Traditional Programming Model Research Articles

Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model

In many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same period. Consequently, traditional production planning models enforce minimum demand constraints by product and period rather than by individual orders. An important drawback of this aggregation procedure is that it requires a fixed order fulfillment period, potentially missing opportunities for more efficient resource use through early completion. This paper introduces a novel mathematical formulation that preserves the integrity of customer orders, allowing for early fulfillment when possible. We compare a traditional linear programming model with a new mixed-integer programming approach using a sawmill case study. Although more complex than the traditional model, the proposed formulation reduces costs by approximately 6% by enabling early order completion and offers greater flexibility and control over the production process. This approach leads to better resource utilization and more precise order management, presenting a valuable alternative to conventional production planning models.

Population based metaheuristics in Spark: Towards a general framework using PSO as a case study

Over the years metaheuristics have been successfully applied to optimization problems in many real-world applications. The increasing complexity and scale of the problems addressed has posed new challenges to researchers in the field. The application of distributed metaheuristics is a common approach to speed up the time to solution or improve its quality by leveraging traditional parallel programming models on platforms like multicore processors or computer clusters. More recently, the emergence of Cloud Computing and new programming models and frameworks for Big Data has facilitated access to an unprecedented amount of computational resources, which led to a growing interest in optimization frameworks that support the development and execution of distributed metaheuristics taking advantage of this potential. In this paper, we present the current status of development of one such framework that aims to provide support for the application of distributed population-based metaheuristics to the global optimization of large-scale problems in Spark. The framework provides a reduced set of abstractions to represent the general structure of population-based metaheuristics as templates and strategies to particularize them into concrete metaheuristics, as well as other nice features like out of the box implementations of the most common distributed models, full configurability through a human-friendly format, and the possibility of rapid prototyping and testing metaheuristics in the Spark shell. To validate the approach, a template for Particle Swarm Optimization (PSO) was implemented as a proof of concept, which includes strategies for instantiating different variants of the algorithm, configurable topologies, and sequential and distributed execution models.

Deep Learning-Based Prediction and Revenue Optimization for Online Platform User Journeys

<abstract> <p>In today's digital landscape, businesses must allocate online resources efficiently. Data-driven AI methods are increasingly adopted for customer journey management. This study enhances existing frameworks with three key propositions, integrating deep learning and optimization to create a three-step revenue optimization model using online customer data. First, we apply K-means clustering to analyze online user data, constructing a behavior model. Then, convolutional neural networks (CNN) and long short-term memory (LSTM) networks predict user behavior and conversion values from sequential data. Finally, the heuristic algorithm optimizes revenue within budget constraints based on conversions. From an academic perspective, our study provides an empirical, theory-grounded model for service and marketing management. Technologically, we identify three key findings: stacking LSTM with CNN effectively processes sequential online user data, outperforming traditional machine learning methods; optimization methods and decision trees improve model interpretability and address marketing attribution challenges by understanding user behavior and channel impacts; and traditional integer programming models fall short in solving high-dimensional online channel planning problems, necessitating heuristic algorithms. Our model aids companies in setting online channel standards and budgets, offering valuable insights and practical guidance to decision-makers.</p> </abstract>

VOLUMETRIC LIGHT TRANSFER IN FUNCTIONALLY DEFINED SCENES

In computer graphics, the main goals are high realism and rendering speed. In terms of realism, physically correct rendering is important, which calculates the transmission of light from the source to the observer. A method of modeling global illumination is presented, which takes into account light coming directly from sources, as well as light redirected through other parts of the scene. This allows you to create various optical effects, such as the flow of color from one surface to another, indirect lighting and caustics. The photon display method is designed for functionally defined scenes using graphics processors, thereby achieving an interactive rendering mode. The aim of the work is to implement a method for displaying photons in interactive rendering mode using graphics processors. It was necessary to find a compromise between physical accuracy and the speed of displaying scenes. As the number of parallel computing cores increases, traditional programming models become less efficient. GPUs based on the parallel processing model are being expanded by adding improved support for general-purpose computing to their cores. CUDA is a multicore computing platform. GPU-enabled hardware provides low-cost access to many computations. The method presented in this paper extends the photon-mapping algorithm for the CUDA platform to volumetric photon mapping. The beam brightness estimate used to efficiently calculate the density is recovered with the correct physical parameters. Photons are traced and bandwidth is selected. Performance increases due to calculations on multiple cores and the use of large compacted blocks.

