Exploiting Local Optimality and Strong Inequalities for Solving Bilevel Combinatorial and Submodular Optimization Problems

Bilevel combinatorial and submodular optimization problems arise in a broad range of real-life applications including price setting, network design, information gathering, viral marketing, and so on. However, the current state-of-the-art solution approaches still have difficulties to solve them exactly for many broad classes of practically relevant problems. In this dissertation, using the concepts of local optimality and strong valid inequalities, we explore the fundamental mathematical structure of these problems and boost the computational performance of exact solution methods for these two important classes of optimization problems. In our initial study, we focus on a class of bilevel spanning tree (BST) problems, motivated by a hierarchical (namely, bilevel) generalization of the classical minimum spanning tree problem. We show that depending on the type of the objective function involved at each level, BST can be solved to optimality either in polynomial time by a specialized algorithm or via a mixed-integer linear programming (MILP) model solvable by an off-the-shelf solver. The latter case corresponds to an NP-hard class of the problem. Our second study proposes a hierarchy of upper and lower bounds for the bilevel problems, where the follower’s variables are all binary. In particular, we develop a generalized bilevel framework that explores the local optimality conditions at the lower level. Submodularity and disjunctive-based approach are then exploited to derive strong MILP formulations for the resulting framework. Computational experiments indicate that the quality of our newly proposed bounds is superior to the current standard approach. Furthermore, we generalize our aforementioned results for BST and show that the proposed bounds are sharp for bilevel matroid problems. Finally, to address the computational challenges in the submodular maximization problem, we present the polyhedral study of its mixed 0–1 set. Specifically, we strengthen some existing results in the literature by finding two families of facet-defining inequalities through the lens of sequence independent lifting. We further extend the scope of this work and describe the multi-dimensional sequence independent lifting for a more complex set. The developed polyhedral results complement the classical results from the literature for the mixed0–1 knapsack and single-node flow sets

Consolidation considering clogging

In land reclamation projects, the vacuum preloading method has been widely used to strengthen dredged fills by removing water. However, during the improvement process, clogging inevitably occurs in the drains and soils, hindering water drainage and causing inhomogeneous consolidation results. Therefore, it is essential to evaluate the effect of clogging on the consolidation behavior of dredged slurry at different radii. In this study, analytical solutions are derived under an uneven strain assumption to calculate the consolidation in the clogging zone and the normal zone, with time-dependent discharge capacity and clogging in the soil considered. Results calculated by the proposed solutions indicated that the clogging effect slows down the development of consolidation, reduces the final consolidation degree, and increases the difference between consolidations at different radii. It is found that the influence of the clogging effect's varies with the speed of the discharge capacity decay, the value of the initial discharge capacity of the drain, the permeability, and the radius of the clogging zone. Finally, a practical application of the proposed solution is discussed, and the proposed solution is suggested for the calculation of consolidation when treating high-water-content slurry

Dual‐Salt Electrolyte Additives Enabled Stable Lithium Metal Anode/Lithium–Manganese‐Rich Cathode Batteries

Although lithium (Li) metal anode/lithium–manganese-rich (LMR) cathode batteries have an ultrahigh energy density, the highly active Li metal and structural deterioration of LMR can make the usage of these batteries difficult. Herein, a multifunctional electrolyte containing LiBF4 and LiFSI dual-salt additives is designed, which enables the superior cyclability of Li/LMR cells with capacity retentions of ≈83.4%, 80.4%, and 76.6% after 400 cycles at 0.5, 1, and 2 C, respectively. The dual-salt electrolyte can form a thin, uniform, and inorganic species-rich solid electrolyte interphase (SEI) and cathode electrolyte interphase (CEI). In addition, it alleviates the bulk Li corrosion and enhances the structural sustainability of LMR cathode. Moreover, the electrolyte design strategy provides insights to develop other high-voltage lithium metal batteries (HVLMBs) to enhance the cycle stability

