Linear Programming-based Algorithm Research Articles

Traceability Technology Adoption in Supply Chain Networks

Modern traceability technologies promise to improve supply chain management by simplifying recalls, increasing visibility, and verifying sustainable supplier practices. Initiatives leading the implementation of traceability technologies must choose the least-costly set of firms—or seed set—to target for early adoption. Choosing this seed set is challenging because firms are part of supply chains interlinked in complex networks, yielding an inherent supply chain effect: benefits obtained from traceability are conditional on technology adoption by a subset of firms in a product’s supply chain. We prove that the problem of selecting the least-costly seed set in a supply chain network is hard to solve and even approximate within a polylogarithmic factor. Nevertheless, we provide a novel linear programming-based algorithm to identify the least-costly seed set. The algorithm is fixed-parameter tractable in the supply chain network’s treewidth, which we show to be low in real-world supply chain networks. The algorithm also enables us to derive easily computable bounds on the cost of selecting an optimal seed set. We leverage our toolbox to conduct large-scale numerical experiments that provide insights into how the supply chain network structure influences diffusion. These insights can help managers optimize their technology diffusion strategy. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01759 .

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory’s Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. 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.2022.0233 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0233 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

A new approach to state bounding for coupled differential-difference equations with bounded disturbances

In this paper, we present a new method to the state bounding problem for a class of coupled differential-difference equations (CDDEs) with bounded disturbances and time-varying delays. Instead of using the state transformation to reformulate the considered problem into the one for non-perturbed CDDEs, our novel idea is to construct suitable comparison systems, from which the state vector can be estimated directly and the information on the initial value is exploited more effectively in order to derive a sharper state bound. For computing and minimising the state bound, a numerical linear programming-based algorithm is also presented. The effectiveness of the presented method is verified via two numerical examples.

Sufficient Matrices: Properties, Generating and Testing

This paper investigates various aspects of sufficient matrices, one of the most relevant matrix classes introduced in connection with linear complementarity problems. We summarize the most important theoretical results and properties related to sufficient matrices. Based on these, we propose different construction rules that can be used to generate new matrices that belong to this class. A nonnegative number can be assigned to each sufficient matrix, which is called its handicap and works as a measure of sufficiency. The handicap plays a crucial role in proving convergence and complexity results for interior point algorithms for linear complementarity problems. For a particular sufficient matrix, called Csizmadia’s matrix, we give the exact value of the handicap, which is exponential in the size of the matrix. Another important topic that we address is deciding whether a matrix is sufficient. Tseng proved in 2000 that this decision problem is co-NP hard. We investigate three different algorithms for determining the sufficiency of a given matrix: Väliaho’s algorithm, a linear programming-based algorithm, and an algorithm that facilitates nonlinear programming reformulations of the definition of sufficiency. We tested the efficiency of these methods on our recently launched benchmark data set that consists of four different sets of matrices. In this paper, we give the description and most important properties of the benchmark set, which can be used in the future to compare the performance of different interior point algorithms for linear complementarity problems.

Optimizing bend loss in optical waveguide channel routing on photonic integrated circuits

Silicon photonics (Si-photonics) has been established as a potential technology that integrates both electronic and optical circuits on single integrated circuits (ICs) in order to satisfy the increasing demand for high speed and low power in the emerging market of ICs. It has opened up the research directions in the domain of design automation for photonic ICs. On the physical layout of the optical circuits, it is a challenging task to obtain the optimal routing of optical waveguides, while minimizing all the parameters like the number of tracks, total bend loss, worst signal loss, total propagation loss and total crossing loss. In this paper, we proposed two non-Manhattan grid-based methods for reducing the bend loss, worst signal loss and tracks in optical channel routing. First, a 0–1 integer linear programming-based algorithm called minimizing bend loss (MBL) is proposed, which minimizes the total bend loss (TBL) and the worst signal loss (WSL) while reducing the number of tracks (T) over the state-of-the-art technique. The execution time of MBL is very high for the large input. Hence next, a scalable heuristic called reducing bend loss (RBL) is presented that provides a better balance between the reduction of the TBL and T over the state-of-the-art and MBL algorithms. Simulation results show that MBL can reduce the TBL and the WSL by an average of 57.9% and 63.1%, respectively, with an average increase of 12% in T over state-of-the-art algorithms. The simulation results show that the RBL reduces the TBL and the WSL by an average of 39.7% and 41.3%, respectively, with an average increase of 23.7% in T over state-of-the-art algorithms.

