Search

In this paper, a new mixed integer programming (MIP) formulation is developed for balancing and scheduling of mixed model assembly lines with disjunctive precedence constraints among assembly tasks. To represent alternative precedence relations, AND/OR assembly graph was adopted. In case of alternative precedence relations, for each product multiple assembly plans exist, which can be represented by a set of alternative precedence subgraphs and only one of such subgraphs should be selected for each product. As the number of subgraphs exponentially increases with the number of disjunctive relations among the tasks, the computational complexity of simultaneous balancing and scheduling along with the assembly subgraph selection increases with the number of alternative precedence relations. Unlike the other MIP approaches known from the literature, the new model does not need the alternative assembly subgraphs to be to explicitly enumerated as input data and then used for indexing the variables. Instead, a new disjunctive precedence selection and task assignment variable and new constraints are introduced to optimally choose one relation for each subset of alternative precedence relations. The optimal solutions for computational examples of balancing and scheduling problems illustrate a superior performance of the new modelling approach. [ABSTRACT FROM AUTHOR]

Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study the problem of unconstrained maximum polarization on compact sets. In particular, we discuss necessary conditions for local optimality, such as that a locally optimal configuration is always contained in the convex hull of the respective darkest points. Building on this, we propose two sequences of mixed-integer linear programs in order to compute lower and upper bounds on the maximal polarization, where the lower bound is constructive. Moreover, we prove the convergence of these sequences towards the maximal polarization. [ABSTRACT FROM AUTHOR]

Most tourist destinations are facing regular and consistent seasonality with significant economic and social impacts. This phenomenon is more pronounced in the post-covid era, where demand for travel has increased but unevenly among different geographic areas. To counter these problems that both customers and hoteliers are facing, we have developed two auctioning systems that allow hoteliers of lower popularity tier areas or during low season periods to auction their rooms in what we call a forward auction model, and also allows customers to initiate a bidding process whereby hoteliers in an area may make offers to the customer for their rooms, in what constitutes a reverse auction model initiated by the customer, similar to the bidding concept of priceline.com. We develop mathematical programming models that define explicitly both types of auctions, and show that in each type, there are significant benefits to be gained both on the side of the hotelier as well as on the side of the customer. We discuss algorithmic techniques for the approximate solution of these optimization problems, and present results using exact optimization solvers to solve them to guaranteed optimality. These techniques could be beneficial to both customer and hotelier reducing seasonality during middle and low season and providing the customer with attractive offers. We have integrated these techniques in a fully functional working prototype web application (). [ABSTRACT FROM AUTHOR]

This paper considers a single machine identical-jobs order scheduling problem with a position-dependent learning effect (SIOSLE) to minimize the total tardiness. A learning effect is common in the identical-jobs order manufacturing, such as clothing, bicycles, shoes, and so on, but its impact on the order scheduling problem has not been studied, especially for orders with different numbers of the same type of jobs. A mixed integer programming (MIP) model is first formulated for SIOSLE and serves as a benchmark. A new branch-and-bound algorithm was developed to handle computational complexity based on the Dominance, Split, Elimination, and Decomposition rules revised from the traditional job scheduling problem and new lower and upper bounds. Numerical experiments demonstrate that the proposed branch-and-bound algorithm is computationally better than the performance of using Gurobi, a popular commercial solver, to solve the MIP. The experiments for large-sized problems found that the proposed branch-and-bound algorithm can solve instances with up to 120 orders. The algorithm is more efficient for instances with a strong or weak learning effect, with tight or loose due dates, or with heterogeneous due dates. The effectiveness of the Dominance, Split, Elimination, and Decomposition rules varies with parameter settings. In addition, the proposed branch-and-bound algorithm can yield better solutions than traditional meta-heuristic algorithms but may require longer run time for large instances. [ABSTRACT FROM AUTHOR]

We describe a diving heuristic framework based on constraint propagation for mixed integer linear programs. The proposed approach is an extension of the common fix-and-propagate scheme, with the addition of solution repairing after each step. The repair logic is loosely based on the WalkSAT strategy for boolean satisfiability. Different strategies for variable ranking and value selection, as well as other options, yield different diving heuristics. The overall method is relatively inexpensive, as it is basically LP-free: the full linear programming relaxation is solved only at the beginning (and only for the ranking strategies that make use of it), while additional, typically much smaller, LPs are only used to compute values for the continuous variables (if any), once at the bottom of a dive. While individual strategies are not very robust in finding feasible solutions on a heterogeneous testbed, a portfolio approach proved quite effective. In particular, it could consistently find feasible solutions in 189 out of 240 instances from the public MIPLIB 2017 benchmark testbed, in a matter of a few seconds of runtime. The framework has also been implemented inside the commercial MIP solver Xpress and shown to give a small performance improvement in time to optimality on a large internal heterogeneous testbed. [ABSTRACT FROM AUTHOR]

