Search results for " Simulation"
showing 10 items of 4034 documents
Qualitative investigations of boundary value problem for self‐similar second order system which arises from modeling of surface chemical reactions
1997
„Qualitative investigations of boundary value problem for self‐similar second order system which arises from modeling of surface chemical reactions" Mathematical Modelling Analysis, 2(1), p. 41-47 First Published Online: 14 Oct 2010
GRASP and path relinking for the max–min diversity problem
2010
The max-min diversity problem (MMDP) consists in selecting a subset of elements from a given set in such a way that the diversity among the selected elements is maximized. The problem is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in the social and biological sciences. We propose a heuristic method-based on the GRASP and path relinking methodologies-for finding approximate solutions to this optimization problem. We explore different ways to hybridize GRASP and path relinking, including the recently proposed variant known as GRASP with evolutionary p…
A comparison of different solution approaches to the vehicle scheduling problem in a practical case
2000
Abstract The Vehicle Scheduling Problem (VSP) consists in assigning a set of scheduled trips to a set of vehicles, satisfying a set of constraints and optimizing an objective function. A wide literature exists for the VSP, but usually not all the practical requirements of the real cases are taken into account. In the present paper a practical case is studied, and for it a traditional method is tailored and two innovative heuristics are developed. As the problem presents a multicriteria nature, each of the three algorithms adopts a different approach to multicriteria optimization. Scalarization of the different criteria is performed by the traditional algorithm. A lexicographic approach is f…
Hybridizing the cross-entropy method: An application to the max-cut problem
2009
Cross-entropy has been recently proposed as a heuristic method for solving combinatorial optimization problems. We briefly review this methodology and then suggest a hybrid version with the goal of improving its performance. In the context of the well-known max-cut problem, we compare an implementation of the original cross-entropy method with our proposed version. The suggested changes are not particular to the max-cut problem and could be considered for future applications to other combinatorial optimization problems.
Using a TSP heuristic for routing order pickers in warehouses
2010
In this paper, we deal with the sequencing and routing problem of order pickers in conventional multi-parallel-aisle warehouse systems. For this NP-hard Steiner travelling salesman problem (TSP), exact algorithms only exist for warehouses with at most three cross aisles, while for other warehouse types literature provides a selection of dedicated construction heuristics. We evaluate to what extent reformulating and solving the problem as a classical TSP leads to performance improvements compared to existing dedicated heuristics. We report average savings in route distance of up to 47% when using the LKH (Lin-Kernighan-Helsgaun) TSP heuristic. Additionally, we examine if combining problem-sp…
Numerical solution of a multi-class model for batch settling in water resource recovery facilities
2017
In Torfs et al. (2017) a new unified framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial differential equations (PDEs) modelling different settling unit processes in wastewater treatment such as primary and secondary settling tanks (PSTs and SSTs). The extension to a multi-class framework to deal with the distributed properties of the settling particles leads to a system of non-linear hyperbolic-parabolic PDEs whose solutions may contain very sharp transitions. This necessitates the use of a consistent and robust numerical method to obtain well-resolved and reliable approximations to the PDE solutions. The use of implicit–explicit …
Boundary Element Crystal Plasticity Method
2017
A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and har…
The multiple vehicle pickup and delivery problem with LIFO constraints
2015
Abstract This paper approaches a pickup and delivery problem with multiple vehicles in which LIFO conditions are imposed when performing loading and unloading operations and the route durations cannot exceed a given limit. We propose two mixed integer formulations of this problem and a heuristic procedure that uses tabu search in a multi-start framework. The first formulation is a compact one, that is, the number of variables and constraints is polynomial in the number of requests, while the second one contains an exponential number of constraints and is used as the basis of a branch-and-cut algorithm. The performances of the proposed solution methods are evaluated through an extensive comp…
A two-slope achievement scalarizing function for interactive multiobjective optimization
2012
The use of achievement (scalarizing) functions in interactive multiobjective optimization methods is very popular, as indicated by the large number of algorithmic and applied scientific papers that use this approach. Key parameters in this approach are the reference point, which expresses desirable objective function values for the decision maker, and weights. The role of the weights can range from purely normalizing to fully preferential parameters that indicate the relative importance given by the decision maker to the achievement of each reference value. Technically, the influence of the weights in the solution generated by the achievement scalarizing function is different, depending on …
Fuzzy green vehicle routing problem for designing a three echelons supply chain
2020
Abstract In this study, a three-echelon fuzzy green vehicle routing problem (3E-FGVRP) is considered for designing a regional agri-food supply chain on a time horizon. To account for the variability associated with the quantities requested by customers, it is assumed that the demands are fuzzy numbers simulated by a time-dependent algorithm. Moreover, the vehicle fleet and distribution centres are considered with a defined capacity. The credibility theory of fuzzy sets is used to implement a multi-objective fuzzy chance-constrained programming model, where the total costs and carbon emissions are minimised. The resolution of the 3E-FGVRP is conducted by using a non-dominated sorting genetic…