Developing a New Reformulation of Single Level Capacitated Lot Sizing Problem (SLCLSP) with Set up, Shortage and Inventory Costs

Formulation of SLCLSP given by Pochet and Wolsey [1] had set up, variables, inventory and shortage cost. We give a new reformulation where SLCLSP is reduced to set up and inventory variables. We find that this reformulation has less number of real variables than the reformulation of Pochet and Wolsey [1]. It is argued that this leads to computations advantages, and this is supported by the empirical investigation that we carried out.

A Reformulation of Newton Second Law for Charged Particles and Its Application to Quantum Dynamics

We propose a reformulation of Newton’s second law of motion for charged particles and possible applications of the reformulation to quantum dynamics. We show that the negative energy states arising from the Dirac equation in relativistic quantum mechanics can be verified using the reformulating framework. We also discuss possible hidden dynamics underlying the concept of quantum jumps in quantum mechanics as outlined in Schrödinger’s article: ARE THERE QUANTUM JUMPS? In this case, we show that the hidden dynamics of quantum jumps are also determined by the Coulomb interaction between charged particles.

Decomposition and Reformulation of Banxia Baizhu Tianma Decoction:A Vasodilatory Approach

Objective To decompose and reformulate Banxia Baizhu Tianma Decoction（BBT） in order to optimize its ratio for vasodilatory effect.The fingerprints of these six component herbs were also studied via Tri-step FTIR analysis.Methods The herbal components of BBT were extracted separately with different solvents,such as 95%ethanol,50%ethanol,and distilled water.The vasodilatory effect of the extracts was studied using the in vitro pre-contracted aortic ring model.Among these extracts,the water extracts of Pinellia ternata[PT（W）]and Citri reticulatae[CR（W）],50%ethanol extracts of Castrodia elata[GE（50）]and Clycyrrhiza uralensis[GU（50）],and 95%ethanol extracts of Atractylodes macrocephala[AM（E）],and Poria cocos[PC（E）]were selected for the orthogonal stimulus-response compatibility group study due to their high effectiveness in vasodilation.Results The best combination ratio（G2） was GE（50）,GU（50）,AM（E）,PC（E）,CR（W）,and PT（W） at EC0,EC5,EC5,EC5,EC5,and EC5,with EC50 of（0.06 ± 0.01） mg/mL.Comparison between the vasodilatory effects of extracts derived from G2 and BBT were also studied.From the results,the 50%ethanol extract following G2 ratio was found to be most potent extract with the highest vasodilatory effect compared with other extracts derived from G2 or BBT,with EC50 of（0.05 ±0.005） mg/mL.Conclusion The optimum ratio and appropriate extraction method for the new BBT formulae are obtained.G2 is determined as the best formulae with the highest potency in producing the vasodilatory effect on isolated rat aortic rings.The results obtained suggest that 50%ethanol is found to be the best solvent to extract the vasoactive compounds of G2 in order to exhibit the highest efficacy of vasodilatory effect.

Convex Reformulation for Two-sided Distributionally Robust Chance Constraints with Inexact Moment Information

Constraints on each node and line in power systems generally have upper and lower bounds,denoted as twosided constraints.Most existing power system optimization methods with the distributionally robust(DR)chance-constrained program treat the two-sided DR chance constraint separately,which is an inexact approximation.This letter derives an equivalent reformulation for the generic two-sided DR chance constraint under the interval moment based ambiguity set,which does not require the exact moment information.The derived reformulation is a second-order cone program(SOCP)formulation and is then applied to the optimal power flow(OPF)problem under uncertainty.Numerical results on several IEEE systems demonstrate the effectiveness of the proposed SOCP formulation and show the differences with other DR chance-constrained OPF approaches.

Study on reformulation of fluid catalytic cracking gasoline and increasing production of light olefins

The effects of reaction temperature,mass ratio of catalystto oil,space velocity,andmass ratio of water to oil on the product distribution,the yields of light olefins(light olefins including ethylene,propylene and butylene)and the composition of the fluid catalytic cracking(FCC)gasoline upgraded over the self-made catalyst GL in a confined fluidized bed reactor were investigated.The experimental results showed that FCC gasoline was obviously reformulated under appropriate reaction con-ditions.The olefins(olefins with C atom number above 4)content of FCC gasoline was markedly reduced,and the aromaticscontent andoctanenumber were increased.The upgraded gasoline met the new standard of gasoline,and meanwhile,higher yields of light olefins were obtained.Furthermore,higher reaction temperature,higher mass ratio of catalyst to oil,higher mass ratio of water to oil,and lower space velocity were found to be beneficial to FCC gasoline reformulation and light olefins production.

