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Fair integer programming under dichotomous and cardinal preferences

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第3期320卷 465-478页

作者： Demeulemeester, Tom Goossens, Dries Hermans, Ben Leus, Roel Katholieke Univ Leuven Res Ctr Operat Res & Stat Leuven Belgium Univ Ghent Dept Business Informat & Operat Management Ghent Belgium FlandersMake UGent Corelab CVAMO Ghent Belgium ORTEC Boortmeerbeek Belgium

One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables represent agents with dichotomous preferences, who only care about whether they are selected in the final solution. We develop several general-purpose algorithms to fairly select optimal solutions, for example, by maximizing the Nash product or the minimum selection probability, or by using a random ordering of the agents as a selection criterion (Random Serial Dictatorship). We also discuss in detail how to extend the proposed methods when agents have cardinal preferences. As such, we embed the "black-box"procedure of solving an integer linear program into a framework that is explainable from start to finish. Lastly, we evaluate the proposed methods on two specific applications, namely kidney exchange (dichotomous preferences), and the scheduling problem of minimizing total tardiness on a single machine (cardinal preferences). We find that while the methods maximizing the Nash product or the minimum selection probability outperform the other methods on the evaluated welfare criteria, methods such as Random Serial Dictatorship perform reasonably well in computation times that are similar to those of finding a single optimal solution.

关键词： integer programming Fairness Inequity Randomization Column generation

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Relaxations and duality for multiobjective integer programming

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MATHEMATICAL programming 2024年第1-2期207卷 577-616页

作者： Dunbar, Alex Sinha, Saumya Schaefer, Andrew J. Emory Univ Atlanta GA USA Univ Minnesota Minneapolis MN 55455 USA

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a weighted-sum scalarization of the MOIP. At unsupported solutions, the convex hull relaxation is not tight and a Lagrangian relaxation may provide a tighter bound. Using the Lagrangian relaxation, we define a Lagrangian dual of an MOIP that satisfies weak duality and is strong at supported solutions under certain conditions on the primal feasible region. We include a numerical experiment to illustrate that bound sets obtained via Lagrangian duality may yield tighter bounds than those from a convex hull relaxation. Subsequently, we generalize the integer programming value function to MOIPs and use its properties to motivate a set-valued superadditive dual that is strong at supported solutions. We also define a simpler vector-valued superadditive dual that exhibits weak duality but is strongly dual if and only if the primal has a unique nondominated point.

关键词： Multiobjective optimization integer programming Lagrangian relaxation Lagrangian duality Superadditive duality

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Optimum renewable oil for biodiesel production as integer programming problem

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ENERGY EXPLORATION & EXPLOITATION 2025年第1期43卷 340-353页

作者： Sagbansua, Lutfu Balo, Figen Southern Univ A&M Coll 801 Harding Blvd Baton Rouge LA 70813 USA Firat Univ Elazig Turkiye

During the last decades, the apprehension about environmental pollution and consuming of the global fossil resource reserves has raised the requisition to improve an environmental friendly and renewable fuel. Bio-based diesel fuel, which primarily occurs of methyl-esters in fatty acid is one of the finest replaces for fossil-based diesel fuel. Nowadays, plant oils are the primary source of bio-sourced diesel fuel. The fatty acid formation of manufactured bio-based diesel fuel from different plant-based sources and their features are disparate. The aim of the existent research is to choose the optimal plant oil as bio-based diesel through utilizing mathematical modeling technique. Amon plant-based oil kinds, the question of choosing the optimal plant oil is assessed, utilizing many criteria concerned with their features. This study spotlights a new perception into evaluating the optimal plant oil-derived bio-based diesels for the decision-makers like engine manufacturers and development and research engineers to strengthen the green reformation to provide the fuel economy and emission standards.

关键词： Biomass renewable energy sustainability biodiesel plant oil integer programming

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A mixed integer programming approach to address cumulative threats in multi action management plans for biodiversity recovery

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2025年 133卷

作者： Salgado-Rojas, Jose alvarez-Miranda, Eduardo Hermoso, Virgilio Forest Sci & Technol Ctr Catalonia CTFC Solsona Spain Univ Politecn Cataluna Dept Stat & Operat Res E-08028 Barcelona Spain CSIC Estn Biol Donana Seville Spain Griffith Univ Australian Rivers Inst Brisbane Qld Australia Univ Talca Sch Engn Dept Ind Engn Curico Chile Inst Sistemas Complejos Ingn ISCI Santiago Chile Inst Ecol & Biodivers IEB Concepcion Chile

