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A generic optimization framework for resilient systems

OPTIMIZATION METHODS & SOFTWARE 2023年第2期38卷 356-385页

作者： Pfetsch, Marc E. Schmitt, Andreas TU Discrete Optimizat Grp Dept Math Darmstadt Germany Tech Univ Darmstadt Dept Math Discrete Optimizat Grp Dolivostr 15 D-64293 Darmstadt Germany

This paper addresses the optimal design of resilient systems, in which components can fail. The system can react to failures and its behaviour is described by general mixed integer nonlinear programs, which allows for applications to many (technical) systems. This then leads to a three-level optimization problem. The upper level designs the system minimizing a cost function, the middle level represents worst-case failures of components, i.e. interdicts the system, and the lowest level operates the remaining system. We describe new inequalities that characterize the set of resilient solutions and allow to reformulate the problem. The reformulation can then be solved using a nested branch-and-cut approach. We discuss several improvements, for instance, by taking symmetry into account and strengthening cuts. We demonstrate the effectiveness of our implementation on the optimal design of water networks, robust trusses, and gas networks, in comparison to an approach in which the failure scenarios are directly included into the model.

关键词： Multi-level optimization mixed-integer nonlinear programming interdiction problems gas and water network design truss topology optimization

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Aeromedical Battlefield Evacuation Under Endogenous Uncertainty in Casualty Delivery Times

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MANAGEMENT SCIENCE 2018年第12期64卷 5481-5496页

作者： Lejeune, Miguel A. Margot, Francois George Washington Univ Washington DC 20052 USA Carnegie Mellon Univ Pittsburgh PA 15213 USA

We propose a new medical evacuation (MEDEVAC) model with endogenous uncertainty in the casualty delivery times. The goal is to provide timely evacuation and medical treatment to injured soldiers. The model enforces the "Golden Hour" evacuation doctrine, attempts to maximize the expected number of severely injured soldiers evacuated within one hour without delay, and represents the availability of air ambulances as an endogenous source of uncertainty. The MEDEVAC model is a mixed-integer nonlinear programming problem whose continuous relaxation is in general nonconvex and for which we develop an algorithmic method articulated around (i) new bounding techniques obtained through the solution of restriction and relaxation problems and (ii) a spatial branch-and-bound algorithm solving conic mixed-integer programs at each node. The computational study, based on data from Operation Enduring Freedom, reveals that the bounding problems can be quickly solved regardless of problem size, the bounds are tight, and the spatial branch-and-bound dominates the CPLEX and BARON solvers in terms of computational time and robustness. Compared to the MEDEVAC myopic policy, our approach increases the number of casualties treated timely and can contribute to reducing the number of deaths on the battlefield. The benefits increase as the MEDEVAC resources become tighter and the combats intensify. The model can be used at the strategic level to design an efficient MEDEVAC system and at the tactical level for intelligent tasking and dispatching.

关键词： MEDEVAC military trauma care endogenous uncertainty mixed-integer nonlinear programming spatial branch-and-bound algorithm relaxation and restriction problems

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A decomposition approach for a new test-scenario in complex problem solving

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JOURNAL OF COMPUTATIONAL SCIENCE 2013年第4期4卷 245-254页

作者： Engelhart, Michael Funke, Joachim Sager, Sebastian Heidelberg Univ Interdisciplinary Ctr Sci Comp IWR D-69120 Heidelberg Germany Heidelberg Univ Dept Psychol D-69117 Heidelberg Germany Univ Magdeburg Inst Math Optimizat D-39106 Magdeburg Germany

Over the last years, psychological research has increasingly used computer-supported tests, especially in the analysis of complex human decision making and problem solving. The approach is to use computerbased test scenarios and to evaluate the performance of participants and correlate it to certain attributes, such as the participant's capacity to regulate emotions. However, two important questions can only be answered with the help of modern optimization methodology. The first one considers an analysis of the exact situations and decisions that led to a bad or good overall performance of test persons. The second important question concerns performance, as the choices made by humans can only be compared to one another, but not to the optimal solution, as it is unknown in general. Additionally, these test-scenarios have usually been defined on a trial-and-error basis, until certain characteristics became apparent. The more complex models become, the more likely it is that unforeseen and unwanted characteristics emerge in studies. To overcome this important problem, we propose to use mathematical optimization methodology not only as an analysis and training tool, but also in the design stage of the complex problem scenario. We present a novel test scenario, the IWR Tailorshop, with functional relations and model parameters that have been formulated based on optimization results. We also present a tailored decomposition approach to solve the resulting mixed-integer nonlinear programs with nonconvex relaxations and show some promising results of this approach. (C) 2012 Elsevier B.V. All rights reserved.

