LP-based Approach Research Articles

A robust LP-based approach for a dynamic surgical case scheduling problem with sterilisation constraints

The purpose of this article is to investigate a practical scheduling problem in which a group of elective surgical cases are scheduled over time, while considering their unpredictable durations and potential delays in the sterilisation of surgical instruments. The primary objectives were to schedule the maximum number of surgeries and decrease overtime for the surgical staff, as well as limit the number of instruments requiring emergency sterilisation. The study was conducted in collaboration with the University Hospital of Angers in France, which also contributed historical data for the experiments. We propose two robust mixed integer linear programming models, which are then solved iteratively through a rolling horizon approach, in which the objective functions are taken into account in lexicographic order. Experiments on randomly generated instances indicated which of the two approaches had better performance. Comparison of the results for a real-world scenario involving actual planning at the hospital indicated a greater than 69% decrease in overtime, and a minimum of 92% fewer stressful situations in the sterilising unit.

An Efficient LP-Based Approach for Spatial-Temporal Coordination of Electric Vehicles in Electricity-Transportation Nexus

A growing integration of electric vehicles (EV) and fast charging stations (FCS) has paved the way for the emergence of transportation and power distribution networks. However, previous work on the coordination of EV in the transportation system mainly focuses on static traffic assignment (STA) models which are unable to characterize the temporal evolution of EV flows on traffic links. Meanwhile, limited prior effort in dynamic traffic assignment (DTA) employs a static FCS model which is unable to describe the temporal evolution of charging and discharging (C&D) behavior of EV flows, while respecting the state-of-charge (SoC) related operating constraints, hindering full exploitation of EV flexibility potentials. To bridge the knowledge gap, this paper proposes a novel DTA model to optimize the spatial-temporal distribution of EV flows on roads and at FCSs, taking into account their flexible C&D options and SoC-related constraints, through the solution of only a single linear program. Case studies validate the effectiveness of the proposed DTA model by benchmarking its performance against traditional STA models, and corroborate the core benefits from the proposed spatial-temporal coordination of EV C&D demand in the power distribution network in terms of peak demand reduction, improved RES absorption, reduced carbon emission as well as more efficient network congestion management.

Hierarchical Decision-Making for Qualification Management in Wafer Fabs: A Simulation Study

A qualification management problem arising in semiconductor wafer fabrication facilities (wafer fabs) is discussed. The stepper equipment needs to be qualified to process lots that belong to different families. Stepper- and family dependent qualification time windows exist. Time windows can be reinitialized if required and can be extended by on-time processing of lots from qualified families. A hierarchical approach is proposed. The base-level provides a dispatching strategy that takes into account qualification decisions, while the mid-level consists of a mixed integer linear program (MILP) for making qualification decisions. The top-level comprises a linear program (LP) that computes target quantities for the families on the steppers in each period of the planning window taking into account fab-wide objectives. In addition to an LP formulation with conventional capacity constraints, we provide a formulation where clearing functions are used to represent the congestion of the wafer fab. We also discuss how to anticipate the behavior of the mid-level on the top-level. Results of simulation experiments where the hierarchical approach is applied in a rolling horizon manner demonstrate that the LP-based approaches outperform a heuristic to determine the target quantities. Among the LP formulations, the ones with clearing functions perform best. We also demonstrate the value of anticipation. Note to Practitioners—A hierarchical approach is designed to decide when tools in wafer fabs have to be qualified for a certain lot family. Qualification-related decisions are highly relevant because qualifications are costly and take a lot of time. The top-level determines target quantities for each family based on linear programming. The mid-level is formed by a MILP. A dispatching scheme to implement the qualification decisions provides the base-level. The hierarchical approach is assessed in a rolling horizon setting using a simulation model of a 200mm wafer fab. The benefit of the different levels of the hierarchy is demonstrated by simulation experiments.