Adjusting the deployment of each server in a server cluster in real-time and online based on a changing load has important considerations. In response to the deficiencies in the existing research on server switch jitter and real-time optimization, this paper proposes a periodic energy consumption optimization strategy based on mixed integer programming (MIP) for server clusters. During an optimization period, the strategy allows the CPU of the server to switch between adjacent frequencies to optimize cluster energy consumption at a granular level. First, we describe cluster energy optimization as a basic MIP model, with a reasonable definition of the decision variables and the modeling of the server load and power. Then, we include the server switch overhead in the objective function of the model, considering the joint optimization of multiple periods. Finally, we design an efficient solution scheme based on Gurobi and create two solution adjustment schemes that can reduce CPU frequency switching. The test results reveal that the proposed strategy can effectively suppress server switch jitter and can be carried out in real-time. The extra power cost of reducing CPU frequency switching is also evaluated and analyzed in the testing section. [ABSTRACT FROM AUTHOR]

This paper introduces a novel mixed integer programming (MIP) reformulation for the joint chance-constrained optimal power flow problem under uncertain load and renewable energy generation. Unlike traditional models, our approach incorporates a comprehensive evaluation of system-wide risk without decomposing joint chance constraints into individual constraints, thus preventing overly conservative solutions and ensuring robust system security. A significant innovation in our method is the use of historical data to form a sample average approximation that directly informs the MIP model, bypassing the need for distributional assumptions to enhance solution robustness. Additionally, we implement a model improvement strategy to reduce the computational burden, making our method more scalable for large-scale power systems. Our approach is validated against benchmark systems, i.e., IEEE 14-, 57- and 118-bus systems, demonstrating superior performance in terms of cost-efficiency and robustness, with lower computational demand compared to existing methods. [ABSTRACT FROM AUTHOR]

The adoption of battery electric trucks (BETs) as a replacement for diesel trucks has potential to significantly reduce greenhouse gas (GHG) emissions from the freight transportation sector. However, BETs have shorter driving range and lower payload capacity, which need to be taken into account when dispatching them. This paper addresses the energy-efficient dispatching of BET fleets, considering backhauls and time windows. To optimize vehicle utilization, customers are categorized into two groups: linehaul customers requiring deliveries and backhaul customers requiring pickups, where the deliveries need to be made following the last-in-first-out principle. The objective is to determine a set of energy-efficient routes that integrate both linehaul and backhaul customers, while considering factors such as limited driving range, payload capacity of BETs and the possibility of en route recharging. The problem is formulated as a mixed-integer linear programming (MILP) model and propose an adaptive large neighborhood search (ALNS) metaheuristic algorithm to solve it. The effectiveness of the proposed strategy is demonstrated through extensive experiments using a real-world case study from a logistics company in Southern California. The results indicate that the proposed strategy leads to a significant reduction in total energy consumption compared to the baseline strategy, ranging from 7% to 40%, while maintaining reasonable computational time. This research contributes to the development of sustainable transportation solutions in the freight sector by providing a practical and more efficient approach for dispatching BET fleets. The findings emphasize the potential of BETs in achieving energy savings and advancing the goal of green logistics.  View the NCST Project Webpage

We review existing approaches to optimizing the deployment of genetic biocontrol technologies-tools used to prevent vector-borne diseases such as malaria and dengue-and formulate a mathematical program that enables the incorporation of crucial ecological and logistical details. The model is comprised of equality constraints grounded in discretized dynamic population equations, inequality constraints representative of operational limitations including resource restrictions, and an objective function that jointly minimizes the count of competent mosquito vectors and the number of transgenic organisms released to mitigate them over a specified time period. We explore how nonlinear programming (NLP) and mixed integer nonlinear programming (MINLP) can advance the state of the art in designing the operational implementation of three distinct transgenic public health interventions, two of which are presently in active use around the world.

