Single Integer Research Articles

A novel approach to pessimistic bilevel problems. An application to the rank pricing problem with ties

This paper introduces a novel method to address the pessimistic approach to the bilevel problem. It consists of considering a lexicographic biobjective optimization problem at the lower level. To emphasize the significance of this approach, we implement it in the context of the Rank Pricing Problem with Ties. This problem can be formulated as a bilevel problem that inherently demands the use of the pessimistic approach. Considering the properties of the lexicographic biobjective problem involved, we formulate this problem as a single level mixed integer optimization problem, deriving also valid values for the big-Ms involved and valid inequalities for this formulation. The computational experiment carried out confirms the relevance of the proposed method.

Triggered integer charge transfer: energy-level alignment at an organic-2D material interface.

Weakly interacting systems such as organic molecules on monolayers of hexagonal boron nitride (h-BN) offer the possibility of single integer charge transfer leading to the formation of organic ions. Such open-shell systems exhibit unique optical and electronic properties which differ from their neutral counterparts. In this study, we used a joint experimental and theoretical approach to investigate the charge transfer of perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) molecules on h-BN/Ni(111) by using differential reflectance spectroscopy (DRS), scanning tunneling spectroscopy (STS), and photoelectron orbital tomography (POT) measurements in combination with density functional theory (DFT) calculations. Our results show that the PTCDA monolayer consists of highly ordered organic radical anions and neutral molecules. In addition, the occurrence of the integer charge transfer is discussed based on the energy-level alignment. Since the integer charge transfer is not limited to PTCDA, we propose that the h-BN covered Ni(111) surface is a promising substrate for studying the optical and electronic properties of highly ordered organic anions.

ElectAnon: A Blockchain-based, Anonymous, Robust, and Scalable Ranked-choice Voting Protocol

Remote voting has become more critical in recent years, especially since the COVID-19 outbreak. Blockchain technology and its benefits such as decentralization, security, and transparency have given rise to proposals for blockchain-based voting systems. However, the traceability of blockchain transactions violates voter anonymity in existing proposals. Besides, transaction costs also need to be considered. Solutions that may cause repeated elections should be avoided for a low-cost scalable voting system. In this work, we propose ElectAnon, a blockchain-based, self-tallying, and ranked-choice voting protocol focusing on anonymity, robustness, and scalability. ElectAnon achieves anonymity by enabling voters to register with identity commitments and cast their votes via zero-knowledge proofs. Robustness is realized by removing the direct control of the authorities in the voting process by using timed-state machines. Each voter encodes the ballot into a single integer and blinds the vote off-chain while making the verification on-chain. This makes the protocol infinitely scalable in the number of voters. ElectAnon is also a solution for governance in Decentralized Autonomous Organizations (DAO): It includes a candidate proposal module and an algorithm-agnostic mechanism to plug-in different tallying methods easily. The Merkle forest extension is proposed for conducting even more trustless elections. ElectAnon is implemented with smart contracts based on Ethereum Virtual Machine (EVM) and a zero-knowledge gadget, Semaphore. The implementation also includes two different sophisticated tallying methods, Borda Count and Tideman. Experimental results show that a 40-voter and 10-candidate election can be implemented with the gas consumption reduced up to 89% compared to previous works. While other studies could not exceed a 25,000-voter setup, ElectAnon has been observed to run safely for 1,000,000 voters. The implementation can be found at https://github.com/ceyonur/electanon .

The Hot Spot Coverage Patrol Problem: Formulations and Solution Approaches

When designing a patrol route, it is often necessary to pay more attention to locations with high crime rates. In this paper, we study a patrol routing problem for a fleet of patrol cars patrolling a region with a high-crime neighborhood (HCN) consisting of multiple hot spots. Considering the disorder and chaos in the HCN, at least one patrol car is required in the HCN at any given time during the patrol. We call this routing problem the hot spot coverage patrol problem (HSCPP). In the HSCPP, the importance of a patrol location is quantified by a prize, and the prize is collected if a patrol car visits the location. Our objective is to maximize the sum of prizes collected by the patrol cars, obeying all operational requirements. We propose mathematical formulations and develop several solution approaches for the HSCPP. The global approach consists of finding the routing solution for all patrol cars with a single integer programming (IP) formulation. The partition approach involves first partitioning the region geographically and solving the routing problem in each subregion with two IP formulations. Next, we strengthen the partition approach by developing a column generation (CG) approach in which the initial columns of the CG approach are the solutions generated from the partition approach. We conduct a detailed computational case study using instances based on real crime data from Montgomery County, Maryland. To further understand the computational tractability of our solution approaches, we also perform a sensitivity analysis using synthetic instances under various scenarios. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0192 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0192 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

