High-Level Relay Hybrid Metaheuristic Method for Multi-Depot Vehicle Routing Problem with Time Windows

This paper presents an efficient hybrid metaheuristic solution for multi-depot vehicle routing with time windows (MD-VRPTW). MD-VRPTW involves the routing of a set of vehicles with limited capacity from a set of depots to a set of geographically dispersed customers with known demands and predefined time windows. The present work aims at using a hybrid metaheuristic algorithm in the class of High-Level Relay Hybrid (HRH) which works in three levels and uses an efficient genetic algorithm as the main optimization algorithm and tabu search as an improvement method. In the genetic algorithm various heuristics incorporate local exploitation in the evolutionary search. An operator deletion- retrieval strategy is executed which shows the efficiency of the inner working of the proposed method. The proposed algorithm is applied to solve the problems of the standard Cordeau??s Instances. Results show that proposed approach is quite effective, as it provides solutions that are competitive with the best known in the literature.     

Attached primes of the top local cohomology modules with respect to an ideal

Let be a Noetherian local ring and let be an ideal of R. Let M be an R-module of dimension n. In this paper we study the attached primes of the top local cohomology module Received: 12 May 2004     

Modeling action-interdependence in multiple criteria decision making

A problem of subset selection when actions are interdependent is formulated within a multiple criteria framework. More specifically, a novel definition and characterization of interdependence of actions applicable to Multiple Criteria Decision Making (MCDM) are presented. The effects of interdependence of actions on the modeling and resolution of a subset choice problem are shown, and the importance of taking interdependence of actions into account is discussed. Most of the discussion is generalized to independence and interdependence of sets of actions, which are then compared to the case of individual actions. A general approach to evaluate a combination of interdependent actions is proposed and the use of the multiple criteria structure to eliminate some difficulties in evaluating a set of interdependent actions is explained.     

On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem

Most commonly used boundary integral formulations of the exterior problem in time-harmonic acoustics, which are valid for all wave-numbers, involve a non-zero coupling parameter. In this paper we analyse the qualitative behaviour of the direct boundary integral formulation due to Burton and Miller. In particular we include a regularised formulation for the Neumann problem. By deriving the eigensystems of the operators we are able to obtain ′almost optimal′ values for the coupling parameter, as a function of the wave-number, so as to minimize the condition number of various formulations     

On the h-triangles of sequentially (S r ) simplicial complexes via algebraic shifting

Recently, Haghighi, Terai, Yassemi, and Zaare-Nahandi introduced the notion of a sequentially (S _r ) simplicial complex. This notion gives a generalization of two properties for simplicial complexes: being sequentially Cohen–Macaulay and satisfying Serre’s condition (S _r ). Let Δ be a (d?1)-dimensional simplicial complex with Γ(Δ) as its algebraic shifting. Also let (h _i,j (Δ))_{0≤j≤i≤d} be the h-triangle of Δ and (h _i,j (Γ(Δ)))_{0≤j≤i≤d} be the h-triangle of Γ(Δ). In this paper, it is shown that for a Δ being sequentially (S _r ) and for every i and j with 0≤j≤i≤r?1, the equality h _i,j (Δ)=h _i,j (Γ(Δ)) holds true.     

Gorenstein Homological Dimension with Respect to a Semidualizing Module and a Generalization of a Theorem of Bass

Let C be a semidualizing module for a commutative ring R. In this paper, we study the resulting modules of finite G _C -projective dimension in Bass class, showing that they admit G _C -projective precover. Over local ring, we prove that dim _R (M) ≤ 𝒢? _C  ? id _R (M) for any nonzero finitely generated R-module M, which generalizes a result due to Bass.     

Tilting modules under special base changes

Given a non-unit, non-zero-divisor, central element x of a ring Λ, it is well known that many properties or invariants of Λ determine, and are determined by, those of $\mathrm{\Lambda }/x\mathrm{\Lambda }$ and ${\mathrm{\Lambda }}_x$. In the present paper, we investigate how the property of “being tilting” behaves in this situation. It turns out that any tilting module over Λ gives rise to tilting modules over ${\mathrm{\Lambda }}_x$ and $\mathrm{\Lambda }/x\mathrm{\Lambda }$ after localization and passing to quotient respectively. On the other hand, it is proved that under some mild conditions, a module over Λ is tilting if its corresponding localization and quotient are tilting over ${\mathrm{\Lambda }}_x$ and $\mathrm{\Lambda }/x\mathrm{\Lambda }$ respectively.     

Linearized and non‐linear acoustic/viscous splitting techniques for low Mach number flows

Computation of the acoustic disturbances generated by unsteady low‐speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two‐step acoustic/viscous splitting technique. An optimized high order dispersion–relation–preserving scheme is used for the solution of the acoustic field. The acoustic field generated by a corotating vortex pair is obtained using the above technique. The computed sound field is compared with the existing analytic solution. Results are in good agreement with the analytic solution except near the centre of the vortices where the acoustic pressure becomes singular. The governing equations for acoustic fluctuations are then linearized and solved for the same model problem. The difference between non‐linear and linearized solutions falls below the numerical error of the simulation. However, a considerable saving in CPU time usage is achieved in solving the linearized equations. The results indicate that the linearized acoustic/viscous splitting technique for the simulation of acoustic fluctuations generation and propagation by low Mach number flow fields seems to be very promising for three‐dimensional problems involving complex geometries. Copyright © 2003 John Wiley & Sons, Ltd.     

Theoretical study on thermal behavior of passively Q-switched microchip Nd:YAG laser

This study deals with the thermal characterization of a continuous wave (CW-) and end-pumped passively Q-switched microchip Nd:YAG laser crystal by solving the rate and heat transfer equations in the laser cavity. In this approach, a parametric study has been performed to investigate the influence of the pumping parameters, cooling metal dimension and also the crystal dimension and doping concentration on the thermal behavior of the laser crystal. Obtained results reveal a closed correlation between the mentioned parameters and the thermal behavior of the crystal indicating that a proper selection of the laser parameters is essential to control the crystal's temperature and improve the performance of the laser accordingly.