We study the problem of category space location-allocation in the retail industry. We introduce a new attractiveness factor to reflect the product-based visibility level in designing the optimal allocation policy. This factor will be determined for each aisle by the lineup of product categories allocated to that aisle and all other aisles sharing a shopping path with it. We explore how considering the classical location-based attractiveness and the proposed product-based attractiveness can improve a retailer's overall space profitability. We develop a modelling framework that integrates both location-based and product-based attractiveness factors in a mixed-integer nonlinear program. Due to the non-linearity and non-convexity of the proposed model, large-scale instances are computationally challenging to solve using the state-of-the-art commercial solvers. We thus introduce a two-stage heuristic solution method that generates a near-optimal solution in a reasonable amount of time. Using the two-stage model, we explore the optimal store design for an illustrative case study. The results couple the optimal category space allocation to customers' shopping paths and create a profitability-maximising balance between the placement of high-demand and high-impulse product categories. We show that focussing on product-based attractiveness exposes the store to congestion risks, which can be prevented by adding constraints limiting congestion in different aisles of the store. [ABSTRACT FROM AUTHOR]

Purpose: In this research, a modular hub location problem has been investigated where the objective is to reduce the transportation costs in the hub network. The proposed model determines the location of hubs, allocation of the non-hub nodes to the hubs, and the optimal vehicle traffic, i.e., the number of flights or the number of trucks traveling in the network, considering the appropriate capacity for each vehicle. Also, decisions regarding the percentage of the traffic volume sent via multiple network routes are made by the presented model.Methodology: The mathematical model, including the objective function and constraints, is constructed and solved by GAMS software. The effect of different parameters on the results is investigated. Due to long solution times for the MIP model, a heuristic solution method based on LP relaxation of the integer variables is developed for the proposed problem, which is able to obtain near-optimal solutions in less time.Findings: The developed mathematical model is implemented on the air passenger transportation data for the airports of the United States of America, which is known as the CAB data set. The results give the optimal number of hubs, as well as the optimal number of transportation units on each arc of the network, which depend on the capacity of the means of transportation.Originality/Value: In this research, a mixed integer programming model is developed for the multiple allocation modular hub location problem. Numerical experiments are conducted with the use of GAMS software and the results are discussed.

The subject of this paper is to develop a method for synthesizing stable neural network controllers with optimization of transient process parameters. The goal is to develop a method for synthesizing a neural network controller for control systems that guarantees the closed-loop system stability through automated selection of Lyapunov function with the involvement of an additional neural network trained on the data obtained in the solving process the integer linear programming problem. The tasks to be solved are: study the stability of a closed-loop control system with a neural network controller, train the neurocontroller and Lyapunov neural network function, create an optimization model for the loss function minimization, and conduct a computational experiment as an example of the neural network stabilizing controller synthesis. The methods used are: a neural network-based control object simulator training method described by an equations system taking into account the SmoothReLU activation function, a direct Lyapunov method to the closed-loop system stability guarantee, and a mixed integer programming method that allows minimizing losses and ensuring stability and minimum time regulation for solving the optimization problem. The following results were obtained: the neural network used made it possible to obtain results related to the transient process time reduction to 3.0 s and a 2.33-fold reduction in overregulation compared to the traditional controller (on the example of the TV3-117 turboshaft engine fuel consumption model). The results demonstrate the proposed approach's advantages, remarkably increasing the dynamic stability and parameter maintenance accuracy, and reducing fuel consumption fluctuations. Conclusions. This study is the first to develop a method for synthesizing a stabilizing neural network controller for helicopter turboshaft engines with guaranteed system stability based on Lyapunov theory. The proposed method's novelty lies in its linear approximation of the SmoothReLU activation function using binary variables, which allowed us to reduce the stability problem to an optimization problem using the mixed integer programming method. A system of constraints was developed that considers the control signal and stability conditions to minimize the system stabilization time. The results confirmed the proposed approach's effectiveness in increasing engine adaptability and energy efficiency in various operating modes.

