants including the latest pheromone level on the links to each of the place ants. The solution agent uses available information to decide which node to visit next and informs the place ant of its decision to move to a given destination and update better tour previously sampled while information about where to go next also obtained. The place ant updates its pheromone value for that link using the equivalent of the algorithm for local pheromone update. The cycle continues until solution agent arrives at its destination. The main advantage of our approach is that it permits the use of mixed integer programming and combinatorial optimization techniques to compute real optimal routing path, solving the problem in practice by returning actual shortest route with its numerical value and not the best effort result as provided by some previous models and analytical methods. The implementation was carried out using C# programming language. Data used were generated and the performance evaluation of the model was carried out through simulation using Matlab 7.0. The result shows that by considering all possible paths between a node as the source and another as the destination, all possible routes for a particular journey with shortest route in each case were generated. Keywords: Ant Colony, Combinatorial Optimization, Mixed Integer Programming, Pheromone, Search Algorithm and Traveling Salesman
Population Diversity in Ant-inspired Optimization Algorithms
Finding a balance between exploration and exploitation is very important in the case of metaheuristics optimization, especially in the systems leveraging population of individuals expressing (as in Evolutionary Algorithms, etc.) or constructing (as in Ant Colony Optimization) solutions. Premature convergence is a real problem and finding means of its automatic detection and counteracting are of great importance. Measuring diversity in Evolutionary Algorithms working in real-value search space is often computationally complex, but feasible while measuring diversity in combinatorial domain is practically impossible (cf. Closest String Problem). Nevertheless, we propose several practical and feasible diversity measurement techniques dedicated to Ant Colony Optimization algorithms, leveraging the fact that even though analysis of the search space is at least an NP problem, we can focus on the pheromone table, where the direct outcomes of the search are expressed and can be analyzed. Besides proposing the measurement techniques, we apply them to assess the diversity of several variants of ACO, and closely analyze their features for the classic ACO. The discussion of the results is the first step towards applying the proposed measurement techniques in auto-adaptation of the parameters affecting directly the exploitation and exploration features in ACO in the future
Breakout Local Search for the Travelling Salesman Problem
The travelling salesman problem (TSP), a famous NP-hard combinatorial optimisation problem (COP), consists of finding a minimum length tour that visits n cities exactly once and comes back to the starting city. This paper presents a resolution of the TSP using the breakout local search metaheuristic algorithm (BLS), which is based on the iterated local search (ILS) framework and improves it by introducing some fundamental features of several well-established metaheuristics such as tabu search (TS) and variable neighbourhood search (VNS). BLS moves from a local optimum of a neighbourhood to another by applying perturbation jumps whose type and number are determined adaptively. It has already been applied to many COP and gives good results. This innovative hybridisation resolved well 41 instances from the commonly used benchmark library TSPLIB. The high quality of experimental results shows the competitiveness of the proposed algorithm compared to other algorithms based on local search
Hybridization of Biologically Inspired Algorithms for Discrete Optimisation Problems
In the field of Optimization Algorithms, despite the popularity of hybrid designs, not enough consideration has been given to hybridization strategies. This paper aims to raise awareness of the benefits that such a study can bring. It does this by conducting a systematic review of popular algorithms used for optimization, within the context of Combinatorial Optimization Problems. Then, a comparative analysis is performed between Hybrid and Base versions of the algorithms to demonstrate an increase in optimization performance when hybridization is employed
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
A nonmonotone GRASP
A greedy randomized adaptive search procedure (GRASP) is an itera-
tive multistart metaheuristic for difficult combinatorial optimization problems. Each
GRASP iteration consists of two phases: a construction phase, in which a feasible
solution is produced, and a local search phase, in which a local optimum in the
neighborhood of the constructed solution is sought. Repeated applications of the con-
struction procedure yields different starting solutions for the local search and the
best overall solution is kept as the result. The GRASP local search applies iterative
improvement until a locally optimal solution is found. During this phase, starting from
the current solution an improving neighbor solution is accepted and considered as the
new current solution. In this paper, we propose a variant of the GRASP framework that
uses a new “nonmonotone” strategy to explore the neighborhood of the current solu-
tion. We formally state the convergence of the nonmonotone local search to a locally
optimal solution and illustrate the effectiveness of the resulting Nonmonotone GRASP
on three classical hard combinatorial optimization problems: the maximum cut prob-
lem (MAX-CUT), the weighted maximum satisfiability problem (MAX-SAT), and
the quadratic assignment problem (QAP)
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