A MILP Model for Optimal Conductor Selection and Capacitor Banks Placement in Primary Distribution Systems

Power distribution systems (PDS) are the infrastructure and equipment used to distribute electricity from the transmission system to end-users, such as homes and businesses. PDS are usually designed to operate in a radial mode, where power flows from one substation to the end user through a series of feeders. The extension of distribution lines to attend new customers along with the growing demand for electricity result in increased energy losses and voltage reductions. Various solutions have been proposed to solve these issues, such as selecting the optimal set of conductors, optimizing the placement of voltage regulators, using capacitor banks, reconfiguring the distribution system, and implementing distributed generation. A well-known approach for reducing energy losses and enhancing voltage profile is the optimal conductor selection (OCS). While this can be beneficial, it may not be sufficient to fully reduce technical losses and improve the system voltage profile; therefore, it must be combined with other strategies. This paper presents a new approach that combines the OCS with the optimal placement of capacitor banks (OPCB) to minimize technical losses and improve the voltage profile in PDS. The main contribution of this paper is the integration of these two problems into a single mixed integer linear programming (MILP) model, therefore guaranteeing the achievement of globally optimal solutions. Three test systems of 27, 69, and 85 buses were used to illustrate the effectiveness of the proposed modeling approach. The results indicate that the combination of OCS and OPCB effectively minimizes energy losses and enhances the voltage profile. In all cases, the solutions obtained by the proposed MILP approach were better than those previously reported through metaheuristics for the combined OCS and OPCB problem.

Utility Preference Robust Optimization with Moment-Type Information Structure

Utility Preference Robust Optimization with Moment-Type Information Structure In some decision-making problems, information on the true utility function of the decision maker may be incomplete, which may bring potential modeling risk. In “Utility Preference Robust Optimization with Moment-Type Information Structure,” Guo, Xu, and Zhang propose a maximin utility preference robust optimization model where information about the DM’s preference is constructed by moment-type conditions. The authors propose a piecewise linear approximation approach to tackle the maximin problem, reformulate the approximate problem as a single mixed integer linear program, and derive error bounds for the approximate ambiguity set, the optimal value, and the optimal solutions. To examine the performance of the model and the computational schemes, they carry out extensive numerical tests and demonstrate the effectiveness of the model and efficiency of the computational methods.

Tunable spatial fractional derivatives with graphene-based transmit arrays.

The optical implementation of mathematical spatial operators is a critical step toward achieving practical high-speed, low-energy analog optical processors. In recent years, it has been shown that using fractional derivatives in many engineering and science applications leads to more accurate results. In the case of optical spatial mathematical operators, the derivatives of the first and second orders have been investigated. But no research has been performed on fractional derivatives. On the other hand, in previous studies, each structure is dedicated to a single integer order derivative. This paper proposes a tunable structure made of graphene arrays on silica to implement fractional derivative orders smaller than two, as well as first and second orders. The approach used for derivatives implementation is based on the Fourier transform with two graded index lenses positioned at the structure's sides and three stacked periodic graphene-based transmit arrays in middle. The distance between the graded index lenses and the nearest graphene array is different for the derivatives of order smaller than one and between one and two. In fact, to implement all derivatives, we need two devices with the same structure having a slight difference in parameters. Simulation results based on the finite element method closely match the desired values. Given the tunability of the transmission coefficient of the proposed structure in the approximate amplitude range of [0,1] and phase range of [-180, 180], on top of the acceptable implementation of the derivative operator, this structure allows obtaining other spatial multi-purpose operators, which are a prelude to achieving analog optical processors and even improving the optical studies performed in image processing.

Using multiple reference vectors and objective scaling in the Feasibility Pump

The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate the usage of multiple reference vectors in all stages of the FP algorithm. In particular, we use LP-feasible vectors obtained during the main loop to tighten the variable domains before entering the computationally expensive enumeration stage, a procedure we refer to as mRENS. Moreover, we consider multiple integer reference vectors to explore further optimizing directions and introduce alternative objective scaling terms to balance the contributions of the distance functions and the original MIP objective.Our computational experiments demonstrate that the new method can improve performance on general MIP test sets. In detail, our modifications provide a 29.3% solution quality improvement and 4.0% running time improvement in an embedded setting, needing 16.0% fewer iterations over a large test set of MIP instances. In addition, the method's success rate increases considerably within the first few iterations. In a standalone setting, we also observe a moderate performance improvement, which makes our version of FP suitable for the two main use-cases of the algorithm.

