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On clustering and interpreting with rules by means of mathematical optimization

COMPUTERS & OPERATIONS RESEARCH 2023年 154卷

作者： Carrizosa, Emilio Kurishchenko, Kseniia Marin, Alfredo Morales, Dolores Romero Univ Seville Inst Matemat Seville Spain Copenhagen Business Sch Dept Econ Frederiksberg Denmark Univ Murcia Dept Estadist & Invest Operat Murcia Spain

In this paper, we make Cluster Analysis more interpretable with a new approach that simultaneously allocates individuals to clusters and gives rule-based explanations to each cluster. The traditional homogeneity metric in clustering, namely the sum of the dissimilarities between individuals in the same cluster, is enriched by considering also, for each cluster and its associated explanation, two explainability criteria, namely, the accuracy of the explanation, i.e., how many individuals within the cluster satisfy its explanation, and the distinctiveness of the explanation, i.e., how many individuals outside the cluster satisfy its explanation. Finding the clusters and the explanations optimizing a joint measure of homogeneity, accuracy, and distinctiveness is formulated as a multi-objective mixed integer Linear Optimization problem, from which non-dominated solutions are generated. Our approach is tested on real-world datasets.

关键词： Machine learning Interpretability Cluster analysis Rules mixed-integer programming

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Improvements for decomposition based methods utilized in the development of multi-scale energy systems

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COMPUTERS & CHEMICAL ENGINEERING 2023年第1期170卷

作者： Allen, R. Cory Iseri, Funda Demirhan, C. Doga Pappas, Iosif Pistikopoulos, Efstratios N. Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA Texas A&M Univ Texas A&M Energy Inst College Stn TX 77843 USA Shell Int Explorat & Prod Inc Shell Technol Ctr Houston TX USA Shell Global Solut Int BV Shell Technol Ctr Amsterdam Netherlands

The optimal design of large-scale energy systems can be found by posing the problem as an integrated multi-period planning and scheduling mathematical programming problem. Due to the complexity of the accompanying mathematical programming problem, decomposition techniques are often required, unfortu-nately they to are often plagued with converge issues. To address these issues we have derived a set of valid inequalities to strengthen the formulation, and we have developed a machine learning framework to identify which subproblems should be solved in each iteration of the decomposition procedure. We illustrate the effectiveness of the valid inequalities and the machine learning framework through the use of a case study wherein we examine the development of an industrial scale hydrogen-based energy system. The results show that the valid inequalities and the machine learning framework significantly reduce the computational burden of the procedure.

关键词： mixed-integer programming Benders decomposition Valid inequalities Integrated planning and scheduling Machine learning

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mixed integer programming of generalized hydro-thermal self-scheduling of generating units

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ELECTRICAL ENGINEERING 2013年第2期95卷 109-125页

作者： Aghaei, J. Ahmadi, A. Shayanfar, H. A. Rabiee, A. Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran Iran Univ Sci & Technol Ctr Excellence Power Syst Automat & Operat Dept Elect Engn Tehran Iran Shahrekord Univ Fac Engn & Technol Dept Elect Engn Shahrekord Iran

This paper presents the application of mixed-integer programming (MIP) approach for solving the hydrothermal self scheduling (HTSS) problem of generating units. In the deregulated environment, the generation companies schedule their generators to maximize their profit while satisfying loads is not an obligation. The HTSS is a high dimensional mixed-integer optimization problem. Therefore, in the large-scale power systems, solving the HTSS is very difficult. In this paper, MIP formulation is adopted for precise modeling of dynamic ramp rate limits, prohibited operating zones, operating services, valve loading effects, variable fuel cost, non-linear start-up cost functions of thermal units, fuel and emission limits of thermal units, multi head power-discharge characteristics of hydro plants and spillage of reservoir. The modified IEEE 118-bus system is used to demonstrate the performance of the proposed method.