Budget-Conscious Fine-Grained Configuration Optimization for Spatio-Temporal Applications

Based on the performance requirements of modern spatio-temporal data mining applications, in-memory database systems are often used to store and process the data. To efficiently utilize the scarce DRAM capacities, modern database systems support various tuning possibilities to reduce the memory footprint (e.g., data compression) or increase performance (e.g., additional indexes). However, the selection of cost and performance balancing configurations is challenging due to the vast number of possible setups consisting of mutually dependent individual decisions. In this paper, we introduce a novel approach to jointly optimize the compression, sorting, indexing, and tiering configuration for spatio-temporal workloads. Further, we consider horizontal data partitioning, which enables the independent application of different tuning options on a fine-grained level. We propose different linear programming (LP) models addressing cost dependencies at different levels of accuracy to compute optimized tuning configurations for a given workload and memory budgets. To yield maintainable and robust configurations, we extend our LP-based approach to incorporate reconfiguration costs as well as a worst-case optimization for potential workload scenarios. Further, we demonstrate on a real-world dataset that our models allow to significantly reduce the memory footprint with equal performance or increase the performance with equal memory size compared to existing tuning heuristics.

Lagrangian Integro-Difference Equation Model for Precipitation Nowcasting

Abstract Delivering reliable nowcasts (short-range forecasts) of severe rainfall and the resulting flash floods is important in densely populated urban areas. The conventional method is advection-based extrapolation of radar echoes. However, during rapidly evolving convective rainfall this so-called Lagrangian persistence (LP) approach is limited to deterministic and very short-range nowcasts. To address these limitations in the 1-h time range, a novel extension of LP, called Lagrangian Integro-Difference equation model with Autoregression (LINDA), is proposed. The model consists of five components: 1) identification of rain cells, 2) advection, 3) autoregressive process describing growth and decay of the cells, 4) convolution describing loss of predictability at small scales, and 5) stochastic perturbations to simulate forecast uncertainty. Advection is separated from the other components that are applied in the Lagrangian coordinates. The reliability of LINDA is evaluated using the NEXRAD WSR-88D radar that covers the Dallas–Fort Worth metropolitan area, as well as the NEXRAD mosaic covering the continental United States. This is done with two different configurations: LINDA-D for deterministic and LINDA-P for probabilistic nowcasts. The validation dataset consists of 11 rainfall events during 2018–20. For predicting moderate to heavy rainfall (5–20 mm h−1), LINDA outperforms the previously proposed LP-based approaches. The most significant improvement is seen for the ETS and POD statistics with the 5 mm h−1 threshold. For 30-min nowcasts, they show 15% and 16% increases, respectively, to the second-best method and 48% and 34% increases compared to LP. For the 5 mm h−1 threshold, the increase in the relative operating characteristic (ROC) skill score of 30-min nowcasts from the second-best method is 10%. Significance Statement Delivering reliable forecasts of severe rainfall for the next few hours has a major societal importance. This is particularly true for densely populated urban areas, where flash floods can cause property damage and loss of lives. Such forecasts are conventionally produced by direct extrapolation of weather radar measurements. However, for intense localized rainfall this approach has low prediction ability beyond 30 min. To extend this limit, we propose a novel method that combines machine vision with a statistical model for growth and decay of rainfall. The method is designed for predicting highly localized rain cells and bands. In addition, a stochastic extension for producing probabilistic forecasts is developed. Using several verification metrics, we demonstrate that for predicting moderate to heavy rainfall (5–20 mm h−1), the proposed method has significantly improved forecast skill compared to the reference methods. The evaluation is done by using the NEXRAD WSR-88D that covers the Dallas–Fort Worth urban metroplex with a population of over 7 million. Demonstration of the applicability of LINDA in a larger domain is done by using the NEXRAD radar network that covers the continental United States.

Maximal quadratic-free sets

The intersection cut paradigm is a powerful framework that facilitates the generation of valid linear inequalities, or cutting planes, for a potentially complex set S. The key ingredients in this construction are a simplicial conic relaxation of S and an S-free set: a convex zone whose interior does not intersect S. Ideally, such S-free set would be maximal inclusion-wise, as it would generate a deeper cutting plane. However, maximality can be a challenging goal in general. In this work, we show how to construct maximal S-free sets when S is defined by a general quadratic inequality. Our maximal S-free sets are such that efficient separation of a vertex in LP-based approaches to quadratically constrained problems is guaranteed.

