Showing papers on "Integer programming published in 2008"

Optimal Transmission Switching

Abstract: In this paper, we formulate the problem of finding an optimal generation dispatch and transmission topology to meet a specific inflexible load as a mixed integer program. Our model is a mixed-integer linear program because it employs binary variables to represent the state of the equipment and linear relationships to describe the physical system. We find that on the standard 118-bus IEEE test case a savings of 25% in system dispatch cost can be achieved.

Generalized Integer Linear Programming Formulation for Optimal PMU Placement

Abstract: Based on the integer linear programming formulation proposed for optimal PMU placement, this paper presents a generalized integer linear programming formulation for cases including redundant PMU placement, full observability and incomplete observability. Due to accurate voltage phasor measurement and current phasor measurements provided by PUM units, the accuracy, redundancy and thus the robustness of state estimation will be enhanced with the integration of PMU measurements. The problem of optimal placement of PMU for the redundant PMU placement, full observability and incomplete observability analysis needs to be studied, for various purposes and considerations. The proposed modeling approach by the author in another paper, which models PMU placement as an integer linear programming problem, is extended and generalized to satisfy different needs. Cases with and without zero injection measurements are considered. Simulation results on different power systems show that the proposed algorithm can be used in practice.

Efficient Sensor Placement Optimization for Securing Large Water Distribution Networks

Abstract: The problem of deploying sensors in a large water distribution network is considered, in order to detect the malicious introduction of contaminants. It is shown that a large class of realistic objective functions—such as reduction of detection time and the population protected from consuming contaminated water—exhibits an important diminishing returns effect called submodularity. The submodularity of these objectives is exploited in order to design efficient placement algorithms with provable performance guarantees. The algorithms presented in this paper do not rely on mixed integer programming, and scale well to networks of arbitrary size. The problem instances considered in the approach presented in this paper are orders of magnitude (a factor of 72) larger than the largest problems solved in the literature. It is shown how the method presented here can be extended to multicriteria optimization, selecting placements robust to sensor failures and optimizing minimax criteria. Extensive empirical evidence ...

Optimal Multistage Scheduling of PMU Placement: An ILP Approach

Abstract: This paper addresses various aspects of optimal phasor measurement unit (PMU) placement problem. We propose a procedure for multistaging of PMU placement in a given time horizon using an integer linear programming (ILP) framework. Hitherto, modeling of zero injection constraints had been a challenge due to the intrinsic nonlinearity associated with it. We show that zero injection constraints can also be modeled as linear constraints in an ILP framework. Minimum PMU placement problem has multiple solutions. We propose two indices, viz, BOI and SORI, to further rank these multiple solutions, where BOI is bus observability index giving a measure of number of PMUs observing a given bus and SORI is system observability redundancy index giving sum of all BOI for a system. Results on IEEE 118 bus system have been presented. Results indicate that: (1) optimal phasing of PMUs can be computed efficiently; (2) proposed method of modeling zero injection constraints improve computational performance; and (3) BOI and SORI help in improving the quality of PMU placement.

Global inference for sentence compression an integer linear programming approach

Abstract: Sentence compression holds promise for many applications ranging from summarization to subtitle generation. Our work views sentence compression as an optimization problem and uses integer linear programming (ILP) to infer globally optimal compressions in the presence of linguistically motivated constraints. We show how previous formulations of sentence compression can be recast as ILPs and extend these models with novel global constraints. Experimental results on written and spoken texts demonstrate improvements over state-of-the-art models.

Optimal Placement of PMUs by Integer Linear Programming

Abstract: This letter presents a simple optimal placement algorithm of phasor measurement units (PMU) by using integer linear programming. Cases with and without conventional power flow and injection measurements are considered. The measurement placement problems under those cases are formulated as an integer linear programming which saves the CPU computation time greatly. Simulation results show that the proposed algorithm can be used in practice.

An MILP Approach for Short-Term Hydro Scheduling and Unit Commitment With Head-Dependent Reservoir

Abstract: The paper deals with a unit commitment problem of a generation company whose aim is to find the optimal scheduling of a multiunit pump-storage hydro power station, for a short term period in which the electricity prices are forecasted. The problem has a mixed-integer nonlinear structure, which makes very hard to handle the corresponding mathematical models. However, modern mixed-integer linear programming (MILP) software tools have reached a high efficiency, both in terms of solution accuracy and computing time. Hence we introduce MILP models of increasing complexity, which allow to accurately represent most of the hydroelectric system characteristics, and turn out to be computationally solvable. In particular we present a model that takes into account the head effects on power production through an enhanced linearization technique, and turns out to be more general and efficient than those available in the literature. The practical behavior of the models is analyzed through computational experiments on real-world data.