Algorithm and System Development for Robotic Micro-Volume Herbicide Spray Towards Precision Weed Management

Weed competition is one of the most limiting factors affecting crop yield and profitability. Robotic weeding systems have demonstrated their potential to save herbicide usage and thereby minimize costs and adverse impacts on the environment. We introduce the software and hardware design of an automatic system for micro-volume herbicide spray using a mobile robot for early-stage weed control. The system is equipped with a stereo camera, one inertial measurement unit, and multiple linearly actuating spray nozzles. To enable the system, we propose a new scene representation from the perspective of spray operation. We represent the space occupied by weeds as candidate line segments for spray and then construct a directed acyclic graph (DAG) that embraces the feasible nozzle paths among weeds. Based on the new scene representation, we formulate an optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -nozzle assignment/motion planning problem and develop a binary linear programming-based algorithm to assign nozzles to the candidate line segments for optimal coverage. We built the system and conducted both simulation and field experiments. Evaluation on rough soil surfaces with artificial targets has shown that the lateral errors of herbicide spray are at sub-centimeter levels. Simulation results demonstrate that the proposed assignment algorithm can provide good coverage within the intra-row regions.

Link State Estimation Under Cyber-Physical Attacks: Theory and Algorithms

Effective defense against cyber-physical attacks in power grids requires accurate damage assessment. While some solutions have been proposed to recover the line states within the attacked area, existing solutions are limited by the assumption of a connected post-attack grid and the lack of verifiable performance guarantees. To fill this gap, we study the recovery of line states under a cyber-physical attack that disconnects lines while blocking information from the attacked area. In contrast to existing solutions assuming a connected post-attack grid or known post-attack power injections, we consider a more challenging scenario where the attack may partition the grid into islands, which causes unknown changes in power injections. To address this problem, under the DC model we (i) propose a linear programming-based algorithm to recover the line states within the attacked area under unknown post-attack power injections, (ii) characterize the accuracy of the proposed recovery algorithm under certain conditions, and (iii) develop efficient algorithms to verify the recovery results using observable information. Then, we extend the DC-based algorithms to AC model. Our numerical evaluations demonstrate that the proposed recovery algorithm is highly accurate in localizing failed lines, most of which can be successfully verified by the proposed verification algorithms.

Coordinate sizing of energy storage and transmission line for a remote renewable power plant

To protect the environment and reduce carbon emissions, renewable power generation has been growing rapidly during the past decade. Renewable energy resources are sometimes far away from the main grid, leading to expensive grid-connection transmission lines. Deploying on-site energy storage can smooth the output power and help to reduce the renewable power spillage and the requirement of transmission line capacity. This paper presents a method to coordinately size on-site energy storage and grid-connection transmission line for a remote renewable power plant, minimising the total investment cost subject to the constraint of renewable curtailment risk. Through an optimal operation model, the renewable curtailment is proven to be a piecewise affine function of capacity parameters and renewable power generation, and a linear programming-based algorithm is proposed to generate an approximate expression. A distributionally robust optimisation model is proposed to determine the sizes. The renewable generation uncertainty is modelled by a Wasserstein-metric-based ambiguity set containing probability distributions around the empirical distribution constructed from the historical data. The utilisation rate is ensured in the worst-case distribution. The sizing problem is transformed into a tractable linear program. The case study demonstrates the effectiveness of the proposed method.

On the complexity of dynamic mechanism design

We introduce a simple dynamic mechanism design problem in which the designer offers two items in two consecutive stages to a single buyer. The buyer's joint distribution of valuations for the two items is known, and the buyer knows the valuation for the current item, but not for the one in the future. The designer seeks to maximize expected revenue, and the mechanism must be deterministic, truthful, and ex-post individually rational. We show that finding the optimum deterministic mechanism in this situation — arguably one of the simplest meaningful dynamic mechanism design problems imaginable — is NP-hard. We also prove several positive results, including a polynomial-time linear programming-based algorithm for the revenue optimal randomized mechanism (even for many buyers and many stages). We prove strong separations in revenue between non-adaptive, adaptive, and randomized mechanisms, even when the valuations in the two stages are independent.

Data-Driven Multimodal Patrol Planning for Anti-poaching

Wildlife poaching is threatening key species that play important roles in the ecosystem. With historical ranger patrol records, it is possible to provide data-driven predictions of poaching threats and plan patrols to combat poaching. However, the patrollers often patrol in a multimodal way, which combines driving and walking. It is a tedious task for the domain experts to manually plan such a patrol and as a result, the planned patrol routes are often far from optimal. In this paper, we propose a data-driven approach for multimodal patrol planning. We first use machine learning models to predict the poaching threats and then use a novel mixed-integer linear programming-based algorithm to plan the patrol route. In a field test focusing on the machine learning prediction result at Jilin Huangnihe National Nature Reserve (HNHR) in December 2019, the rangers found 42 snares, which is significantly higher than the historical record. Our offline experiments show that the resulting multimodal patrol routes can improve the efficiency of patrol and thus they can serve as the basis for future deployment in the field.

