Fire field modelling using the SMARTFIRE automated dynamic solution control environment

SMARTFIRE is a fire field model based on an open architecture integrated CFD code and knowledge-based system. It makes use of the expert system to assist the user in setting up the problem specification and new computational techniques such as Group Solvers to reduce the computational effort involved in solving the equations. This paper concentrates on recent research into the use of artificial intelligence techniques to assist in dynamic solution control of fire scenarios being simulated using fire field modelling techniques. This is designed to improve the convergence capabilities of the software while further decreasing the computational overheads. The technique automatically controls solver relaxations using an integrated production rule engine with a blackboard to monitor and implement the required control changes during solution processing. Initial results for a two-dimensional fire simulation are presented that demonstrate the potential for considerable savings in simulation run-times when compared with control sets from various sources. Furthermore, the results demonstrate enhanced solution reliability due to obtaining acceptable convergence within each time step unlike some of the comparison simulations.

A multilevel approach to the travelling salesman problem

We motivate, derive, and implement a multilevel approach to the travelling salesman problem.The resulting algorithm progressively coarsens the problem, initialises a tour, and then employs either the Lin-Kernighan (LK) or the Chained Lin-Kernighan (CLK) algorithm to refine the solution on each of the coarsened problems in reverse order.In experiments on a well-established test suite of 80 problem instances we found multilevel configurations that either improved the tour quality by over 25% as compared to the standard CLK algorithm using the same amount of execution time, or that achieved approximately the same tour quality over seven times more rapidly. Moreover, the multilevel variants seem to optimise far better the more clustered instances with which the LK and CLK algorithms have the most difficulties.

Case base adaptation using solution-space metrics

In this paper we propose a generalisation of the k-nearest neighbour (k-NN) retrieval method based on an error function using distance metrics in the solution and problem space. It is an interpolative method which is proposed to be effective for sparse case bases. The method applies equally to nominal, continuous and mixed domains, and does not depend upon an embedding n-dimensional space. In continuous Euclidean problem domains, the method is shown to be a generalisation of the Shepard's Interpolation method. We term the retrieval algorithm the Generalised Shepard Nearest Neighbour (GSNN) method. A novel aspect of GSNN is that it provides a general method for interpolation over nominal solution domains. The performance of the retrieval method is examined with reference to the Iris classification problem,and to a simulated sparse nominal value test problem. The introducion of a solution-space metric is shown to out-perform conventional nearest neighbours methods on sparse case bases.

Multilevel refinement for the vehicle routing problem

Multilevel approaches to computational problems are pervasive across many areas of applied mathematics and scientific computing. The multilevel paradigm uses recursive coarsening to create a hierarchy of approximations to the original problem, then an initial solution is found for the coarsest problem and iteratively refined and improved at each level, coarsest to finest. The solution process is aided by the global perspective (or `global view') imparted to the optimisation by the coarsening. This paper looks at their application to the Vehicle Routing Problem.

Multilevel approaches applied to the capacitated clustering problem

This paper presents two multilevel refinement algorithms for the capacitated clustering problem. Multilevel refinement is a collaborative technique capable of significantly aiding the solution process for optimisation problems. The central methodologies of the technique are filtering solutions from the search space and reducing the level of problem detail to be considered at each level of the solution process. The first multilevel algorithm uses a simple tabu search while the other executes a standard local search procedure. Both algorithms demonstrate that the multilevel technique is capable of aiding the solution process for this combinatorial optimisation problem.

Vibrational spectra of α-amino acids in the zwitterionic state in aqueous solution and the solid state: DFT calculations and the influence of hydrogen bonding

The zwitterionic forms of the two simplest alpha-amino acids, glycine and l-alanine, in aqueous solution and the solid state have been modeled by DFT calculations. Calculations of the structures in the solid state, using PW91 or PBE functionals, are in good agreement with the reported crystal structures, and the vibrational spectra computed at the optimized geometries provide a good fit to the observed IR and Raman spectra in the solid state. DFT calculations of the structures and vibrational spectra of the zwitterions in aqueous solution at the B3-LYP/cc-pVDZ level were found to require both explicit and implicit solvation models. Explicit solvation was modeled by inclusion of five hydrogen-bonded water molecules attached to each of the five possible hydrogen-bonding sites in the zwitterion and the integration equation formalism polarizable continuum model (IEF-PCM) was employed, providing a satisfactory fit to observed IR and Raman spectra. Band assignments are reported in terms of potential-energy distributions, which differ in some respects to those previously reported for glycine and l-alanine.

The parallel solution of early-exercise Asian options with stochastic volatility

This paper describes an parallel semi-Lagrangian finite difference approach to the pricing of early exercise Asian Options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices. Asian options are contingent claims with payoffs that depend on the average price of an asset over some time interval. The payoff may depend on this average and a fixed strike price (Fixed Strike Asians) or it may depend on the average and the asset price (Floating Strike Asians). The option may also permit early exercise (American contract) or confine the holder to a fixed exercise date (European contract). The Fixed Strike Asian with early exercise is considered here where continuous arithmetic averaging has been used. Pricing such an option where the asset price has a stochastic volatility leads to the requirement to solve a tri-variate partial differential inequation in the three state variables of asset price, average price and volatility (or equivalently, variance). The similarity transformations [6] used with Floating Strike Asian options to reduce the dimensionality of the problem are not applicable to Fixed Strikes and so the numerical solution of a tri-variate problem is necessary. The computational challenge is to provide accurate solutions sufficiently quickly to support realtime trading activities at a reasonable cost in terms of hardware requirements.