Assessing Source Evaluation Skills of Middle School Students Using Learning Progressions

ABSTRACT Effectively evaluating the credibility and accuracy of multiple sources is critical for college readiness. We developed 24 source evaluation tasks spanning four predicted difficulty levels of a hypothesized learning progression (LP) and piloted these tasks to evaluate the utility of an LP-based approach to designing formative literacy assessments. Sixth, seventh, and eighth grade students (N = 360, 120 per grade) completed 12 of the 24 tasks in an online testing session. Analyses examined the tasks’ reliability and validity and whether patterns of performance aligned to predicted LP levels (i.e., recovery of the LP) using task progression maps derived from item response theory (IRT). Results suggested that the LP tasks were reliable and correlated with external measures; however, some lower level tasks proved unexpectedly difficult. Possible explanations for low performance are discussed, followed by implications for future LP and task revisions. This work provides a model for designing and evaluating LP-based literacy assessments.

New partial aggregations for multicommodity network flow problems: An application to the fixed-charge network design problem

When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in the speed at which the LP can be solved, as it is linear in the number of constraints and variables. The conventional approach to improve the solve time of the LP relaxation of a Mixed Integer Programming (MIP) model that encodes such an instance is to aggregate all commodities that have the same origin or the same destination. However, the bound of the resulting LP relaxation can significantly worsen, which tempers the efficiency of aggregating techniques. In this paper, we introduce the concept of partial aggregation of commodities that aggregates commodities over a subset of the network instead of the conventional aggregation over the entire underlying network. This offers a high level of control on the trade-off between size of the aggregated MIP model and quality of its LP bound. We apply the concept of partial aggregation to two different MIP models for the multicommodity network design problem. Our computational study on benchmark instances confirms that the trade-off between solve time and LP bound can be controlled by the level of aggregation, and that choosing a good trade-off can allow us to solve the original large-scale problems faster than without aggregation or with full aggregation.

An LP-Based Approach for Goal Recognition as Planning

Goal recognition aims to recognize the set of candidate goals that are compatible with the observed behavior of an agent. In this paper, we develop a method based on the operator-counting framework that efficiently computes solutions that satisfy the observations and uses the information generated to solve goal recognition tasks. Our method reasons explicitly about both partial and noisy observations: estimating uncertainty for the former, and satisfying observations given the unreliability of the sensor for the latter. We evaluate our approach empirically over a large data set, analyzing its components on how each can impact the quality of the solutions. In general, our approach is superior to previous methods in terms of agreement ratio, accuracy, and spread. Finally, our approach paves the way for new research on combinatorial optimization to solve goal recognition tasks.

On the plausibility of using linear programming to trace important input–output coefficients in the framework of tolerable limits

Recent input–output (IO) literature offers original proposals on using linear programming (LP) to make ‘tolerable limits’ approach suitable for measuring the importance of IO coefficients to an economy. In this paper, I focus on one of such influential proposals presented in Tarancón et al. [(2008). A revision of the tolerable limits approach: searching for the important coefficients. Economic Systems Research, 20, 75–95]. In the theoretical part of this paper, I provide exact analytical solutions to the LP problems formulated in Tarancón et al. The main result proves that the classification of IO coefficients with respect to their importance in the sense of the LP-based indicators of Tarancón et al. does not depend on the benchmark welfare measure of interest. This fact, in turn, severely reduces practical applicability of the discussed LP-based approach to tracing important IO coefficients.