AbstractByproduct hydrogen offers a cost-effective entry into hydrogen energy. However, the inherent complexity of hydrogen supply chain (HSC) presents hurdles in production, transport, and utilization, leading to low utilization and increased costs. Hydrogen supply chain network design (HSCND) and hydrogen fueling station planning (HFSP) both aim to optimize HSC from different angles, but integrating these two into a single framework poses challenges. Furthermore, HSC design directly influences hydrogen fuel cell vehicle (HFCV) adoption, influenced by factors like vehicle registration, driving tolerance range, traveling range, and more. The aim of this study is to develop an end-to-end supply chain framework that simultaneously considers HSCND and HFSP, encompassing all segments of the HSC. We design a two-stage model that aligns with each stage of HSC. From the end-user’s (station) perspective, we find optimal locations of Hydrogen Refueling Stations (HRSs) on expressways by means of a capacitated flow-refueling location model (CFRLM) combined with a hydrogen vehicle refueling station logic. This model considers government policy and consumer adoption factors with the goal of striking a balance between consumer interests and HRS decision-makers. For transporting byproduct production, we use a Voronoi Diagram (VD)-based capacitated vehicle routing model (CVRP) to deliver byproduct hydrogen from industrial areas to stations. The VD is employed to determine the assignment of HRSs in different target periods. Finally, we propose a modified branch-and-cut (BC) algorithm to solve the VD-based CVRP, which significantly outperforms commercial solvers in both speed and solution quality. Through sensitivity analysis, we identify critical factors impacting overall cost and hydrogen utilization. Tested on real and benchmark datasets, our algorithm increases byproduct hydrogen utilization by over 10% overall, reaching up to 70% in key industrial areas, while also achieving maximum path and flow coverage. [ABSTRACT FROM AUTHOR]

Inland waterway transportation plays a crucial role in Europe's transportation network and economy. It is an efficient and sustainable mode of transportation, with lower emissions and energy consumption than other modes of transportation, such as road and air. However, the services provided by inland waterway transport can be significantly impacted by adverse weather conditions such as heavy rain, strong winds, and flooding. These disruptions can cause delays, cancellations, or even damage to vessels or infrastructure. To improve the system reliability, we propose a set of revenue management based (demand itinerary) rerouting mechanisms for intermodal barge transportation optimisation. Revenue Management policies including several customer categories and fare differentiation are applied. Sequential accept/reject decisions are made based on a probabilistic mixed integer programming model maximising the expected revenue of a carrier. A booking framework is defined over a rolling horizon and capacity allocation/reallocation decisions are made for a set of demands including the current and relevant past and potential future transportation requests. Several (demand) rerouting mechanisms are defined and implemented on different service network configurations. The service network status is regularly updated, in particular with respect to barge capacity variations due to changing water levels. An extensive set of experiments is performed and numerical results are analysed. The study results emphasise the added value but also the need for data availability and information sharing between the different stakeholders of Inland Waterway Transportation systems. [ABSTRACT FROM AUTHOR]

Copyright of Operations Research Transactions / Yunchouxue Xuebao is the property of Editorial office of Operations Research Transactions and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Purpose: In this research, a modular hub location problem has been investigated where the objective is to reduce the transportation costs in the hub network. The proposed model determines the location of hubs, allocation of the non-hub nodes to the hubs, and the optimal vehicle traffic, i.e., the number of flights or the number of trucks traveling in the network, considering the appropriate capacity for each vehicle. Also, decisions regarding the percentage of the traffic volume sent via multiple network routes are made by the presented model. Methodology: The mathematical model, including the objective function and constraints, is constructed and solved by GAMS software. The effect of different parameters on the results is investigated. Due to long solution times for the MIP model, a heuristic solution method based on LP relaxation of the integer variables is developed for the proposed problem, which is able to obtain near-optimal solutions in less time. Findings: The developed mathematical model is implemented on the air passenger transportation data for the airports of the United States of America, which is known as the CAB data set. The results give the optimal number of hubs, as well as the optimal number of transportation units on each arc of the network, which depend on the capacity of the means of transportation. Originality/Value: In this research, a mixed integer programming model is developed for the multiple allocation modular hub location problem. Numerical experiments are conducted with the use of GAMS software and the results are discussed. [ABSTRACT FROM AUTHOR]

The fragmentation of natural environments, generally a consequence of human activity, is one of the main threats to biodiversity. The conservation or creation of ecological corridors is essential in an attempt to remedy this fragmentation. We propose a multi-species model to help decision-makers select an optimal network of corridors from a very general potential network, within a budgetary constraint. The selected network must link a given set of biodiversity reservoirs both spatially and biologically. It must therefore be adapted to a given set of species, i.e. it must take account of the fact that certain corridors and reservoirs are more or less suitable for certain species. The quality of the selected network is measured against the quality of the potential network. This network must also take into account the distance certain species have to travel to connect reservoirs, as well as the possibility for certain species to connect reservoirs even when certain corridors have become impassable, thanks to redundant paths. The proposed model is formulated by a mixed-integer mathematical program. A small example illustrates the model and its resolution in detail. Experiments on larger examples using one of the efficient commercial solvers currently available demonstrate the model's practicability. [ABSTRACT FROM AUTHOR]

