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Using hyper populated ant colonies for solving the TSP
Vietnam J Comput Sci
Using hyper populated ant colonies for solving the TSP
Andrzej Siemi n´ski 0
0 Faculty of Computer Science and Management, Wroclaw University of Technology , Wroclaw , Poland
The paper discusses the application of hyper populated ant colonies to the well-known traveling salesman problem (TSP). The ant colony optimization (ACO) approach offers reasonably good quality solutions for the TSP, but it suffers from its inherent non-determinism and as a consequence the processing time is unpredictable. The paper tries to mitigate the problem by a substantial increase in the number of used ants. This approach is called ant hyper population and it could be obtained by increasing the number of ants in a single colony assigning more than one colony to solve the same task or both. In all cases the level of nondeterminism decreases and thus the number iterations could be reduced. Parallel implementation of the ACO makes it possible to reduce drastically the processing time. The paper compares two ways of implementation of the parallelism using the sockets or the RMI-remote method invocation mechanisms. The paper concentrates on the classical static version of the TSP, but preliminary experiments indicate that such an approach could be even more useful for dynamic TPSs.
Ant colony optimization; Traveling salesmen problem; Parallelization strategies for ACO; Ant colony community (ACC)
1 Introduction
The aim of the paper is to discuss the problem of
optimizing the performance of the ant colony optimization (ACO)
used for the traveling salesman problem (TSP).
Metaheuristics such as the ACO solve a complex problem by iteratively
improving candidate solutions. They do not guarantee the
selection of an optimum or even a satisfactory near-optimal
solution. In the case of the NP-hard or even NP-complete
problems they are often the only available choice that we
have.
Usually the quality of solutions is measured by exclusively
by the length of the selected route. The ACO works in a
nondeterministic way. Usually a predefined number of iterations
are executed and the best found solution is selected. The
quality of solutions improves with time, but the process is
not uniform. A high quality solution could be found after a
few thousands of iterations, but it is not uncommon that we
can have it after just a few dozens of them. Therefore, it is so
hard to tell when to stop the operation of the ACO. There is
a great incentive to prolong the execution time. The reported
experiment results look more impressive. This is certainly
possible in an university environment. It may not be the case
for the real life applications. The time needed to execute
a great number of iterations may simply not be available.
Moreover, the longer we run the ACO, the solution updates
are the less and less frequent. This demerit is even more acute
for the dynamic TSP. In that case the ACO may not be able
to catch up with the changing environment.
The paper addresses the problem using a drastically
increased number of ants. In what follows such ACOs are
called hyper populated Ant Colonies. They come in two
flavors. In the first one the ant number increases in just one
colony and in the second we have a number of
cooperating colonies—the so-called ant colony community (ACC). In
both cases the results converge faster so the number of
iterations could be limited. The main contribution of the paper
is a detailed presentations of a model for the ACC and
verification of its efficiency. The Socket mechanism was used to
implement the model and its advantages over the competing
RMI mechanism are discussed. The complexity of
interactions between individual ants or even ant colonies make a
theoretical analysis extremely hard even with a number of
simplifying assumptions. Therefore, this paper demonstrates
empirically the performance and convergence aspects of the
proposed model.
The paper is organized as follows. The second Section
briefly introduces the TSP. The next one is devoted to the
ACO—a metaheuristics commonly used to solve it. This
section presents its general operational principles and the role
played by its parameters. Attempts to optimize their values
are also mentioned. It ends with the discussion of the
stopping conditions. In the fourth Section we provide experiment
results that justify the increase in the number of used ants.
The prolonged execution time resulting from increasing of
ant population could be mitigated by the parallel
implementation of the ACO. The fifth Section contains the taxonomy of
parallel ACOs and introduces the coarse-grained ACC
proposed in the paper. The conducted experiments, their results
with the criteria used to evaluate them are presented in the
6th Section. The paper concludes with the resume of research
work done so far and the plans for future investigation.
2 Traveling salesman problem specification
The TSP could be stated in a remarkably simple way: given
a list of cities and the distances sepa (...truncated)