A Single Path Digital-IF Receiver Supporting Inter/Intra 5-CA With a Single Integer LO-PLL in 14-nm CMOS FinFET

The world’s first 5-carrier aggregation (CA) supporting digital-intermediate frequency (IF) receiver (RX) to support 5G sub-6 GHz new radio (NR) and CA/E-UTRA NR dual connectivity (CA/EN-DC) maintaining 2G and 3G in 14-nm FinFET CMOS technology is presented. Three digital-IF RXs with a shared local oscillator-phase-locked loop (LO-PLL) are integrated for supporting inter-/intra-band 5-CA to reduce power consumption and area of the massive number of RX paths. The RX features nine single-ended low-noise amplifiers (LNAs) with low/mid/high band (L/M/HB) characteristics. It achieves noise figure (NF) of 1.5 dB with 18 dB external LNA gain and +7.6-dBm out-of-band (OOB) input intercept point 3 (IIP3), and input intercept point 2 (IIP2) calibration is not required thanks to IF planning. The RX achieves an error vector magnitude (EVM) of 2.5% by intra-4CA for B1 LTE10MHz and LTE20MHz in one single RX path, as well as inter-3CA for B3, B5, and B7 long-term evolution (LTE) 20 MHz with a shared LO-PLL. The estimated power saving by sharing a single LO-PLL is 17% compared to 3-CA RXs with three separate LO-PLLs.

BFF: foundational and automated verification of bitfield-manipulating programs

Low-level systems code often needs to interact with data, such as page table entries or network packet headers, in which multiple pieces of information are packaged together as bitfield components of a single machine integer and accessed via bitfield manipulations (e.g., shifts and masking). Most existing approaches to verifying such code employ SMT solvers, instantiated with theories for bit vector reasoning: these provide a powerful hammer, but also significantly increase the trusted computing base of the verification toolchain. In this work, we propose an alternative approach to the verification of bitfield-manipulating systems code, which we call BFF. Building on the RefinedC framework, BFF is not only highly automated (as SMT-based approaches are) but also foundational---i.e., it produces a machine-checked proof of program correctness against a formal semantics for C programs, fully mechanized in Coq. Unlike SMT-based approaches, we do not try to solve the general problem of arbitrary bit vector reasoning, but rather observe that real systems code typically accesses bitfields using simple, well-understood programming patterns: the layout of a bit vector is known up front, and its bitfields are accessed in predictable ways through a handful of bitwise operations involving bit masks. Correspondingly, we center our approach around the concept of a structured bit vector---i.e., a bit vector with a known bitfield layout---which we use to drive simple and predictable automation. We validate the BFF approach by verifying a range of bitfield-manipulating C functions drawn from real systems code, including page table manipulation code from the Linux kernel and the pKVM hypervisor.

An experimental extension to the discrete Laplace method for Y-STR haplotype frequency estimation

Frequency estimation for Y-STR haplotypes is a challenging problem because limited data are available and complex dependencies exist within the data. As a result, various statistical methods have been proposed for frequency estimation. The discrete Laplace method has been recommended in some contexts by the DNA commission of the ISFG. This method is limited to haplotypes with single integer repeat alleles only at all loci. We propose a generalisation of the method that handles duplicated loci such as DYS385 and less common alleles that are not integer repeats. The extension is implemented in an experimental R package called disclapmix2.

The scientific value of numerical measures of human feelings

Human feelings measured in integers (my happiness is an 8 out of 10, my pain 2 out of 6) have no objective scientific basis. They are "made-up" numbers on a scale that does not exist. Yet such data are extensively collected-despite criticism from, especially, economists-by governments and international organizations. We examine this paradox. We draw upon longitudinal information on the feelings and decisions of tens of thousands of randomly sampled citizens followed through time over four decades in three countries (n = 700,000 approximately). First, we show that a single feelings integer has greater predictive power than does a combined set of economic and social variables. Second, there is a clear inverse relationship between feelings integers and subsequent get-me-out-of-here actions (in the domain of neighborhoods, partners, jobs, and hospital visits). Third, this feelings-to-actions relationship takes a generic form, is consistently replicable, and is fairly close to linear in structure. Therefore, it seems that human beings can successfully operationalize an integer scale for feelings even though there is no true scale. How individuals are able to achieve this is not currently known. The implied scientific puzzle-an inherently cross-disciplinary one-demands attention.

