Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Optimal Paths on Urban Networks Using Travelling Times Prevision
2012
We deal with an algorithm that, once origin and destination are fixed, individuates the route that permits to reach the destination in the shortest time, respecting an assigned maximal travel time, and with risks measure below a given threshold. A fluid dynamic model for road networks, according to initial car densities on roads and traffic coefficients at junctions, forecasts the future traffic evolution, giving dynamical weights to a constrained 𝐾 shortest path algorithm. Simulations are performed on a case study to test the efficiency of the proposed procedure.
Representation of capacity drop at a road merge via point constraints in a first order traffic model
2018
We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by c…
Online Metric Learning Methods Using Soft Margins and Least Squares Formulations
2012
Online metric learning using margin maximization has been introduced as a way to learn appropriate dissimilarity measures in an efficient way when information as pairs of examples is given to the learning system in a progressive way. These schemes have several practical advantages with regard to global ones in which a training set needs to be processed. On the other hand, they may suffer from a poor performance depending on the quality of the examples and the particular tuning or other implementation details. This paper formulates several online metric learning alternatives using a passive-aggressive schema. A new formulation of the online problem using least squares is also introduced. The…
The Rural Postman Problem on mixed graphs with turn penalties
2002
In this paper we deal with a problem which generalizes the Rural Postman Problem defined on a mixed graph (MRPP). The generalization consists of associating a non-negative penalty to every turn as well as considering the existence of forbidden turns. This new problem fits real-world situations more closely than other simpler problems. A solution tour must traverse all the requiring service arcs and edges of the graph while not making forbidden turns. Its total cost will be the sum of the costs of the traversed arcs and edges together with the penalties associated with the turns done. The Mixed Rural Postman Problem with Turn Penalties (MRPPTP) consists of finding such a tour with a total mi…
Using penalties instead of rewards: Solving OCST problems with guided local search
2012
Abstract This paper considers the optimal communication spanning tree (OCST) problem. Previous work analyzed features of high-quality solutions and found that edges in optimal solutions have low weight and point towards the center of a tree. Consequently, integrating this problem-specific knowledge into a metaheuristic increases its performance for the OCST problem. In this paper, we present a guided local search (GLS) approach which dynamically changes the objective function to guide the search process into promising areas. In contrast to traditional approaches which reward promising solution features by favoring edges with low weights pointing towards the tree’s center, GLS penalizes low-…
Robust and Efficient IMEX Schemes for Option Pricing under Jump-Diffusion Models
2013
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump diffusion process. The schemes include the families of IMEX-midpoint, IMEXCNAB and IMEX-BDF2 schemes. Each family is defined by a convex parameter c ∈ [0, 1], which divides the zeroth-order term due to the jumps between the implicit and explicit part in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restrictions, the IMEX-midpoint fa…
Robust model calibration using determinist and stochastic performance metrics
2016
International audience; The aeronautics industry has benefited from the use of numerical models to supplement or replace the costly design-build-test paradigm. These models are often calibrated using experimental data to obtain optimal fidelity-to-data but compensating effects between calibration parameters can complicate the model selection process due to the non-uniqueness of the solution. One way to reduce this ambiguity is to include a robustness requirement to the selection criteria. In this study, the info-gap decision theory is used to represent the lack of knowledge resulting from compensating effects and a robustness analysis is performed to investigate the impact of uncertainty on…
A Highly Flexible Trajectory Model Based on the Primitives of Brownian Fields—Part II: Analysis of the Statistical Properties
2016
In the first part of our paper, we have proposed a highly flexible trajectory model based on the primitives of Brownian fields (BFs). In this second part, we study the statistical properties of that trajectory model in depth. These properties include the autocorrelation function (ACF), mean, and the variance of the path along each axis. We also derive the distribution of the angle-of-motion (AOM) process, the incremental traveling length process, and the overall traveling length. It is shown that the path process is in general non-stationary. We show that the AOM and the incremental traveling length processes can be modeled by the phase and the envelope of a complex Gaussian process with no…
Optimization of the objective function –surface quality by end-milling dimensional machining of some aluminum alloys
2019
Abstract In the aerospace industry, the milling of aluminum alloy parts is a machining process with the primary purpose of removing high volumes of material. Aluminum alloys are materials that have relatively good machinability, which helps the process because many of the components of the aircraft are of high dimensions. These parts have many pockets more or less deep, and the removal by cutting off about 90% of the initial volume of the workpiece is a matter of consideration. The manufacturing process is protracted and involves long semi-finishing and finishing operations, so it is recommended that any researcher who begins and finishes an experimental study should do it base on a specifi…
Necessary conditions for extremality and separation theorems with applications to multiobjective optimization
1998
The aim of this paper is to give necessary conditions for extremality in terms of an abstract subdifferential and to obtain general separation theorems including both finite and infinite classical separation theorems. This approach, which is mainly based on Ekeland's variational principle and the concept of locally weak-star compact cones, can be considered as a generalization f the notions of optima in problems of scalar or vector optimization with and without constraints. The results obtained are applied to derive new necessary optimality conditions for Pareto local minimum and weak Pareto minimum of nonsmooth multlobjectivep rogramming problems.