Showing papers on "Integer programming published in 2015"
TL;DR: The works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC are reviewed to help transform research advances into real-world applications.
Abstract: Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC’s birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.
519 citations
TL;DR: A unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station.
Abstract: This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin–destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases.
329 citations
TL;DR: In this article, the main novelty is the simultaneous management of energy production and energy demand within a reactive scheduling approach to deal with the presence of uncertainty associated to production and consumption, where delays in nominal energy demands are allowed under associated penalty costs to tackle flexible and fluctuating demand profiles.
241 citations
TL;DR: The main contribution of the proposed methodology, when compared with the traditional vehicle routing problem’s (VRP) solutions, is the fact that the method solves some practical problems only encountered during the execution of the task with actual UAVs.
Abstract: This paper presents a solution for the problem of minimum time coverage of ground areas using a group of unmanned air vehicles (UAVs) equipped with image sensors. The solution is divided into two parts: (i) the task modeling as a graph whose vertices are geographic coordinates determined in such a way that a single UAV would cover the area in minimum time; and (ii) the solution of a mixed integer linear programming problem, formulated according to the graph variables defined in the first part, to route the team of UAVs over the area. The main contribution of the proposed methodology, when compared with the traditional vehicle routing problem’s (VRP) solutions, is the fact that our method solves some practical problems only encountered during the execution of the task with actual UAVs. In this line, one of the main contributions of the paper is that the number of UAVs used to cover the area is automatically selected by solving the optimization problem. The number of UAVs is influenced by the vehicles’ maximum flight time and by the setup time, which is the time needed to prepare and launch a UAV. To illustrate the methodology, the paper presents experimental results obtained with two hand-launched, fixed-wing UAVs.
235 citations
TL;DR: In this paper, a wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques, but in some cases the resulting MIP can be either too weak or...
Abstract: A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or ...
211 citations
01 Feb 2015
TL;DR: This survey reviews advanced MIP formulation techniques that result in stronger and/or smaller formulations for a wide class of problems.
Abstract: A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or too large to be effectively solved by state of the art solvers. In this survey we review advanced MIP formulation techniques that result in stronger and/or smaller formulations for a wide class of problems.
209 citations
TL;DR: The authors use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models, which are trained on a small set of word problems and their answers, without any manual annotation.
Abstract: This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as ALGES. We compare ALGES with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. In addition, ALGES overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.
193 citations
TL;DR: A robust energy and reserve dispatch (RERD) model is proposed in this paper, in which the operating decisions are divided into pre-dispatch and re- Dispatch, and a robust feasibility constraint set is imposed on pre-Dispatch variables, such that operation constraints can be recovered by adjusting re-dispatches after wind generation realizes.
Abstract: Global warming and environmental pollution concerns have promoted dramatic integrations of renewable energy sources all over the world. Associated with benefits of environmental conservation, essentially uncertain and variable characteristics of such energy resources significantly challenge the operation of power systems. In order to implement reliable and economical operations, a robust energy and reserve dispatch (RERD) model is proposed in this paper, in which the operating decisions are divided into pre-dispatch and re-dispatch. A robust feasibility constraint set is imposed on pre-dispatch variables, such that operation constraints can be recovered by adjusting re-dispatch after wind generation realizes. The model is extended to more general dispatch decision making problems involving uncertainties in the framework of adjustable robust optimization. By revealing the convexity of the robust feasibility constraint set, a comprehensive mixed integer linear programming based oracle is presented to verify the robust feasibility of pre-dispatch decisions. A cutting plane algorithm is established to solve associated optimization problems. The proposed model and method are applied to a five-bus system as well as a realistic provincial power grid in China. Numeric experiments demonstrate that the proposed methodology is effective and efficient.
193 citations
Posted Content•
TL;DR: 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.
Abstract: We study the problem of optimal multi-robot path planning on graphs MPP over four distinct minimization objectives: the makespan (last arrival time), the maximum (single-robot traveled) distance, the total arrival time, and the total distance. In a related paper, we show that these objectives are distinct and NP-hard to optimize. In this work, we focus on efficiently algorithmic solutions for solving these optimal MPP problems. Toward this goal, we first establish a one-to-one solution mapping between MPP and network-flow. 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 such that is capable of solving extremely challenging problems with robot-vertex ratio 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 some 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.
190 citations
TL;DR: A parallel simulated annealing algorithm that includes a Residual Capacity and Radial Surcharge insertion-based heuristic is developed and applied to solve a variant of the vehicle routing problem in which customers require simultaneous pickup and delivery of goods during specific individual time windows.