Topological Chern vectors in three-dimensional photonic crystals.

The paradigmatic example of a topological phase of matter, the two-dimensional Chern insulator1-5, is characterized by a topological invariant consisting of a single integer, the scalar Chern number. Extending the Chern insulator phase from two to three dimensions requires generalization of the Chern number to a three-vector6,7, similar to the three-dimensional (3D) quantum Hall effect8-13. Such Chern vectors for 3D Chern insulators have never been explored experimentally. Here we use magnetically tunable 3D photonic crystals to achieve the experimental demonstration of Chern vectors and their topological surface states. We demonstrate Chern vector magnitudes of up to six, higher than all scalar Chern numbers previously realized in topological materials. The isofrequency contours formed by the topological surface states in the surface Brillouin zone form torus knots or links, whose characteristic integers are determined by the Chern vectors. We demonstrate a sample with surface states forming a (2, 2) torus link or Hopf link in the surface Brillouin zone, which is topologically distinct from the surface states of other 3D topological phases. These results establish the Chern vector as an intrinsic bulk topological invariant in 3D topological materials, with surface states possessing unique topological characteristics.

On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes

The paper considers the problem of unique recovery of sparse finite-valued integer signals using a single linear integer measurement. For l-sparse signals in {mathbb {Z}}^n, 2l<n, with absolute entries bounded by r, we construct an 1times n measurement matrix with maximum absolute entry Delta =O(r^{2l-1}). Here the implicit constant depends on l and n and the exponent 2l-1 is optimal. Additionally, we show that, in the above setting, a single measurement can be replaced by several measurements with absolute entries sub-linear in Delta. The proofs make use of results on admissible (n-1)-dimensional integer lattices for m-sparse n-cubes that are of independent interest.

A robust approximation for yard template optimization under uncertainty

This paper considers a container yard template optimization problem when the arrival schedule of vessels calling at the port is uncertain. First, container storage locations in the yard need to be assigned to vessels, which essentially forms the yard template. When the arrival of the vessels becomes firmed, the operation schedule to store and retrieve containers from the yard is determined, taking into account the vessel turnaround time requirements and activity congestion in the yard. We develop a two-stage robust approximation model in the form of a single linear mixed integer program to minimize the maximum cost associated with excessive activity concentrations and travel distance from the vessel berth to the container storage locations. An accelerated column generation meta-heuristic solution approach is then proposed, which integrates adaptive large neighborhood search, evolutionary algorithm, and column generation algorithm to generate near-optimal solutions in a reasonable time. Numerical results show that the proposed solution algorithm performs favorably compared to other standalone approaches.

On Generating Lagrangian Cuts for Two-Stage Stochastic Integer Programs

We investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. Lagrangian cuts can be added to a Benders reformulation and are derived from solving single scenario integer programming subproblems identical to those used in the nonanticipative Lagrangian dual of a stochastic integer program. Although Lagrangian cuts have the potential to significantly strengthen the Benders relaxation, generating Lagrangian cuts can be computationally demanding. We investigate new techniques for generating Lagrangian cuts with the goal of obtaining methods that provide significant improvements to the Benders relaxation quickly. Computational results demonstrate that our proposed method improves the Benders relaxation significantly faster than previous methods for generating Lagrangian cuts and, when used within a branch-and-cut algorithm, significantly reduces the size of the search tree for three classes of test problems.