A Constraint Programming Solution to the Guillotine Rectangular Cutting Problem

The guillotine rectangular cutting problem deals with a single rectangular plate of raw material and a collection of rectangular items to be cut from the plate. Each item is associated with a profit and a demand. The problem searches for a feasible layout of a subset of items on the plate so as to maximize the total profit of selected items. The guillotine constraint restricts feasible layouts to those that can be obtained via guillotine edge-to-edge cuts that run parallel to an edge of the plate. We propose a novel constraint programming model that is suitable for guillotine cutting with an arbitrary number of stages of alternating horizontal and vertical guillotine cuts. This is an assignment-based model that models guillotine cuts using a constant number of rectangular regions, with some regions allocated to items. It treats the entire plate as a primary region and decides on the guillotine cuts required to split the regions recursively till they produce space for the items. To speed the search, the model explores the strength of cumulative scheduling relaxations of the cutting problem. Our model is a successful alternative to more traditional mixed-integer linear programming (MILP) models. It outperforms a number of state-of-the-art MILPs on a set of small and moderate size benchmark instances and proves optimality for several instances that remain challenging for these MILPs.

Mixed-Integer Programming vs. Constraint Programming for Shop Scheduling Problems: New Results and Outlook

Constraint programming (CP) has been recently in the spotlight after new CP-based procedures have been incorporated into state-of-the-art solvers, most notably the CP Optimizer from IBM. Classical CP solvers were only capable of guaranteeing the optimality of a solution, but they could not provide bounds for the integer feasible solutions found if interrupted prematurely due to, say, time limits. New versions, however, provide bounds and optimality guarantees, effectively making CP a viable alternative to more traditional mixed-integer programming (MIP) models and solvers. We capitalize on these developments and conduct a computational evaluation of MIP and CP models on 12 select scheduling problems. 1 We carefully chose these 12 problems to represent a wide variety of scheduling problems that occur in different service and manufacturing settings. We also consider basic and well-studied simplified problems. These scheduling settings range from pure sequencing (e.g., flow shop and open shop) or joint assignment-sequencing (e.g., distributed flow shop and hybrid flow shop) to pure assignment (i.e., parallel machine) scheduling problems. We present MIP and CP models for each variant of these problems and evaluate their performance over 17 relevant and standard benchmarks that we identified in the literature. The computational campaign encompasses almost 6,623 experiments and evaluates the MIP and CP models along five dimensions of problem characteristics, objective function, decision variables, input parameters, and quality of bounds. We establish the areas in which each one of these models performs well and recognize their conceivable reasons. The obtained results indicate that CP sets new limits concerning the maximum problem size that can be solved using off-the-shelf exact techniques. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. 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.2023.1287 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0326 ) at ( http://dx.doi.org/10.5281/zenodo.7541223 ).

Two-stage distributionally robust optimization for disaster relief logistics under option contract and demand ambiguity

Disaster relief logistics (DRL) provides adequate relief supplies to victims of natural disasters (e.g., earthquakes and volcanic eruptions). This study explicitly considers supplier selection and inventory pre-positioning corresponding to static preparedness decisions, and post-disaster procurement and delivery associated with dynamic response decisions in actual DRL operations. To tackle issues triggered by shortage and surplus of multi-class relief resources, a flexible option contract is adopted to purchase relief items from suppliers. To measure the risk of demand ambiguity, a worst-case mean-quantile-deviation criterion is introduced to reflect the decision-maker’s risk-averse attitude. To handle the ambiguity in the probability distribution of demand, a novel two-stage distributionally robust optimization (DRO) model is developed for the addressed DRL problem. The proposed DRO model can be transformed into equivalent mixed-integer linear programs when the ambiguity sets incorporate all distributions within L1-norm and joint L1- and L∞-norms from a nominal (reference) distribution. A computational study of earthquakes in Iran is conducted to illustrate the applicability of the proposed DRO model to real-world problems. The experimental results demonstrate that our proposed DRO model has superior out-of-sample performance and can mitigate the effect of Optimization Bias compared to the traditional stochastic programming model. Some managerial insights regarding the proposed approach are provided based on numerical results.