Traditionally, most of the prioritization models used by researchers and practitioners, rely on spatially dichotomous settings for threats, for species and for actions' benefit;i.e., threats and species are present with equal intensity in some territorial units (while in the other units are not present at all), and actions have impact only on those units where they are applied. However, when dealing with ecological phenomena on large and complex territories, characterized by different areas (such as multiple realms or large river basins) and different spatial connectivity patterns among them, such a dichotomous setting does not capture the spatial (cumulative) diffusion of threats and thus actions' benefits. Hence, common conservation planning tools are likely to misestimate the benefits of actions and the impact of threats, yielding less effective solutions. In order to address this issue, we develop a framework for designing multi-action prioritization plans featuring threats and actions' benefit spatial diffusion. Our framework relies on a mathematical programming model that identifies priority areas for the implementation of management actions for multiple threats across a complex and large landscape. We consider the particular case an ecological setting characterized by different realms, multiple threats, and multiple species. We use the Tagus River (Iberian Peninsula) as a case study, including four realms (terrestrial, freshwater, estuary, and marine), where we integrate three different types of spatial connectivity: longitudinal along rivers, and multidimensional in the estuary and marine realms. We simulate the spatial diffusion of threats across the study area using four types of decay models (dispersal kernels): one exponential kernel, two negative triangular kernels (medium and high), and no dispersal. The results show how the MIP-based methodology offers a flexible and practical strategy for incorporating the cumulative effects of threats into action ma

关键词： Cumulative effects Mathematical programming Multi-realm management integer programming conservation planning

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integer programming Approaches to an Issue of Scheduling for a Truck-Drone Last-Mile Delivery System with Parcel Pickup Service 13

Integer Programming Approaches to an Issue of Scheduling for...

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Joint 13th International Conference on Soft Computing and Intelligent Systems and 25th International Symposium on Advanced Intelligent Systems, SCIS and ISIS 2024

作者： Yamada, Kotaro Karuno, Yoshiyuki Iima, Hitoshi Graduate School of Science and Technology Kyoto Institute of Technology Mechanodesign Program Kyoto Japan Kyoto Institute of Technology Faculty of Mechanical Engineering Kyoto Japan Kyoto Institute of Technology Faculty of Information and Human Sciences Kyoto Japan

ISBN: (纸本)9798350373332

In this paper, we consider a scheduling issue for parcel delivery and pickup services by a truck-drone last-mile delivery system. We are given a single carrier truck and multiple identical drones to serve a finite set of customers. The single carrier truck plays the role of a mobile depot for the drones, and it visits several stops in a given order of them. The given order of stops constitutes a fixed truck route, and the carrier truck is allowed to launch (resp., to retrieve) a drone to (resp., from) a customer at a stop. For each sortie of a drone, the launching stop and the retrieving stop must be the same. The load capacity of a drone is limited to one, and for a sortie of a drone at a stop, there are three options: (i) only deliver a parcel to a customer, (ii) only pick up a parcel from a customer, and (iii) deliver a parcel to a customer, and then pick up a parcel from a customer. The scheduling problem asks to find an assignment of customers to drones with sortie options and a choice of a truck stop for each sortie in the assignment. The objective is to minimize the total duration of the carrier truck over all the stops, which is equivalent to minimizing the makespan. In this paper, we first propose an extended integer program for the case with both delivery and pickup services from an existing one for the case with delivery service only. We also conduct numerical experiments to demonstrate the solution quality of the proposed integer program by utilizing an integer programming solver, and report the results. © 2024 IEEE.

关键词： integer programming

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Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期313卷 69-91页

作者： Lastra-Diaz, Juan J. Ortuno, M. Teresa Univ Complutense Madrid UCM Res Grp HUMLOG Dept Stat & Operat Res Inst Interdisciplinary Math Madrid Spain

The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-integer programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, there is room to improve the efficiency of the current family of exact MIP models for nesting. In order to bridge this gap, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Ten instances are solved up to optimality within one hour for the first time, including one with 27 pieces. Finally, we provide a detailed reproducibility protocol and dataset as supplementary material to allow the exact replication of our models, experiments, and results. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )

关键词： Packing integer programming Irregular strip packing Nesting Cutting

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3D Mesh Animation Optimization Algorithm Based on integer programming and Nonlinear Constraints

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IEEE ACCESS 2024年 12卷 86649-86661页

作者： Jiang, Jing Wang, Xiaojun Anhui Xinhua Univ Coll Arts Hefei 230088 Peoples R China

With the rapid development of digital media and entertainment industry, the importance of 3D mesh animation has become increasingly prominent. However, the traditional production methods are faced with problems such as high computational complexity and unnatural effects when dealing with complex motion. To improve the production efficiency and quality of 3D mesh animation, this study innovatively integrates integer programming, nonlinear constraint optimization, and machine learning algorithms to construct a new 3D mesh animation optimization algorithm. Comparative analysis of the improved machine learning algorithm shows that the mean absolute error of the algorithm is 0.00048 and the fit degree is 98.8%, which is better than the comparison algorithm. Then, the performance of the proposed 3D mesh animation optimization algorithm is analyzed. The results show that the rendering speed and average frame rate of the proposed algorithm are 29.5 FPS and 28.7 FPS, respectively, which is superior to the comparison algorithm. The algorithm can effectively improve the efficiency and quality of animation production, and inject new vitality into the development of digital media and entertainment industry. This study not only provides new ideas and methods for optimizing 3D mesh animation, but also provides useful references for research and applications in related fields.

