Abstract: The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CNmaxn2) where C is the iterations, Nmax is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.
Abstract: Traveling salesman problem (TSP) is a combinatorial integer optimization problem that asks "What is the optimal route for a vehicle to traverse in order to deliver requests to a given set of customers?”. It is widely used by the package carrier companies’ distribution centers. The main goal of applying the TSP in courier organizations is to minimize the time that it takes for the courier in each trip to deliver or pick up the shipments during a day. In this article, an optimization model is constructed to create a new TSP variant to optimize the routing in a courier organization with a consideration of congestion in Amman, the capital of Jordan. Real data were collected by different methods and analyzed. Then, concert technology - CPLEX was used to solve the proposed model for some random generated data instances and for the real collected data. At the end, results have shown a great improvement in time compared with the current trip times, and an economic study was conducted afterwards to figure out the impact of using such models.
Abstract: It is very common to observe, especially in Computer
Science studies that students have difficulties to correctly understand
how some mechanisms based on Artificial Intelligence work. In
addition, the scope and limitations of most of these mechanisms
are usually presented by professors only in a theoretical way,
which does not help students to understand them adequately. In this
work, we focus on the problems found when teaching Evolutionary
Algorithms (EAs), which imitate the principles of natural evolution,
as a method to solve parameter optimization problems. Although
this kind of algorithms can be very powerful to solve relatively
complex problems, students often have difficulties to understand
how they work, and how to apply them to solve problems in
real cases. In this paper, we present two interactive graphical
applications which have been specially designed with the aim of
making Evolutionary Algorithms easy to be understood by students.
Specifically, we present: (i) TSPS, an application able to solve the
”Traveling Salesman Problem”, and (ii) FotEvol, an application able
to reconstruct a given image by using Evolution Strategies. The
main objective is that students learn how these techniques can be
implemented, and the great possibilities they offer.
Abstract: Chemical Reaction Optimization (CRO) is an
optimization metaheuristic inspired by the nature of chemical
reactions as a natural process of transforming the substances from
unstable to stable states. Starting with some unstable molecules with
excessive energy, a sequence of interactions takes the set to a state of
minimum energy. Researchers reported successful application of the
algorithm in solving some engineering problems, like the quadratic
assignment problem, with superior performance when compared with
other optimization algorithms. We adapted this optimization
algorithm to the Printed Circuit Board Drilling Problem (PCBDP)
towards reducing the drilling time and hence improving the PCB
manufacturing throughput. Although the PCBDP can be viewed as
instance of the popular Traveling Salesman Problem (TSP), it has
some characteristics that would require special attention to the
transactions that explore the solution landscape. Experimental test
results using the standard CROToolBox are not promising for
practically sized problems, while it could find optimal solutions for
artificial problems and small benchmarks as a proof of concept.
Abstract: The expanded Invasive Weed Optimization algorithm (exIWO) is an optimization metaheuristic modelled on the original IWO version created by the researchers from the University of Tehran. The authors of the present paper have extended the exIWO algorithm introducing a set of both deterministic and non-deterministic strategies of individuals’ selection. The goal of the project was to evaluate the exIWO by testing its usefulness for solving some test instances of the traveling salesman problem (TSP) taken from the TSPLIB collection which allows comparing the experimental results with optimal values.
Abstract: Imperial competitive algorithm (ICA) simulates a multi-agent algorithm. Each agent is like a kingdom has its country, and the strongest country in each agent is called imperialist, others are colony. Countries are competitive with imperialist which in the same kingdom by evolving. So this country will move in the search space to find better solutions with higher fitness to be a new imperialist. The main idea in this paper is using the peculiarity of ICA to explore the search space to solve the kinds of combinational problems. Otherwise, we also study to use the greed search to increase the local search ability. To verify the proposed algorithm in this paper, the experimental results of traveling salesman problem (TSP) is according to the traveling salesman problem library (TSPLIB). The results show that the proposed algorithm has higher performance than the other known methods.
Abstract: Genetic Algorithm (GA) is a powerful technique for solving optimization problems. It follows the idea of survival of the fittest - Better and better solutions evolve from previous generations until a near optimal solution is obtained. GA uses the main three operations, the selection, crossover and mutation to produce new generations from the old ones. GA has been widely used to solve optimization problems in many applications such as traveling salesman problem, airport traffic control, information retrieval (IR), reactive power optimization, job shop scheduling, and hydraulics systems such as water pipeline systems. In water pipeline systems we need to achieve some goals optimally such as minimum cost of construction, minimum length of pipes and diameters, and the place of protection devices. GA shows high performance over the other optimization techniques, moreover, it is easy to implement and use. Also, it searches a limited number of solutions.
