Performance comparison of adapted delaunay triangulation method over nurbs for surface optimization problems

Traditionally NURBS (Non-Uniform Rational Basis Spline) are used as the basis for defining free-form surfaces as they can define non-regular surfaces with minimal control points. However, they require parameters such as knot vectors and weights to configure a surface. Similarly, DT (Delaunay Triangulation) is proven and used widely for meshing, rendering and surface reconstruction applications, but its capability in freeform surface design for optimization is untested. Thus, this paper proposes Adapted Delaunay Triangulation (ADT) method which can generate a surface from scattered data points without any parameters. The paper presents a comparison of the performance of ADT method and NURBS fitting method for surface generation from scattered 3D coordinate points. This method was suggested so that the generated surface could be used in Stochastic Optimization Algorithm (SOA) methods and computational fluid dynamics applications (CFD) simultaneously. Data points that other 3D point clouds fitting methods would ignore as outliers are included in ADT method. Small change in each data point during optimization cycle should show a distinctive change in its output as SOA approaches depend on such differences for its optimal performance. Special consideration has been made for fast processing and rendering of the surface with minimum complexity (removing parameters such as knots and weights) and storage requirements as SOA methods demand generation of numerous surfaces to solve any problem

Adapted Delaunay triangulation method for free-form surface generation from random point clouds for stochastic optimization applications

Free-form surfaces are defined with NURBS (non-uniform rational basis spline) for most computer-aided engineering (CAE) applications. The NURBS method requires the definition of parameters such as weights, knot vectors and degree of the curves which make the configuration of the surface computationally expensive and complex. When the control points are randomly spaced in the point cloud and the topology of the desired surface is unknown, surface configuration with NURBS method becomes a challenging task. Optimization attempts for such surfaces create enormous amounts of computing data when coupled with physics solvers such as finite element analysis (FEA) tools and computational fluid dynamics (CFD) tools. In this paper, an adapted Delaunay triangulation (ADT) method for surface generation from the random points cloud is proposed and compared with widely used implicit functions based NURBS fitting method. The surface generated from ADT method can be simultaneously used with stochastic optimization algorithms (SOA) and CFD applications to search for the optimal results with minimum computational costs. It was observed while comparing ADT with NURBS-based geometry configuration that the computation time can be reduced by 3 folds. The corresponding deviation between both geometry configuration methods has been observed as low as 5% for all optimisation scenarios during the comparison. In addition, ADT method can provide light weight CFD approach as any instance of design iteration has at least half storage footprint as compared to corresponding NURBS surface. The proposed approach provides novel methodology towards establishing light weight CFD geometry, absence of which currently isolates methodologies for optimization and CFD analysis

A multi-objective evolutionary optimisation model for heterogeneous vehicles routing and relief items scheduling in humanitarian crises

In a disaster scenario, relief items distribution is required as early as possible for the disaster victims to reduce the associated risks. For the distribution tasks, an effective and efficient relief items distribution model to generated relief items distribution schedules is essential to minimise the impact of disaster to the disaster victims. However, developing efficient distribution schedules is challenging as the relief items distribution problem has multiple objectives to look after where the objectives are mostly contradictorily creating a barrier to simultaneous optimisation of each objective. Also, the relief items distribution model has added complexity with the consideration of multiple supply points having heterogeneous and limited vehicles with varying capacity, cost and time. In this paper, multi-objective evolutionary optimisation with the greedy heuristic search has been applied for the generation of relief items distribution schedules under heterogeneous vehicles condition at supply points. The evolutionary algorithm generates the disaster region distribution sequence by applying a global greedy heuristic search along with a local search that finds the efficient assignment of heterogeneous vehicles for the distribution. This multi-objective evolutionary approach provides Pareto optimal solutions that decision-makers can apply to generate effective distribution schedules that optimise the distribution time and vehicles’ operational cost. In addition, this optimisation also incorporated the minimisation of unmet relief items demand at the disaster regions. The optimised distribution schedules with the proposed approach are compared with the single-objective optimisation, weighted single-objective optimisation and greedy multi-objective optimisation approaches. The comparative results showed that the proposed multi-objective evolutionary approach is an efficient alternative for finding the distribution schedules with optimisation of distribution time and operational cost for the relief items distribution with heterogeneous vehicles