A reinforcement learning approach to a single leg airline revenue management problem with multiple fare classes and overbooking

The airline industry strives to maximize the revenue obtained from the sale of tickets on every flight. This is referred to as revenue management and it forms a crucial aspect of airline logistics. Ticket pricing, seat or discount allocation, and overbooking are some of the important aspects of a revenue management problem. Though ticket pricing is usually heavily influenced by factors beyond the control of an airline company, significant amount of control can be exercised over the seat allocation and the overbooking aspects. A realistic model for a single leg of a flight should consider multiple fare classes, overbooking of the flight, concurrent demand arrivals of passengers from the different fare classes, and class-dependent, random cancellations. Accommodating all these factors in one optimization model is a challenging task because that makes it a very large-scale stochastic optimization problem. Almost all papers in the existing literature either accommodate only a subset of these factors or use a discrete approximation in order to make the model tractable. We consider all these factors and cast the single leg problem as a semi-Markov Decision Problem (SMDP) under the average reward optimizing criterion over an infinite time horizon. We solve it using a stochastic optimization technique called Reinforcement Learning. Not only is Reinforcement Learning able to scale up to a huge state-space but because it is simulation-based it can also handle complex modeling assumptions such as the ones mentioned above. The state-space of the numerical test problem scenarios considered here is non-denumerable; its countable part being of the order of 10⁹. Our solution procedure involves a multi-step extension of the SMART algorithm which is based on the one-step Bellman equation. Numerical results presented here show that our approach is able to outperform a heuristic, namely the nested version of the EMSR heuristic, which is widely used in the airline industry. We also present a detailed study of the sensitivity of some modeling parameters via a full factorial experiment.     

On the reformulation of topology optimization problems as linear or convex quadratic mixed 0–1 programs

We consider equivalent reformulations of nonlinear mixed 0–1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. We show that the considered problems can equivalently be cast as either linear or convex quadratic mixed 0–1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design of structures subjected to static or periodic loads, design of composite materials with prescribed homogenized properties using the inverse homogenization approach, optimization of fluids in Stokes flow, design of band gap structures, and multi-physics problems involving coupled steady-state heat conduction and linear elasticity. Several numerical examples of maximum stiffness design of truss structures are presented. The research is funded by the Danish Natural Science Research Council and the Danish Research Council for Technology and Production Sciences.     

Pricing and location decisions in multi-objective facility location problem with M/M/m/k queuing systems

This article presents a new multi-objective model for a facility location problem with congestion and pricing policies. This model considers situations in which immobile service facilities are congested by a stochastic demand following M/M/m/k queues. The presented model belongs to the class of mixed-integer nonlinear programming models and NP-hard problems. To solve such a hard model, a new multi-objective optimization algorithm based on a vibration theory, namely multi-objective vibration damping optimization (MOVDO), is developed. In order to tune the algorithms parameters, the Taguchi approach using a response metric is implemented. The computational results are compared with those of the non-dominated ranking genetic algorithm and non-dominated sorting genetic algorithm. The outputs demonstrate the robustness of the proposed MOVDO in large-sized problems.     

Statistical evaluation of resilient models characterizing coarse granular materials

Consistent material modeling is a prerequisite for a mechanistic approach to pavement design. The scope of this investigation was to statistically evaluate the efficiency of various resilient models commonly encountered in highway engineering. These models were categorized as describing either resilient modulus or shear and volumetric strains. Triaxial tests using constant and cyclic confining pressure were performed on coarse granular materials of various gradings (maximum particle size 90 mm). Two statistical methods, the extra sum of squares F-test and the Akaike information criterion, were used for model comparison. Concerning resilient modulus, the Uzan model provided, in general, a statistically significant improvement compared to the k–θ model. However, this improvement is lost if a constant Poisson ratio is used to predict shear and volumetric strains. In case of the shear–volumetric approach, no single model was most likely to be the best model for all gradings studied.     