关键词： Hydro-thermal self scheduling mixed-integer programming Dynamic ramp rate Prohibited operating zones Valve loading effect

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Dynamic rebalancing for Bike-sharing systems under inventory interval and target predictions

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EURO JOURNAL ON TRANSPORTATION AND LOGISTICS 2024年 13卷

作者： Liang, Jiaqi Silva, Maria Clara Martins Aloise, Daniel Jena, Sanjay Dominik Polytech Montreal 2500 Chemin Polytech Montreal PQ H3T 1J4 Canada Univ Quebec Montreal Sch Management 315 Rue St Catherine Est Montreal PQ H2X 3X2 Canada Ctr Interuniv Rech Reseaux Entreprise Logist & Tra 2920 Chemin Tour Montreal PQ H3T 1J4 Canada Canada Excellence Res Chair Data Sci Real time Dec 2500 Chemin Polytech Montreal PQ H3T 1J4 Canada Grp Etud & Rech Anal decis GERAD 2920 Chemin Tour Montreal PQ H3T 1N8 Canada

Bike-sharing systems have become a popular transportation alternative. Unfortunately, station networks are often unbalanced, with some stations being empty, while others being congested. Given the complexity of the underlying planning problems to rebalance station inventories via trucks, many mathematical optimizations models have been proposed, mostly focusing on minimizing the unmet demand. This work explores the benefits of two alternative objectives, which minimize the deviation from an inventory interval and a target inventory, respectively. While the concepts of inventory intervals and targets better fit the planning practices of many system operators, they also naturally introduce a buffer into the station inventory, therefore better responding to stochastic demand fluctuations. We report on extensive computational experiments, evaluating the entire pipeline required for an automatized and data-driven rebalancing process: the use of synthetic and real-world data that relies on varying weather conditions, the prediction of demand and the computation of inventory intervals and targets, different reoptimization modes throughout the planning horizon, and an evaluation within a fine-grained simulator. Results allow for unanimous conclusions, indicating that the proposed approaches reduce unmet demand by up to 34% over classical models.

关键词： Bike-sharing systems Dynamic rebalancing Inventory intervals Target inventories Reoptimization modes mixed-integer programming

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Impact of Incorporating Returns into Pre-Disaster Deployments for Rapid-Onset Predictable Disasters

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PRODUCTION AND OPERATIONS MANAGEMENT 2021年第2期30卷 451-474页

作者： Stauffer, Jon M. Kumar, Subodha Texas A&M Univ Mays Business Sch Dept Informat & Operat Management College Stn TX 77845 USA Temple Univ Fox Sch Business Dept Mkt & Supply Chain Management Philadelphia PA 19122 USA

Initial deployment decisions are critical to humanitarian organizations as they pre-position resources and prepare for predictable disasters, such as hurricanes, floods, and wildfires. Deploying too few resources results in unmet demand, bad publicity, and unhappy donors. However, deploying a large number of resources can also result in bad publicity and unhappy donors due to high costs and wasted resources when disasters do not occur as expected and deployed items are not managed efficiently. We use a stochastic optimization model to investigate the initial deployment decision and resulting costs. The stochastic model forces the initial deployment decision to be made after the disaster warning, but before the disaster occurs and true demand is realized. We find that afull optimization model(incorporating returns and disposal into the model) will increase the initial deployment level from the level obtained without incorporating returns and disposal (referred to as apartial optimization model). This allows more beneficiaries to be served when using a full optimization model. We also find that fixed return costs do not have a large impact on initial deployment levels, but can result in a more consolidated pre-positioning strategy. Using the results of our models, we present several other interesting managerial insights that may be useful for humanitarian organizations in pre-positioning inventory for predictable disasters.

