Lagrangian Relaxation for Mixed-Integer Linear Programming: Importance, Challenges, Recent Advancements, and Opportunities

Operations in areas of importance to society are frequently modeled as Mixed-Integer Linear Programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve the associated difficulties through decomposition. Due to the non-smooth nature of Lagrangian dual functions, the coordination aspect of the method has posed serious challenges. This paper presents several significant historical milestones (beginning with Polyak's pioneering work in 1967) toward improving Lagrangian Relaxation coordination through improved optimization of non-smooth functionals. Finally, this paper presents the most recent developments in Lagrangian Relaxation for fast resolution of MILP problems. The paper also briefly discusses the opportunities that Lagrangian Relaxation can provide at this point in time

On the Influence of Corpuscular Fluxes and of Electron Photoloosening Reaction on the Formation of the D-Layer of the Ionosphere

Effect of corpuscular fluxes and electron photoloosening reaction on formation of ionospheric D laye

Electron-positron annihilation into two photons in an intense plane-wave field

The process of electron-positron annihilation into two photons in the presence of an intense classical plane wave of an arbitrary shape is investigated analytically by employing light-cone quantization and by taking into account the effects of the plane wave exactly. We introduce a general description of second-order 2-to-2 scattering processes in a plane-wave background field, indicating the necessity of considering the localization of the colliding particles and achieving that by means of wave packets. We define a local cross section in the background field, which generalizes the vacuum cross section and which, though not being directly an observable, allows for a comparison between the results in the plane wave and in vacuum without relying on the shape of the incoming wave packets. Two possible cascade or two-step channels have been identified in the annihilation process and an alternative way of representing the two-step and one-step contributions via a "virtuality" integral has been found. Finally, we compute the total local cross section to leading order in the coupling between the electron-positron field and the quantized photon field, excluding the interference between the two leading-order diagrams arising from the exchange of the two final photons, and express it in a relatively compact form. In contrast to processes in a background field initiated by a single particle, the pair annihilation into two photons, in fact, also occurs in vacuum. Our result naturally embeds the vacuum part and reduces to the vacuum expression, known in the literature, in the case of a vanishing laser field.Comment: 26 pages, 2 figure

Toward Efficient Transportation Electrification of Heavy-Duty Trucks: Joint Scheduling of Truck Routing and Charging

The timely transportation of goods to customers is an essential component of economic activities. However, heavy-duty diesel trucks used for goods delivery significantly contribute to greenhouse gas emissions within many large metropolitan areas, including Los Angeles, New York, and San Francisco. To reduce GHG emissions by facilitating freight electrification, this paper proposes Joint Routing and Charging scheduling for electric trucks. The objective of the associated optimization problem is to minimize the cost of transportation, charging, and tardiness. A large number of possible combinations of road segments as well as a large number of combinations of charging decisions and charging durations leads to a combinatorial explosion in the possible decisions electric trucks can make. The resulting mixed-integer linear programming problem is thus extremely challenging because of the combinatorial complexity even in the deterministic case. Therefore, a Surrogate Level-Based Lagrangian Relaxation (SLBLR) method is employed to decompose the overall problem into significantly less complex truck subproblems. In the coordination aspect, each truck subproblem is solved independently of other subproblems based on the values of Lagrangian multipliers. In addition to serving as a means of guiding and coordinating trucks, multipliers can also serve as a basis for transparent and explanatory decision-making by trucks. Testing results demonstrate that even small instances cannot be solved using the off-the-shelf solver CPLEX after several days of solving. The SLBLR method, on the other hand, can obtain near-optimal solutions within a few minutes for small cases, and within 30 minutes for large ones. Furthermore, it has been demonstrated that as battery capacity increases, the total cost decreases significantly; moreover, as the charging power increases, the number of trucks required decreases as well

Quantitative Estimation of the Ratio of GABA-Immunoreactive Cells in Neocortical Grafts

