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: Ants are fascinating creatures that demonstrate the
ability to find food and bring it back to their nest. Their ability as a
colony, to find paths to food sources has inspired the development of
algorithms known as Ant Colony Systems (ACS). The principle of
cooperation forms the backbone of such algorithms, commonly used
to find solutions to problems such as the Traveling Salesman
Problem (TSP). Ants communicate to each other through chemical
substances called pheromones. Modeling individual ants- ability to
manipulate this substance can help an ACS find the best solution.
This paper introduces a Dynamic Ant Colony System with threelevel
updates (DACS3) that enhance an existing ACS. Experiments
were conducted to observe single ant behavior in a colony of
Malaysian House Red Ants. Such behavior was incorporated into the
DACS3 algorithm. We benchmark the performance of DACS3 versus
DACS on TSP instances ranging from 14 to 100 cities. The result
shows that the DACS3 algorithm can achieve shorter distance in
most cases and also performs considerably faster than DACS.
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.
Abstract: Combinatorial optimization problems arise in many scientific and practical applications. Therefore many researchers try to find or improve different methods to solve these problems with high quality results and in less time. Genetic Algorithm (GA) and Simulated Annealing (SA) have been used to solve optimization problems. Both GA and SA search a solution space throughout a sequence of iterative states. However, there are also significant differences between them. The GA mechanism is parallel on a set of solutions and exchanges information using the crossover operation. SA works on a single solution at a time. In this work SA and GA are combined using new technique in order to overcome the disadvantages' of both algorithms.