Showing papers on "Integer programming published in 2016"
TL;DR: In this article, a discrete extension of modern first-order continuous optimization methods is proposed to find high quality feasible solutions that are used as warm starts to a MIO solver that finds provably optimal solutions.
Abstract: In the period 1991–2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MIO problems. We present a MIO approach for solving the classical best subset selection problem of choosing $k$ out of $p$ features in linear regression given $n$ observations. We develop a discrete extension of modern first-order continuous optimization methods to find high quality feasible solutions that we use as warm starts to a MIO solver that finds provably optimal solutions. The resulting algorithm (a) provides a solution with a guarantee on its suboptimality even if we terminate the algorithm early, (b) can accommodate side constraints on the coefficients of the linear regression and (c) extends to finding best subset solutions for the least absolute deviation loss function. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with $n$ in the 1000s and $p$ in the 100s in minutes to provable optimality, and finds near optimal solutions for $n$ in the 100s and $p$ in the 1000s in minutes. We also establish via numerical experiments that the MIO approach performs better than Lasso and other popularly used sparse learning procedures, in terms of achieving sparse solutions with good predictive power.
441 citations
TL;DR: Two Mixed Integer Linear Programming (MILP) approaches to generate configurable square-based fiducial marker dictionaries maximizing their inter-marker distance are proposed.
415 citations
TL;DR: An appropriate framework is devised and the roles and tasks of different management entities in a multi-microgrids system are introduced and the effectiveness in confronting with different outage events is demonstrated through realistic case studies.
Abstract: This paper proposes a hierarchical outage management scheme to enhance the resilience of a smart distribution system comprised of multi-microgrids against unexpected disaster events. In this regard, after identifying the main features and requirements for a resilient outage management scheme, an appropriate framework is devised and the roles and tasks of different management entities in a multi-microgrids system are introduced. Based on this framework, the microgrids schedule their available resources in the first stage using a novel model predictive control-based algorithm. In the second stage, distribution system operator coordinates the possible power transfers among the microgrids and utilizes the unused capacities of microgrids’ resources for feeding the unserved loads in stage I. The general optimization model that needs to be run is formulated as a mixed integer linear programming problem and a novel index is presented to quantify the performance of the proposed method. The developed scheme is implemented on a test system and its effectiveness in confronting with different outage events is demonstrated through realistic case studies.
308 citations
Proceedings Article•
12 Feb 2016TL;DR: This work proposes a machine learning (ML) framework for variable branching in MIP, and observes the decisions made by Strong Branching, a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree.
Abstract: The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic. To address these issues, we propose a machine learning (ML) framework for variable branching in MIP. Our method observes the decisions made by Strong Branching (SB), a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Based on the collected data, we learn an easy-to-evaluate surrogate function that mimics the SB strategy, by means of solving a learning-to-rank problem, common in ML. The learned ranking function is then used for branching. The learning is instance-specific, and is performed on-the-fly while executing a branch-and-bound search to solve the instance. Experiments on benchmark instances indicate that our method produces significantly smaller search trees than existing heuristics, and is competitive with a state-of-the-art commercial solver.
262 citations
TL;DR: The Random EMbedding Bayesian Optimization (REMBO) algorithm as mentioned in this paper applies to domains with both categorical and continuous variables and achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver.
Abstract: Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high-dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple, has important invariance properties, and applies to domains with both categorical and continuous variables. We present a thorough theoretical analysis of REMBO. Empirical results confirm that REMBO can effectively solve problems with billions of dimensions, provided the intrinsic dimensionality is low. They also show that REMBO achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver.
227 citations
TL;DR: In this paper, the authors study optimal multirobot path planning on graphs over four minimization objectives: the makespan (last arrival time), the maximum (single-robot traveled) distance, the total arrival time, and the total distance.
Abstract: We study optimal multirobot path planning on graphs ( $\text{MPP}$ ) over four minimization objectives: the makespan (last arrival time), the maximum (single-robot traveled) distance, the total arrival time, and the total distance. Having established previously that these objectives are distinct and NP-hard to optimize, in this paper, we focus on efficient algorithmic solutions for solving these optimal $\text{MPP}$ problems. Toward this goal, we first establish a one-to-one solution mapping between $\text{MPP}$ and a special type of multiflow network. Based on this equivalence and integer linear programming (ILP), we design novel and complete algorithms for optimizing over each of the four objectives. In particular, our exact algorithm for computing optimal makespan solutions is a first that is capable of solving extremely challenging problems with robot-vertex ratios as high as $100\%$ . Then, we further improve the computational performance of these exact algorithms through the introduction of principled heuristics, at the expense of slight optimality loss. The combination of ILP model based algorithms and the heuristics proves to be highly effective, allowing the computation of $1.x$ -optimal solutions for problems containing hundreds of robots, densely populated in the environment, often in just seconds.
215 citations
TL;DR: This paper constructs a special model known as RELAX-RSMN with a totally unimodular constraint coefficient matrix to solve the relaxed 0-1 ILP rapidly through linear programming.
Abstract: Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest. However, in certain applications, barrier coverage cannot be satisfied after random deployment. In this paper, we study how mobile sensors can be efficiently relocated to achieve k-barrier coverage. In particular, two problems are studied: relocation of sensors with minimum number of mobile sensors and formation of k-barrier coverage with minimum energy cost. These two problems were formulated as 0–1 integer linear programming (ILP). The formulation is computationally intractable because of integrality and complicated constraints. Therefore, we relax the integrality and complicated constraints of the formulation and construct a special model known as RELAX-RSMN with a totally unimodular constraint coefficient matrix to solve the relaxed 0–1 ILP rapidly through linear programming. Theoretical analysis and simulation were performed to verify the effectiveness of our approach.
202 citations
TL;DR: In this paper, a hybrid algorithm of MIP and iterated neighborhood search is proposed to solve the green vehicle routing and scheduling problem (GVRSP) which allows vehicles to stop on arcs, which is shown to reduce emissions up to additional 8% on simulated data.
Abstract: The green vehicle routing and scheduling problem (GVRSP) aims to minimize green-house gas emissions in logistics systems through better planning of deliveries/pickups made by a fleet of vehicles. We define a new mixed integer liner programming (MIP) model which considers heterogeneous vehicles, time-varying traffic congestion, customer/vehicle time window constraints, the impact of vehicle loads on emissions, and vehicle capacity/range constraints in the GVRSP. The proposed model allows vehicles to stop on arcs, which is shown to reduce emissions up to additional 8% on simulated data. A hybrid algorithm of MIP and iterated neighborhood search is proposed to solve the problem.
195 citations
TL;DR: A stochastic optimization model for optimal bidding strategies of electric vehicle (EV) aggregators in day-ahead energy and ancillary services markets with variable wind energy and a game theoretic approach is developed for analyzing the competition among the EV aggregators.
Abstract: This paper proposes a stochastic optimization model for optimal bidding strategies of electric vehicle (EV) aggregators in day-ahead energy and ancillary services markets with variable wind energy. The forecast errors of EV fleet characteristics, hourly loads, and wind energy as well as random outages of generating units and transmission lines are considered as potential uncertainties, which are represented by scenarios in the Monte Carlo Simulation (MCS). The conditional value at risk (CVaR) index is utilized for measuring EV aggregators risks caused by the uncertainties. The EV aggregators optimal bidding strategy is formulated as a mathematical programming with equilibrium constraints (MPEC), in which the upper level problem is the aggregators CVaR maximization while the lower level problem corresponds to the system operation cost minimization. The bi-level problem is transformed into a single-level mixed integer linear programming (MILP) problem using the prime-dual formulation with linearized constraints. The progressive hedging algorithm (PHA) is utilized to solve the resulting single-level MILP problem. A game theoretic approach is developed for analyzing the competition among the EV aggregators. Numerical cases are studied for a modified 6-bus system and the IEEE 118-bus system. The results show the validity of the proposed approach and the impact of the aggregators bidding strategies on the stochastic electricity market operation.
179 citations
TL;DR: In this paper, a stochastic multi-objective ORPD (SMO-ORPD) problem is studied in a wind integrated power system considering the loads and wind power generation uncertainties.
177 citations
TL;DR: In this paper, a Supersparse Linear Integer Model (SLIM) is proposed for scoring linear classification models, which can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce acceptable models without parameter tuning.
Abstract: Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM scoring systems are built by using an integer programming problem that directly encodes measures of accuracy (the 0---1 loss) and sparsity (the $$\ell _0$$l0-seminorm) while restricting coefficients to coprime integers. SLIM can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce acceptable models without parameter tuning because of the direct control provided over these quantities. We provide bounds on the testing and training accuracy of SLIM scoring systems, and present a new data reduction technique that can improve scalability by eliminating a portion of the training data beforehand. Our paper includes results from a collaboration with the Massachusetts General Hospital Sleep Laboratory, where SLIM is being used to create a highly tailored scoring system for sleep apnea screening.
TL;DR: The disjunctive MIP model is most efficient, and MIP is efficient for solving moderate-size problems, while constraint programming is compared to constraint programming and the best known algorithm to provide a broad view among different approaches.
TL;DR: This work considers secure resource allocations for orthogonal frequency division multiple access (OFDMA) two-way relay wireless sensor networks (WSNs) and proposes an asymptotically optimal algorithm based on the dual decomposition method and a suboptimal algorithm with lower complexity.
Abstract: We consider secure resource allocations for orthogonal frequency division multiple access (OFDMA) two-way relay wireless sensor networks (WSNs). The joint problem of subcarrier (SC) assignment, SC pairing and power allocations, is formulated under scenarios of using and not using cooperative jamming (CJ) to maximize the secrecy sum rate subject to limited power budget at the relay station (RS) and orthogonal SC allocation policies. The optimization problems are shown to be mixed integer programming and nonconvex. For the scenario without CJ, we propose an asymptotically optimal algorithm based on the dual decomposition method and a suboptimal algorithm with lower complexity. For the scenario with CJ, the resulting optimization problem is nonconvex, and we propose a heuristic algorithm based on alternating optimization. Finally, the proposed schemes are evaluated by simulations and compared with the existing schemes.
13 Jun 2016
TL;DR: A general formulation of the optimal DSP placement (for short, ODP) as an Integer Linear Programming problem which takes explicitly into account the heterogeneity of computing and networking resources and which encompasses - as special cases - the different solutions proposed in the literature.
Abstract: Data Stream Processing (DSP) applications are widely used to timely extract information from distributed data sources, such as sensing devices, monitoring stations, and social networks. To successfully handle this ever increasing amount of data, recent trends investigate the possibility of exploiting decentralized computational resources (e.g., Fog computing) to define the applications placement. Several placement policies have been proposed in the literature, but they are based on different assumptions and optimization goals and, as such, they are not completely comparable to each other.In this paper we study the placement problem for distributed DSP applications. Our contributions are twofold. We provide a general formulation of the optimal DSP placement (for short, ODP) as an Integer Linear Programming problem which takes explicitly into account the heterogeneity of computing and networking resources and which encompasses - as special cases - the different solutions proposed in the literature. We present an ODP-based scheduler for the Apache Storm DSP framework. This allows us to compare some well-known centralized and decentralized placement solutions. We also extensively analyze the ODP scalability with respect to various parameter settings.
TL;DR: A mixed integer programming formulation as well as an Adaptive Large Neighborhood Search (ALNS) heuristic for the E-VSP are presented and result shows that the proposed heuristic can provide good solutions to large E-vSP instances and optimal or near-optimal solutions to small E- VSP instances.
TL;DR: This paper presents an incremental scheduling approach, based on the demand bound test for asynchronous tasks, which significantly improves the scalability of the scheduling problem and demonstrates the performance of the approach with an extensive evaluation of industrial-sized synthetic configurations using alternative state-of-the-art SMT and MIP solvers.
Abstract: Ethernet-based time-triggered networks (e.g. TTEthernet) enable the cost-effective integration of safety-critical and real-time distributed applications in domains where determinism is a key requirement, like the aerospace, automotive, and industrial domains. Time-Triggered communication typically follows an offline and statically configured schedule (the synthesis of which is an NP-complete problem) guaranteeing contention-free frame transmissions. Extending the end-to-end determinism towards the application layers requires that software tasks running on end nodes are scheduled in tight relation to the underlying time-triggered network schedule. In this paper we discuss the simultaneous co-generation of static network and task schedules for distributed systems consisting of preemptive time-triggered tasks which communicate over switched multi-speed time-triggered networks. We formulate the schedule problem using first-order logical constraints and present alternative methods to find a solution, with or without optimization objectives, based on satisfiability modulo theories (SMT) and mixed integer programming (MIP) solvers, respectively. Furthermore, we present an incremental scheduling approach, based on the demand bound test for asynchronous tasks, which significantly improves the scalability of the scheduling problem. We demonstrate the performance of the approach with an extensive evaluation of industrial-sized synthetic configurations using alternative state-of-the-art SMT and MIP solvers and show that, even when using optimization, most of the problems are solved within reasonable time using the incremental method.
TL;DR: This paper shows that by estimating jointly and globally the trajectories of different types of objects, the presence of the ones which were not initially detected based solely on image evidence can be inferred from the detections of the others.
Abstract: In this paper, we show that tracking different kinds of interacting objects can be formulated as a network-flow mixed integer program This is made possible by tracking all objects simultaneously using intertwined flow variables and expressing the fact that one object can appear or disappear at locations where another is in terms of linear flow constraints Our proposed method is able to track invisible objects whose only evidence is the presence of other objects that contain them Furthermore, our tracklet-based implementation yields real-time tracking performance We demonstrate the power of our approach on scenes involving cars and pedestrians, bags being carried and dropped by people, and balls being passed from one player to the next in team sports In particular, we show that by estimating jointly and globally the trajectories of different types of objects, the presence of the ones which were not initially detected based solely on image evidence can be inferred from the detections of the others
01 Dec 2016
TL;DR: The authors have proposed an integer linear programming formulation for the scheduling problem and a greedy randomised adaptive search procedure-based heuristic for the routing problem that have been evaluated using several test cases.
Abstract: In this study the authors are interested in safety-critical real-time applications implemented on distributed architectures supporting the time-sensitive networking (TSN) standard. The on-going standardisation of TSN is an IEEE effort to bring deterministic real-time capabilities into the IEEE 802.1 Ethernet standard supporting safety-critical systems and guaranteed quality-of-service. TSN will support time-triggered (TT) communication based on schedule tables, audio-video-bridging (AVB) flows with bounded end-to-end latency as well as best-effort messages. The authors first present a survey of research related to the optimisation of distributed cyber-physical systems using real-time Ethernet for communication. Then, the authors formulate two novel optimisation problems related to the scheduling and routing of TT and AVB traffic in TSN. Thus, the authors consider that they know the topology of the network as well as the set of TT and AVB flows. The authors are interested to determine the routing of both TT and AVB flows as well as the scheduling of the TT flows such that all frames are schedulable and the AVB worst-case end-to-end delay is minimised. The authors have proposed an integer linear programming formulation for the scheduling problem and a greedy randomised adaptive search procedure-based heuristic for the routing problem. The proposed approaches have been evaluated using several test cases.
Posted Content•
TL;DR: MILP method is extended to search integral distinguishers of block ciphers based on division property with block size larger than 32 to solve the challenge of solving bit-based division property of SIMON32.
Abstract: Division property is a generalized integral property proposed by Todo at EUROCRYPT 2015, and very recently, Todo et al. proposed bit-based division property and applied to SIMON32 at FSE 2016. However, this technique can only be applied to block ciphers with block size no larger than 32 due to its high time and memory complexity. In this paper, we extend Mixed Integer Linear Programming (MILP) method, which is used to search differential characteristics and linear trails of block ciphers, to search integral distinguishers of block ciphers based on division property with block size larger than 32.
TL;DR: In this article, a new rich vehicle routing problem that could arise in a real life context is introduced and formalized: the Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet.
Abstract: In this paper, a new rich Vehicle Routing Problem that could arise in a real life context is introduced and formalized: the Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet. The goal of the problem is to minimize the total delivery cost. A heterogeneous fleet composed of vehicles with different capacity, characteristics (i.e. refrigerated vehicles) and hourly costs is considered. A limit on the maximum route duration is imposed. Unlike what happens in classical multi-depot VRP, not every customer may/will be served by all the vehicles or from all the depots. The planning horizon, as in most real life applications, consists of multiple periods, and the period in which each route is performed is a variable of the problem. The set of periods, within the time horizon, in which the delivery may be carried out is known for each customer. A Mixed Integer Programming (MIP) formulation for MDMPVRPHF is presented in this paper, and an Adaptive Large Neighborhood Search (ALNS) based Matheuristic approach is proposed, in which different destroy operators are defined. Computational results, pertaining to realistic instances, which show the effectiveness of the proposed method, are provided.
TL;DR: This work model the cold supply chain design problem as a mixed-integer concave minimization problem with dual objectives of minimizing the total cost - including capacity, transportation, and inventory costs - and the global warming impact and proposes a novel hybrid simulation-optimization approach to solve the problem.
20 Mar 2016
TL;DR: This paper proposes an MILP-based method for automatic search for differential characteristics and linear approximations in ARX ciphers and presents a method to describe the differential characteristic and linear approximation with linear inequalities under the assumptions of independent inputs to the modular addition and independent rounds.
Abstract: In recent years, Mixed Integer Linear Programming MILP has been successfully applied in searching for differential characteristics and linear approximations in block ciphers and has produced the significant results for some ciphers such as SIMON a family of lightweight and hardware-optimized block ciphers designed by NSA etc. However, in the literature, the MILP-based automatic search algorithm for differential characteristics and linear approximations is still infeasible for block ciphers such as ARX constructions. In this paper, we propose an MILP-based method for automatic search for differential characteristics and linear approximations in ARX ciphers. By researching the properties of differential characteristic and linear approximation of modular addition in ARX ciphers, we present a method to describe the differential characteristic and linear approximation with linear inequalities under the assumptions of independent inputs to the modular addition and independent rounds. We use this representation as an input to the publicly available MILP optimizer Gurobi to search for differential characteristics and linear approximations for ARX ciphers. As an illustration, we apply our method to Speck, a family of lightweight and software-optimized block ciphers designed by NSA, which results in the improved differential characteristics and linear approximations compared with the existing ones. Moreover, we provide the improved differential attacks on Speck48, Speck64, Speck96 and Speck128, which are the best attacks on them in terms of the number of rounds.
01 Dec 2016
TL;DR: Simulation results show that the online algorithms can reduce the blocking probability of SC requests and increase the service provider's profit from SC deployment effectively.
Abstract: This paper studies the problem of service chain (SC) deployment. Specifically, we try to place virtual network functions (vNFs) on network nodes and connect the vNFs in sequence through link mapping. We start with the offline problem. An integer linear programming (ILP) model is formulated to minimize the total SC deployment cost. With the ILP, we prove that the offline problem is NP-hard and propose a time-efficient heuristic based on affiliation-aware vNF placement. Then, we move to the online problem, and design a forecast-assisted online SC deployment algorithm that includes the prediction of future vNF requirements. Simulation results show that the online algorithms can reduce the blocking probability of SC requests and increase the service provider's profit from SC deployment effectively.
TL;DR: This study studies the provisioning algorithms to realize tree-type virtual network function forwarding graphs (VNF-FGs), i.e., multicast NFV trees (M-NFV-Ts), in inter-DC elastic optical networks (IDC-EONs) cost-effectively and designs two additional online algorithms based on AFM-GS and RB to serve M-NFv-Ts in a dynamic IDC- EON, with the consideration of spectrum fragmentation.
Abstract: It is known that by incorporating network function virtualization (NFV) in inter-datacenter (inter-DC) networks, service providers can use their network resources more efficiently and adaptively and expedite the deployment of new services. This paper studies the provisioning algorithms to realize tree-type virtual network function forwarding graphs (VNF-FGs), i.e., multicast NFV trees (M-NFV-Ts), in inter-DC elastic optical networks (IDC-EONs) cost-effectively. Specifically, we try to optimize the VNF placement and multicast routing and spectrum assignment jointly for orchestrating M-NFV-Ts in an IDC-EON with the lowest cost. Our study addresses both static network planning and dynamic network provisioning. For network planning, we first formulate a mixed integer linear programming (MILP) model to solve the problem exactly, and then propose three heuristic algorithms, namely, auxiliary frequency slot matrix (AFM)-MILP, AFM-GS, and RB. Extensive simulations show that AFM-MILP and AFM-GS can approximate the MILP's performance on low-cost M-NFV-T provisioning with much shorter running time. For network provisioning, we design two additional online algorithms based on AFM-GS and RB to serve M-NFV-Ts in a dynamic IDC-EON, with the consideration of spectrum fragmentation.
TL;DR: A comprehensive two-stage robust security-constrained unit commitment (SCUC) approach, which minimizes the operation cost of the base case while guaranteeing that the robust solution can be adaptively and securely adjusted in response to continuous load and wind uncertainty intervals as well as discrete N-K generation and transmission contingency security criteria.
Abstract: This paper presents a comprehensive two-stage robust security-constrained unit commitment (SCUC) approach, which minimizes the operation cost of the base case while guaranteeing that the robust solution can be adaptively and securely adjusted in response to continuous load and wind uncertainty intervals as well as discrete $N-K$ generation and transmission contingency security criteria. In addition, corrective capabilities of both non-quick-start and quick-start units are rigorously formulated. Specifically, unit commitment of quick-start units is adaptively adjusted in the recourse stage for satisfying security constraints under various uncertainties, which introduces mixed-integer recourse to the proposed two-stage robust SCUC model. The proposed model is solved by the combination of modified Benders decomposition (BD) method and column-and-constraint generation (C&CG) algorithm, which decompose the original problem into a master UC problem for the base case and security checking subproblems for uncertainties. Numerical case studies on the modified IEEE 118-bus system illustrate the effectiveness of the proposed robust SCUC approach. Although the modified BD does not provide the tightest lower bound and may not guarantee the global optimality, robustness performance tests indicate that a reasonable threshold on the violation of security checking subproblems would guarantee good enough solutions from engineering point of view.
TL;DR: In this paper, the authors demonstrate that ILP outperforms SA with respect to both solution quality (how close it is to optimality) and processing time over a range of problem sizes.
TL;DR: This work presents an MIQO-based approach for designing high quality linear regression models that explicitly addresses various competing objectives and demonstrates the effectiveness of the approach on both real and synthetic data sets.
Abstract: Linear regression models are traditionally built through trial and error to balance many competing goals such as predictive power, interpretability, significance, robustness to error in data, and sparsity, among others. This problem lends itself naturally to a mixed integer quadratic optimization (MIQO) approach but has not been modeled this way because of the belief in the statistics community that MIQO is intractable for large scale problems. However, in the last 25 years (1991–2015), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving mixed integer optimization problems. We present an MIQO-based approach for designing high quality linear regression models that explicitly addresses various competing objectives and demonstrate the effectiveness of our approach on both real and synthetic data sets.
TL;DR: In this paper, the authors proposed a convex model for active distribution network expansion planning integrating dispersed energy storage systems (DESS), where four active management schemes, distributed generation curtailment, demand side management, on-load tap changer tap adjustment and reactive power compensation are considered.
Abstract: This study proposes the convex model for active distribution network expansion planning integrating dispersed energy storage systems (DESS). Four active management schemes, distributed generation (DG) curtailment, demand side management, on-load tap changer tap adjustment and reactive power compensation are considered. The optimisation of DESS for peak shaving and operation cost decreasing is also integrated. The expansion model allows alternatives to be considered for new wiring, new substation, substation expansion and DG installation. The distribution network expansion planning (DNEP) problem is a mixed integer non-linear programming problem. Active management and uncertainties especially with the DG integration make the DNEP problem much complex. To find the suitable algorithm, this study converts the DNEP problem to a second-order cone programming model through distflow equations and constraints relaxation. A modified 50-bus application example is used to verify the proposed model.
TL;DR: A hierarchical framework for timetable design which combines a microscopic and a macroscopic model of the network is proposed which shows the ability of the approach to automatically compute a feasible, stable and robust timetable.
Abstract: With the increasing demand for railway transportation infrastructure managers need improved automatic timetabling tools that provide feasible timetables with enhanced performance in short computation times. This paper proposes a hierarchical framework for timetable design which combines a microscopic and a macroscopic model of the network. The framework performs an iterative adjustment of train running and minimum headway times until a feasible and stable timetable has been generated at the microscopic level. The macroscopic model optimizes a trade-off between minimal travel times and maximal robustness using an Integer Linear Programming formulation which includes a measure for delay recovery computed by an integrated delay propagation model in a Monte Carlo setting. The application to an area of the Dutch railway network shows the ability of the approach to automatically compute a feasible, stable and robust timetable. Practitioners can use this approach both for effective timetabling and post-evaluation of existing timetables.
TL;DR: In this paper, the restoration problem is transformed into a mixed integer second-order cone programming problem, which can be solved efficiently using several commercial solvers based on the efficient optimization technique family branch and bound.
Abstract: This paper presents a comprehensive mathematical model to solve the restoration problem in balanced radial distribution systems. The restoration problem, originally modeled as mixed integer nonlinear programming, is transformed into a mixed integer second-order cone programming problem, which can be solved efficiently using several commercial solvers based on the efficient optimization technique family branch and bound. The proposed mathematical model considers several objectives in a single objective function, using parameters to preserve the hierarchy of the different objectives: 1) maximizing the satisfaction of the demand, 2) minimizing the number of switch operations, 3) prioritizing the automatic switch operation rather than a manual one, and 4) prioritizing especial loads. General and specialized tests were carried out on a 53-node test system, and the results were compared with other previously proposed algorithms. Results show that the mathematical model is robust, efficient, flexible, and presents excellent performance in finding optimal solutions.