Elastoviscoplastic constitutive frameworks for generalized continua

Summary.  A unifying thermomechanical constitutive framework for generalized continua including additional degrees of freedom or/and the second gradient of displacement is presented. Based on the analysis of the dissipation, state laws, flow rules and evolution equations are proposed for Cosserat, strain gradient and micromorphic continua. The case of the gradient of internal variable approach is also incorporated by regarding the nonlocal internal variable as an actual additional degree of freedom. The consistency of the continuum thermodynamical framework is ensured by the introduction of a viscoplastic pseudo–potential of dissipation, thus extending the classical class of so–called standard material models to generalized continua. Variants of the higher order and higher grade theories are also reported based on the explicit introduction of the plastic strain tensor as additional degree of freedom. Within this new class of models, called here gradient of strain models, one recognizes the fact that, in a second grade theory for instance, the plastic part of the strain gradient can be identified with the gradient of plastic strain. Simple examples dealing with bending and shearing of Cosserat or second grade media are given to illustrate two types of extensions of classical J ₂-plasticity : single-criterion and multi-mechanism generalized elastoplasticity. Finally, formulations at finite deformation of the proposed models are provided focusing on proper decompositions of Cosserat curvature, strain gradient and gradient of micromorphic deformation into elastic and viscoplastic parts. Received March 11, 2002 Published online: January 16, 2003     

H 8 fuzzy control for time‐delay affine Takagi‐Sugeno fuzzy models: An ILMI approach

Abstract

This paper deals with the fuzzy based H₈ control problem for time‐delay affine Takagi‐Sugeno (T‐S) fuzzy models. A class of nonlinear time‐delay systems is approximated by a time‐delay affine T‐S fuzzy model in this paper. Based on Lyapunov‐Razumikhin theorem and S‐procedure, the stability and stabilization problems are solved by employing a Parallel Distributed Compensation (PDC) type H₈ fuzzy controller. The synthesis for the time‐delay affine T‐S fuzzy models is a Bilinear Matrix Inequality (BMI) problem and it can not be solved via a convex optimization algorithm. Hence, an Iterative Linear Matrix Inequality (ILMI) algorithm is used to solve the BMI problems in this paper. Finally, a numerical simulation for a delayed pendulum system is given to show the applications of the present approach.     

On the Applicability of the Magnetic Susceptibility Models for the Magnetic Superconductor Ru-1212

The applicability of theoretical models for the ac susceptibility measurements of polycrystalline RuSr₂GdCu₂O₈ superconductor has been examined within the temperature range between 8–50 K, ac magnetic field 0.5–25 G, and frequency 20–12500 Hz. In general, a reasonable qualitative agreement between theory and experiment was attained. An evident and detectable asymmetry was observed within the Cole–Cole polar plots with a peak enhancement for both theoretical and experimental data. The modified critical state models are found to generate much better explanation of the ac susceptibility measured data than Bean’s model. For fields above 20 G, the results are agreed roughly with the Bean critical state model, while below 20 G, the Kim–Anderson model is more suitable to account of the magnetic performance. The temperature and field amplitude dependencies of the flux-creep exponent, n, were extracted from the real part of susceptibility, χ′, dependence on frequency. The flux-creep exponent was found to decrease with both temperature and ac field amplitude in accordance to a power-law of the form: n(T,H)=n ₀(H)T ^−s(H). Such dependence might be an indication of a crossover to flux-creep bundles regime.     

J resistance behavior in functionally graded materials using cohesive zone and modified boundary layer models

This paper describes elastic–plastic crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) under mode I loading conditions using cohesive zone and modified boundary layer (MBL) models. For this purpose, we first explore the applicability of two existing, phenomenological cohesive zone models for FGMs. Based on these investigations, we propose a new cohesive zone model. Then, we perform crack growth simulations for TiB/Ti FGM SE(B) and SE(T) specimens using the three cohesive zone models mentioned above. The crack growth resistance of the FGM is characterized by the J-integral. These results show that the two existing cohesive zone models overestimate the actual J value, whereas the model proposed in the present study closely captures the actual fracture and crack growth behaviors of the FGM. Finally, the cohesive zone models are employed in conjunction with the MBL model. The two existing cohesive zone models fail to produce the desired K–T stress field for the MBL model. On the other hand, the proposed cohesive zone model yields the desired K–T stress field for the MBL model, and thus yields J _R curves that match the ones obtained from the SE(B) and SE(T) specimens. These results verify the application of the MBL model to simulate crack growth resistance in FGMs.     