关键词： Animation Three-dimensional displays Machine learning algorithms Optimization integer programming Production Mathematical models Digital communication Mesh networks 3D mesh animation integer programming nonlinear constraints machine learning optimization algorithms

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A Method for Inferring Polymers Based on Linear Regression and integer programming

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2024年第6期21卷 1623-1632页

作者： Ido, Ryota Cao, Shengjuan Zhu, Jianshen Azam, Naveed Ahmed Haraguchi, Kazuya Zhao, Liang Nagamochi, Hiroshi Akutsu, Tatsuya Kyoto Univ Grad Sch Informat Dept Appl Math & Phys Kyoto 6068501 Japan Quaid I Azam Univ Dept Math Islamabad 45320 Pakistan Kyoto Univ Grad Sch Adv Integrated Studies Human Survivabil S Kyoto 6068306 Japan Kyoto Univ Inst Chem Res Bioinformat Ctr Uji 6110011 Japan

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In this paper, we design a new method for inferring a polymer based on the framework. For this, we introduce a new way of representing a polymer as a form of monomer and define new descriptors that feature the structure of polymers. We also use linear regression as a building block of constructing a prediction function in the framework. The results of our computational experiments reveal a set of chemical properties on polymers to which a prediction function constructed with linear regression performs well. We also observe that the proposed method can infer polymers with up to 50 non-hydrogen atoms in a monomer form.

关键词： Cheminformatics integer programming linear regression machine learning materials informatics molecular design polymers QSAR/QSPR integer programming linear regression machine learning materials informatics molecular design polymers QSAR/QSPR

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integer programming-based non-uniform window decoding schedules for spatially coupled low-density parity-check codes

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IET COMMUNICATIONS 2022年第17期16卷 2019-2035页

作者： Khittiwitchayakul, Sirawit Phakphisut, Watid Supnithi, Pornchai King Mongkuts Inst Technol Ladkrabang Sch Engn Bangkok 10520 Thailand

Spatially coupled low-density parity-check (SC-LDPC) codes generally use a window decoding scheme, which is known to yield a near-optimal decoding, compared to full block decoding. Recently, a non-uniform schedule has been proposed to eliminate unnecessary updates of variable nodes within a window: this schedule is generated based on the behaviour of variable node updates analysed by density evolution. Here, the authors present a new non-uniform schedule based on integer programming, whereby the objective functions and constraints are derived from a protograph-based extrinsic information transfer chart. Our design is more flexible than the previous design, because the integer programming-based design allows reduction of update numbers and performance losses through the constraints function, whereas the previous design requires observation of variable node update behaviour. The authors report the performance of their designs of non-uniform schedules in additive white Gaussian noise (AWGN) and inter-symbol interference (ISI) channels. Particularly, in the ISI channel, the authors' non-uniform schedules are designed with cooperative decoding between a Bahl-Cocke-Jelinek-Raviv (BCJR) detector and an SC-LDPC decoder.

关键词： integer programming-based design block decoding protograph-based extrinsic information transfer chart additive white Gaussian noise channels Bahl-Cocke-Jelinek-Raviv detector SC-LDPC decoder nonuniform window decoding schedules AWGN channels telecommunication scheduling density evolution parity check codes integer programming decoding intersymbol interference channels channel coding intersymbol interference cooperative communication spatially coupled low-density parity-check codes near-optimal decoding variable node update behaviour ISI channels low-density parity-check codes BCJR detector

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A mixed-integer programming formulation for optimizing the double row layout problem

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OPTIMIZATION METHODS & SOFTWARE 2024年第6期39卷 1428-1444页

作者： Amaral, Andre R. S. Fed Univ Espirito Santo UFES Grad Sch Comp Sci BR-29075910 Vitoria Brazil

The Double Row Layout Problem (DRLP) asks for an arrangement of machines on both sides of a straight line corridor so as to minimize the total cost for transferring materials among machines. The DRLP is NP-Hard and has practical relevance, specially in manufacturing systems design. In this paper, we drastically reduce the time required to solve the problem by constructing a new and effective mixed-integer linear programming (MILP) model of the DRLP. The new model was obtained by reformulating an existing MILP model. This includes tightening some constraints, introducing new variables, implementing constraints to link the new and original variables;and adding valid inequalities and a valid system of equations. To reduce the size of the reformulated model, we eliminate several of the new introduced variables by a substitution using the system of equations. The computational results demonstrate that the proposed model requires considerably smaller computational times compared to the ones in the literature. As a consequence, optimal solutions can now be efficiently found for larger instances of the problem. Previous studies have been able to optimally solve, within reasonable time, instances with size up to 16 machines, while with the new model four instances with 20 machines could be optimally solved.

关键词： integer programming discrete optimization facility layout

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