Revealing the Various Electrochemical Behaviors of Sn4P3 Binary Alloy Anodes in Alkali Metal Ion Batteries

Sn4P3 binary alloy anode has attracted much attention, not only because of the synergistic effect of P and Sn, but also its universal popularity in alkali metal ion batteries (AIBs), including lithium-ion batteries (LIBs), sodium-ion batteries (SIBs), and potassium-ion batteries (PIBs). However, the alkali metal ion (A+) storage and capacity attenuation mechanism of Sn4P3 anodes in AIBs are not well understood. Herein, a combination of ex situ X-ray diffraction, transmission electron microscopy, and density functional theory calculations reveals that the Sn4P3 anode undergoes segregation of Sn and P, followed by the intercalation of A+ in P and then in Sn. In addition, differential electrochemical curves and ex situ XPS results demonstrate that the deep insertion of A+ in P and Sn, especially in P, contributes to the reduction in capacity of AIBs. Serious sodium metal dendrite growth causes further reduction in the capacity of SIBs, while in PIBs it is the unstable solid electrolyte interphase and sluggish dynamics that lead to capacity decay. Not only the failure mechanism, including structural deterioration, unstable SEI, dendrite growth, and sluggish kinetics, but also the modification strategy and systematic analysis method provide theoretical guidance for the development of other alloy-based anode materials. © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH Gmb

Strain regulating and kinetics accelerating of micro-sized silicon anodes via dual-size hollow graphitic carbons conductive additives

Micro-sized silicon (mu Si) anode features fewer interfacial side reactions and lower costs compared to nanosized silicon, and has higher commercial value when applied as a lithium-ion battery (LIB) anode. However, the high localized stress generated during (de)lithiation causes electrode breakdown and performance deterioration of the mu Si anode. In this work, hollow graphitic carbons with tailored dual sizes are employed as conductive additives for the mu Si anode to overcome electrode failure. The dual-size hollow graphitic carbons (HGC) additives consist of particles with micrometer size similar to the mu Si particles; these additives are used for strain regulation. Additionally, nanometer-size particles similar to commercial carbon black Spheron (SP) are used mainly for kinetics acceleration. In addition to building an efficient conductive network, the dual-size hollow graphitic carbon conductive additive prevents the fracture of the electrode by reducing local stress and alleviating volume expansion. The mu Si anode with dual-size hollow graphitic carbons as conductive additives achieves an impressive capacity of 651.4 mAh g(-1) after 500 cycles at a high current density of 2 A g(-1). These findings suggest that dual-size hollow graphitic carbons are expected to be superior conductive additives for micro-sized alloy anodes similar to mu Si.Web of Scienc

Revealing the various electrochemical behaviors of Sn4P3 binary alloy anodes in alkali metal ion batteries

Sn4P3 binary alloy anode has attracted much attention, not only because of the synergistic effect of P and Sn, but also its universal popularity in alkali metal ion batteries (AIBs), including lithium-ion batteries (LIBs), sodium-ion batteries (SIBs), and potassium-ion batteries (PIBs). However, the alkali metal ion (A(+)) storage and capacity attenuation mechanism of Sn4P3 anodes in AIBs are not well understood. Herein, a combination of ex situ X-ray diffraction, transmission electron microscopy, and density functional theory calculations reveals that the Sn4P3 anode undergoes segregation of Sn and P, followed by the intercalation of A(+) in P and then in Sn. In addition, differential electrochemical curves and ex situ XPS results demonstrate that the deep insertion of A(+) in P and Sn, especially in P, contributes to the reduction in capacity of AIBs. Serious sodium metal dendrite growth causes further reduction in the capacity of SIBs, while in PIBs it is the unstable solid electrolyte interphase and sluggish dynamics that lead to capacity decay. Not only the failure mechanism, including structural deterioration, unstable SEI, dendrite growth, and sluggish kinetics, but also the modification strategy and systematic analysis method provide theoretical guidance for the development of other alloy-based anode materials.Web of Science3131art. no. 210204