Online Coloring and a New Type of Adversary for Online Graph Problems

We introduce a new type of adversary for online graph problems thus allowing parametrized analysis of online algorithms with respect to a natural parameter. The new adversary is parameterized by a single integer \(\kappa \), which upper bounds the number of connected components that the adversary can use at any time during the presentation of the online graph G. We call this adversary “\(\kappa \)-components-bounded”, or \(\kappa \)-CB for short. On one hand, this adversary is restricted compared to the classical adversary because of the \(\kappa \)-CB constraint. On the other hand, we seek competitive ratios parameterized only by \(\kappa \) with no dependence on the input length n, thereby giving the new adversary power to use arbitrarily large inputs. We study online coloring under the \(\kappa \)-CB adversary. We obtain a finer analysis of the existing algorithms FirstFit and CBIP by computing their competitive ratios on trees and bipartite graphs under the new adversary: (1) Perhaps surprisingly, FirstFit outperforms CBIP on trees; (2) The competitive ratio of CBIP on bipartite graphs is simply \(\kappa \). We also study several well known classes of graphs, such as 3-colorable, \(C_k\)-free, d-inductive, planar, and bounded treewidth, with respect to online coloring under the \(\kappa \)-CB adversary. We demonstrate that the extra adversarial power of unbounded input length outweighs the restriction on the number of connected components leading to non-existence of competitive algorithms for these classes.

A multi-objective integrated procurement, production, and distribution problem of supply chain network under fuzziness uncertainties

In this paper, we devoted a design under uncertainty of a four-echelon supply chain network including multiple suppliers, multiple plants, multiple distributors and multiple customers. The proposed model is a bi-objective mixed integer linear programming which considers several constraints and aims to minimize the total costs including the procurement, production, storage and distribution costs as well as to maximize on-time deliveries (OTD). To bring the model closer to real-world planning problems, the objective function coefficients (e.g. procurement cost, production cost, inventory holding and transport costs) and other parameters (e.g., demand, production capacity and safety stock level), are all considered triangular fuzzy numbers. Besides, a hybrid mathematical model-based on credibility approach is constructed for the problem, i.e., expected value and chance constrained models. Moreover, to build the crisp equivalent model, we use different property of the credibility measure. The resulted crisp equivalent model is a bi-objective mixed integer linear programs (BOMILP). To transform this crisp BOMILP into a single objective mixed integer linear programs (MILP) model, we apply three different aggregation functions. Finally, numerical results are reported for a real case study to demonstrate the efficiency and applicability of the proposed model.

Efficient and sustainable closed-loop supply chain network design: A two-stage stochastic formulation with a hybrid solution methodology

In recent years, consumers and legislators have pushed companies to design their supply chain networks to consider environmental and social impacts as an important performance outcome. Due to the role of resource utilization as a key component of logistics network design, another primary goal of design is ensuring available scarce resources are used as efficiently as possible across all facilities. To address efficiency issues in a sustainable closed-loop supply chain network, a stochastic integrated multi-objective mixed integer nonlinear programming model is developed in this paper, in which sustainability outcomes as well as efficiency of facility resource utilization are considered in the design of a sustainable supply chain network. In doing so, efficiency is assessed using a bi-objective output-oriented data envelopment analysis model. A hybrid three-step solution methodology is presented that creates a linear form of the original mixed integer nonlinear programming problem using piecewise McCormick envelopes approach. In the second step, an aggregated single objective programming model is derived by exploiting the multi-choice goal programming. Finally, a Lagrangian relaxation algorithm is developed to effectively solve the latter stochastic single objective mixed integer linear programming problem. The application of the proposed approach is investigated with data drawn from a case study in the electronics industry. This case study illustrates how firms may balance sustainability and efficiency in the supply chain network design problem. Further, it demonstrates the integration of efficiency results in improving economic aspects of sustainability as well as social responsibility outcomes, but also highlights the trade-offs that exist between efficiency and environmental impacts.

Design and implementation of parallel MSD integer divider in ternary optical computer

Division is one of the four basic operations. It is a very important operation in the field of numerical calculation, such as numerical calculation, large integer decomposition and so on. How to divide quickly has been a hot issue in electronic computers, embedded systems and other new computing systems. It is of great significance to give full play to the advantages of ternary optical computer processors, such as a large number of bits, reconfigurable operation functions, bit allocation, etc. by designing the efficient parallel MSD number divider to improve the division operation efficiency of large data and promote the application of ternary optical computer in the field of numerical calculation. In this paper, the symbol decision algorithm for MSD numbers is proposed first time, and based on the SRT algorithm, the scheme for implementing a parallel division of multiple MSD integers using a parallel carry free SJ-MSD adder and an MSD comparator, which is called as parallel MSD integer division, is designed first time. For the corresponding parallel MSD integer divider, the machine cycles required to run multiple MSD integer division in parallel is the same as the machine cycles required for the operation of a single MSD integer division. Experiments show that the parallel SRT integer division scheme is feasible. It will effectively improve the efficiency of large data processing and accelerate TOC to enter practical applications such as numerical computation.