839 research outputs found
An analysis of various elastic net algorithms
The Elastic Net Algorithm (ENA) for solving the Traveling Salesman Problem is analyzed applying statistical mechanics. Using some general properties of the free energy function
of stochastic Hopfield Neural Networks, we argue why Simic's derivation of the ENA from a Hopfield network is incorrect. However, like the Hopfield-Lagrange method, the ENA may be considered a specific dynamic penalty method, where, in this case, the weights of the various penalty terms decrease during execution of the algorithm. This view on the ENA corresponds to the view resulting from the theory on `deformable templates', where the term stochastic penalty method seems to be most appropriate. Next, the ENA is analyzed both on the level of the energy function as well as on the level of the motion equations. It will be proven and shown experimentally, why a non-feasible solution is sometimes found. It can be caused either by a too rapid lowering of the
temperature parameter (which is avoidable), or by a peculiar property of the algorithm,namely, that of adhering to equidistance of the elastic net points. Thereupon, an alternative, Non-equidistant Elastic Net Algorithm (NENA) is presented and analyzed. It has a correct distance measure and it is hoped to guarantee feasibility in a more natural way. For small problem instances, this conjecture is confirmed
experimentally. However, trying larger problem instances, the pictures changes: our
experimental results show that the elastic net points appear to become `lumpy' which may
cause non-feasibility again. Moreover, in cases both algorithms yield a feasible solution,
the quality of the solution found by the NENA is often slightly worse than the one found
by the original ENA. This motivated us to try an Hybrid Elastic Net Algorithm (HENA),
which starts using the ENA and, after having found a good approximate solution, switches
to the NENA in order to guarantee feasibility too. In practice, the ENA and HENA perform
more or less the same. Up till now, we did not find parameters of the HENA, which invariably guarantee the desired feasibility of solutions
Parallel ACO with a Ring Neighborhood for Dynamic TSP
The current paper introduces a new parallel computing technique based on ant
colony optimization for a dynamic routing problem. In the dynamic traveling
salesman problem the distances between cities as travel times are no longer
fixed. The new technique uses a parallel model for a problem variant that
allows a slight movement of nodes within their Neighborhoods. The algorithm is
tested with success on several large data sets.Comment: 8 pages, 1 figure; accepted J. Information Technology Researc
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
Flexible protein folding by ant colony optimization
Protein structure prediction is one of the most challenging topics in bioinformatics.
As the protein structure is found to be closely related to its functions,
predicting the folding structure of a protein to judge its functions is meaningful to
the humanity. This chapter proposes a flexible ant colony (FAC) algorithm for solving
protein folding problems (PFPs) based on the hydrophobic-polar (HP) square lattice
model. Different from the previous ant algorithms for PFPs, the pheromones in the
proposed algorithm are placed on the arcs connecting adjacent squares in the lattice.
Such pheromone placement model is similar to the one used in the traveling salesmen
problems (TSPs), where pheromones are released on the arcs connecting the cities.
Moreover, the collaboration of effective heuristic and pheromone strategies greatly
enhances the performance of the algorithm so that the algorithm can achieve good
results without local search methods. By testing some benchmark two-dimensional
hydrophobic-polar (2D-HP) protein sequences, the performance shows that the proposed
algorithm is quite competitive compared with some other well-known methods
for solving the same protein folding problems
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