关键词： mixed-integer nonlinear programming Complex problem solving Decomposition approach

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Optimal power flow problem considering multiple-fuel options and disjoint operating zones: A solver-friendly MINLP model

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2019年第0期113卷 45-55页

作者： Pourakbari-Kasmaei, Mahdi Lehtonen, Matti Fotuhi-Firuzabad, Mahmud Marzband, Mousa Sanches Mantovani, Jose Roberto Aalto Univ Dept Elect Engn & Automat Maarintie 8 Espoo 02150 Finland Sharif Univ Technol Dept Elect Engn Tehran Iran Northumbria Univ Newcastle Dept Maths Phys & Elect Engn Fac Engn & Environm Newcastle Upon Tyne Tyne & Wear England Islamic Azad Univ Lahijan Branch Dept Elect Engn Lahijan Iran State Univ Sao Paulo UNESP Dept Elect Engn Ilha Solteira Brazil

This paper proposes a solver-friendly model for disjoint, non-smooth, and nonconvex optimal power flow (OPF) problems. The conventional OPF problem is considered as a nonconvex and highly nonlinear problem for which finding a high-quality solution is a big challenge. However, considering practical logic-based constraints, namely multiple-fuel options (MFOs) and prohibited operating zones (POZs), jointly with the non-smooth terms such as valve point effect (VPE) results in even more difficulties in finding a near-optimal solution. In complex problems, the nonlinearity itself is not a big issue in finding the optimal solution, but the nonconvexity does matter and considering MFO, POZ, and VPE increase the degree of nonconvexity exponentially. Another primary concern in practice is related to the limitations of the existing commercial solvers in handling the original logic-based models. These solvers either fail or show intractability in solving the equivalent mixed integer nonlinear programming (MINLP) models. This paper aims at addressing the existing gaps in the literature, mainly handling the MFOs and POZs simultaneously in OPF problems by proposing a solver-friendly MINLP (SF-MINLP) model. In this regard, due to the actions that are done in the pre-solve step of the existing commercial MINLP solvers, the most adaptable model is obtained by melting the primary integer decision variables, associated with the feasible region, into the objective function. For the verification and didactical purposes, the proposed SF-MINLP model is applied to the IEEE 30-bus system under two different loading conditions, namely normal and increased, and details are provided. The model is also tested on the IEEE 118-bus system to reveal its effectiveness and applicability in larger-scale systems. Results show the effectiveness and tractability of the model in finding a high-quality solution with high computational efficiency.

关键词： mixed-integer nonlinear programming Multiple-fuel option Non-smooth terms Optimal power flow Prohibited operating zones

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Energy-efficient task scheduling for mobile edge computing with virtual machine I/O interference

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FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2023年第1期148卷 538-549页

作者： Lu, Baoshan Fang, Junli Hong, Xuemin Shi, Jianghong Guangxi Normal Univ Sch Elect & Informat Engn Guangxi Key Lab Brain Inspired Comp & Intelligent Guilin 541004 Peoples R China Xiamen Univ Dept Informat & Commun Engn Xiamen 361005 Fujian Peoples R China

Mobile edge computing (MEC) is expected to support the computation-intensive and delay-sensitive applications of mobile internet users. In this paper, we investigate the resource allocation of MEC with the effect of I/O interference among parallel virtual machines (VMs) while satisfying the quality of service (QoS) of tasks. Different from existing works, we propose a flexible task scheduling approach that combining parallel and sequential computing to minimize the computing energy consumption of MEC server. We formulate the task scheduling problem as a mixed-integer nonlinear programming (MINLP) and decompose it as a CPU resource allocation subproblem, a computing time slot subproblem, and a VM selection subproblem. We show the first subproblem is a convex problem and propose a CPU frequency allocation (CFA) algorithm based on the Karush-Kuhn-Tucker (KKT) conditions to obtain the optimal CPU frequency resource allocation. For the time slot allocation and VM selection subproblems, we propose the three step allocation (TSA) and urgency based adjusting (UBA) algorithms to obtain the near-optimal solutions, respectively. Simulation results show that compared with several time slot allocations and VM selections, the proposed TSA and UBA algorithms can save up to 21.7% and 95.8% of energy consumption, respectively.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： Mobile edge computing Virtual machine I O interference Task scheduling mixed-integer nonlinear programming Karush-Kuhn-Tucker

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Natural gas production network infrastructure development under uncertainty

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OPTIMIZATION AND ENGINEERING 2017年第1期18卷 35-62页

作者： Li, Xiang Tomasgard, Asgeir Barton, Paul I. MIT Proc Syst Engn Lab Dept Chem Engn 77 Massachusetts Ave Cambridge MA 02139 USA Queens Univ Dept Chem Engn 19 Div St Kingston ON K7L 3N6 Canada Norwegian Univ Sci & Technol Dept Ind Econ & Technol Management N-7491 Trondheim Norway

Mathematical programming has been widely applied for the planning of natural gas production infrastructure development. As the production infrastructure involves large investments and is expected to remain in operation over several decades, the factors that will impact the gas production but cannot be foreseen before the development of the infrastructure need to be taken into account in the planning. Therefore, two scenario-based two-stage stochastic programming models are developed to facilitate natural gas production infrastructure development under uncertainty. One is called the stochastic pooling model, which tracks the qualities of gas streams throughout the production network via a generalized pooling model. The other is an enhancement of the stochastic pooling model with the consideration of pressure. Either model results in a large-scale nonconvex mixed-integer nonlinear programming (MINLP) problem, for which a global optimal solution, although very important for a problem that involves large investments, is very difficult to obtain. A novel optimization method, called nonconvex generalized Benders decomposition (NGBD), is developed for efficient global optimization of the large-scale nonconvex MINLP. Case studies of a real industrial natural gas production system show the advantages of the proposed stochastic programming models over deterministic optimization models, as well as the dramatic computational advantages of NGBD over a state-of-the-art global optimization solver.

关键词： Natural gas production network mixed-integer nonlinear programming Stochastic programming Benders decomposition Global optimization

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Extension of the hybrid linear programming method to optimize simultaneously the design and operation of groundwater utilization systems

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ENGINEERING OPTIMIZATION 2015年第4期47卷 550-560页

作者： Bostan, Mohamad Afshar, Mohamad Hadi Khadem, Majed Iran Univ Sci & Technol Sch Civil Engn Tehran Iran

This article proposes a hybrid linear programming (LP-LP) methodology for the simultaneous optimal design and operation of groundwater utilization systems. The proposed model is an extension of an earlier LP-LP model proposed by the authors for the optimal operation of a set of existing wells. The proposed model can be used to optimally determine the number, configuration and pumping rates of the operational wells out of potential wells with fixed locations to minimize the total cost of utilizing a two-dimensional confined aquifer under steady-state flow conditions. The model is able to take into account the well installation, piping and pump installation costs in addition to the operational costs, including the cost of energy and maintenance. The solution to the problem is defined by well locations and their pumping rates, minimizing the total cost while satisfying a downstream demand, lower/upper bound on the pumping rates, and lower/upper bound on the water level drawdown at the wells. A discretized version of the differential equation governing the flow is first embedded into the model formulation as a set of additional constraints. The resulting mixed-integer highly constrained nonlinear optimization problem is then decomposed into two subproblems with different sets of decision variables, one with a piezometric head and the other with the operational well locations and the corresponding pumping rates. The binary variables representing the well locations are approximated by a continuous variable leading to two LP subproblems. Having started with a random value for all decision variables, the two subproblems are solved iteratively until convergence is achieved. The performance and ability of the proposed method are tested against a hypothetical problem from the literature and the results are presented and compared with those obtained using a mixed-integer nonlinear programming method. The results show the efficiency and effectiveness of the proposed method for s

关键词： confined aquifer decomposition mixed-integer nonlinear programming groundwater management total cost

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On the optimal design of water distribution networks: a practical MINLP approach

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OPTIMIZATION AND ENGINEERING 2012年第2期13卷 219-246页

