Abstract: Ant colony optimization (ACO) and its variants are
applied extensively to resolve various continuous optimization
problems. As per the various diversification and intensification
schemes of ACO for continuous function optimization, researchers
generally consider components of multidimensional state space to
generate the new search point(s). However, diversifying to a new
search space by updating only components of the multidimensional
vector may not ensure that the new point is at a significant distance
from the current solution. If a minimum distance is not ensured
during diversification, then there is always a possibility that the
search will end up with reaching only local optimum. Therefore, to
overcome such situations, a Mahalanobis distance-based
diversification with Nelder-Mead simplex-based search scheme for
each ant is proposed for the ACO strategy. A comparative
computational run results, based on nine nonlinear standard test
problems, confirms that the performance of ACO is improved
significantly with the integration of the proposed schemes in the
ACO.
Abstract: There are two common types of operational research techniques, optimisation and metaheuristic methods. The latter may be defined as a sequential process that intelligently performs the exploration and exploitation adopted by natural intelligence and strong inspiration to form several iterative searches. An aim is to effectively determine near optimal solutions in a solution space. In this work, a type of metaheuristics called Ant Colonies Optimisation, ACO, inspired by a foraging behaviour of ants was adapted to find optimal solutions of eight non-linear continuous mathematical models. Under a consideration of a solution space in a specified region on each model, sub-solutions may contain global or multiple local optimum. Moreover, the algorithm has several common parameters; number of ants, moves, and iterations, which act as the algorithm-s driver. A series of computational experiments for initialising parameters were conducted through methods of Rigid Simplex, RS, and Modified Simplex, MSM. Experimental results were analysed in terms of the best so far solutions, mean and standard deviation. Finally, they stated a recommendation of proper level settings of ACO parameters for all eight functions. These parameter settings can be applied as a guideline for future uses of ACO. This is to promote an ease of use of ACO in real industrial processes. It was found that the results obtained from MSM were pretty similar to those gained from RS. However, if these results with noise standard deviations of 1 and 3 are compared, MSM will reach optimal solutions more efficiently than RS, in terms of speed of convergence.
Abstract: Collateralized Debt Obligations are not as widely used
nowadays as they were before 2007 Subprime crisis. Nonetheless
there remains an enthralling challenge to optimize cash flows
associated with synthetic CDOs. A Gaussian-based model is used
here in which default correlation and unconditional probabilities of
default are highlighted. Then numerous simulations are performed
based on this model for different scenarios in order to evaluate the
associated cash flows given a specific number of defaults at different
periods of time. Cash flows are not solely calculated on a single
bought or sold tranche but rather on a combination of bought and
sold tranches. With some assumptions, the simplex algorithm gives
a way to find the maximum cash flow according to correlation of
defaults and maturities. The used Gaussian model is not realistic in
crisis situations. Besides present system does not handle buying or
selling a portion of a tranche but only the whole tranche. However the
work provides the investor with relevant elements on how to know
what and when to buy and sell.