A Distributed Hardware Monitoring System for Runtime Verification on Multi-Tile MPSoCs

Exhaustive verification techniques do not scale with the complexity of today’s multi-tile Multi-processor Systems-on-chip (MPSoCs). Hence, runtime verification (RV) has emerged as a complementary method, which verifies the correct behavior of applications executed on the MPSoC during runtime. In this article, we propose a decentralized monitoring architecture for large-scale multi-tile MPSoCs. In order to minimize performance and power overhead for RV, we propose a lightweight and non-intrusive hardware solution. It features a new specialized tracing interconnect that distributes and sorts detected events according to their timestamps. Each tile monitor has a consistent view on a globally sorted trace of events on which the behavior of the target application can be verified using logical and timing requirements. Furthermore, we propose an integer linear programming-based algorithm for the assignment of requirements to monitors to exploit the local resources best. The monitoring architecture is demonstrated for a four-tiled MPSoC with 20 cores implemented on a Virtex-7 field-programmable gate array (FPGA).

Minimizing the variance of flow series using a genetic algorithm for reliability-based design of looped water distribution networks

ABSTRACTA network design based on the flow uniformity in various pipes improves the reliability of the network. One way to obtain such a flow distribution is by minimizing the variance of pipe flows. The available analytical method is critically studied, and observed to fail in providing global minimum variance of flow series. The analytical method accounts for the flow directions, while a variance evaluation requires that only the magnitude of flows is considered. A general nonlinear programming approach is tried, and it is observed that it requires correct knowledge of the flow direction. This article presents a genetic algorithm-based method to avoid this limitation. A linear programming-based algorithm is then suggested for selecting the optimal pipe sizes considering reliability. The proposed method is found to provide better design solutions than those obtained using some of the methodologies previously suggested for expansion of a water main system.

Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings

The intuitionistic multiplicative preference relation (IMPR), which takes into account both the ratio degree to which an alternative is preferred to another and the ratio degree to which an alternative is non-preferred to another, is a useful tool for decision makers to elicit their preference information using Saaty’s 1–9 scale. In this paper, we focus on group decision making with IMPRs. First, we analyze the flaws of the consistency definition of an IMPR in previous work and then propose a new definition to overcome the flaws. On this basis, a linear programming-based algorithm is developed to check and improve the consistency of an IMPR. Second, we discuss the relationships between an IMPR and a normalized intuitionistic multiplicative weight vector and develop two approaches to group decision making based on complete and incomplete IMPRs, respectively. Based on the proposed algorithm and approaches, a general framework for group decision making with IMPRs is proposed. Finally, some numerical examples are provided to demonstrate the proposed approaches. The results show that the proposed approaches can deal with group decision-making problems with IMPRs effectively.

Rebalancing the assembly lines: exact solution approaches

In this study, we consider an assembly line rebalancing problem with disruptions caused by workstation breakdowns or shutdowns. After the disruption, we aim to find a rebalance so as to catch the trade-off between the efficiency measure of cycle time and stability measure of number of tasks assigned to different workstations in the original and new balances. Our aim is to generate all nondominated objective vectors with respect to the efficiency and stability measures. We develop two optimisation algorithms: a Mixed Integer Linear Programming-based algorithm and a Branch and Bound algorithm. The results of our experiments have shown the favourable performances of both algorithms and the superiority of the Branch and Bound algorithm.

A Simple and Effective Heuristic Method for Threshold Logic Identification

In this paper, a straightforward and effective method to identify threshold logic function (TLF) is presented. Threshold logic is a promising alternative to conventional Boolean logic due to its suitability for emerging technologies, like memristors, quantum-dot cellular automata, resonant tunneling device, and spintronic devices. Identification and synthesis of TLF are essential tasks in a design flow based on such a logic strategy. The proposed method relies on irredundant sum-of-products Boolean function description form and exploits both ordering of variables and system of inequalities to assign the variable weights and the function threshold value. This is the first heuristic algorithm able to identify all threshold functions with up to six variables, being also more effective than other heuristic methods for functions with a larger number of variables. For functions obtained from ${k}$ -cuts of benchmark circuits, experimental results demonstrated effectiveness near to 100% when compared to exact methods, even when the number of function variables increases. The execution time of the proposed approach is similar to related heuristic methods, being faster than integer linear programming-based algorithms.