An Enhanced Conic Reformulation for Capacity-Constrained Assortment Optimization Under the Mixture of Multinomial Logit Model

In this work,we study the conic quadratic mixed-integer formulation for assortment optimization problem under the mixture of multinomial logit(MMNL)model.The MMNL model generalizes the widely studied multinomial logit choice model and can approximate any random utility model with an arbitrary additive error.An important operational decision problem in revenue management is assortment optimization problem,which aims to find a subset of products to make available to customers that maximizes the expected revenue of the retailer.It is known that assortment optimization problem under the MMNL model is NP-hard and inapproximable within any constant performance guarantee.Commonly used methods for solving such problem are heuristical approaches or customized combinatorial optimization approaches.In the meanwhile,studies related to global optimization approaches are relatively scarce.We propose an enhanced conic quadratic mixed-integer formulation for solving assortment optimization problem under the MMNL model with a higher computational efficiency.Furthermore,we conduct extensive numerical experiments to demonstrate that the proposed reformulation significantly outperforms the existing conic reformulations for assortment optimization under the MMNL model.

Mathematical treatment of wave propagation in acoustic waveguides with n curved interfaces

There are some curved interfaces in ocean acoustic waveguides. To compute wave propagation along the range with some marching methods, a flattening of the internal interfaces and a transforming equation are needed. In this paper a local orthogonal coordinate transform and an equation transformation are constructed to flatten interfaces and change the Helmholtz equation as a solvable form. For a waveguide with a flat top, a fiat bottom and n curved interfaces, the coefficients of the transformed Helmholtz equation are given in a closed formulation which can be thought of as an extension of the formal work related to the equation transformation with two curved internal interfaces. In the transformed horizontally stratified waveguide, the one-way reformulation based on the Dirichlet-to-Neumann （DtN） map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method to discretize the range variable and a truncated local eigenfunction expansion to approximate the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. Furthermore, the method can also be applied to wave propagation problems in acoustic waveguides associated with varied density.

Conceptual Design of a Butyl-levulinate Reactive Distillation Process by Incremental Refinement

Butyl-levulinate has been identified as a promising fuel candidate with high oxygen content. Its com- bustion in diesel engines yields very low soot and NOx emissions. It can be produced by the esterification of butanol and levulinic acid, which themselves are platform chemicals in a biorenewables-based chemical supply chain. Since the equilibrium of esterification limits the conversion in a conventional reactor, reactive distillation can be applied to overcome this limitation. The presence of the high-boiling catalyst sulfuric acid requires a further separation step downstream of the reactive distillation column to recover the catalyst for recycle. Optimal design specifications and an optimal operating point are determined using rigorous flowsheet optimization. The challenging optimization problem is solved by a favorable initialization strategy and continuous reformulation. The design identified has the potential to produce a renewable transportation fuel at reasonable cost.

Chinese college students' Web querying behaviors:A case study of Peking University

This study examined users' querying behaviors based on a sample of 30 Chinese college students from Peking University. The authors designed 5 search tasks and each participant conducted two randomly selected search tasks during the experiment. The results show that when searching for pre-designed search tasks, users often have relatively clear goals and strategies before searching. When formulating their queries, users often select words from tasks, use concrete concepts directly, or extract 'central words' or keywords. When reformulating queries, seven query reformulation types were identified from users' behaviors, i.e. broadening, narrowing, issuing new query, paralleling, changing search tools, reformulating syntax terms, and clicking on suggested queries. The results reveal that the search results and/or the contexts can also influence users' querying behaviors.

Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory

A new size-dependent axially functionally graded(AFG) micro-beam model is established with the application of a reformulated strain gradient elasticity theory(RSGET). The new micro-beam model incorporates the strain gradient, velocity gradient,and couple stress effects, and accounts for the material variation along the axial direction of the two-component functionally graded beam. The governing equations and complete boundary conditions of the AFG beam are derived based on Hamilton's principle. The correctness of the current model is verified by comparing the static behavior results of the current model and the finite element model(FEM) at the micro-scale. The influence of material inhomogeneity and size effect on the static and dynamic responses of the AFG beam is studied. The numerical results show that the static and vibration responses predicted by the newly developed model are different from those based on the classical model at the micro-scale. The new model can be applied not only in the optimization of micro acoustic wave devices but also in the design of AFG micro-sensors and micro-actuators.