HIGHLIGHTS Some forest harvest scheduling processes that have been used for many years in practice and research employ rules that emulate human behaviour. Linear programming and mixed integer programming represent sophisticated mathematical procedures, yet there is arguably nothing intelligent inherent in the search process to allow them to emulate human behaviour. With basic random search, no intelligence is employed, and the search process lacks functions that would allow adaptation of search behaviour based on knowledge gained. With hill-climbing search, very little intelligence is employed, and the search process lacks functions that would allow adaptation of search behaviour based on knowledge gained. With other heuristic search processes and evolutionary computation methods, some intelligence is employed, and the search processes may contain functions that would allow adaptation of search behaviour based on knowledge gained. While some forest harvest scheduling processes are similar in how they solve a complex problem, the degree to which they emulate artificial intelligence (learning from search history, adapting the search behaviour) varies. SUMMARY Contemporary tactical forest harvest scheduling efforts address planning problems that generally have an economic or commodity production objective, accounting routines to accumulate outcomes or to assess the extent of forest conditions, and constraints (policy or resource) that limit the assignment of management actions to subdivisions of a forest (stands or strata). Operations research methods have proven useful for addressing these problems and providing guidance, in the form of a harvest schedule, to people managing forests. Heuristic search and simulation methods have also shown promise for addressing these types of problems. Artificial intelligence includes some of these forms of search processes. When concepts of learning, adaptation, and emulation of human thought describe certain search processes, they can be considered under the broad umbrella of artificial intelligence. In this work, many of the operations research, heuristic search, and simulation methods that have been demonstrated as useful for forest harvest scheduling efforts are assessed for their association with artificial intelligence. In some cases, it is argued that the forestry profession has been using artificial intelligence for quite some time to develop tactical forest harvest schedules. Les efforts contemporains de planification pour une récolte forestière tactique font face à des problèmes de planification ayant en général un objectif économique ou de production de commodité, des routines comptables pour accumuler les résultats ou pour évaluer l'étendue des conditions forestières, et des contraintes (de politique ou de ressources) qui limitent l'octroi d'actions de gestion à des subdivisions de forêt (parcelles ou données). Les méthodes de recherche d'observation se sont montrées être utiles pour faire face à ces problèmes et pour offrir de l'aide, sous forme d'une planification de la récolte aux personnes gérant la forêt. Une recherche heuristique et des méthodes de simulation ont également été prometteuses pour faire face à ces types de problèmes. L'intelligence artificielle inclut certaine de ces formes de processus de recherche. Quand les concepts d'apprentissage, d'adaptation et d'émulation de la pensée humaine décrivent certain processus de recherche, ils peuvent être considérés comme étant sous la large égide de l'intelligence artificielle. Dans ce travail, plusieurs des recherches d'opérations, la recherche heuristique et les méthodes de simulation qui ont prouvé être utiles aux efforts de planification de la récolte forestière sont évaluées du point de vue de leur association avec l'intelligence artificielle. Dans certains cas, il est avancé que la profession de foresterie a utilisé l'intelligence artificielle depuis longtemps pour développer des planifications tactiques de récolte forestière. Los esfuerzos contemporáneos de programación táctica de aprovechamientos forestales abordan problemas de planificación que generalmente tienen un objetivo económico o de producción de materias primas, rutinas contables para acumular resultados o evaluar el alcance de las condiciones forestales, y restricciones (políticas o de recursos) que limitan la asignación de acciones de gestión a subdivisiones de un bosque (rodales o estratos). Los métodos de investigación operativa han demostrado su utilidad para abordar estos problemas y ofrecer orientación, en forma de calendario de aprovechamientos, a quienes gestionan los bosques. La búsqueda heurística y los métodos de simulación también han demostrado ser prometedores para abordar este tipo de problemas. La inteligencia artificial incluye algunas de estas formas de procesos de búsqueda. Cuando los conceptos de aprendizaje, adaptación y emulación del pensamiento humano describen ciertos procesos de búsqueda, pueden considerarse parte del amplio abanico de la inteligencia artificial. En este trabajo se evalúan muchos de los métodos de investigación operativa, búsqueda heurística y simulación que se han demostrado útiles para la programación de los aprovechamientos forestales por su asociación con la inteligencia artificial. En algunos casos, se sostiene que la silvicultura lleva bastante tiempo utilizando la inteligencia artificial para elaborar programas tácticos de aprovechamientos forestales. [ABSTRACT FROM AUTHOR]