Distributional robustness and lateral transshipment for disaster relief logistics planning under demand ambiguity

AbstractThis paper considers facility location, inventory pre‐positioning and vehicle routing as strategic and operational decisions corresponding to preparedness and response phases in disaster relief logistics planning. For balancing surpluses and shortages, an effective lateral transshipment strategy is proposed to evenly distribute the relief resources between warehouses after the disaster occurs. To handle ambiguity in the probability distribution of demand, we develop a risk‐averse two‐stage distributionally robust optimization (DRO) model for the disaster relief logistics planning problem, which specifies the worst‐case mean‐conditional value‐at‐risk (CVaR) as a risk measure. For computationally tractability, we transform the robust counterpart into its equivalent linear mixed‐integer programming model under the discrepancy‐based ambiguity set centered at the nominal (empirical) distributions on the observed demand from the historical data. We verify the effectiveness of the proposed DRO model and the value of lateral transshipment strategy by an illustrative small‐scale example. The numerical results show that the proposed DRO model has advantage on avoiding over‐conservative solutions compared to the classic robust optimization model. We also illustrate the applicability of the proposed DRO model by a real‐world case study of hurricanes in the southeastern United States. The computational results demonstrate that the proposed DRO model has superior out‐of‐sample performance and can mitigate the adverse effects of Optimizers' Curse compared with the traditional stochastic programming model.

Distributed robust optimization scheduling of a steel plant integrated energy system considering the uncertainty of byproduct coal gas

The steel plant integrated energy system (SPIES) is an important form in the steel industry. Improving the utilization efficiency of steam, electricity, coal gas and other energy flows is of great significance for both economic and environmental benefits. In this paper, a SPIES scheduling model is established according to the operation characteristics of coal gas holders, boilers and other equipment in steel plants. Meanwhile, to cope with the uncertainty of byproduct coal gas, this paper adopts an imprecise Dirichlet model (IDM) to construct a fuzzy set containing multisource coal gas production information. Then, according to duality theory and the big-M method, the original distributed robust optimization (DRO) model is transformed into a traditional mixed integer linear programming (MILP) model, which is solved by the column-and-constraint generation (CC&G) algorithm. Finally, a real steel production system is given in a case study. Case study illustrate that compared with the traditional robust method, the method proposed in this paper for a SPIES can effectively reduce the conservatism of the scheduling decision. Numerical simulation show that the proposed method can reduce total cost by 55,307.1¥, accounting for 1.91% of the total cost compared with robust optimization method and save 1,326.94 s of computational time compared with the stochastic optimization method, thus reaching balance between conservatism and computational efficiency.

Multi-stage stochastic programming based offering strategy for hydrogen fueling station in joint energy, reserve markets

Hydrogen fueling stations (HFSs) with onsite hydrogen production systems, which are usually composed of electrolyzers, hydrogen storage tanks and fuel cells, not only supply hydrogen for hydrogen-powered vehicles but also serve as a dispatchable technology that can bid in electricity markets. Except participating in energy market, joining in reserve market can compensate the cost in energy market and increase the total revenue of HFS. This paper proposes a multi-stage stochastic programming model to find the optimal offering strategy of the HFS in energy, reserve markets taking into account a series of uncertainties: day-ahead price, secondary reserve price, system imbalance price and hydrogen demand. Nonanticipativity constraints are employed to guarantee the decisions are made according to the realized uncertainty information up to the present stage. Compared with traditional stochastic programming model, the proposed model adequately considers the sequential bidding decisions with the gradual revealing of the uncertainty over time. Numerical experiments based on one case study indicate that the participation of reserve market greatly increase the revenue of HFS. In addition, the proposed multi-stage stochastic programming model is effective in characterizing the sequential decision.

