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Vehicle routing problem considering equity of demand satisfaction

OPTIMIZATION LETTERS 2021年第6期15卷 2275-2297页

作者： Ibarra-Rojas, O. J. Silva-Soto, Y. Av Univ S-N San Nicolas De Los Garza Nuevo Leon Mexico

Planning of distribution processes has been represented by vehicle routing problems (VRP), where objective functions are commonly related to the cost of routes and delivery times involved in those processes. However, other objectives, such as equity of demand satisfaction, are of particular interest in social or non-profit distribution systems. This study addresses a VRP focused on an egalitarian distribution among all demand centroids considering a heterogeneous fleet. In particular, our goal is to maximize the minimum fraction of fulfilled demand to foster the equity of demand satisfaction while minimizing the delivery times as a secondary objective. We formulate our optimization problem as a mixed-integer linear program that is intractable by using a commercial solver for large instances. Therefore, we design three variants of the biased random-key genetic algorithm, and one of them can obtain near-optimal solutions for instances up to 120 demand points and 15 routes in less than one minute of computational time. Finally, we present an analysis of the trade-off between egalitarian demand satisfaction and total delivery time for a scenario based on an economically deprived region in Mexico.

关键词： Vehicle routing problem Equity of demand satisfaction mixed-integer linear programming BRKGA

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mixed-integer optimal control under minimum dwell time constraints

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MATHEMATICAL programming 2021年第2期188卷 653-694页

作者： Zeile, Clemens Robuschi, Nicolo Sager, Sebastian Otto von Guericke Univ Dept Math D-39106 Magdeburg Germany Politecn Milan Dept Mech Engn Via Giuseppe La Masa 1 I-20156 Milan Italy

Tailored mixed-integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems (MIOCPs) to epsilon-optimality by solving one continuous nonlinear program and one mixed-integer linear program (MILP). Within this work, we analyze the integrality gap of MIOCPs under MDT constraints by providing tight upper bounds on the MILP subproblem. We suggest different rounding schemes for constructing MDT feasible control solutions, e.g., we propose a modification of Sum Up Rounding. A numerical study supplements the theoretical results and compares objective values of integer feasible and relaxed solutions.

关键词： mixed-integer linear programming Optimal control Discrete approximations Switched dynamic systems Approximation methods and heuristics Minimum dwell time constraints

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Electrification seeds-A fiexible approach for decentralized electricity supply in developing countries

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ENERGY FOR SUSTAINABLE DEVELOPMENT 2021年 62卷 176-185页

作者： Huber, Matthias Namockel, Nils Rezgui, Rim Kueppers, Martin Heger, Hans Joerg Siemens AG Corp Technol Munich Germany Deggendorf Inst Technol European Campus Pfarrkirchen Germany Univ Cologne Inst Energy Econ Cologne Germany Tech Univ Munich Ctr Energy Markets Munich Germany

There are currently more than 500 million people without access to electricity on the African continent alone. With an expected strong population growth and the global goals for reducing carbon emissions, the challenge of providing electricity for all is tremendous. We present an approach that tackles electrification bottom-up in a decentral approach from so-called electrification seeds: Business owners or public institutions that invest in an electricity system to ensure reliable electricity supply for themselves may serve as a seed by also selling elec-tricity in their surroundings via mini-or microgrids. This approach will allow for cheaper solutions due to economies of scale. While private households can also be addressed by simple solutions e.g. solar home systems, the power of the "electrification seed" approach is that it can also provide enough secure power for small and medium enterprises (SME) and thus drive economic development. It is important to address the individual environment of the respective electrification seed, since there is no standard solution. To do so, the method includes an entire toolchain from estimating demands and structures with satellite data and Geographic Information System (GIS) software over employing an energy system model for finding the optimal technological design. As a last step, the viability of the electrification seed concept is verified with an exemplary business plan. The results show positive business cases for the electrification seed and a reduction of electricity costs for end-customers by 11.3 %. Altogether, this gives a very optimistic outlook of the suggested approach to support the great challenge of sustainable electrification for economic growth in developing countries. (c) 2021 International Energy Initiative. Published by Elsevier Inc. All rights reserved.

关键词： Rural electrification Mini-grids Microgrids Geo-spatial modeling Mini-grid business model Energy system development mixed-integer linear programming

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mixed-integer linear optimization for full truckload pickup and delivery

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OPTIMIZATION LETTERS 2021年第6期15卷 1847-1863页

作者： Wang, Akang Ferro, Nicholas Majewski, Rita Gounaris, Chrysanthos E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Carnegie Mellon Univ Ctr Adv Proc Decis Making Pittsburgh PA 15213 USA Braskem Digital Ctr BR-05501050 Sao Paulo SP Brazil Braskem Innovat & Technol Pittsburgh PA 15219 USA

This paper is focused on solving an industrially-motivated, rich routing variant of the so-called full truckload pickup and delivery problem. It addresses a setting where the distributor has to transport full truckload shipments between distribution centers and customer locations, yet the distributor's owned fleet is inadequate to perform the totality of the required deliveries and thus a subset of the deliveries has to be outsourced to third-party carriers. In this work, we propose a novel mixed-integer linear programming formulation to model this problem. Using datasets inspired from industrial practice, we evaluate the computational tractability of this model and demonstrate its potential to serve as a decision-support system for real-life operations. Furthermore,we hypothesize that the distributor may realize cost savings when the later portion of the distribution period is utilized to pre-load cargo for delivery during the following period. To that end, we augment the original model to allow for such cargo pre-loading, and we conduct a rolling horizon-based simulation study to quantify its overall economic effect.