Mixed integer programming is inherently involved in solving a significant number of practical problems. This paper focuses on mixed integer programming, where the objective function is the summation of N functions, and the constraints include both scalar coupling and set constraints. Given the potentially large scale of these problems, the goal of this work is to propose a distributed method to solve large-scale problems more efficiently. The right-hand side allocation decomposition approach is employed to address the large-scale mixed integer programming problem. Algorithms are then proposed for solving these problems, based on the analysis of the continuity, differentiability, and local convexity properties of the decomposed subproblems. Simulation experiments with randomly generated coefficients demonstrate the superior performance of the proposed algorithms compared to the Gurobi solver, offering higher solution accuracy and faster processing time for large-scale mixed integer programming problems with nonlinear objective and constraint functions. [ABSTRACT FROM AUTHOR]

To guarantee the safety of flight operations, decision-support systems for air traffic control must be able to improve the usage of airspace capacity and handle increasing demand. This study addresses the aircraft conflict avoidance and trajectory recovery problem. The problem of finding the least deviation conflict-free aircraft trajectories that guarantee the return to a target waypoint is highly complex due to the nature of the nonlinear trajectories that are sought. We present a two-stage iterative algorithm that first solves initial conflicts by manipulating their speed and heading control and then identifying each aircraft's optimal time to recover its trajectory towards their nominal one. We extend existing mixed-integer programming formulations by modelling speed and heading control as continuous variables while recovery time is treated as a discrete variable. We develop a novel iterative approach which shows that the trajectory recovery costs can be anticipated by inducing avoidance trajectories with higher deviation, therefore obtaining earlier recovery time within a few iterations. Numerical results on benchmark conflict resolution problems show that this approach can solve instances with up to 30 aircraft within 10 min. [ABSTRACT FROM AUTHOR]

Copyright of GeSec: Revista de Gestao e Secretariado is the property of Sindicato das Secretarias e Secretarios do Estado de Sao Paulo (SINSESP) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a framework for classifying and comparing instances of integer linear programs (ILPs) based on their mathematical structure. It has long been observed that the structure of ILPs can play an important role in determining the effectiveness of certain solution techniques; those that work well for one class of ILPs are often found to be effective in solving similarly structured problems. In this work, the structure of a given ILP instance is captured via a graph-based representation, where decision variables and constraints are described by nodes, and edges denote the presence of decision variables in certain constraints. Using machine learning techniques for graph-structured data, we introduce two approaches for leveraging the graph representations for relating ILPs. In the first approach, a graph convolutional network (GCN) is used to classify ILP graphs as having come from one of a known number of problem classes. The second approach makes use of latent features learned by the GCN to compare ILP graphs to one another directly. As part of the latter approach, we introduce a formal measure of graph-based structural similarity. A series of empirical studies indicate strong performance for both the classification and comparison procedures. Additional properties of ILP graphs, namely, losslessness and permutation invariance, are also explored via computational experiments. 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.2023.0255) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2023.0255). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

The subject of this paper is to develop a method for synthesizing stable neural network controllers with optimization of transient process parameters. The goal is to develop a method for synthesizing a neural network controller for control systems that guarantees the closed-loop system stability through automated selection of Lyapunov function with the involvement of an additional neural network trained on the d ata obtained in the solving process the integer linear programming problem. The tasks to be solved are: study the stability of a closed-loop control system with a neural network controller, train the neurocontroller and Lyapunov neural network function, create an optimization model for the loss function minimization, and conduct a computational experiment as an example of the neural network stabilizing controller synthesis. The methods used are: a neural network - based control object simulator training method described by an equations system taking into account the Smooth-ReLU activation function, a direct Lyapunov method to the closed-loop system stability guarantee, and a mixed integer programming method that allows minimizing losses and ensuring stability a nd minimum time regulation for solving the optimization problem. The following results were obtained: the neural network used made it possible to obtain results related to the transient process time reduction to 3.0 s and a 2.33 -fold reduction in overregulation compared to the traditional controller (on the example of the TV3 -117 turboshaft engine fuel consumption model). The results demonstrate the proposed approach's advantages, remarkably increasing the dynamic stability and parameter maintenance accuracy, and reducing fuel consumption fluctuations. Conclusions. This study is the first to develop a method for synthesizing a stabilizing neural network controller for helicopter turboshaft engines with guaranteed system stability based on Lyapunov theory. The proposed method's novelty lies in its linear approximation of the SmoothReLU activation function using binary variables, which allowed us to reduce the stability problem to an optimization problem using the mixed integer programming method. A system of constraints was developed that considers the control signal and stability conditions to minimize the system stabilization time. The results confirmed the proposed approach's effectiveness in increasing engine adaptability and energy efficiency in various operating modes. [ABSTRACT FROM AUTHOR]