State-Variable Modeling for a Class of Two-Stage Stochastic Optimization Problems

This paper considers a class of two-stage stochastic mixed-integer optimization problems where, for a given first-stage solution, we can determine the optimal values of recourse variables sequentially. This class of problems arises in a wide variety of applications. In the case of multivariate discrete distributions for uncertain parameters, a standard stochastic programming formulation of these problems involves an exponential number of scenarios, therefore an exponential number of variables and constraints. We propose a new mixed-integer programming modeling approach where the number of variables and constraints is independent of the number of scenarios and scales at most pseudopolynomially with the problem size. The proposed modeling approach relies on state variables that track the system’s state as the uncertainty realizes sequentially. We demonstrate the advantages of the proposed approach in two applications arising in project scheduling and operating room allocation. Summary of Contribution: This paper proposes a new modeling approach for a class of two-stage stochastic optimization problems that is computationally more efficient than the traditional scenario-based stochastic integer programming models. The proposed modeling approach relies on state variables that track the system's state as the uncertainty realizes sequentially. We demonstrated the efficiency of the proposed approach by computational results on two applications in project scheduling and operating room allocation.

A bivariate stochastic optimization model of bidding strategy considering the competition among renewable power producers

The competition among renewable power producers (RPPs) may lead the cleared power of RPPs to be less than the bidding power while the impacts of competition are neglected in the existing price-taker methods. To overcome the above deficiency, this paper develops an optimal bidding strategy considering the competition among RPPs. First, a bivariate stochastic optimization (BSO) model of bidding strategy is proposed by considering the variable power output of RPPs and the competition among RPPs. Particularly, the cleared power estimated by the demand-supply ratio is a random variable in the proposed BSO model. Then, the Newton method and particle swarm optimization (PSO) are combined to solve the BSO model in which various probability distribution functions (PDFs) of renewable energy generation are considered. Finally, the effectiveness of the proposed method is verified based on the results of a case study and the proposed model is performed better than the traditional chance-constrained programming (CCP) model in power market competition.

Randomized Objective Function Linear Programming in Risk Management

The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.

A Birandom Chance-Constrained Linear Programming Model for CCHP System Operation Management: A Case Study of Hotel in Shanghai, China

Due to its capability to reduce fuel consumption and increase energy efficiency, the combined cooling, heating, and power (CCHP) system has obtained great concern during the last decade. A large number of deterministic and stochastic optimization models were proposed for supporting the operation management of the CCHP system, but few studies noticed that users’ demands in the real world may be subjected to twofold randomness with incomplete or uncertain information. In this study, a birandom chance-constrained linear programming (BCCLP) model is developed for identifying optimal operation strategies under random uncertainties. Compared with traditional stochastic programming models, the BCCLP model made the improvement through describing the energy demands as the birandom variables firstly, instead of traditional random variables. This way effectively avoided potential imbalance between energy supply and demand caused by oversimplified expression of uncertain parameters. A gas-fired CCHP system of a hotel in Shanghai, China, was used as a study case for demonstration. A variety of operation strategies are obtained under specific constraints-satisfaction conditions. It is concluded that the BCCLP model was capable of generating the cost-effective operation strategies and evaluating the tradeoffs between system economy and reliability. The influence imposed by some critical parameters on the system performance was examined through the sensitivity analysis, which provided the important guidance to the design and operational management of other similar CCHP systems in the future.

Transparent many‐core partitioning for high‐performance big data I/O

SummaryAs the number of cores equipped in a single computing node is rapidly increasing, utilizing many cores for contemporary applications in an efficient manner is a challenging issue. We need to consider both parallelization and locality to fully exploit many cores for multifarious operations of emerging applications. In particular, big data applications perform computation and I/O intensive operations alternately. For instance, Apache Hadoop MapReduce assumes local persistent storage for each computing node. Thus, unlike traditional parallel programming models, the MapReduce framework performs not only networking but also storage I/O. In this study, we aim to improve the locality of network and storage I/O operations on many‐core systems by partitioning cores for I/O system calls and event handlers. In order to implement fine‐grained many‐core partitioning, we decouple the system call context from the user‐level process by suggesting message‐based system calls. The suggested design provides user‐level transparency and does not require any kernel‐level modifications. In addition, we propose a scheme that dynamically decides the core affinity of system calls and event handlers by considering locality, run‐time loads, and hardware architectures. The experimental results show that the proposed many‐core partitioning can improve the locality of network and storage I/O operations in an integrated manner for MapReduce applications.