An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts

Abstract: This paper presents a new exact algorithm for the Capacitated Vehicle Routing Problem (CVRP) based on the set partitioning formulation with additional cuts that correspond to capacity and clique inequalities. The exact algorithm uses a bounding procedure that finds a near optimal dual solution of the LP-relaxation of the resulting mathematical formulation by combining three dual ascent heuristics. The first dual heuristic is based on the q-route relaxation of the set partitioning formulation of the CVRP. The second one combines Lagrangean relaxation, pricing and cut generation. The third attempts to close the duality gap left by the first two procedures using a classical pricing and cut generation technique. The final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between an upper bound and the lower bound achieved. The resulting problem is solved by an integer programming solver. Computational results over the main instances from the literature show the effectiveness of the proposed algorithm.

Multistage Model for Distribution Expansion Planning With Distributed Generation—Part I: Problem Formulation

Abstract: This paper presents a model for use in the problem of multistage planning of energy distribution systems including distributed generation. The expansion model allows alternatives to be considered for increasing the capacity of existing substations, for installing new ones, for using distributed generation, and for the possible change to feeders in terms of addition and removing feeders sections; combining, subdividing, and load transfer between feeders; and replacement of conductors. The objective function to be minimized is the present value of total installation costs (feeders and substations), of operating and maintaining the network, and of distributed generation. The model takes operational constraints on equipment capacities and voltage limits together into account with logical constraints, aimed at reducing the search space. This paper presents: (1) an extension to the linear disjunctive formulation to represent the inclusion, exclusion, and replacement of branches and (2) a generalization of constraints related to the creation of new paths which can be applied in more complex topologies. The resulting mixed integer linear model allows the optimal solution to be found using mathematical programming methods, such as the branch-and-bound algorithm. The validity and efficiency of the model are demonstrated in Part II of this paper.

Spectrum Sharing for Multi-Hop Networking with Cognitive Radios

Abstract: Cognitive radio (CR) capitalizes advances in signal processing and radio technology and is capable of reconfiguring RF and switching to desired frequency bands. It is a frequency-agile data communication device that is vastly more powerful than recently proposed multi-channel multi-radio (MC-MR) technology. In this paper, we investigate the important problem of multi-hop networking with CR nodes. For such a network, each node has a pool of frequency bands (typically of unequal size) that can be used for communication. The potential difference in the bandwidth among the available frequency bands prompts the need to further divide these bands into sub-bands for optimal spectrum sharing. We characterize the behavior and constraints for such a multi-hop CR network from multiple layers, including modeling of spectrum sharing and sub-band division, scheduling and interference constraints, and flow routing. We develop a mathematical formulation with the objective of minimizing the required network-wide radio spectrum resource for a set of user sessions. Since the formulated model is a mixed-integer non-linear program (MINLP), which is NP-hard in general, we develop a lower bound for the objective by relaxing the integer variables and using a linearization technique. Subsequently, we design a near-optimal algorithm to solve this MINLP problem. This algorithm is based on a novel sequential fixing procedure, where the integer variables are determined iteratively via a sequence of linear programs. Simulation results show that solutions obtained by this algorithm are very close to the lower bounds obtained via the proposed relaxation, thus suggesting that the solution produced by the algorithm is near-optimal.

Orchestrating the execution of stream programs on multicore platforms

Abstract: While multicore hardware has become ubiquitous, explicitly parallel programming models and compiler techniques for exploiting parallelism on these systems have noticeably lagged behind. Stream programming is one model that has wide applicability in the multimedia, graphics, and signal processing domains. Streaming models execute as a set of independent actors that explicitly communicate data through channels. This paper presents a compiler technique for planning and orchestrating the execution of streaming applications on multicore platforms. An integrated unfolding and partitioning step based on integer linear programming is presented that unfolds data parallel actors as needed and maximally packs actors onto cores. Next, the actors are assigned to pipeline stages in such a way that all communication is maximally overlapped with computation on the cores. To facilitate experimentation, a generalized code generation template for mapping the software pipeline onto the Cell architecture is presented. For a range of streaming applications, a geometric mean speedup of 14.7x is achieved on a 16-core Cell platform compared to a single core.

Path Planning of Autonomous Underwater Vehicles for Adaptive Sampling Using Mixed Integer Linear Programming

Abstract: The goal of adaptive sampling in the ocean is to predict the types and locations of additional ocean measurements that would be most useful to collect. Quantitatively, what is most useful is defined by an objective function and the goal is then to optimize this objective under the constraints of the available observing network. Examples of objectives are better oceanic understanding, to improve forecast quality, or to sample regions of high interest. This work provides a new path-planning scheme for the adaptive sampling problem. We define the path-planning problem in terms of an optimization framework and propose a method based on mixed integer linear programming (MILP). The mathematical goal is to find the vehicle path that maximizes the line integral of the uncertainty of field estimates along this path. Sampling this path can improve the accuracy of the field estimates the most. While achieving this objective, several constraints must be satisfied and are implemented. They relate to vehicle motion, intervehicle coordination, communication, collision avoidance, etc. The MILP formulation is quite powerful to handle different problem constraints and flexible enough to allow easy extensions of the problem. The formulation covers single- and multiple-vehicle cases as well as single- and multiple-day formulations. The need for a multiple-day formulation arises when the ocean sampling mission is optimized for several days ahead. We first introduce the details of the formulation, then elaborate on the objective function and constraints, and finally, present a varied set of examples to illustrate the applicability of the proposed method.