Abstract: The Genetic Algorithm (GA) is one of the most important methods used to solve many combinatorial optimization problems. Therefore, many researchers have tried to improve the GA by using different methods and operations in order to find the optimal solution within reasonable time. This paper proposes an improved GA (IGA), where the new crossover operation, population reformulates operation, multi mutation operation, partial local optimal mutation operation, and rearrangement operation are used to solve the Traveling Salesman Problem. The proposed IGA was then compared with three GAs, which use different crossover operations and mutations. The results of this comparison show that the IGA can achieve better results for the solutions in a faster time.
Abstract: Deoxyribonucleic Acid or DNA computing has
emerged as an interdisciplinary field that draws together chemistry,
molecular biology, computer science and mathematics. Thus, in this
paper, the possibility of DNA-based computing to solve an absolute
1-center problem by molecular manipulations is presented. This is
truly the first attempt to solve such a problem by DNA-based
computing approach. Since, part of the procedures involve with
shortest path computation, research works on DNA computing for
shortest path Traveling Salesman Problem, in short, TSP are reviewed.
These approaches are studied and only the appropriate one is adapted
in designing the computation procedures. This DNA-based
computation is designed in such a way that every path is encoded by
oligonucleotides and the path-s length is directly proportional to the
length of oligonucleotides. Using these properties, gel electrophoresis
is performed in order to separate the respective DNA molecules
according to their length. One expectation arise from this paper is that
it is possible to verify the instance absolute 1-center problem using
DNA computing by laboratory experiments.
Abstract: Ant colony optimization is an ant algorithm framework that took inspiration from foraging behavior of ant colonies. Indeed, ACO algorithms use a chemical communication, represented by pheromone trails, to build good solutions. However, ants involve different communication channels to interact. Thus, this paper introduces the acoustic communication between ants while they are foraging. This process allows fine and local exploration of search space and permits optimal solution to be improved.
Abstract: The conventional GA combined with a local search
algorithm, such as the 2-OPT, forms a hybrid genetic algorithm(HGA)
for the traveling salesman problem (TSP). However, the geometric
properties which are problem specific knowledge can be used to
improve the search process of the HGA. Some tour segments (edges)
of TSPs are fine while some maybe too long to appear in a short tour.
This knowledge could constrain GAs to work out with fine tour
segments without considering long tour segments as often.
Consequently, a new algorithm is proposed, called intelligent-OPT
hybrid genetic algorithm (IOHGA), to improve the GA and the 2-OPT
algorithm in order to reduce the search time for the optimal solution.
Based on the geometric properties, all the tour segments are assigned
2-level priorities to distinguish between good and bad genes. A
simulation study was conducted to evaluate the performance of the
IOHGA. The experimental results indicate that in general the IOHGA
could obtain near-optimal solutions with less time and better accuracy
than the hybrid genetic algorithm with simulated annealing algorithm
(HGA(SA)).
Abstract: This paper presents a new heuristic algorithm for the classical symmetric traveling salesman problem (TSP). The idea of the algorithm is to cut a TSP tour into overlapped blocks and then each block is improved separately. It is conjectured that the chance of improving a good solution by moving a node to a position far away from its original one is small. By doing intensive search in each block, it is possible to further improve a TSP tour that cannot be improved by other local search methods. To test the performance of the proposed algorithm, computational experiments are carried out based on benchmark problem instances. The computational results show that algorithm proposed in this paper is efficient for solving the TSPs.
Abstract: The objective of this paper is the introduction to a
unified optimization framework for research and education. The
OPTILIB framework implements different general purpose algorithms
for combinatorial optimization and minimum search on standard continuous
test functions. The preferences of this library are the straightforward
integration of new optimization algorithms and problems
as well as the visualization of the optimization process of different
methods exploring the search space exclusively or for the real time
visualization of different methods in parallel. Further the usage of
several implemented methods is presented on the basis of two use
cases, where the focus is especially on the algorithm visualization.
