Heuristics for the multi-depot petrol station replenishment problem with time windows

In the multi-depot petrol station replenishment problem with time windows (MPSRPTW), the delivery of petroleum products stored in a number of different petroleum depots to a set of petrol distribution stations has to be optimized. Each depot has its own fleet of heterogeneous and compartmented tank trucks. Stations specify their demand by indicating the minimum and maximum quantities to be delivered for each ordered product and require the delivery within a predetermined time window. Several inter-related decisions must be made simultaneously in order to solve the problem. For this problem, the set of feasible routes to deliver all the demands, the departure depot for each route, the quantities of each product to be delivered, the assignment of these routes to trucks, the time schedule for each trip, and the loading of the ordered products to different tanks of the trucks used need to be determined. In this paper, we propose a mathematical model that selects, among a set of feasible trips, the subset that allows the delivery of all the demands while maximizing the overall daily net revenue. If this model is provided with all possible feasible trips, it determines the optimal solution for the corresponding MPSRPTW. However, since the number of such trips is often huge, we developed a procedure to generate a restricted set of promising feasible trips. Using this restricted set, the model produces a good but not necessarily optimal solution. Thus the proposed solution process can be seen as a heuristic. We report the results of the extensive numerical tests carried out to assess the performance of the proposed heuristic. In addition, we show that, for the special case of only one depot, the proposed heuristic outperforms a previously published solution method.     

An exact method with variable fixing for solving the generalized assignment problem

We propose a simple exact algorithm for solving the generalized assignment problem. Our contribution is twofold: we reformulate the optimization problem into a sequence of decision problems, and we apply variable-fixing rules to solve these effectively. The decision problems are solved by a simple depth-first lagrangian branch-and-bound method, improved by our variable-fixing rules to prune the search tree. These rules rely on lagrangian reduced costs which we compute using an existing but little-known dynamic programming algorithm.     

Genetic algorithm based approach for the integrated airline crew-pairing and rostering problem

Airline crew scheduling problem is a complex and difficult problem faced by all airline companies.To tackle this problem, it was often decomposed into two subproblems solved successively. First, the airline crew-pairing problem, which consists on finding a set of trips – called pairings – i.e. sequences of flights, starting and ending at a crew base, that cover all the flights planned for a given period of time. Secondly, the airline crew rostering problem, which consists on assigning the pairings found by solving the first subproblem, to the named airline crew members. For both problems, several rules and regulations must be respected and costs minimized.It is sure that this decomposition provides a convenient tool to handle the numerous and complex restrictions, but it lacks, however, of a global treatment of the problem. For this purpose, in this study we took the challenge of proposing a new way to solve both subproblems simultaneously. The proposed approach is based on a hybrid genetic algorithm. In fact, three heuristics are developed here to tackle the restriction rules within the GA’s process.     

DNS and LES of spark ignition with an automotive coil

The cycle to cycle combustion variability which is observed in spark-ignition engines is often caused by fluctuations of the early flame development. LES can be exploited for a better understanding and mastering of their origins. For that purpose appropriate models taking into account energy deposition, mixture ignition and transition to propagation are necessary requirements. This paper presents first DNS and LES of spark ignition with a real automotive coil and simplified pin-pin electrodes. The electrical circuit characteristics are provided by ISSIM while the energy deposition is modelled by Lagrangian particles. The ignition model is first evaluated in terms of initial spark radius on a pin-pin ignition experiment in pure air performed at CORIA and EM2C laboratories, showing that it pilots the radius of the torus formed by the initial shock wave. DNS of a quiescent lean propane/air mixture are then performed with this ignition system and a two-step mechanism. The impact of the modelled transferred energy during glow phase as well as the initial arc radius on the minimum ignition energy (MIE) are examined and compared to experimental values. Replacing the two-step chemistry by an analytically reduced mechanism leads to similar MIE but shows a different ignition kernel shape. Finally, LES of turbulent ignition using a Lagrangian arc model show a realistic prediction of the arc shape and its important role on the energy transfer location and thus on the flame kernel shape.     

