Carpooling problem: A new mathematical model,branch-and-bound,and heuristic beam search algorithm

Carpooling is an environmentally friendly transportation system. It can efficaciously help resolve a variety of societal concerns of the urban areas, ranging from traffic congestion to environmental pollution. In this paper, we propose a new mathematical model to solve the carpooling problem. The model simultaneously minimizes the costs of travel times, the vehicle use, and the vehicle delays. An exact solution method based on Branch-and-Bound (B&B) algorithm is proposed to efficiently obtain the optimal solution of the problem. In order to find the near-optimal solutions for large-scale problems, a heuristic beam search algorithm is introduced, which is based on the partial relaxation of some fathoming criteria applied in our proposed B&B. The computational experiments are conducted, based upon the transportation network of Isfahan city, Iran. The results demonstrate the great capability of the proposed exact solution method in terms of both computational solving time required and the number of the evaluated nodes, in comparison with CPLEX software package. The findings of this research can be applied to solve the carpooling problem compatible to the real-life situations.     

An appropriate unidirectional wave spectrum model for the Strait of Hormuz

The objective of this paper is to introduce an appropriate unidirectional wave spectrum model for the Strait of Hormuz. The research is focused on assessing performance of standard wave spectrum models in the region. By evaluating such models based on valuable measurement data recently published, the calibration procedure has been conducted on such standard models to reach a better concordance between a modified standard spectral model and observed field spectra. The calibration is performed initially with respect to four distinct directions related to four available measurement stations. So, it results in four sets of coefficients for a nominated model. Next, it is continued to reach just one model insensitive to directions. Results clearly showed that the International Towing Tank Conference (ITTC) model is more appropriate than Joint North Sea Wave Project (JONSWAP) and Pierson and Moskowitz (PM) models in this area, even without any calibration. However, modifications have been successful on improving the conformity of the model.     

Numerical investigation of transmission of low frequency sound through a smooth air-water interface

It is the traditional belief that sound transmission from water to the air is very weak due to a large contrast between air and water impedances. Recently, the enhanced sound transmission and anomalous transparency of air-water interface have been introduced. Anomalous transparency of air-water interface states that the sound generated by a submerged shallow depth monopole point source localized at depths less than 1/10 sound wavelength, can be transmitted into the air with omni-directional pattern. The generated sound has 35 times higher power compared to the classical ray theory prediction. In this paper, sound transmission through air-water interface for a localized underwater shallow depth source is examined. To accomplish this, two-phase coupled Helmholtz wave equations in two-phase media of air-water are solved by the commercial finite element based COMSOL Multiphysics software. Ratios of pressure amplitudes of different sound sources in two different underwater and air coordinates are computed and analyzed against non-dimensional ratio of the source depth (D) to the sound wavelength (λ). The obtained results are compared with the experimental data and good agreement is displayed.     

Sound scattering from rough bubbly ocean surface based on modified sea surface acoustic simulator and consideration of various incident angles and sub-surface bubbles’ radii

The aim of the present study is to improve the capabilities and precision of a recently introduced Sea Surface Acoustic Simulator (SSAS) developed based on optimization of the Helmholtz–Kirchhoff–Fresnel (HKF) method. The improved acoustic simulator, hereby known as the Modified SSAS (MSSAS), is capable of determining sound scattering from the sea surface and includes an extended Hall–Novarini model and optimized HKF method. The extended Hall–Novarini model is used for considering the effects of sub-surface bubbles over a wider range of radii of sub-surface bubbles compared to the previous SSAS version. Furthermore, MSSAS has the capability of making a three-dimensional simulation of scattered sound from the rough bubbly sea surface with less error than that of the Critical Sea Tests (CST) experiments. Also, it presents scattered pressure levels from the rough bubbly sea surface based on various incident angles of sound. Wind speed, frequency, incident angle, and pressure level of the sound source are considered as input data, and scattered pressure levels and scattering coefficients are provided. Finally, different parametric studies were conducted on wind speeds, frequencies, and incident angles to indicate that MSSAS is quite capable of simulating sound scattering from the rough bubbly sea surface, according to the scattering mechanisms determined by Ogden and Erskine. Therefore, it is concluded that MSSAS is valid for both scattering mechanisms and the transition region between them that are defined by Ogden and Erskine.     

Multiclass fuzzy user equilibrium with endogenous membership functions and risk‐taking behaviors

Over the last decades, several approaches have been proposed in the literature to incorporate users' perceptions of travel costs, their bounded rationality, and risk‐taking behaviors into network equilibrium modeling for traffic assignment problem. While theoretically advanced, these models often suffer from high complexity and computational cost and often involve parameters that are difficult to estimate. This study proposes an alternative approach where users' imprecise perceptions of travel times are endogenously constructed as fuzzy sets based on the probability distributions of random link travel times. Two decision rules are proposed accordingly to account for users' heterogeneous risk‐taking behaviors, that is, optimistic and pessimistic rules. The proposed approach, namely, the multiclass fuzzy user equilibrium, can be formulated as a link‐based variational inequality model. The model can be solved efficiently, and parameters involved can be either easily estimated or treated as factors for calibration against observed traffic flow data. Numerical examples show that the proposed model can be solved efficiently even for a large‐scale network of Mashhad, Iran, with 2538 links and 7157 origin–destination pairs. The example also illustrates the calibration capability of the proposed model, highlighting that the model is able to produce much more accurate flow estimates compared with the Wardropian user equilibrium model. Copyright © 2016 John Wiley & Sons, Ltd.