Recent Advances in Mathematical Programming with Semi-continuous Variables and Cardinality Constraint

Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems.

Polymeric micelle nanocarriers in cancer research

Amphiphilic block copolymers （ABCs） assem- ble into a spherical nanoscopic supramolecular core/shell nanostructure termed a polymeric micelle that has been widely researched as an injectable nanocarrier for poorly water-soluble anticancer agents. The aim of this review article is to update progress in the field of drug delivery towards clinical trials, highlighting advances in polymeric micelles used for drug solubilization, reduced off-target toxicity and tumor targeting by the enhanced permeability and retention （EPR） effect. Polymeric micelles vary in stability in blood and drug release rate, and accordingly play different but key roles in drug delivery. For intravenous （IV） infusion, polymeric micelles that disas- semble in blood and rapidly release poorly water-soluble anticancer agent such as paclitaxel have been used for drug solubilization, safety and the distinct possibility of toxicity reduction relative to existing solubilizing agents, e.g., Cremophor EL. Stable polymeric micelles are long- circulating in blood and reduce distribution to non-target tissue, lowering off-target toxicity. Further, they participate in the EPR effect in murine tumor models. In summary, polymeric micelles act as injectable nanocarriers for poorly water-soluble anticancer agents, achieving reduced toxi- city and targeting tumors by the EPR effect.

Scenario-Based Stochastic Resource Allocation with Uncertain Probability Parameters

The stochastic resource allocation(SRA) problem is an extensive class of combinatorial optimization problems widely existing in complex systems such as communication networks and unmanned systems. In SRA, the ability of a resource to complete a task is described by certain probability,and the objective is to maximize the reward by appropriately assigning available resources to different tasks. This paper is aimed at an important branch of SRA, that is, stochastic SRA(SSRA) for which the probability for resources to complete tasks is also uncertain. Firstly, a general SSRA model with multiple independent uncertain parameters(GSSRA-MIUP) is built to formulate the problem. Then,a scenario-based reformulation which can address multi-source uncertainties is proposed to facilitate the problem-solving process. Secondly, in view of the superiority of the differential evolution algorithm in real-valued optimization, a discrete version of this algorithm was originally proposed and further combined with a specialized local search to create an efficient hybrid optimizer. The hybrid algorithm is compared with the discrete differential evolution algorithm, a pure random sampling method, as well as a restart local search method. Experimental results show that the proposed hybrid optimizer has obvious advantages in solving GSSRA-MIUP problems.

A numerical local orthogonal transform method forstratified waveguides

Flattening of the interfaces is necessary in computing wave propagation along strati?ed waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight line in two adjacent interfaces does not hold, the previously suggested local orthogonal transform method with an analytical formulation is not feasible. This paper presents a numerical coordinate transform and an equation transform to perform the transforms numerically for waveguides without satisfying the supposition. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This method is applicable in solving long-range wave propagation problems in slowly varying waveguides with a multilayered medium structure.

Online gasoline blending with EPA Complex Model for predicting emissions

The empirical Complex Model developed by the US Environmental Protection Agency （EPA） is used by refiners to predict the toxic emissions of reformulated gasoline with respect to gasoline properties. The difficulty in implementing this model in the blending process stems from the implicit definition of Complex Model through a series of disjunctions assembled by the EPA in the form of spreadsheets. A major breakthrough in the refinery-based Complex Model implementation occurred in 2008 and 2010 through the use of generalized disjunctive and mixed- integer nonlinear programming （MINLP）. Nevertheless, the execution time of these MINLP models remains prohibitively long to control emissions with our online gasoline blender. The first objective of this study is to present a new model that decreases the execution time of our online controller. The toxic thresholds as hard second objective is to consider constraints to be verified and search for blends that verify them. Our approach introduces a new way to write the Complex Model without any binary or integer variables. Sigmoid functions are used herein to approximate step functions until the measurement precision for each blend property is reached. By knowing this level of precision, we are able to propose an extremely good and differentiable approximation of the Complex Model. Next, a differentiable objective function is introduced to penalize emission values higher than the threshold emissions. Our optimization module has been implemented and tested with real data. The execution time never exceeded 1 s, which allows the online regulation of emissions the same way as other traditional properties of blended gasoline.