Accelerating O-redox kinetics with carbon nanotubes for stable lithium-rich cathodes

Lithium-rich cathodes (LRCs) show great potential to improve the energy density of commercial lithium-ion batteries owing to their cationic and anionic redox characteristics. Herein, a complete conductive network using carbon nanotubes (CNTs) additives to improve the poor kinetics of LRCs is fabricated. Ex situ X-ray photoelectron spectroscopy first demonstrates that the slope at a low potential and the following long platform can be assigned to the transition metal and oxygen redox, respectively. The combination of galvanostatic intermittent titration technique and electrochemical impedance spectroscopy further reveal that a battery with CNTs exhibited accelerated kinetics, especially for the O-redox process. Consequently, LRCs with CNTs exhibit a much better rate and cycling performance (approximate to 89% capacity retention at 2 C for over 200 cycles) than the Super P case. Eventually, TEM results imply that the improved electrochemical performance of the CNTs case also benefits from its more stable bulk and surface structures. Such a facile conductive additive modification strategy also provides a universal approach for the enhancement of the electron diffusion properties of other electrode materials.Web of Science67art. no. 220044

Investigating the jamming of particles in a three-dimensional fluid-driven flow via coupled CFD–DEM simulations

The clogging of a dense stream of particles when passing through an orifice occurs ubiquitously in both natural and industrial fields. Since most of the jamming phenomena lead to the negative effects, studying and preventing jamming is of great importance. There are two typical types of jamming due to different types of driving force: (a) gravity-driven jamming and (b) fluid-driven jamming. Among these two types of jamming, the fluid-driven jamming occurs in fluid-driven particle flows, and the initial solid concentration, the fluid velocity, and the orifice-particle size ratio has been demonstrated to have effects on the occurrence of this jamming. Although the individual influence of the initial solid concentration and orifice-particle size ratio on jamming has been studied, the coupled effects of these two factors on jamming are little known. In addition, the complex effects of the fluid velocity on jamming have not been fully discussed. To address these problems, this work performs a three-dimensional simulation of the fluid-driven jamming using the coupled Computational Fluid Dynamics–Discrete Element Method (CFD–DEM) model. At first, the jamming probability under different initial conditions is studied. The jamming probability is displayed on the solid concentration–orifice size ratio plane to illustrate the coupled effects of these two factors on jamming. The simulation results show that the critical solid concentration, at which the jamming probability increases to 1, increases with the orifice-particle size ratio. This is because an orifice with a larger orifice size ratio has a greater particle discharge capacity, which allows more particles to pass through without jamming. Then, we reveal the influence of fluid velocity over a wide range on the fluid-driven jamming type, jamming probability and shape of the jamming dome. To the author’s knowledge, this is the first time that the shape of the jamming dome has been related to the fluid velocity. The jamming dome formed in the higher-speed flow has a greater curvature due to the greater fluid drag acting on the particles

The equivalent stiffness of a saturated poroelastic halfspace interacting with an infinite beam under a moving point load

The equivalent stiffness of a saturated poroelastic halfspace that supports an infinite Euler-Bernoulli beam under a moving point load has been investigated in this paper. The smooth contact condition is assumed for the interface of beam and halfspace, however, with an improved continuity condition, i.e. the continuities of contact normal stress and contact vertical displacements are imposed across the width of the beam. The equivalent stiffness of the halfspace has been evaluated using a contour integration approach such that contributions of the Rayleigh pole and the dispersion branches can be explicitly taken into account. Influences of the continuity condition and the permeability on the equivalent stiffness have been studied. It is found that the imaginary part of the equivalent stiffness is nonzero since the viscous coupling between two phases of the saturated halfspace has been considered. This observation fundamentally differentiates the present paper to the work by Shi and Selvadurai (2016) where an infinite permeability has been assumed for the halfspace, i.e. null viscous coupling

DEDICATION To my parents:

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