First it is demonstrated how different methods can be compared
conveniently using OPTILIB on the example of different iterative
improvement schemes for the TRAVELING SALESMAN PROBLEM.
A second study emphasizes how the framework can be used to find
global minima in the continuous domain.
Abstract: A novel method of individual level adaptive mutation rate control called the rank-scaled mutation rate for genetic algorithms is introduced. The rank-scaled mutation rate controlled genetic algorithm varies the mutation parameters based on the rank of each individual within the population. Thereby the distribution of the fitness of the papulation is taken into consideration in forming the new mutation rates. The best fit mutate at the lowest rate and the least fit mutate at the highest rate. The complexity of the algorithm is of the order of an individual adaptation scheme and is lower than that of a self-adaptation scheme. The proposed algorithm is tested on two common problems, namely, numerical optimization of a function and the traveling salesman problem. The results show that the proposed algorithm outperforms both the fixed and deterministic mutation rate schemes. It is best suited for problems with several local optimum solutions without a high demand for excessive mutation rates.
Abstract: In this paper, we address the problem of reducing the
switching activity (SA) in on-chip buses through the use of a bus
binding technique in high-level synthesis. While many binding
techniques to reduce the SA exist, we present yet another technique for
further reducing the switching activity. Our proposed method
combines bus binding and data sequence reordering to explore a wider
solution space. The problem is formulated as a multiple traveling
salesman problem and solved using simulated annealing technique.
The experimental results revealed that a binding solution obtained
with the proposed method reduces 5.6-27.2% (18.0% on average) and
2.6-12.7% (6.8% on average) of the switching activity when compared
with conventional binding-only and hybrid binding-encoding
methods, respectively.
Abstract: The well known NP-complete problem of the Traveling Salesman Problem (TSP) is coded in genetic form. A software system is proposed to determine the optimum route for a Traveling Salesman Problem using Genetic Algorithm technique. The system starts from a matrix of the calculated Euclidean distances between the cities to be visited by the traveling salesman and a randomly chosen city order as the initial population. Then new generations are then created repeatedly until the proper path is reached upon reaching a stopping criterion. This search is guided by a solution evaluation function.
Abstract: Very Large and/or computationally complex optimization problems sometimes require parallel or highperformance computing for achieving a reasonable time for computation. One of the most popular and most complicate problems of this family is “Traveling Salesman Problem". In this paper we have introduced a Branch & Bound based algorithm for the solution of such complicated problems. The main focus of the algorithm is to solve the “symmetric traveling salesman problem". We reviewed some of already available algorithms and felt that there is need of new algorithm which should give optimal solution or near to the optimal solution. On the basis of the use of logarithmic sampling, it was found that the proposed algorithm produced a relatively optimal solution for the problem and results excellent performance as compared with the traditional algorithms of this series.
Abstract: By introducing the concept of Oracle we propose an approach for improving the performance of genetic algorithms for large-scale asymmetric Traveling Salesman Problems. The results have shown that the proposed approach allows overcoming some traditional problems for creating efficient genetic algorithms.
Abstract: The multiple traveling salesman problem (mTSP) can be used to model many practical problems. The mTSP is more complicated than the traveling salesman problem (TSP) because it requires determining which cities to assign to each salesman, as well as the optimal ordering of the cities within each salesman's tour. Previous studies proposed that Genetic Algorithm (GA), Integer Programming (IP) and several neural network (NN) approaches could be used to solve mTSP. This paper compared the results for mTSP, solved with Genetic Algorithm (GA) and Nearest Neighbor Algorithm (NNA). The number of cities is clustered into a few groups using k-means clustering technique. The number of groups depends on the number of salesman. Then, each group is solved with NNA and GA as an independent TSP. It is found that k-means clustering and NNA are superior to GA in terms of performance (evaluated by fitness function) and computing time.
Abstract: Traveling salesman problem (TSP) is hard to resolve
when the number of cities and routes become large. The frequency
graph is constructed to tackle the problem. A frequency graph
maintains the topological relationships of the original weighted graph.
The numbers on the edges are the frequencies of the edges emulated
from the local optimal Hamiltonian paths. The simplest kind of local
optimal Hamiltonian paths are computed based on the four vertices
and three lines inequality. The search algorithm is given to find the
optimal Hamiltonian circuit based on the frequency graph. The
experiments show that the method can find the optimal Hamiltonian
circuit within several trials.