关键词： Pickup and delivery routing Full truckload shipments mixed-integer linear programming Pre-loading policy

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Approximate Kernel Learning Uncertainty Set for Robust Combinatorial Optimization

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INFORMS JOURNAL ON COMPUTING 2024年第3期36卷 705-937, C2页

作者： Loger, Benoit Dolgui, Alexandre Lehuede, Fabien Massonnet, Guillaume IMT Atlantique LS2N F-44300 Nantes France

Support vector clustering (SVC) has been proposed in the literature as a datadriven approach to build uncertainty sets in robust optimization. Unfortunately, the resulting SVC-based uncertainty sets induces a large number of additional variables and constraints in the robust counterpart of mathematical formulations. We propose a two-phase method to approximate the resulting uncertainty sets and overcome these tractability issues. This method is controlled by a parameter defining a trade-off between the quality of the approximation and the complexity of the robust models formulated. We evaluate the approximation method on three distinct, well-known optimization problems. Experimental results show that the approximated uncertainty set leads to solutions that are comparable to those obtained with the classic SVC-based uncertainty set with a significant reduction of the computation time.

关键词： data-driven robust optimization machine learning mixed-integer linear programming

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Optimal location, sizing and scheduling of distributed energy storage in a radial distribution network

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JOURNAL OF ENERGY STORAGE 2024年 94卷

作者： Binini, Giscard M. Munda, Josiah L. Popoola, Olawale M. Tshwane Univ Technol Dept Elect Engn Pretoria West South Africa

Research has shown the effective use of storage technologies to support the operation of a network with a large share of renewable sources of energy. This is done by storing excess energy when generation exceeds demand and delivering the extra energy stored when demand exceeds generation. This ensures that renewable resources are used even when renewable generation is not sufficient to satisfy the demand. To maximise the benefit of storage units in the network, their size and location within the network need to be optimised to the characteristics of the network, the demand and generation profiles. The optimisation is done to minimise network congestion and losses while maximising the benefits of the storage elements in the network. Several optimisation processes have been employed to perform this task but consideration of the storage technology and storage utilisation were not sufficiently explored. The proposed method considered optimising the size and location of distributed energy storage resources in a radial distribution network taking into consideration the effect of storage technology. The results showed that the location and sizes of distributed energy storage depend not only on the aggregated size of the technology but also on the technology types. The results also show that the size of the aggregated storage influences the overall network losses. Generally, the larger the aggregated size of distributed storage, the more the storage units are distributed resulting in a greater reduction of network losses. Among the storage technologies considered, Lithium-Ion batteries presented the most improvement in network losses due to their higher-rated power delivery and charging capacity relative to the energy storage size.

关键词： Distributed storage Battery technologies Optimal placement mixed-integer linear programming

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The Continuous Time-Resource Trade-off Scheduling Problem with Time Windows

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INFORMS JOURNAL ON COMPUTING 2024年第6期36卷 1359-1756, C2页

作者： Artigues, Christian Hebrard, Emmanuel Quilliot, Alain Toussaint, Helene Univ Toulouse Lab Anal & Architecture Syst Ctr Natl Rech Sci F-31031 Toulouse France Ctr Natl Rech Sci Lab Informat Modelisat & Optimisat Syst F-63178 Clermont Ferrand France Univ Clermont Auvergne F-63178 Clermont Ferrand France

We introduce a variant of the cumulative scheduling problem (CuSP) characterized by continuous modes, time windows, and a criterion that involves safety margin maximization. The study of this variant is motivated by the Geospatial based Environment for Optimisation Systems Addressing Fire Emergencies Horizon 2020 Project, which is devoted to the design of evacuation plans in the face of natural disasters and more specifically, wildfire. People and goods have to be transferred from endangered places to safe places, and evacuation planning consists of scheduling evacuee moves along precomputed paths under arc capacities and deadlines. The resulting model is relevant in other contexts, such as project or industrial process scheduling. We consider here several formulations of the continuous time -resource trade-off scheduling problem (CTRTP-TW) with a safety maximization objective. We establish a complete complexity characterization distinguishing polynomial and NP -hard special cases depending on key parameters. We show that the problem with fixed sequencing (i.e., with predetermined overlap or precedence relations between activities) is convex. We then show that the preemptive variant is polynomial, and we propose lower and upper bounds based on this relaxation. A flow -based mixed -integer linear programming formulation is presented, from which a branch -and -cut exact method and an insertion heuristic are derived. An exact dedicated branch -andbound algorithm is also designed. Extensive computational experiments are carried out to compare the different approaches on evacuation planning instances and on general CTRTP-TW instances. The experiments also show the interest of the continuous model compared with a previously proposed discrete approximation.