An Integer Linear Programming approach to the single and bi-objective Next Release Problem

ContextThe Next Release Problem involves determining the set of requirements to implement in the next release of a software project. When the problem was first formulated in 2001, Integer Linear Programming, an exact method, was found to be impractical because of large execution times. Since then, the problem has mainly been addressed by employing metaheuristic techniques. ObjectiveIn this paper, we investigate if the single-objective and bi-objective Next Release Problem can be solved exactly and how to better approximate the results when exact resolution is costly. MethodsWe revisit Integer Linear Programming for the single-objective version of the problem. In addition, we integrate it within the Epsilon-constraint method to address the bi-objective problem. We also investigate how the Pareto front of the bi-objective problem can be approximated through an anytime deterministic Integer Linear Programming-based algorithm when results are required within strict runtime constraints. Comparisons are carried out against NSGA-II. Experiments are performed on a combination of synthetic and real-world datasets. FindingsWe show that a modern Integer Linear Programming solver is now a viable method for this problem. Large single objective instances and small bi-objective instances can be solved exactly very quickly. On large bi-objective instances, execution times can be significant when calculating the complete Pareto front. However, good approximations can be found effectively. ConclusionThis study suggests that (1) approximation algorithms can be discarded in favor of the exact method for the single-objective instances and small bi-objective instances, (2) the Integer Linear Programming-based approximate algorithm outperforms the NSGA-II genetic approach on large bi-objective instances, and (3) the run times for both methods are low enough to be used in real-world situations.

Developing an integrated revenue management and customer relationship management approach in the hotel industry

Revenue management (RM) and customer relationship management (CRM) are the standard strategies of many hotels to increase their profitability. Although the objectives and time horizons of RM and CRM are different, they can be considered as complimentary business strategies. However, the integration has received little attention both practically and theoretically. In this study, we develop an approach to jointly make the capacity allocation and overbooking decisions considering CRM strategies over a hotel network. Hotel customers are divided based on their lifetime value into two major groups of occasional and loyal customers. Price discounts and room availability guarantee (RAG) are offered to loyal customers, who are the hotel’s essential source of profit. The main problem is tackled by a stochastic dynamic programming model whose expected value of objective function is approximated by two deterministic linear programming-based algorithms. The computational results indicate that the loyalty programs may lead to decrease in short-term net revenue. However, another analysis is required to decide upon cost-effectiveness of loyalty programs in an extended planning horizon. On the basis of an estimated discount-RAG response function, the cost-effectiveness of different loyalty programs is compared, which shows potential increase in hotel expected net revenue up to 3.5 per cent. The analytical long-term evaluation of loyalty programs introduced is capable of determining the most appropriate loyalty program factors. Moreover, it suggests discount-RAG response function and the level of tightness as sensitive parameters.

Linear Integer Programming Approach to Construction of Balanced Incomplete Block Designs

This article proposes a linear integer programming-based algorithm to construct balanced incomplete block designs. Working of the algorithm is illustrated with the help of an example. The algorithm is able to generate balanced incomplete block designs very fast in most of the cases. The performance of the proposed algorithm is compared with other algorithms proposed in the literature. It is demonstrated that the proposed algorithm is competitive with the existing algorithms.

Linear programming-based algorithms for the minimum makespan high multiplicity jobshop problem

We study a generalized version of the minimum makespan jobshop problem in which multiple instances of each job are to be processed. The system starts with specified inventory levels in all buffers and finishes with some desired inventory levels of the buffers at the end of the planning horizon. A schedule that minimizes the completion time of all the operations is sought. We develop a polynomial time asymptotic approximation procedure for the problem. That is, the ratio between the value of the delivered solution and the optimal one converge into one, as the multiplicity of the problem increases. Our algorithm uses the solution of the linear relaxation of a time-indexed Mixed-Integer formulation of the problem. In addition, a heuristic method inspired by this approximation algorithm is presented and is numerically shown to out-perform known methods for a large set of standard test problems of moderate job multiplicity.

Escape Routing for Staggered-Pin-Array PCBs

To accommodate the ever-growing pin number of complex printed circuit board (PCB) designs, the staggered pin array is introduced for modern designs with higher pin density. However, the escape routing for staggered pin arrays, which is a key component of PCB routing, is significantly different from that for grid arrays. This paper presents a routing algorithm for the escape routing for staggered-pin-array PCBs. We first analyze the properties of staggered pin arrays, and propose an orthogonal-side wiring style that fully utilizes the routing resource of the staggered pin array. A linear programming/integer linear programming-based algorithm is presented to solve the staggered-pin-array escape routing problem. Experimental results show that our approach successfully routes all test cases efficiently and effectively.