Local proper generalized decomposition

One of the main difficulties that a reduced‐order method could face is the poor separability of the solution. This problem is common to both a posteriori model order reduction (proper orthogonal decomposition, reduced basis) and a priori [proper generalized decomposition (PGD)] model order reduction. Early approaches to solve it include the construction of local reduced‐order models in the framework of POD. We present here an extension of local models in a PGD—and thus, a priori—context. Three different strategies are introduced to estimate the size of the different patches or regions in the solution manifold where PGD is applied. As will be noticed, no gluing or special technique is needed to deal with the resulting set of local reduced‐order models, in contrast to most proper orthogonal decomposition local approximations. The resulting method can be seen as a sort of a priori manifold learning or nonlinear dimensionality reduction technique. Examples are shown that demonstrate pros and cons of each strategy for different problems.     

Interaction study of indigo carmine with albumin and dextran by NMR relaxation

In this study, the interaction processes between a dye (indigo carmine) and two different macromolecular models were studied with the aim to obtain physical-chemistry information about the dyeing of textiles. Two macromolecules, albumin and dextran (DX), were chosen to simulate wool and cotton fibers during the coloration procedure in water. Proton NMR selective and non-selective spin–lattice relaxation rate measurements were used to monitor the strength of the overall complexation behavior of indigo carmine toward albumin or DX. The affinity index, a quantitative parameter related to the strength of the ligand–macromolecule interaction, was determined from selective spin–lattice relaxation rate enhancements due to the bound ligand molar fraction. Moreover, this approach allowed the calculation of the equilibrium constant of the complex formation (K) between the dye and macromolecular models. NMR data suggested a higher indigo carmine–albumin complex thermodynamic stability with respect to the indigo carmine–DX adduct. These results indicate a stronger persistence of the dyeing process in wool with respect to cotton fibers, in agreement with literature data.     

Pair Excitations and Vertex Corrections in Fermi Fluids

Based on an equations–of–motion approach for time–dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known “correlated” random–phase approximation (CRPA), our approach has the following properties: (i) The CRPA is reproduced when pair fluctuations are neglected. (ii) The first two energy–weighted sumrules are fulfilled implying a correct static structure. (iii) No ad–hoc assumptions for the effective mass are needed to reproduce the experimental dispersion of the zero sound mode in ³He. (iv) The density response function displays a novel form, arising from vertex corrections in the proper polarisation. Our theory is presented here with special emphasis on this latter point. We have also extended the approach to the single particle self-energy and included pair fluctuations in the same way. The theory provides a diagrammatic superset of the familiar GW approximation. It aims at a consistent calculation of single particle excitations with an accuracy that has previously only been achieved for impurities in Bose liquids.     

Optimization of a Graphite Tube Blackbody Heater for a Thermogage Furnace

Design modifications are presented for a 289-mm long, 25.4-mm inner diameter blackbody heater element of a 48 kW Thermogage blackbody furnace, based on (i) cutting a small “heater zone” into the ends of the tube and (ii) using a mixture of He and Ar or N₂ to “tune” the heat losses and, hence, gradients in the furnace. A simple numerical model for the heater tube is used to model and optimize these design changes, and experimental measurements of the modified temperature profile are presented. The convenience of the Thermogage graphite-tube furnace, commonly used in many NMIs as a blackbody source for radiation–thermometer calibration and as a spectral irradiance standard, is limited by its effective emissivity, typically between 99.5% and 99.9%. The design simplicity of the furnace is that the blackbody cavity, heater, and electrical and mechanical connections are achieved through a single piece of machined graphite. As the heater also performs a mechanical function, the required material thickness leads to significant axial heat flux and resulting temperature gradients. For operation at a single temperature, changes to the tube profile could be used to optimize the gradient. However, it is desired to use the furnace over a wide temperature range (1,000–2,900°C), and the temperature-dependence of the electrical conductivity and thermal conductivity, and that of the insulation, makes this approach much more complex; for example, insulation losses are proportional to T ⁴, whereas conduction losses are proportional to T. In the results presented here, a slightly thinner graphite region near each end of the tube was used to “inject heat” to compensate for the axial conduction losses, and the depth, width, and position of this region was adjusted to achieve a compromise in performance over a wide temperature range. To assist with this optimization, the insulation purging gas was changed from N₂ to He at the lower temperatures to change the thermal conductivity of the felt insulation, and the effectiveness of this approach has been experimentally confirmed.     