Reallocating multiple facilities on the line

We study the K-Facility Reallocation problem on the real line, where we maintain K facility locations over T stages, based on the stage-dependent locations of n agents. Each agent is connected to the nearest facility at each stage, and the facilities may move from one stage to another, to accommodate different agent locations. The objective is to minimize the connection cost of the agents plus the total moving cost of the facilities, over all stages. The K-Facility Reallocation problem was introduced by de Keijzer and Wojtczak, where they mostly focused on the special case of a single facility. Using an LP-based approach, we present a polynomial time algorithm that computes the optimal solution for any number of facilities. We also consider the online K-Facility Reallocation problem, where the algorithm becomes aware of agent locations in a stage-by-stage fashion. By exploiting an interesting connection to the classical K-server problem, we present a constant-competitive algorithm for K=2 facilities.

A MaxSAT-Based Framework for Group Testing

The success of MaxSAT (maximum satisfiability) solving in recent years has motivated researchers to apply MaxSAT solvers in diverse discrete combinatorial optimization problems. Group testing has been studied as a combinatorial optimization problem, where the goal is to find defective items among a set of items by performing sets of tests on items. In this paper, we propose a MaxSAT-based framework, called MGT, that solves group testing, in particular, the decoding phase of non-adaptive group testing. We extend this approach to the noisy variant of group testing, and propose a compact MaxSAT-based encoding that guarantees an optimal solution. Our extensive experimental results show that MGT can solve group testing instances of 10000 items with 3% defectivity, which no prior work can handle to the best of our knowledge. Furthermore, MGT has better accuracy than the LP-based approach. We also discover an interesting phase transition behavior in the runtime, which reveals the easy-hard-easy nature of group testing.

Linear Programming Based Near-Optimal Pricing for Laminar Bayesian Online Selection

In the Bayesian online selection problem, the goal is to design a pricing scheme for a sequence of arriving buyers that maximizes the expected social-welfare (or revenue) subject to different types of structural constraints. Inspired by applications in operations management, the focus of this paper is on the cases where the set of served customers is characterized by a laminar matroid. We give the first Polynomial-Time Approximation Scheme (PTAS) for the problem when the laminar matroid has constant depth. Our approach is based on rounding the solution of a hierarchy of linear programming relaxations that approximate the optimum online solution with any degree of accuracy plus a concentration argument that shows the rounding incurs a small loss. We also study another variation, which we call the production constrained problem, for which the allowable set of served customers is characterized by a collection of production and shipping constraints forming a certain form of laminar matroid. Using a similar LP-based approach, we design a PTAS for this problem even when the depth of the laminar matroid is not constant. The analysis exploits the negative dependency of the optimum selection rule in the lower-levels of the laminar family. Finally, we conclude with a discussion of the linear programming based approach employed in the paper and re-derive some of the classic prophet inequalities known in the literature.

Glottal Vocoding With Frequency-Warped Time-Weighted Linear Prediction

Linear prediction (LP) is a prevalent source-filter separation method of speech production. One of the drawbacks of conventional LP-based approaches is the biasing of estimated formants by harmonic peaks. Methods such as discrete all-pole modeling and weighted LP have been proposed to overcome this problem, but they all use a linear frequency scale. This study proposes a new LP technique, frequency-warped time-weighted linear prediction (WWLP), to provide spectral envelope estimates robust to harmonic peaks that work on a warped frequency scale that approximates the sensitivities of the human auditory system. Experiments are performed within the context of vocoding in statistical parametric speech synthesis. Subjective listening test results show that WWLP-based spectral envelope modeling increases quality over previously developed methods.

An integrated genetic algorithm approach to 1D-cutting stock problem

Manufacturing industries face trim minimisation problem, which if not effectively dealt results in loss of revenue. In this paper, we propose a new genetic-based approach to solve one dimensional cutting stock problem. The approach involves effective column generation techniques to stabilise and accelerate the solution process. This acceleration is achieved by imposing penalty function on the fitness value for evolution of better population. The GA capability is enhanced by using dynamic behaviour in crossover and mutation operators. The dynamism helps to improve the solution convergence rate to a great extend and controls the random behaviour to acceptable levels. Our approach reduces the rate by 60%. The computation comparison with the existing similar LP-based hybrid approach and other existing and recent meta heuristic approaches from literature proves the feasibility and validity of the algorithm. The proposed approach proves its efficiency and applicability on benchmark as well as industrial problems.