关键词： humanitarian operations multiple deployments inventory pre-positioning mixed-integer programming predictable disasters

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Application of Fuzzy Multi-Objective programming to Regional Sewer System Planning

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PROCESSES 2023年第1期11卷 183页

作者： Huang, Chung-Fu Chen, Wei-Ting Kao, Chuan-Ksing Chang, Han-Jung Kao, Po-Min Wan, Terng-Jou Zhaoqing Univ Sch Environm & Chem Engn Zhaoqing 526061 Peoples R China Zhaoqing Univ Guangdong Prov Key Lab Environm Hlth & Land Resour Zhaoqing 526061 Peoples R China St Marys Jr Coll Med Nursing & Management Dept Cosmet Applicat & Management Yilan 26644 Taiwan Natl Yunlin Univ Sci & Technol Dept Safety Hlth & Environm Engn Yunlin 64002 Taiwan Natl Yunlin Univ Sci & Technol Ctr Green Sustainable & Innovat Yunlin 64002 Taiwan Natl Yunlin Univ Sci & Technol Bachelor Program Ind Technol Yunlin 64002 Taiwan

Planning of sewer systems typically involves limitations and problems, regardless of whether traditional planning methods or optimization models are used. Such problems include non-quantifiability, fuzzy objectives, and uncertainties in decision-making variables which are commonly applied in the planning of any process. Particularly, uncertainties have prevented the inclusion of these variables in models. Consequently, the theoretical optional solution of the mathematical models is not the true optimum solution to practical problems. In this study, to solve the above problems for regional sewer system planning, multi-objective programming (MOP), nonlinear programming, mixed-integer programming, and compromise fuzzy programming were used. The objectives of this study were two-fold: (1) determination of the necessary decision-making variables or parameters, such as the optimum number of plants, piping layout, size of the plant, and extent of treatment;(2) establishment of a framework and methodology for optimal planning for designing a regional sewer system, matching demanded targets with the lowest cost, which would achieve the aim of lower space and energy requirements as well as consumption and high treatment efficiency for the purpose of meeting effluent standards. The findings of this study revealed that individual regional sewage treatment plants could be merged to form a centralized system. Land acquisition was difficult;thus, reducing the number of plants was required. Therefore, the compromise-fuzzy-based MOP method could effectively be used to build a regional sewer system plan, and the amount of in-plant establishment reached its maximized value with a minimized cost.

关键词： regional sewer system planning multi-objective programming nonlinear programming mixed-integer programming compromise fuzzy programming

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Strip based compact formulation for two-dimensional guillotine cutting problems

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COMPUTERS & OPERATIONS RESEARCH 2023年 149卷

作者： Rodrigues, Carlos Diego Cherri, Adriana Cristina Araujo, Silvio Alexandre de Univ Fed Ceara Ctr Ciencias Campus PiciBloco 910 BR-60440900 Fortaleza CE Brazil Univ State Sao Paulo UNESP Fac Ciencias Ave Eng Luis Edmundo Carrijo Coube 14-01 Vargem L BR-17033360 Bauru SP Brazil Univ State Sao Paulo UNESP Inst Biociencias Letras & Ciencias Exatas R Cristovao Colombo 2265 Jardim Nazareth BR-15054000 Sao Jose Do Rio Preto SP Brazil

In this paper, we present a new mixed integer programming formulation for two-dimensional guillotine cutting and packing problems based on a strip decomposition of the rectangular spaces. The formulation covers most of the main related problems in the literature by setting parameters accordingly. The strip concept commonly used for problems with a limited number of stages (two or three stages) has been, in this study, extended to a general concept that can cover an arbitrary number of stages. Due to the easy adaptation of the proposed formulation, which is presented in both heuristic and exact version, an extensive set of computational experiments was performed with instances for the two-dimensional guillotine knapsack, cutting stock and bin packing problems. The experiments, which involve existing benchmark instances and randomly generated instances from the literature, showed that our proposed formulation, considering its heuristic version, can output competitive results both in terms of computational time and percentage of optimally solved instances.