Intensity-modulated radiotherapy – a large scale multi-criteria programming problem

Abstract. Radiation therapy planning is often a tight rope walk between dangerous insufficient dose in the target volume and life threatening overdosing of organs at risk. Finding ideal balances between these inherently contradictory goals challenges dosimetrists and physicians in their daily practice. Todays inverse planning systems calculate treatment plans based on a single evaluation function that measures the quality of a radiation treatment plan. Unfortunately, such a one dimensional approach cannot satisfactorily map the different backgrounds of physicians and the patient dependent necessities. So, too often a time consuming iterative optimization process between evaluation of the dose distribution and redefinition of the evaluation function is needed. In this paper we propose a generic multi-criteria approach based on Pareto's solution concept. For each entity of interest – target volume or organ at risk – a structure dependent evaluation function is defined measuring deviations from ideal doses that are calculated from statistical functions. A reasonable bunch of clinically meaningful Pareto optimal solutions are stored in a data base, which can be interactively searched by physicians. The system guarantees dynamic planning as well as the discussion of tradeoffs between different entities. Mathematically, we model the inverse problem as a multi-criteria linear programming problem. Because of the large scale nature of the problem it is not possible to solve the problem in a 3D-setting without adaptive reduction by appropriate approximation schemes. Our approach is twofold: First, the discretization of the continuous problem results from an adaptive hierarchical clustering process which is used for a local refinement of constraints during the optimization procedure. Second, the set of Pareto optimal solutions is approximated by an adaptive grid of representatives that are found by a hybrid process of calculating extreme compromises and interpolation methods. Correspondence to: K.-H. Küfer     

A finite strain framework for the simulation of polymer curing. Part II. Viscoelasticity and shrinkage

A phenomenologically inspired, elastic finite strain framework to simulate the curing of polymers has been developed and discussed in the first part (Hossain et al. in Comput Mech 44(5):621–630, 2009) of this work. The present contribution provides an extension of the previous simulation concept towards the consideration of viscoelastic effects and the phenomenon of curing shrinkage. The proposed approach is particularly independent of the type of the free energy density, i.e. any phenomenologically or micromechanically based viscoelastic polymer model can be utilised. For both cases the same representatives that have been used for the elastic curing models, i.e. the Neo-Hookean model and the 21-chain microsphere model, are reviewed and extended accordingly. The governing equations are derived as well as the corresponding tangent operators necessary for the numerical implementation within the finite element method. Furthermore, we investigate two different approaches—a shrinkage strain function and a multiplicative decomposition of the deformation gradient–to capture the phenomenon of curing shrinkage, i.e. the volume reduction induced by the polymerisation reaction which may lead to significant residual stresses and strains in the fully cured material. Some representative numerical examples conclude this work and prove the capability of our approach to correctly capture inelastic behaviour and shrinkage effects in polymers undergoing curing processes.     

A Thermodynamic Property Model for the Binary Mixture of Methane and Hydrogen Sulfide

A thermodynamic property model with new mixing rules using the Helmholtz free energy is presented for the binary mixture of methane and hydrogen sulfide based on experimental P_ρ T_x data, vapor–liquid equilibrium data, and critical-point properties. The binary mixture of methane and hydrogen sulfide shows vapor–liquid–liquid equilibria and a divergence of the critical curve. The model represents the existing experimental data accurately and describes the complicated behavior of the phase equilibria and the critical curve. The uncertainty in density calculations is estimated to be 2%. The uncertainty in vapor–liquid equilibrium calculations is 0.02 mole fraction in the liquid phase and 0.03 mole fraction in the vapor phase. The model also represents the critical points with an uncertainty of 2% in temperature and 3% in pressure. Graphical and statistical comparisons between experimental data and the available thermodynamic models are discussed     

MQSPR modeling in materials informatics: a way to shorten design cycles?

We demonstrate applications of quantitative structure–property relationship (QSPR) modeling to supplement first-principles computations in materials design. We have here focused on the design of polymers with specific electronic properties. We first show that common materials properties such as the glass transition temperature (T _g) can be effectively modeled by QSPR to generate highly predictive models that relate polymer repeat unit structure to T _g. Next, QSPR modeling is shown to supplement and guide first-principles density functional theory (DFT) computations in the design of polymers with specific dielectric properties, thereby leveraging the power of first-principles computations by providing high-throughput capability. Our approach consists of multiple rounds of validated MQSPR modeling and DFT computations to optimize the polymer skeleton as well as functional group substitutions thereof. Rigorous model validation protocols insure that the statistical models are able to make valid predictions on molecules outside the training set. Future work with inverse QSPRs has the potential to further reduce the time to optimize materials properties.     

ADAPTIVE RESPONSE SURFACE METHOD - A GLOBAL OPTIMIZATION SCHEME FOR APPROXIMATION-BASED DESIGN PROBLEMS

For design problems involving computation-intensive analysis or simulation processes, approximation models are usually introduced to reduce computation lime. Most approximation-based optimization methods make step-by-step improvements to the approximation model by adjusting the limits of the design variables. In this work, a new approximation-based optimization method for computation-intensive design problems - the adaptive response surface method(ARSM), is presented. The ARSM creates quadratic approximation models for the computation-intensive design objective function in a gradually reduced design space. The ARSM was designed to avoid being trapped by local optima and to identify the global design optimum with a modest number of objective function evaluations. Extensive tests on the ARSM as a global optimization scheme using benchmark problems, as well as an industrial design application of the method, are presented. Advantages and limitations of the approach are also discussed     

Rheological and hydrodynamic characteristics of high-concentration suspensions of water-soluble polymers

Investigation is made of rheological and hydrodynamic characteristics of the high-concentration suspensions of water-soluble polymers used to solve one of the most important problems of energy conservation: to decrease conservationsin pipeline transport of liquids and in external flows around bodies. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 3, pp. 436–441, May–June, 1997.     

Simultaneous optimal design of structural topology, actuator locations and control parameters for a plate structure

 Simultaneous optimization with respect to the structural topology, actuator locations and control parameters of an actively controlled plate structure is investigated in this paper. The system consists of a clamped-free plate, a H ₂ controller and four surface-bonded piezoelectric actuators utilized for suppressing the bending and torsional vibrations induced by external disturbances. The plate is represented by a rectangular design domain which is discretized by a regular finite element mesh and for each element the parameter indicating the presence or absence of material is used as a topology design variable. Due to the unavailability of large-scale 0–1 optimization algorithms, the binary variables of the original topology design problem are relaxed so that they can take all values between 0 and 1. The popular techniques in the topology optimization area including penalization, filtering and perimeter restriction are also used to suppress numerical problems such as intermediate thickness, checkerboards, and mesh dependence. Moreover, since it is not efficient to treat the structural and control design variables equally within the same framework, a nested solving approach is adopted in which the controller syntheses are considered as sub processes included in the main optimization process dealing with the structural topology and actuator locations. The structural and actuator variables are solved in the main optimization by the method of moving asymptotes, while the control parameters are designed in the sub optimization processes by solving the Ricatti equations. Numerical examples show that the approach used in this paper can produce systems with clear structural topology and high control performance. Received 16 November 2001 / Accepted 26 February 2002