Simplicité abstraite des groupes de Kac–Moody non affines

We announce the simplicity of non-affine Kac–Moody lattices (modulo center). The groups under consideration are minimal Kac–Moody groups. They were defined by Jacques Tits by means of a presentation à la Steinberg. The ground field is finite, assumed to be of cardinality greater than the rank of the buildings these groups naturally act upon. We work in the general combinatorial context of twin root data. To cite this article: P.-E. Caprace, B. Rémy, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov’s ‘homological projective duality.’ Along the way, we shall see how ‘noncommutative spaces’ (in Kontsevich’s sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.     

Constrained regulation of continuous Petri nets

This paper deals with constrained regulation of continuous Petri nets under the so-called infinite servers semantics. Our aim is to design feedback gains that permit us to reach both desired stationary marking vector and desired asymptotic firing rate vector. The proposed approach takes into account constraints on the control, the marking of the Petri net, and the stability of the closed-loop system. The existence of a solution is first expressed geometrically, in terms of the inclusion of two polyhedral sets. They are reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem. Finally, an application to an assembly production system is given.     

Adiabatic and nonadiabatic dynamics in the CH3(CD3)+HCl reaction

The scattering dynamics leading to the formation of Cl (2P(3/2)) and Cl* (2P(1/2)) products of the CH(3)+HCl reaction (at a mean collision energy =22.3 kcal mol(-1)) and the Cl (2P(3/2)) products of the CD(3)+HCl reaction (at =19.4 kcal mol(-1)) have been investigated by using photodissociation of CH(3)I and CD(3)I as sources of translationally hot methyl radicals and velocity map imaging of the Cl atom products. Image analysis with a Legendre moment fitting procedure demonstrates that, in all three reactions, the Cl/Cl* products are mostly forward scattered with respect to the HCl in the center-of-mass (c.m.) frame but with a backward scattered component. The distributions of the fraction of the available energy released as translation peak at f(t)=0.31-0.33 for all the reactions, with average values that lie in the range =0.42-0.47. The detailed analysis indicates the importance of collision energy in facilitating the nonadiabatic transitions that lead to Cl* production. The similarities between the c.m.-frame scattering and kinetic energy release distributions for Cl and Cl* channels suggest that the nonadiabatic transitions to a low-lying excited potential energy surface (PES) correlating to Cl* products occur after passage through the transition state region on the ground-state PES. Branching fractions for Cl* are determined to be 0.14+/-0.02 for the CH(3)+HCl reaction and 0.20+/-0.03 for the CD(3)+HCl reaction. The difference cannot be accounted for by changes in collision energy, mass effects, or vibrational excitation of the photolytically generated methyl radical reagents and instead suggests that the low-frequency bending modes of the CD(3)H or CH(4) coproduct are important mediators of the nonadiabatic couplings occurring in this reaction system.     

Dicobalt hexacarbonyl complexes of alkynyl imines in a sequential Staudinger/Pauson-Khand process. A route to new fused tricyclic beta-lactams

Dicobalt hexacarbonyl complexes of alkynyl imines were allowed to react with ketenes via Staudinger reaction. Sequential [2 + 2] cycloaddition/Pauson-Khand reaction led to structurally new fused-tricyclic beta-lactams and fused-azabicyclic cyclopentenones. Chemoselectivity, scope, and limitation of the process were investigated.     

The acidity functions of trifluoroethanol and hexafluoroisopropanol,and their mixtures with water

Acidity measurements in trifluoroethanol and hexafluoroisopropanol as solvents, and in their mixtures with water, are reported. The hydrogen electrode and the glass electrode were used for pH measurements. The “experimental” autoprotolysis constants were determined from measurements in strongly acidic (trifluoromethanesulfonic) media and in strongly basic (alcoholate) media: for trifluoroethanol, pK = -log K/mol² l^-2 = 15 and for hexafluoroisopropanol, pK = 14.8. Evaluation of the pH-indicator potential systems with reference to the ferrocene/ferricinium couple gives the acidity function R₀(H). The values obtained are compared to the H₀ values evaluated in the same conditions.