4,986 research outputs found
Applications of Bee Colony Optimization
Many computationally difficult problems are attacked using non-exact algorithms, such as approximation algorithms and heuristics. This thesis investigates an ex- ample of the latter, Bee Colony Optimization, on both an established optimization problem in the form of the Quadratic Assignment Problem and the FireFighting problem, which has not been studied before as an optimization problem. Bee Colony Optimization is a swarm intelligence algorithm, a paradigm that has increased in popularity in recent years, and many of these algorithms are based on natural pro- cesses.
We tested the Bee Colony Optimization algorithm on the QAPLIB library of Quadratic Assignment Problem instances, which have either optimal or best known solutions readily available, and enabled us to compare the quality of solutions found by the algorithm. In addition, we implemented a couple of other well known algorithms for the Quadratic Assignment Problem and consequently we could analyse the runtime of our algorithm.
We introduce the Bee Colony Optimization algorithm for the FireFighting problem. We also implement some greedy algorithms and an Ant Colony Optimization al- gorithm for the FireFighting problem, and compare the results obtained on some randomly generated instances.
We conclude that Bee Colony Optimization finds good solutions for the Quadratic Assignment Problem, however further investigation on speedup methods is needed to improve its performance to that of other algorithms. In addition, Bee Colony Optimization is effective on small instances of the FireFighting problem, however as instance size increases the results worsen in comparison to the greedy algorithms, and more work is needed to improve the decisions made on these instances
On Quadratic Programming with a Ratio Objective
Quadratic Programming (QP) is the well-studied problem of maximizing over
{-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures
many known combinatorial optimization problems, and assuming the unique games
conjecture, semidefinite programming techniques give optimal approximation
algorithms. We extend this body of work by initiating the study of Quadratic
Programming problems where the variables take values in the domain {-1,0,1}.
The specific problems we study are
QP-Ratio : \max_{\{-1,0,1\}^n} \frac{\sum_{i \not = j} a_{ij} x_i x_j}{\sum
x_i^2}, and Normalized QP-Ratio : \max_{\{-1,0,1\}^n} \frac{\sum_{i \not = j}
a_{ij} x_i x_j}{\sum d_i x_i^2}, where d_i = \sum_j |a_{ij}|
We consider an SDP relaxation obtained by adding constraints to the natural
eigenvalue (or SDP) relaxation for this problem. Using this, we obtain an
algorithm for QP-ratio. We also obtain an
approximation for bipartite graphs, and better algorithms
for special cases. As with other problems with ratio objectives (e.g. uniform
sparsest cut), it seems difficult to obtain inapproximability results based on
P!=NP. We give two results that indicate that QP-Ratio is hard to approximate
to within any constant factor. We also give a natural distribution on instances
of QP-Ratio for which an n^\epsilon approximation (for \epsilon roughly 1/10)
seems out of reach of current techniques
The quadratic assignment problem and plant layout
Imperial Users onl
- ā¦