Scheduling residential battery storage with solar PV: Assessing the benefits of net metering

In this paper we propose a linear program (LP)-based algorithm to schedule battery storage co-located with residential solar photovoltaics (PV), when excess generation is compensated via net metering. While the objective of this LP-based approach is to maximize the operational savings that accrue to customers, an undesirable consequence to the utility is reverse power flow during the peak pricing period. We show in this paper that it is possible to balance the objective of the utility in limiting reverse power flow, with the customer objective of increasing operational savings, in the context of net metering. To balance the specified utility and customer objectives we employ a quadratic program (QP)-based algorithm, which explicitly penalizes reverse power flow. To complete our assessment of net metering, both the LP-based and QP-based scheduling algorithms are applied to measured load and generation data from 145 residential customers located in an Australian distribution network. The results of this case study confirm the absence of reverse power flow when all customers employ a QP-based battery schedule, with the majority of customers exhibiting operational savings.

Temporal Flexibility Revisited: Maximizing Flexibility by Computing Bipartite Matchings

We discuss two flexibility metrics for Simple Temporal Networks (STNs): the so-called naive flexibility metric based on the difference between earliest and latest starting times of temporal variables, and a recently proposed concurrent flexibility metric. We establish an interesting connection between the computation of these flexibility metrics and properties of the minimal distance matrix DS of an STN S: the concurrent flexibility metric can be computed by finding a minimum weight matching of a weighted bipartite graph completely specified by DS, while the naive flexibility metric corresponds to computing a maximum weight matching in the same graph. From a practical point of view this correspondence offers an advantage: instead of using an O(n5) LP-based approach, reducing the problem to a matching problem we derive an O(n3) algorithm for computing the concurrent flexibility metric.

LP-Based Approaches to Stationary-Constrained Markov Decision Problems

We study a class of Markov Decision Processes (MDPs) under stationary constraints (particularly but not exclusively, chance constraints). Our model focuses on problems where the state space is finite but the control at each state may take real values. It is straightforward to formulate the problem as a constrained nonlinear optimization problem, but solving it requires either projection, penalty or gradient-based methods that may show slow convergence, particularly because this type of problems may not be strictly convex.In this paper we extend results that are known for the discrete control model and show that the solution of a binary randomized control problem is optimal under the assumption that the dependency on the control variable is linear. If the dependency is piecewise linear with several breakpoints, then the randomized problem is not equivalent to the original problem; however we show that a particular solution always exists that is also the solution to the original continuous problem. This special solution takes the form of a two-action control policy for each state. Solving each two-action randomized problem can be done in polynomial time by linear programming (LP). This leads to an efficient solution when the number of states is small, but for a large state space the complexity can be prohibitive. In a restricted yet interesting special case of piecewise linear, multiple actions setting where the actions are linearly ordered, we show that the problem can again be reduced to a single LP.To overcome the computational complexity in the general case, we propose an alternative approach that involves solving a sequence of linear programs modeling the stationary measure and the optimal solution concurrently. We conclude the paper by discussing future extensions of this framework to application settings where the state space is continuous as well.

Positivity of discrete singular systems and their stability: An LP-based approach

In this paper we present an efficient approach to the analysis of discrete positive singular systems. One of our main objectives is to investigate the problem of characterizing positivity of such systems. Previously, this issue was not completely addressed. We provide easily checkable necessary and sufficient conditions for such problem to be solved. On the other hand, we study the stability of discrete positive singular systems. Note that this is not a trivial problem since the set of admissible initial conditions is not the whole space but it is represented by a special cone. All the conditions we provide are necessary and sufficient and are based on a reliable computational approach via linear programming.

Modeling and Optimization of the Multiobjective Stochastic Joint Replenishment and Delivery Problem under Supply Chain Environment

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP) approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA) solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE), hybrid DE (HDE), and genetic algorithm (GA), are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted.