Model Reformulation Research Articles

Optimal battery electric bus system planning considering heterogeneous vehicles, opportunity charging, and battery degradation

Battery electric buses (BEBs) have been seen as a viable alternative for sustainable mobility. The charger placement and fleet configuration play a crucial role in the operational efficiency of BEBs. In this study, a joint optimization model is developed to strategically plan the charger placement and fleet configuration for a BEB system. Distinct from existing research, we simultaneously incorporate opportunity charging, heterogeneous vehicles, and battery degradation to integratively minimize the costs of charger installation, BEB purchase, energy consumption, and battery degradation. Based on a model reformulation, a heuristic-exact hybrid solution method is customized to solve the model. A real-world case study from Oslo, Norway is provided to demonstrate the optimization model and solution method. The results indicate that the proposed model can reduce the total costs by 21.27 % in comparison to the conventional model. Sensitivity analyses are further conducted to provide insightful findings and managerial implications for BEB systems.

Asymptotic preserving semi-Lagrangian discontinuous Galerkin methods for multiscale kinetic transport equations

We propose a new family of asymptotic preserving (AP) discontinuous Galerkin (DG) schemes for kinetic transport equations under a diffusive scaling. They are built upon a characteristics-based model reformulation proposed in Zhang et al. (2023) [27]. The reformulated model comprises a convection-diffusion-like equation for the macroscopic density and another evolution equation for the distribution function. We employ the equations in a weak form to enjoy the advantages of a DG method. We also leverage a semi-Lagrangian (SL) approach to achieve higher efficiency than a fully implicit scheme without loss of unconditional stability. A damping technique is introduced to control spurious numerical oscillations for high-order DG methods. We establish formal AP and Fourier stability analyses for fully discrete schemes in a linear scenario. Numerical experiments, covering one-dimensional to three-dimensional in space problems, confirm the accuracy, AP property, uniformly unconditional stability, and high parallel efficiency of the proposed methods.

Fast and Generic Energy Flow Analysis of the Integrated Electric Power and Heating Networks

Energy flow analysis is a fundamental tool to determine the network states of the integrated energy systems (IES). For the widely deployed IES with coupled power grids (PG) and heating networks (HN), we still lack a generic tool that can be easily employed to calculate the quasi-dynamic energy flows of it. In this paper, we have developed a generic code package (named as MATHN) for energy flow analysis of the quality-regulated HN. After that, a generic solution framework that leverages MATPOWER and MATHN to realize decomposed energy flow calculation of PG and HN is proposed. Behind the MATHN tool, a model reformulation technique is proposed to eliminate the massive indirect variables of the basic HN model discretized by finite difference, which finally derives a compact matrix formulation (similar to the network equation of power grid: I=YU) for generic description of any HN and also slashes the original model scale by around 20 times. Moreover, the solution strategy behind the MATHN tool further converts this matrix formulation into a standard system of non-homogeneous linear equations, with which some existing well-recognized algorithms can be directly applied for efficient and accurate solution. Case studies on three different scales of test systems demonstrate the generality, efficiency and accuracy of our methods. All the codes and input data are packaged into the MATHN tool and are made open-source for non-commercial use.

Probabilistic Forecasting-Based Reserve Determination Considering Multi-Temporal Uncertainty of Renewable Energy Generation

Operating reserve, among the most important ancillary services, is a powerful prescription for mitigating increasing uncertainty of renewable generation. Traditional reserve determination neglects uncertainty of renewable generation variations within the dispatch interval, which cannot gurantee sufficient reserve deliverability in real-time operation. This paper proposes a probabilistic forecasting-based reserve determination method to efficiently deal with multi-temporal uncertainty of renewable energy in power systems. A novel probabilistic forecasting approach is proposed by integrating Dirichlet process Gaussian mixture model into bootstrap-based extreme learning machine. A unified uncertainty model is constructed for depicting both interval-averaged uncertainty and intra-interval uncertainty by combing the probabilistic forecasts and linearized Itô-process model. In current business practices of many independent system operators, the coordinated determination of two well-designed reserve products, including regulating reserve and ramp capability reserve, is formulated in a two-stage robust optimization framework. A Bernstein polynomial-based model reformulation approach is then employed to handle the existing heterogeneity in the sub-models of each stage. Consequently, the integrated reserve determination is embedded in a generic two-stage robust optimization problem, which can be efficiently solved by the adopted modified column-and-constraint generation method. Finally, numerical simulations are implemented to validate the effectiveness and profitability of the proposed approach.

A region-based low-carbon operation analysis method for integrated electricity-hydrogen-gas systems

A region-based low-carbon operation analysis method for integrated electricity‑hydrogen-gas systems (IEHGSs) is proposed in this paper. The committed carbon emission operation region (CCE_OR) and the economic CCE_OR (ECCE_OR) are proposed to evaluate the low-carbon feasible space (LCFS) from the low-carbon, secure, and economic perspectives, which provides powerful tools for the low-carbon operation analyses of IEHGSs. Firstly, a coordinated mechanism of carbon flow and hydrogen flow is developed to excavate the low-carbon operation potential of IEHGSs. Then, based on the distributionally robust chance-constrained approach, the concepts and models of CCE_OR and ECCE_OR are defined and formulated considering uncertainties and hydrogen merits. Furthermore, a region model reformulation method is proposed to reformulate the uncertain and non-convex CCE_OR and ECCE_OR models into the deterministic and mixed-integer linear region models. The geometric properties of CCE_OR and ECCE_OR are both theoretically proven, which are the union set of finite convex and bounded polytopes. The united region solution methodology considering the geometric properties of CCE_OR and ECCE_OR is presented to effectively characterize CCE_OR and ECCE_OR. Finally, the numerical results on two test systems verify the effectiveness and applicability of the proposed methods. Simulation results indicate that the proposed methods can improve the LCFS, characterize visual coupling relationships between LCFS and observation variables, and provide comprehensive low-carbon operation information of operation points.

Distributed low-carbon economic dispatch of integrated power and transportation system

Electric vehicles (EVs) are widely recognized as promising solutions to reduce carbon emissions from the transportation sector. The rapid proliferation of EVs intensifies the interdependency between the power distribution system (PDS) and transportation system (TS). This paper proposes a distributed low-carbon economic dispatch scheme for the integrated power and transportation system (IPTS). Carbon emissions from the TS are quantified by a carbon dioxide calculation model, and the emissions from the PDS are determined by the electricity generation of fossil-fueled generators and the carbon reduction of carbon capture and storage (CCS) devices. An integrated model reformulation method is employed to transform the original non-convex model into a tractable one. Then a distributed solution method based on the spectral penalty parameter based adaptive alternating direction method of multipliers (SPPA-ADMM) is developed to protect the privacy of the PDS and TS. The reformulated model is solved iteratively, and the penalty parameter of the SPPA-ADMM is adjusted adaptively to improve the convergence performance of the method. Numerical results on three test systems demonstrate the effectiveness of the proposed scheme in achieving low-carbon economic dispatch of IPTS. Moreover, case studies validate the superiority of the SPPA-ADMM based distributed solution method in computation performance.

Air cargo network planning and scheduling problem with minimum stay time: A matrix-based ALNS heuristic

In air cargo delivery, cargo usually needs to stay in hubs after unloading operations until the designated outbound flight is ready to leave. The stay time may account for a significant part of the overall delivery time and is closely related to the service level of the cargo delivery. However, the prior studies on the air cargo network planning and scheduling problem mainly focused on the cost and revenue but paid little attention to the stay time. To bridge this gap, we introduce a new facet to the air cargo network planning and scheduling literature. The air cargo network planning and scheduling problem with minimum stay time involves the optimization of the hub location, flight deployment, flight timetabling, and flight-sequence-based cargo distribution to minimize the total stay time of freighter cargoes while guaranteeing a rational cost level. We develop a hierarchical modeling framework to handle this problem, where a time–space network is built to model the cargo stay time and the flight departure time. Next, to efficiently address the framework, the concept of the capacity matrix is introduced for model reformulation, and a matrix-based ALNS heuristic is proposed for model solving. The heuristic designs eight destroy operators from the column, row, and element perspectives, and develops a repair model for the repair operation. Finally, the proposed framework and algorithm are tested with a real-life instance from a leading express company in China.

Green hydrogen-based energy storage service via power-to-gas technologies integrated with multi-energy microgrid

Power-to-gas (P2G) is a promising solution to the issue of non-dispatchable renewable power generation. However, the high investment costs and low energy efficiency of P2G systems pose challenges. This study designs a green hydrogen-based Energy Storage as a Service (ESaaS) mode to improve the economic efficiency of P2G systems. In this ESaaS mode, the P2G system acts as an energy trading hub. The ESaaS operator manages the system and enables microgrids to access energy storage services. In return, the ESaaS operator generates revenue through electricity and hydrogen trading. To characterize stakeholders' behaviors, we develop a cost-minimizing model for multi-energy microgrid operation and a revenue-maximizing model for P2G investment and operation. To coordinate stakeholders involved in cooperation, we employ Nash bargaining-based model reformulation to determine investment and operation decisions and benefit distribution. Then, logarithm transformation and trading price discretization are introduced to efficiently solve the non-convex and nonlinear reformulated model. Simulation experiments using Shanghai's electricity market and meteorological data demonstrate that the ESaaS mode achieves 100% recovery of surplus renewable electricity and increases the proportion of renewable energy in microgrids from 59% to 83%. The results suggest that green hydrogen-based ESaaS is a feasible solution to increase the utilization rate of renewable energy and bring considerable economic and environmental benefits to all stakeholders.

An MINLP formulation to identify thermodynamically-efficient distillation configurations

Designing configurations for separation of multicomponent mixtures by distillation is challenging because of (i) combinatorial explosion of the choice set, and (ii) nonconvex nature of the governing equations. This work proposes a novel Mixed Integer Nonlinear Program (MINLP) that is formulated to identify configurations that minimize the total exergy loss/maximize thermodynamic efficiency of the separation process. The formulation in its default form has several nonlinear nonconvex equations. We propose a model reformulation via a simple variable elimination technique to reduce the system of nonlinear equations to a single equation, which we refer to as the exergy constraint. We describe the properties of exergy constraints and exploit them in deriving additional valid cuts for the problem. Finally, we use the model for a case study concerning the recovery of Natural Gas Liquids (NGLs) from shale gas.

A novel two-stage approach for energy-efficient timetabling for an urban rail transit network

Urban rail transit (URT) is the backbone transport mode in metropolitan areas to accommodate large travel demands. The high energy consumption of URT becomes a hotspot problem due to the ever-increasing operation mileages and pressing agendas of carbon neutralization. The high model complexity and inconsistency in the objectives of minimizing passenger travel time and operational energy consumption are the main challenges for energy-efficient timetabling for a URT network with multiple interlinked lines. This study proposes a general model framework of timetabling and passenger path choice in a URT network to minimize energy consumption under passenger travel time constraints. To obtain satisfactory energy-efficient nonuniform timetables, we suggest a novel model reformulation as a tree knapsack problem to determine train running times by a pseudo-polynomial dynamic programming algorithm in the first stage. Furthermore, a heuristic sequencing method is developed to determine nonuniform headways and dwell times in the second stage. The suggested model framework and solution algorithm are tested using a real-world URT network, and the results show that energy consumption can be considerably reduced given certain travel time increments.

Day-Ahead Strategic Operation of Hydrogen Energy Service Providers

The green hydrogen provides a pathway to the 100% sustainable energy future, rendering hydrogen energy service providers (HESPs) an important role in energy supply. Different from the conventional electricity service providers, HESP is not only responsible for the production, purchase and retailing but also the transportation of hydrogen, which makes its operation a challenging problem. To this end, this paper proposes a bi-level strategic operation model for HESPs. In the operation level, the bidding, hydrogen production and hydrogen transportation are coordinated to minimize the overall cost of HESPs. In the market level, the market clearing is simulated to estimate the influence of HESP behavior on electricity prices in the market. Then, a model reformulation technique is developed to connect the discrete-time based hydrogen production and continuous-time based hydrogen transportation. The bi-level optimization model is transformed into a single-level mixed-integer linear programming (MILP) problem with Karush-Kuhn-Tucker (KKT) conditions. The case studies with the modified IEEE-RTS-79 system were given to validate the proposed model and confirm the necessity to coordinate the hydrogen production and transportation in the strategic operation of HESPs. Sensitivity analysis is also conducted to study the potential influencing factors.

Strategy and Business Model Reformulation for Development of Zakat, Infaq, Alms, and Waqf (ZISWAF) (Case Study Bank XYZ, Pekanbaru)

Indonesia has enormous potential for zakat and waqf, but Bank XYZ has not maximized the collection through the sharia business unit (UUS). Therefore, it is necessary to reformulate the strategy and business model of developing ZISWAF Bank XYZ in order to obtain optimal results. This study used a qualitative descriptive method with a case study at Bank XYZ. The research was conducted from February 2021 to October 2021. The response survey was determined based on purposive sampling consisting of internal practitioners, academics, BWI, BAZNAS, and ziswaf institutions affiliated with Islamic banks. The data collection technique was based on observation, in-depth interviews, and questionnaires to respondents. Data analysis used IPA, BMC, SWOT, and QSPM approaches. Based on IPA analysis, this study recommends that three selected elements be developed: value proposition, channel, and critical resource. Technology adjustment and strengthening of bank image as ZISWAF recipients, improving bank channels through optimizing office networks and utilizing social media marketing and customer databases, as well as improving SOPs to improve the business model of Bank XYZ in the future.

Finding [formula omitted] dissimilar paths: Single-commodity and discretized flow formulations

While finding a path between two nodes is the basis for several applications, the need for alternative paths also may have various motivations. For instance, it can be of interest to ensure reliability in a telecommunications network, to reduce the consequences of possible accidents in the transportation of hazardous materials or to decrease the risk of robberies in money distribution. All these applications involve the search for a set of paths that are as dissimilar as possible, with respect to the arcs in them. In this work, we present linear integer programming formulations that intend to find K dissimilar paths. The new models derive from a straightforward single-commodity flow formulation of the K paths problem, to which extra constraints are added to account for the concept of dissimilarity. In particular, in each formulation a different measure of the similarity between the K paths is minimized: the number of repeated arcs, the number of arc reuses and the number of pairwise arc overlaps. The third measure originates a non-linear model that is linearized through a discretized model reformulation technique. These formulations are complemented by a polynomial algorithm that allows to extract K loopless paths from the solutions output by each of them.The formulations are tested for random and grid networks with respect to the solutions’ average and minimum dissimilarity and the run time. Two of them stand out in terms of both those measures, when compared to an iterative approach from the literature. The best one regarding the average dissimilarity finds 20 paths with average dissimilarity of 99.5% in about 168 s for random networks of 5000 nodes and 100000 arcs. The same approach finds 20 paths for grid instances of size 100 × 100 in less than 18 s. The other formulation requires about 11 s for the same random instances, with a 0.7% deviation from the best known average dissimilarity; while it requires less than 7 s to compute 20 paths in 100 × 100 grids with a 0.6% deviation to the optimal dissimilarity.

Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics

We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest and provide an overview of various settings leading to tractable formulations. Some of the arising side results, such as the mathematical programming expressions for robustified risk measures in a discrete space, are also of independent interest. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications, and present a numerical study for a novel risk-averse scheduling problem with controllable processing times. Summary of Contribution: In this study, we introduce a new class of optimization problems that simultaneously address distributional and decision-dependent uncertainty. We present a unified modeling framework along with a discussion on possible ways to specify the key model components, and discuss the main computational challenges in solving the complex problems of interest. Special care has been devoted to identifying the settings and problem classes where these challenges can be mitigated. In particular, we provide model reformulation results, including mathematical programming expressions for robustified risk measures, and describe how these results can be utilized to obtain tractable formulations for specific applied problems from the fields of humanitarian logistics and machine scheduling. Toward demonstrating the value of the modeling approach and investigating the performance of the proposed mixed-integer linear programming formulations, we conduct a computational study on a novel risk-averse machine scheduling problem with controllable processing times. We derive insights regarding the decision-making impact of our modeling approach and key parameter choices.

Estimation of older-adult mortality from information distorted by systematic age misreporting

Testing theories about human senescence and longevity demands accurate information on older-adult mortality; this is rare in low- to middle-income countries where raw data may be distorted by defective completeness and systematic age misreporting. For this reason, such populations are frequently excluded from empirical tests of mortality and longevity theories, thus limiting their reach, as they reflect only a small and selected human mortality experience. In this paper we formulate an integrated method to compute estimates of older-adult mortality when vital registration and population counts are defective due to inaccurate coverage and/or systematic age misreporting. The procedure is validated with a simulation study that identifies a strategy to compute adjustments, which, under some assumptions, performs quite well. While the paper focuses on Latin American and Caribbean countries, the method is quite general and, with additional information and some model reformulation, could be applied to other populations with similar problems.

Takagi–Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs

AbstractThis article presents a new observer design framework for a class of nonlinear descriptor systems with unknown but bounded inputs. In the presence of unmeasured nonlinearities, that is, premise variables, designing nonlinear observers is known as particularly challenging. To solve this problem, we rewrite the nonlinear descriptor system in the form of a Takagi–Sugeno (TS) fuzzy model with nonlinear consequents. This model reformulation enables an effective use of the differential mean value theorem to deal with the mismatching terms involved in the estimation error dynamics. These nonlinear terms, issued from the unmeasured nonlinearities of the descriptor system, cause a major technical difficulty for TS fuzzy‐model‐based observer design. The descriptor form is treated through a singular redundancy representation. For observer design, we introduce into the Luenberger‐like observer structure a virtual variable aiming at estimating the one‐step ahead state. This variable introduction allows for free‐structure decision variables involved in the observer design to further reduce the conservatism. Using Lyapunov‐based arguments, the observer design is reformulated as an optimization problem under linear matrix inequalities with a single line search parameter. The estimation error bounds of both the state and the unknown input can be minimized by means of a guaranteed ℓ∞‐gain performance level. The interests of the new ℓ∞ TS fuzzy observer design are clearly illustrated with two physically motivated examples.

A modified collocation modeling framework for dynamic evolution of molecular weight distributions in general polymer kinetic systems

General modeling and optimization with molecular weight distributions (MWDs) are essential to determine optimal designs and operations for polymerization processes. Orthogonal collocation methods in two dimensions can capture the dynamic feature of MWD in time and the distributive feature in chain length. However, there are still computational challenges for complex reactions using this method. This study proposes a general framework based on the collocation methods. For different mathematical operations caused by different types of polymeric reactions, we propose corresponding model reformulation methods with specific coefficient matrices, including moment operations caused by chain propagation and disproportionate termination, moment operation without closure caused by scission, and convolution operation caused by coupling termination. The chain-length dependent rate can also be handled well through this general framework. Case studies show the effectiveness, accuracy, and generality of our approach.

Coastal ocean forecasting on the GPU using a two-dimensional finite-volume scheme

In this work, we take a modern high-resolution finite-volume scheme for solving the rotational shallow-water equations and extend it with features required to run real-world ocean simulations. Our contributions include a spatially varying north vector and Coriolis term required for large scale domains, moving wet-dry fronts, a static land mask, bottom shear stress, wind forcing, boundary conditions for nesting in a global model, and an efficient model reformulation that makes it well-suited for massively parallel implementations. Our model order is verified using a grid convergence test, and we show numerical experiments using three different sections along the coast of Norway based on data originating from operational forecasts run at the Norwegian Meteorological Institute. Our simulation framework shows perfect weak scaling on a modern P100 GPU, and is capable of providing tidal wave forecasts that are very close to the operational model at a fraction of the cost. All source code and data used in this work are publicly available under open licenses.

Robust Frequency and Phase Estimation for Three-Phase Power Systems Using a Bank of Kalman Filters

In this paper we propose a powerful frequency, phase angle, and amplitude estimation solution for an unbalanced three-phase power system based on multiple model adaptive estimation. The proposed model utilizes the existence of a conditionally linear and Gaussian substructure in the power system states by marginalizing out the frequency component. This substructure can be effectively tracked by a bank of Kalman filters where each filter employs a different angular frequency value. Compared to other Bayesian filtering schemes for estimation in three-phase power systems, the proposed model reformulation is simpler, more robust, and more accurate as validated with numerical simulations on synthetic data.

An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation

We study a multi‐period, multi‐item dynamic pricing problem faced by a retailer. The objective is to maximize the total profit by choosing prices, while satisfying several business rules. The strength of our work lies in our graphical model reformulation, which allows us to use ideas from combinatorial optimization. We do not make any assumptions on the structure of the demand function. The complexity of our method depends linearly on the number of time periods but is exponential in the memory of the model (number of past prices that affect current demand) and in the number of items. We prove that the profit maximization problem is NP‐hard by showing an approximation preserving reduction from the weighted Max‐3‐SAT problem. We next introduce the discrete reference price model which is a discretized version of the reference price model, accounting for an exponentially smoothed contribution of all past prices. We show that our problem can be solved efficiently under this model. We then approximate common demand functions using the discrete reference price model. To handle cross‐item effects among multiple items, we propose to use a virtual reference price that assigns a reference price for each category of items (as opposed to a reference price for each item). To enhance the tractability of our approach, we cluster items into blocks and show how to adapt our method to include business constraints across blocks. Finally, we apply our solution approach using demand models calibrated with supermarket data and validate its practical performance.