181 citations
TL;DR: In this article, a generic mixed integer linear programming (MILP) model that integrates the unit commitment problem (UCP) with the long-term generation expansion planning (GEP) framework is presented.
10 Aug 2015
TL;DR: This paper proposes a novel solution to preserve the joint distribution of a high-dimensional dataset using an integer programming relaxation and the constrained concave-convex procedure and proves that selecting the optimal marginals with the goal of minimizing error is NP-hard.
Abstract: Releasing high-dimensional data enables a wide spectrum of data mining tasks. Yet, individual privacy has been a major obstacle to data sharing. In this paper, we consider the problem of releasing high-dimensional data with differential privacy guarantees. We propose a novel solution to preserve the joint distribution of a high-dimensional dataset. We first develop a robust sampling-based framework to systematically explore the dependencies among all attributes and subsequently build a dependency graph. This framework is coupled with a generic threshold mechanism to significantly improve accuracy. We then identify a set of marginal tables from the dependency graph to approximate the joint distribution based on the solid inference foundation of the junction tree algorithm while minimizing the resultant error. We prove that selecting the optimal marginals with the goal of minimizing error is NP-hard and, thus, design an approximation algorithm using an integer programming relaxation and the constrained concave-convex procedure. Extensive experiments on real datasets demonstrate that our solution substantially outperforms the state-of-the-art competitors.
TL;DR: This paper approximate two-stage robust binary programs by their corresponding K -adaptability problems, in which the decision maker precommits to K second-stage policies, here -and-now, and implements the best of these policies once the uncertain parameters are observed.
Abstract: Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multistage problems with continuous recourse. This paper takes a step toward extending the robust optimization methodology to problems with integer recourse, which have largely resisted solution so far. To this end, we approximate two-stage robust binary programs by their corresponding K-adaptability problems, in which the decision maker precommits to K second-stage policies, here -and-now, and implements the best of these policies once the uncertain parameters are observed. We study the approximation quality and the computational complexity of the K-adaptability problem, and we propose two mixed-integer linear programming reformulations that can be solved with off-the-shelf software. We demonstrate the effectiveness of our reformulations for stylized instances o...
TL;DR: In this paper, an energy-saving optimization method that considers machine tool selection and operation sequence for flexible machining job shops is proposed, which aims to reduce the energy consumption for machining operations and reduce the idle energy consumption of machine tools.
Proceedings Article•
04 May 2015TL;DR: This paper studies the interplay between Integer Linear Programming (ILP) and greedy algorithms to generate solutions optimized for latency, pipeline occupancy, or power consumption, and suggests the best greedy approach.
Abstract: Programmable switching chips are becoming more commonplace, along with new packet processing languages to configure the forwarding behavior. Our paper explores the design of a compiler for such switching chips, in particular how to map logical lookup tables to physical tables, while meeting data and control dependencies in the program. We study the interplay between Integer Linear Programming (ILP) and greedy algorithms to generate solutions optimized for latency, pipeline occupancy, or power consumption. ILP is slower but more likely to fit hard cases; further, ILP can be used to suggest the best greedy approach. We compile benchmarks from real production networks to two different programmable switch architectures: RMT and Intel's FlexPipe. Greedy solutions can fail to fit and can require up to 38% more stages, 42% more cycles, or 45% more power for some benchmarks. Our analysis also identifies critical resources in chips. For a complicated use case, doubling the TCAM per stage reduces the minimum number of stages needed by 12.5%.
01 Jun 2015
TL;DR: Ant colony optimization for continuous domains (ACOR) based integer programming is employed for size optimization in a hybrid photovoltaic (PV)-wind energy system and the results prove that the authors' proposed approach outperforms them in terms of reaching an optimal solution and speed.
Abstract: ACOR based integer programming is employed for size optimization.The objective function of the hybrid PV-wind system is the total design cost.Decision variables are number of solar panels, wind turbines and batteries.A complete data set, an optimization formulation and ACOR are benefits of this paper. In this paper, ant colony optimization for continuous domains (ACOR) based integer programming is employed for size optimization in a hybrid photovoltaic (PV)-wind energy system. ACOR is a direct extension of ant colony optimization (ACO). Also, it is the significant ant-based algorithm for continuous optimization. In this setting, the variables are first considered as real then rounded in each step of iteration. The number of solar panels, wind turbines and batteries are selected as decision variables of integer programming problem. The objective function of the PV-wind system design is the total design cost which is the sum of total capital cost and total maintenance cost that should be minimized. The optimization is separately performed for three renewable energy systems including hybrid systems, solar stand alone and wind stand alone. A complete data set, a regular optimization formulation and ACOR based integer programming are the main features of this paper. The optimization results showed that this method gives the best results just in few seconds. Also, the results are compared with other artificial intelligent (AI) approaches and a conventional optimization method. Moreover, the results are very promising and prove that the authors' proposed approach outperforms them in terms of reaching an optimal solution and speed.
TL;DR: A bi-objective mixed integer linear programming (BOMILP) model is developed for a pharmaceutical supply chain network design (PSCND) problem to concurrently minimize the total costs and unfulfilled demands as the first and second objective functions.
TL;DR: The results show that the proposed method can coordinate the scheduling of the three types of handling equipment and can realize the optimal trade-off between time-saving and energy-saving.
Abstract: Energy-saving objective is considered in the container terminal operations.A MIP model for the integrated scheduling of cranes and trucks is developed.A simulation optimization method is proposed to solve the NP-hard problem.Experimental results show that the proposed method can realize port energy-saving. Container terminals mainly include three types of handling equipment, i.e., quay cranes (QCs), internal trucks (ITs) and yard cranes (YCs). Due to high cost of the handling equipment, container terminals can hardly purchase additional handling equipment. Therefore, the reasonable scheduling of these handling equipment, especially coordinated scheduling of the three types of handling equipment, plays an important role in the service level and energy-saving of container terminal. This paper addresses the problem of integrated QC scheduling, IT scheduling and YC scheduling. Firstly, this problem is formulated as a mixed integer programming model (MIP), where the objective is to minimize the total departure delay of all vessels and the total transportation energy consumption of all tasks. Furthermore, an integrated simulation-based optimization method is developed for solving the problem, where the simulation is designed for evaluation and optimization algorithm is designed for searching solution space. The optimization algorithm integrates genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, where the GA is used for global search and the PSO is used for local search. Finally, numerical experiments are conducted to verify the effectiveness of the proposed method. The results show that the proposed method can coordinate the scheduling of the three types of handling equipment and can realize the optimal trade-off between time-saving and energy-saving.
TL;DR: In this paper, a superstructure-based MILP (mixed integer linear programming) model is constructed to achieve simultaneous optimization of synthesis (i.e., type, capacity, number, and location of equipment as well as structure of the energy distribution networks) and operation strategies of the entire system.
TL;DR: In this article, a mixed-integer linear programming model is presented to identify such optimal design for a small residential neighbourhood, where the electricity and the space heating and cooling demands of a residential neighbourhood are satisfied through the consideration and combined use of distributed generation technologies, thermal units and energy storage with an optional interconnection with the central grid.
TL;DR: This study proposes a three-stage hybrid method for selecting an optimal combination of projects and obtains the maximum fitness between the final selection and the project initial rankings while considering various organizational objectives.
Abstract: Project portfolio selection is a complex and difficult task in fuzzy environments.A three-stage hybrid method is used to select an optimal combination of projects.Data Envelopment Analysis is used to screen the available projects.TOPSIS is used to rank the potentially promising projects.Linear Integer Programming is used to select the most suitable project portfolio. Project selection and resource allocation are critical issues in project-based organizations. These organizations are required to plan, evaluate, and control their projects in accordance with the organizational mission and objectives. In this study, we propose a three-stage hybrid method for selecting an optimal combination of projects. We obtain the maximum fitness between the final selection and the project initial rankings while considering various organizational objectives. The proposed model is comprised of three stages and each stage is composed of several steps and procedures. We use Data Envelopment Analysis (DEA) for the initial screening, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for ranking the projects, and linear Integer Programming (IP) for selecting the most suitable project portfolio in a fuzzy environment according to organizational objectives. Finally, a case study is used to demonstrate the applicability of the proposed method and exhibit the efficacy of the algorithms and procedures.
TL;DR: A model predictive control (MPC) based coordinated operation framework for a grid-connected residential microgrid with considering forecast errors with results show that the proposed method is economic and flexible.
TL;DR: In this paper, the authors define a routing problem called the platooning problem and prove that this problem is NP-hard, even when the graph used to represent the road network is planar.
Abstract: We create a mathematical framework for modeling trucks traveling in road networks, and we define a routing problem called the platooning problem. We prove that this problem is NP-hard, even when the graph used to represent the road network is planar. We present integer linear programming formulations for instances of the platooning problem where deadlines are discarded, which we call the unlimited platooning problem. These allow us to calculate fuel-optimal solutions to the platooning problem for large-scale, real-world examples. The problems solved are orders of magnitude larger than problems previously solved exactly in the literature. We present several heuristics and compare their performance with the optimal solutions on the German Autobahn road network. The proposed heuristics find optimal or near-optimal solutions in most of the problem instances considered, especially when a final local search is applied. Assuming a fuel reduction factor of 10% from platooning, we find fuel savings from platooning of 1–2% for as few as 10 trucks in the road network; the percentage of savings increases with the number of trucks. If all trucks start at the same point, savings of up to 9% are obtained for only 200 trucks.