关键词： mixed-integer programming Two-dimensional cutting problems Guillotine cuts Mathematical modeling

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Improvement of demand fulfillment in Advanced Planning System through decentralized decision support system

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JOURNAL OF INDUSTRIAL INFORMATION INTEGRATION 2023年 35卷

作者： Mousavi, Behrouz Alizadeh Heavey, Cathal Millauer, Chirine Tian, Zhikang Ehm, Hans Univ Limerick Confirm Ctr Limerick V94 T9PX Ireland Infineon Technol Ireland Ltd Dublin Ireland Infineon Technol AG Supply Chain Innovat Dept Munich Germany

In a tight supply situation, industries such as the semiconductor sector face challenges in allocating supply to customers through complex hierarchical supply chain planning systems, which involve the use of Advanced Planning Systems (APS) and human planners in updating allocation plans. This article focuses on designing, developing, and testing a prototype Decision Support System (DSS) based on a mathematical model to assist human planners and improve demand fulfillment systems in APS when demand exceeds supply. By incorporating digitalization and supporting human interventions in planning, our approach enhances these systems. The bi-objective mathematical model aims to maximize customer service levels while maintaining a maxi-mum amount of stock available for unforeseen planning situations. We developed the proposed mathematical model into a web application decision support tool, called the Regional Customer Allocation Support Tool (ReCAST). The ReCAST prototype was applied to a semiconductor case study, demonstrating its effectiveness in supporting decision-making processes by planners in a real-world context.

关键词： Advanced Planning System Supply chain planning Decision support tool mixed-integer programming Customer Allocation

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Quantum computing for future real-time building HVAC controls

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APPLIED ENERGY 2023年第1期334卷

作者： Deng, Zhipeng Wang, Xuezheng Dong, Bing Syracuse Univ Dept Mech & Aerosp Engn Syracuse NY 13244 USA

Buildings contribute to more than 70% of overall U.S. electricity usage and greenhouse gas (GHG) emissions. HVAC systems in buildings often consume more than 40% of the total building energy usage. To reduce such high energy use, numerous control strategies including optimal and predictive controls have been developed and demonstrated. To achieve a near real-time solution, most previous research has simplified the non-linearity of building thermodynamics and provided an approximate optimal solution. The future HVAC control optimizes more connected devices in buildings, which requires a rapid and accurate response, not only to the building itself but also to the grid signals. It also poses the challenge of solving non-linear problems with discrete variables. With the recent development of quantum computers, this has become feasible. In this paper, we developed a new optimization solution based on quantum annealing for model predictive control (MPC) of a rooftop unit (RTU). Compared to traditional optimization methods, we obtained similar solutions with less than 2% differences and improved computational speed from hours to seconds. We also demonstrated an 80% reduction in total electricity consumption and a 21% reduction in electricity bills by considering day-ahead price time-of-use demand response signals. Quantum computing has proven capable of solving large-scale non-linear discrete optimization problems for building energy systems.

关键词： Discrete optimization mixed-integer programming Quadratic unconstrained binary optimization Quantum annealing Energy-efficient building

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Optimisation of long-term quarry production scheduling under geological uncertainty to supply raw materials to a cement plant

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MINING TECHNOLOGY-TRANSACTIONS OF THE INSTITUTIONS OF MINING AND METALLURGY 2021年第3期130卷 146-158页

作者： Vu, Trong Bao, Tran Drebenstedt, Carsten Pham, Hien Nguyen, Hoai Nguyen, Duc Quang Ninh Univ Ind Surface Min Dept Dong Trieu 2000 Quang Ninh Vietnam Hanoi Univ Min & Geol Surface Min Dept Hanoi Vietnam TU Freiberg Univ Min & Technol Inst Bergbau & Spezialtiefbau Freiberg Freiberg Germany

The success of a cement production project depends on the supply of raw materials. Long-term quarry production scheduling (LTQPS) based on resource models is essential to maintain a consistent supply to cement plants. Geological uncertainty is inherent due to sparse exploration data in resource models and significant risk factors for not achieving production targets. This research proposes a stochastic framework for LTQPS that considers the impact of geological uncertainty on raw material supply. A clustering algorithm uses multiple simulated deposit models to aggregate blocks into mining cuts. A new stochastic mixed-integer programming model is formulated with two objectives: to minimise the cost for developing the raw mix and the risk of not meeting production targets. The proposed framework is implemented successfully in a limestone deposit in Southern Vietnam, resulting in an increase of 5 million tons (Mt) and a 30% reduction in unit cost over the deterministic mixed-integer programming model.

关键词： Cement raw material supply geological uncertainty stochastic clustering mining cut mixed-integer programming

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