On Providing OS Support to Allow Transparent Use of Traditional Programming Models for Persistent Memory

The advent of persistent memory (PM) into our everyday computing environment is now imminent. New programming models and algorithms based on these models are being developed for such systems. However, current models require programs to be rewritten with persistence related primitives such as clflush and clwb or at least recompiled so that persistent mechanisms can be automatically inserted. This is a burden to program developers. Furthermore, executing legacy programs as-is can lead to application and system inconsistencies as unexpected faults occur. In this article, we propose µSnap, an operating system support that is based on checkpointing that allows legacy applications to be executed as-is without compromising consistency in systems that deploy PM. We implement a prototype of µSnap in the Linux kernel version 4.3.3, and measure and quantify the effect of µSnap for a wide range of applications. We find that µSnap incurs overhead for application execution compared to applications run without any notion of persistency, but that the overhead can be controlled to be minimal by appropriately setting the checkpointing interval. We argue that the benefit for paying this small cost can be tremendous in the sense that one can transparently guarantee the consistency of all legacy software written under the traditional programming model.

Velocity-Based Training: From Theory to Application

ABSTRACT Velocity-based training (VBT) is a contemporary method of resistance training that enables accurate and objective prescription of resistance training intensities and volumes. This review provides an applied framework for the theory and application of VBT. Specifically, this review gives detail on how to: use velocity to provide objective feedback, estimate strength, develop load-velocity profiles for accurate load prescription, and how to use statistics to monitor velocity. Furthermore, a discussion on the use of velocity loss thresholds, different methods of VBT prescription, and how VBT can be implemented within traditional programming models and microcycles is provided.

Robust single machine scheduling problem with uncertain job due dates for industrial mass production

The single machine scheduling problem which involves uncertain job due dates is one of the most important issues in the real make-to-order environment. To deal with the uncertainty, this paper establishes a robust optimization model by minimizing the maximum tardiness in the worst case scenario over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our model only needs the information of due date intervals. The worst case scenario for a given sequence that belongs to a set containing only n scenarios is proved, where n is the number of jobs. Then, the model is simplified and reformulated as an equivalent mixed 0-1 integer linear programming (MILP) problem. To solve the MILP problems efficiently, a heuristic approach is proposed based on a robust dominance rule. The experimental results show that the proposed method has the advantages of robustness and high calculating efficiency, and it is feasible for large-scale problems.

Molecular Dynamics Simulation of Gas Pipeline Steel Based on LAMMPS Parallel Computing Platform

Along with the advent of the fourth industrial revolution, the processing capacity of big is highly demanded in industry community. Compared with the traditional computing and programming model based on serial program, parallel computing is based on heterogeneous architecture and runs in a completely different way from CPU, which has greatly enhanced the processing speed of large-scale data sets. Therefore, parallel computing has been developing dramatically in recent years, and has been favored by all walks of life. In the future, large-scale data processing must belong to parallel computing. Set on LAMMPS (large-scale atomic/molecular massively parallel simulator) as an example, this paper described the technique of establishing parallel computing platform, and applied it on simulated test on fracture process of lamellar structure from gas-pipeline steel.

A linear programming based approach for composite-action Markov decision processes

We study a time homogeneous discrete composite-action Markov decision process (CMDP) which needs to make multiple decisions at each state. In this particular Markov decision process, the state variables are divided into two separable sets and a two-dimensional composite action is chosen at each decision epoch. To solve a composite-action Markov decision process, we propose a novel linear programming model (Contracted Linear Programming Model, CLPM). We show that the CLPM model obtains the optimal state values of a CMDP process. We analyze and compare the number of variables and constraints of the CLPM model and the Traditional Linear Programming Model (TLPM). Computational experiments compare running times and memory usage of the two models. The CLPM model outperforms the TLPM model in both time complexity and space complexity by theoretical analysis and computational experiments.