Somatosensory anlage from 17-18 day old rat embryos were transplanted in place of the removed barrel cortex in adult rats. Six to eight months after transplantation, the grafts were either completely separated by glial scar or partly separated and partly confluent with the host neocortex. Each was studied histologically and immunostained for GABA. It was found that in partly confluent grafts the neuronal density was similar or even higher than in the host cortex, while the cell number in the separate grafts was much lower than in the nearby host cortex. The number of GABA-positive cells, however, was in all grafts significantly lower (2.9% on average) than in the normal cortex (11.8% on average).The decline in GABA-stained nerve cells was highest in separated grafts, but was somewhat less marked in transplants partly confluent with the host tissue. The possible role of partial or total deafferentation as well as the relative vulnerability of the transplanted tissue by temporary hypoxia and other metabolic disturbances are discussed as the probable factors in selective decline of GABA-ergic cells in the transplanted somatosensory cortex

Accelerating Level-Value Adjustment for the Polyak Stepsize

The Polyak stepsize formula has been widely used for convex optimization. However, stepsize computations require the generally unknown optimal value. Dynamic estimations of the optimal value are thus usually needed. In this paper, guided by a decision-based procedure through a novel easy-to-solve ``Polyak Stepsize Violation Detector'' (PSVD) linear constraint satisfaction problem, a series of level values is constructed to successively estimate the optimal value to guarantee convergence for subgradient as well as for approximate subgradient methods. Through a series of empirical tests of convex optimization problems with diverse characteristics, we illustrate the practical advantages of our approach as compared to existing methods

Age-Related Loss of GABA-Positive and GABA-Negative Neurons in Neocortical Transplants

The numerical density of GABA immunopositive and GABA immunonegative neurons was quantitatively determined in 0, 12, 30 and 90 day-old neocortical transplants, derived from E17 rat embryos and transplanted into adult hosts. It was found that the original, very high neuronal density in the fetal transplant declined steadily after transplantation to the somatosensory cortex of adult rat. The decline in numerical density of GABA-positive neurons, however, was disproportionately larger than that of GABA-negative nerve cells: At 90 days the proportion of GABA-positive cells was 2.3% (in contrast to the 11.8% in the adult host cortex). The density of GABA-negative neurons, on the other hand, remained slightly higher than comparable values in the control cortex. The decline in density Of GABA-positive neurons was continuous until the 90th post-transplantation day, while final, close to normal density values of GABA-negative nerve cells were already reached in 30 day-old grafts, with no significant change afterwards

TO THE ISSUE HARDENING OF DRILLING EQUIPMENT PARTS

This paper considers the possibility of optimal hardened layer of parts operating in conditions of high abrasive wear. The experiments on obtaining of parts with a hardened layer, conducted their research of the macro and micro structure of the resulting coating thickness and wear resistance.Южно-Уральский государственный университет выражает благодарность за финансовую поддержку Министерства образования и науки Российской Федерации (грант № 11.9658.2017/БЧ)

Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation

We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations phase-lock with a phase-shift dependent on the strength of local inhibition. Increasing the strength of long-range excitation induces a transition to chaos via period-doubling or quasi-periodic scenarios. In the chaotic regime oscillatory activity undergoes fast temporal decorrelation. The generality of these dynamical properties is assessed in firing-rate models as well as in large networks of conductance-based neurons.Comment: 4 pages, 5 figures. accepted for publication in Physical Review Letter

Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Manufacturing plays a significant role in promoting economic development, production, exports, and job creation, which ultimately contribute to improving the quality of life. The presence of manufacturing defects is, however, inevitable leading to products being discarded, i.e. scrapped. In some cases, defective products can be repaired through rework. Scrap and rework cause a longer completion time, which can contribute to the order being shipped late. In addition, complex manufacturing scheduling becomes much more challenging when the above uncertainties are present. Motivated by the presence of uncertainties as well as combinatorial complexity, this paper addresses the challenge illustrated through a case study of stochastic job-shop scheduling problems arising within low-volume high-variety manufacturing. To ensure on-time delivery, high-quality solutions are required, and near-optimal solutions must be obtained within strict time constraints to ensure smooth operations on the job-shop floor. To efficiently solve the stochastic job-shop scheduling (JSS) problem, a recently-developed Surrogate "Level-Based" Lagrangian Relaxation is used to reduce computational effort while efficiently exploiting the geometric convergence potential inherent to Polyak's step-sizing formula thereby leading to fast convergence. Numerical testing demonstrates that the new method is more than two orders of magnitude faster as compared to commercial solvers