关键词： continuous time-resource trade-off scheduling time windows complexity mixed-integer linear programming branch and cut insertion heuristic evacuation planning

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Matching and Scheduling of Student-Company-Talks for a University IT-Speed Dating Event

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Operations Research Forum 2022年第3期3卷 42页

作者： Ackermann, Christian Hahne, Felix Rieck, Julia Institute for Business Administration and Information Systems Operations Research Group University of Hildesheim Samelsonplatz 1 Hildesheim 31141 Germany

In this paper, the IT-speed dating of a German university is considered, where students have talks with different companies in order to find a suitable internship. The goal is to create a good and fair matching of students and companies for these talks, based on student preferences, and to schedule the resulting talks in order to maintain the given time horizon and minimize the necessary room changes for the students. We solved the problem in two steps. First, we modeled the matching problem as an extended version of the capacitated transportation problem and solved it using a modified stepping stone method. Second, we present two approaches to solve the scheduling problem. A Monte Carlo tree search procedure generates time-constrained schedules with minimal duration, while a genetic algorithm generates longer schedules with individual pauses and fewer room changes. The approaches led to significantly more talks with valuable content, a shorter duration, and greater satisfaction of all participants. © 2022, The Author(s).

关键词： Genetic algorithm Matching and scheduling mixed-integer linear programming Modified stepping stone method Monte Carlo tree search

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Learning Optimal Fair Scoring Systems for Multi-Class Classification 34

Learning Optimal Fair Scoring Systems for Multi-Class Classi...

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34th IEEE International Conference on Tools with Artificial Intelligence (ICTAI)

作者： Rouzot, Julien Ferry, Julien Huguet, Marie-Jose Univ Toulouse CNRS LAAS Toulouse France Univ Toulouse CNRS LAAS INSA Toulouse France

ISBN: (纸本)9798350397444

Machine Learning models are increasingly used for decision making, in particular in high-stakes applications such as credit scoring, medicine or recidivism prediction. However, there are growing concerns about these models with respect to their lack of interpretability and the undesirable biases they can generate or reproduce. While the concepts of interpretability and fairness have been extensively studied by the scientific community in recent years, few works have tackled the general multi-class classification problem under fairness constraints, and none of them proposes to generate fair and interpretable models for multi-class classification. In this paper, we use mixed-integer linear programming (MILP) techniques to produce inherently interpretable scoring systems under sparsity and fairness constraints, for the general multi-class classification setup. Our work generalizes the SLIM (Supersparse linear integer Models) framework that was proposed by Rudin and Ustun to learn optimal scoring systems for binary classification. The use of MILP techniques allows for an easy integration of diverse operational constraints (such as, but not restricted to, fairness or sparsity), but also for the building of certifiably optimal models (or sub-optimal models with bounded optimality gap).

关键词： Machine Learning Fairness Interpretability mixed-integer linear programming Scoring System Multi-class Classification

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Distributed Optimal Energy Management of a Microgrid Community 17

Distributed Optimal Energy Management of a Microgrid Communi...

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IEEE 17th International Conference on Control and Automation (ICCA)

作者： Liu, Yueyang Gao, Shuhua Xiang, Cheng Yu, Ming Tan, Kuan Tak Natl Univ Singapore Dept Elect & Comp Engn Singapore Singapore Power Automat Pte Ltd 438B Alexandra RdAlexandra Technopk Singapore 119968 Singapore Singapore Inst Technol Engn Cluster 10 Dover Dr Singapore 138683 Singapore

ISBN: (数字)9781665495721

ISBN: (纸本)9781665495721

This paper studies optimal scheduling of multiple microgrids using distributed coordination algorithms. Each microgrid is controlled by an individual agent using mixed-integer linear programming (MILP). The algorithm is designed towards a two-level microgrid community (MGC) structure, where the exchange power is adjusted several times through information communication between the upper-level agent and lower-level agents to minimize the operation cost. In the paper, an overview of the system model is first given, followed by a description of the distributed coordination algorithm in detail incorporating the mathematical modeling of the problem. A simulation study of the algorithm is performed based on a real MGC system. We found that the distributed coordination algorithm with multiple iterations can make the operation cost of the MGC system closer to the centralized result if appropriate parameter values are selected. Compared with other hierarchical energy management methods, our approach can achieve a lower cost.

关键词： Energy management systems adjustable power distributed optimization mixed-integer linear programming

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