We consider a staff allocation problem at a sequential sorting facility. In this facility, staff need to be assigned to work areas, through which commodities flow sequentially to be processed. Assigning staff optimally involves a trade-off between several different objectives, such as minimising the overall number of workers, as well as having fewer changes in the staff levels over time. While optimising for these, many operational requirements need to be met, including minimum processing volumes, correct ordering/processing of the commodities, and not exceeding staff resource constraints. We develop a deterministic time-expanded network flow model to solve the staff allocation problem. The model addresses the problem at a more granular timescale and with more operational constraints than previously used models. We use a lexicographical approach to deal with the multiple objectives. To demonstrate the model's value, we apply it to a staff problem of a UK mail centre, showing that in the majority of cases, our model improves on current staffing practises on both objectives. We also show how the model performs in several different scenarios, including increasing total mail volumes and changing the proportion of letters and parcels to be sorted. [ABSTRACT FROM AUTHOR]

Motivated by the operational scenarios of lock scheduling, we propose a serial-lock chain navigation problem (SLCNP) modeled on the Three Gorges-Gezhouba Dam (TGGD) for the first time. Ship grouping, synchronized moving, and grouped waiting operations are integrated into the ship navigation process. A mixed integer programming (MIP) model that incorporates real-world constraints such as ship priority, service fairness, traffic flow equilibrium, and phased ship placement is presented to optimize ship throughput and ship stay time. To solve the SLCNP, a sort-pick strategy-based swarm intelligence algorithm (SPSSIA) framework is developed that integrates the characteristics of SLCNP through a hybrid multi-section encoding method and a two-stage heuristic decoding approach. A swarm intelligence evolution mechanism is used to improve the search ability and robustness of the framework. Several instances are generated based on real data to verify the correctness and effectiveness of the model and algorithm. Computational results demonstrate the applicability and effectiveness of the proposed SPSSIA. Further analysis of the experimental results indicates that the key impact factors significantly influence the navigational performance of the TGGD system. The results of this study will provide practical guidance for the operational processes of inland river hubs with comparable characteristics. [ABSTRACT FROM AUTHOR]

Copyright of Palestine Journal of Mathematics is the property of Palestine Polytechnic University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We consider an integrated batching problem for steel-making and continuous casting process of steel plate manufacturing. For steel-making, slab batching problem is defined to make charges from slabs, and for continuous casting, charge batching problem is defined to make casts from charges. Our batching problem is regarded as a combination of slab batching and charge batching problems. Since steel-making and continuous casting are processes that must be synchronised, two batching problems must be integratedly handled. However, because of their difficulties, most papers solved each batching problem sequentially. We deal with a batching problem under bi-strand casting environment where slabs are cast with two strands. We also consider practical aspects that were barely considered before such as slab length difference constraints between strands and casts having few charges. We propose two mixed integer programming models. The first one is to create frames to define the overall structure of the solution and the second one is to fill the created frames with slabs to concretise the solution. The proposed matheuristic algorithm solves the problem in an integrated manner and finds a near-optimal solution in a reasonable time. It outperforms the company's current practice, as shown in experiments with real and randomly generated data. [ABSTRACT FROM AUTHOR]

In deterministic optimization, it is typically assumed that all problem parameters are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from contextual information. A typical predict-then-optimize approach separates predictions and optimization into two distinct stages. Recently, end-to-end predict-then-optimize has emerged as an attractive alternative. This work introduces the PyEPO package, a PyTorch-based end-to-end predict-then-optimize library in Python. To the best of our knowledge, PyEPO (pronounced like pineapple with a silent "n") is the first such generic tool for linear and integer programming with predicted objective function coefficients. It includes various algorithms such as surrogate decision losses, black-box solvers, and perturbated methods. PyEPO offers a user-friendly interface for defining new optimization problems, applying state-of-the-art algorithms, and using custom neural network architectures. We conducted experiments comparing various methods on problems such as the Shortest Path, the Multiple Knapsack, and the Traveling Salesperson Problem, discussing empirical insights that may guide future research. PyEPO and its documentation are available at https://github.com/khalil-research/PyEPO. [ABSTRACT FROM AUTHOR]