TL;DR: In this paper, a fuzzy multiple-objective network optimization model was proposed to obtain the best profit values and to satisfy the environmental indicator targets in a more holistic manner while also considering environmental issues.
22 Apr 2015
TL;DR: This paper forms the problem of network function placement and routing as a mixed integer linear programming problem, and develops heuristics to solve the problem incrementally, allowing it to support a large number of flows and to solving the problem for incoming flows without impacting existing flows.
Abstract: The integration of network function virtualization (NFV) and software defined networks (SDN) seeks to create a more flexible and dynamic software-based network environment. The line between entities involved in forwarding and those involved in more complex middle box functionality in the network is blurred by the use of high-performance virtualized platforms capable of performing these functions. A key problem is how and where network functions should be placed in the network and how traffic is routed through them. An efficient placement and appropriate routing increases system capacity while also minimizing the delay seen by flows. In this paper, we formulate the problem of network function placement and routing as a mixed integer linear programming problem. This formulation not only determines the placement of services and routing of the flows, but also seeks to minimize the resource utilization. We develop heuristicsto solve the problem incrementally, allowing us to support a large number of flows and to solve the problem for incoming flows without impacting existing flows.
TL;DR: This paper presents a new “all-in-one” approach to joint optimization of product family and supply chain configuration that neglects the complex tradeoffs underlying two different decision making problems and fails to reveal the inherent coupling of PFC and SCC.
TL;DR: In this article, the authors consider the problem of planning preventive maintenance and overhaul for modules that are used in a fleet of assets such as trains or airplanes, and prove that this planning problem is strongly NP-hard, but also provide computational evidence that the mixed integer programming formulation can be solved within reasonable time for real-life instances.
Abstract: We consider the problem of planning preventive maintenance and overhaul for modules that are used in a fleet of assets such as trains or airplanes. Each type of module, or rotable, has its own maintenance program in which a maximum amount of time/usage between overhauls of a module is stipulated. Overhauls are performed in an overhaul workshop with limited capacity. The problem we study is to determine aggregate workforce levels, turn-around stock levels of modules, and overhaul and replacement quantities per period so as to minimize the sum of labor costs, material costs of overhaul, and turn-around stock investments over the entire life-cycle of the maintained asset. We prove that this planning problem is strongly $\mathcal{NP}$
-hard, but we also provide computational evidence that the mixed integer programming formulation can be solved within reasonable time for real-life instances. Furthermore, we show that the linear programming relaxation can be used to aid decision making. We apply the model in a case study and provide computational results for randomly generated instances.
TL;DR: This paper presents an integrated approach that jointly optimizes the airport’s flight schedule at the strategic level and the utilization of airport capacity at the tactical level, subject to scheduling, capacity, and delay-reduction constraints.
Abstract: Most flight delays are created by imbalances between demand and capacity at the busiest airports. Absent large increases in capacity, airport congestion can only be mitigated through scheduling int...
TL;DR: The YC scheduling problem is converted into a vehicle routing problem with soft time windows (VRPSTW) and formulated as a mixed integer programming (MIP) model, whose two objectives minimize the total completion delay of all task groups and the total energy consumption of all YCs.
TL;DR: In this article, a game theoretic consumption scheduling framework based on the use of mixed integer programming (MIP) to schedule consumption plan for residential consumers is presented. But the optimization framework incorporates integration of locally generated renewable energy in order to minimize dependency on conventional energy and the consumption cost.
Abstract: Facilitated by advanced information and communication technologies (ICT) infrastructure and optimization techniques, smart grid has the potential to bring significant benefits to the energy consumption management. This paper presents a game theoretic consumption scheduling framework based on the use of mixed integer programming (MIP) to schedule consumption plan for residential consumers. In particular, the optimization framework incorporates integration of locally generated renewable energy in order to minimize dependency on conventional energy and the consumption cost. The game theoretic model is designed to coordinatively manage the scheduling of appliances of consumers. The Nash equilibrium of the game exists and the scheduling optimization converges to an equilibrium where all consumers can benefit from participating in. Simulation results are presented to demonstrate the proposed approach and the benefits of home demand management.