作者： Bragalli, Cristiana D'Ambrosio, Claudia Lee, Jon Lodi, Andrea Toth, Paolo Univ Bologna DEIS I-40136 Bologna Italy Univ Bologna DISTART I-40136 Bologna Italy IBM TJ Watson Res Ctr Yorktown Hts NY 10598 USA

We propose a practical solution method for real-world instances of a water-network optimization problem with fixed topology using a nonconvex continuous NLP (nonlinear programming) relaxation and a MINLP (mixed integer nonlinear programming) search. Our approach employs a relatively simple and accurate model that pays some attention to the requirements of the solvers that we employ. Our view is that in doing so, with the goal of calculating only good feasible solutions, complicated algorithmics can be confined to the MINLP solver. We report successful computational experience using available open-source MINLP software on problems from the literature and on difficult real-world instances. An important contribution of this paper is that the solutions obtained, besides being low cost, are immediately usable in practice because they are characterized by an allocation of diameters to pipes that leads to a correct hydraulic operation of the network. This is not the case for most of the other methods presented in the literature.

关键词： Water network design mixed-integer nonlinear programming Modeling Computation

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Evaluating shortfalls in mixed-integer programming approaches for the optimal design and dispatch of distributed generation systems

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APPLIED ENERGY 2013年 102卷 386-398页

作者： Pruitt, Kristopher A. Braun, Robert J. Newman, Alexandra M. Colorado Sch Mines Div Econ & Business Golden CO 80401 USA Colorado Sch Mines Coll Engn & Computat Sci Dept Mech Engn Golden CO 80401 USA

The distributed generation (DG) of combined heat and power (CHP) for commercial buildings is gaining increased interest, yet real-world installations remain limited. This lack of implementation is due, in part, to the challenging economics associated with volatile utility pricing and potentially high system capital costs. Energy technology application analyses are also faced with insufficient knowledge regarding how to appropriately design (i.e., configure and size) and dispatch (i.e., operate) an integrated CHP system. Existing research efforts to determine a minimum-cost-system design and dispatch do not consider many dynamic performance characteristics of generation and storage technologies. Consequently, we present a mixed-integer nonlinear programming (MINLP) model that prescribes a globally minimum cost system design and dispatch, and that includes off-design hardware performance characteristics for CHP and energy storage that are simplified or not considered in other models. Specifically, we model the maximum turn-down, start up, ramping, and part-load efficiency of power generation technologies, and the time-varying temperature of thermal storage technologies. The consideration of these characteristics can be important in applications for which system capacity, building demand, and/or utility guidelines dictate that the dispatch schedule of the devices varies over time. We demonstrate the impact of neglecting system dynamics by comparing the solution prescribed by a simpler, linear model with that of our MINLP for a case study consisting of a large hotel, located in southern Wisconsin, retrofitted with solid-oxide fuel cells (SOFCs) and a hot water storage tank. The simpler model overestimates the SOFC operational costs and, consequently, underestimates the optimal SOFC capacity by 15%. Published by Elsevier Ltd.

关键词： Optimization mixed-integer nonlinear programming Distributed generation Combined heat and power Fuel cells Building energy

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Optimal scheduling of copper concentrate operations under uncertainty

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COMPUTERS & CHEMICAL ENGINEERING 2020年 140卷 106919-106919页

作者： Cheng, Pengfei Garcia-Herreros, Pablo Lalpuria, Mangalam Grossmann, Ignacio E. Georgia Inst Technol Sch Chem & Biomol Engn Atlanta GA 30332 USA Carnegie Mellon Univ Ctr Adv Proc Decis Making Dept Chem Engn Pittsburgh PA 15213 USA Aurubis AG Res Dev & Innovat Dept D-20539 Hamburg Germany

We propose a continuous-time scheduling model for the logistic and blending operations of copper concentrates with uncertain composition. The formulation, based on the Multi-Operation Sequencing (MOS) model, gives rise to a large-scale nonconvex mixed-integer nonlinear programming (MINLP) model. We adopt a two-step MILP-NLP decomposition strategy and enhance the MILP relaxation to propose schedules that significantly reduce the optimality gaps. The bounded uncertainty in element composition of the concentrates is addressed by an extended robust MOS model, which combines robust optimization and flexibility analysis techniques. The effectiveness of the models and the solution strategy is validated with an illustrative example and an industrial case study. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Scheduling Copper operations mixed-integer nonlinear programming Robust optimization

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