This research delves into the dynamic landscape of transportation systems, with a specific focus on the integration of drones and conventional vehicles. The study presents a Mixed Integer Programming (MIP) model for the Capacitated Multi-Drone Assisted Vehicle Routing Problem (mDroneCVRP), aiming to minimize the time of the last vehicle's arrival at the warehouse. It is essential to highlight that the proposed model was effectively solved using the CPLEX algorithm within the GAMS framework, underscoring the sophistication of the solution approach. The integration of multiple drones into the routing process proves to be instrumental in significantly reducing service time, demonstrating the efficacy of synergizing drone and truck operations. As the number of nodes escalates, emphasizing the necessity for heuristic approaches to address larger instances, the study provides valuable insights into the judicious use of drones in synchronized routing operations. Furthermore, the research challenges conventional assumptions by permitting drones to take off from and land on different vehicles, thereby augmenting operational capabilities and adeptly tackling contemporary transportation challenges. [ABSTRACT FROM AUTHOR]

Introduction and objectives: Sustainable development is defined as development that meets the needs of the present generation without compromising the ability of future generations to meet their own needs. It encompasses economic, social, and environmental dimensions that must be considered simultaneously. With the increasing importance of sustainable development, many companies worldwide are motivated, either proactively or reactively, to collect their used products. In such circumstances, establishing a reverse logistics network based on sustainable development is essential. The decision to outsource logistics has gained significance due to the need to avoid fixed costs, heavy investment, and achieve economic advantages, with many companies recognizing the potential benefits of high-quality logistics services. Method: This research presents a mixed integer programming model for planning reverse logistics outsourcing in the assembly cycle of the automotive industry, focusing on a cost-oriented objective function. The research scope includes the assembly cycle of production lines, specifically prioritizing high-volume car manufacturers (light vehicles), and focuses on the Saipa Automotive Industrial Group, including the Ryan Saipa Leasing Group. The research period spans from 1389 to 1398 in the Iranian calendar. Variables such as non-commercial receivables, total assets, operating profit, net profit, and market value were evaluated using MATLAB software based on published statistics from Saipa. Findings: The research findings indicate that among the variables of non-commercial receivables, total assets, operating profit, net profit, and market value, net profit to operating profit and sales (operating income) are of significant importance. The highest amount of non-commercial receivables for Saipa occurred in 1398 during the summer, while the highest total assets were recorded in 1392 during the summer. The highest operating profit was observed in 1398 during the winter, and the highest net profit was in 1390 during the spring. The degree of data convergence was calculated in the regression charts of sales (operating income) to operating profit and net profit to operating profit for the years 1389-1398. The degree of data convergence in the regression chart of sales to operating profit based on the conceptual model in 1398 was 0.9895, and for net profit to operating profit in 1398, it was 0.9961. The regression rate for the conceptual model in the test phase was 0.79, and in the overall processing stage, it was also 0.79. The histogram error rate was calculated for all three stages of learning, validation, and testing, with an error rate of 0.002375, which is acceptable due to its proximity to zero. Comparing these results with other studies shows an improvement in the regression and error rate in the analysis of the objective function. Conclusion: Based on the calculated weight of the criteria in two-way assembly line balancing issues, it can be concluded that the decision team pays special attention to strategic issues in addition to production issues. The production rate of the line, which is the inverse of the production cycle time, affects the company's market share in the long term and increases its market share. [ABSTRACT FROM AUTHOR]

In this paper, we address the difficulty of solving large-scale multi-dimensional knapsack instances (MKP), presenting a novel deep reinforcement learning (DRL) framework. In this DRL framework, we train different agents compatible with a discrete action space for sequential decision-making while still satisfying any resource constraint of the MKP. This novel framework incorporates the decision variable values in the 2D DRL where the agent is responsible for assigning a value of 1 or 0 to each of the variables. To the best of our knowledge, this is the first DRL model of its kind in which a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our framework is configured to solve MKP instances of different dimensions and distributions. We propose a K-means approach to obtain an initial feasible solution that is used to train the DRL agent. We train four different agents in our framework and present the results comparing each of them with the CPLEX commercial solver. The results show that our agents can learn and generalize over instances with different sizes and distributions. Our DRL framework shows that it can solve medium-sized instances at least 45 times faster in CPU solution time and at least 10 times faster for large instances, with a maximum solution gap of 0.28% compared to the performance of CPLEX. Furthermore, at least 95% of the items are predicted in line with the CPLEX solution. Computations with DRL also provide a better optimality gap with respect to state-of-the-art approaches. [ABSTRACT FROM AUTHOR]