Improving the accuracy and efficiency of MAP inference for Markov Logic

Abstract: In this work we present Cutting Plane Inference (CPI), a Maximum A Posteriori (MAP) inference method for Statistical Relational Learning. Framed in terms of Markov Logic and inspired by the Cutting Plane Method, it can be seen as a meta algorithm that instantiates small parts of a large and complex Markov Network and then solves these using a conventional MAP method. We evaluate CPI on two tasks, Semantic Role Labelling and Joint Entity Resolution, while plugging in two different MAP inference methods: the current method of choice for MAP inference in Markov Logic, MaxWalkSAT, and Integer Linear Programming. We observe that when used with CPI both methods are significantly faster than when used alone. In addition, CPI improves the accuracy of MaxWalkSAT and maintains the exactness of Integer Linear Programming.

Constraint integer programming: a new approach to integrate CP and MIP

Abstract: This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques.

A Distributed Optimization Algorithm for Multi-Hop Cognitive Radio Networks

Abstract: Cognitive radio (CR) is a revolution in radio technology and is viewed as an enabling technology for dynamic spectrum access. This paper investigates how to design distributed algorithm for a future multi-hop CR network, with the objective of maximizing data rates for a set of user communication sessions. We study this problem via a cross-layer optimization approach, with joint consideration of power control, scheduling, and routing. The main contribution of this paper is the development of a distributed optimization algorithm that iteratively increases data rates for user communication sessions. During each iteration, there are two separate processes, a Conservative Iterative Process (CIP) and an Aggressive Iterative Process (AIP). For both CIP and AIP, we describe our design of routing, minimalist scheduling, and power control/scheduling modules. To evaluate the performance of the distributed optimization algorithm, we compare it to an upper bound of the objective function, since the exact optimal solution to the objective function cannot be obtained via its mixed integer nonlinear programming (MINLP) formulation. Since the achievable performance via our distributed algorithm is close to the upper bound and the optimal solution (unknown) lies between the upper bound and the feasible solution obtained by our distributed algorithm, we conclude that the results obtained by our distributed algorithm are very close to the optimal solution.

Staffing Multiskill Call Centers via Linear Programming and Simulation

Abstract: We study an iterative cutting-plane algorithm on an integer program for minimizing the staffing costs of a multiskill call center subject to service-level requirements that are estimated by simulation. We solve a sample average version of the problem, where the service levels are expressed as functions of the staffing for a fixed sequence of random numbers driving the simulation. An optimal solution of this sample problem is also an optimal solution to the original problem when the sample size is large enough. Several difficulties are encountered when solving the sample problem, especially for large problem instances, and we propose practical heuristics to deal with these difficulties. We report numerical experiments with examples of different sizes. The largest example corresponds to a real-life call center with 65 types of calls and 89 types of agents (skill groups).

Temperature-aware scheduling and assignment for hard real-time applications on MPSoCs

Abstract: Thermal effects in MPSoCs may cause the violation of timing constraints in real-time systems. This paper presents a mixed integer linear programming based solution to this problem. Tasks are assigned and scheduled to an MPSoC to minimize peak temperature, subject to real-time constraints. The proposed approach outperforms existing methods, reducing peak temperature by up to 24.66degC and by an average of 8.75degC when compared to minimal-energy solutions. We also present a heuristic for use on large problem instances. Steady- state thermal analysis is used for tasks with long execution times compared to the RC thermal time constants of the cores. Transient analysis is used otherwise. The steady-state analysis based heuristic finds solutions with at most 3.40degC deviation from optimal peak temperature (0.22degC on average) while improving upon existing technique by as much as 25.71degC and 10.86degC on average. The transient analysis based heuristic further reduce peak temperature by 1degC in the best case and 0.17degC on average.

A mixed integer programming model for remanufacturing in reverse logistics environment

Abstract: Recently, there has been a growing interest in reverse logistics due to environmental deterioration. Firms incorporate reverse flow to their systems for such reasons as ecological and economic factors, government regulations and social responsibilities. In this paper a new mixed integer mathematical model for a remanufacturing system, which includes both forward and reverse flows, is proposed and illustrated on a numerical example. The proposed model provides the optimal values of production and transportation quantities of manufactured and remanufactured products while solving the location problem of dissassembly, collection and distribution facilities. The model is validated by using a set of experimental data reflecting practical business situation. Sensitivity analysis of the model is also presented.

Optimal Boolean Matrix Decomposition: Application to Role Engineering

Abstract: A decomposition of a binary matrix into two matrices gives a set of basis vectors and their appropriate combination to form the original matrix. Such decomposition solutions are useful in a number of application domains including text mining, role engineering as well as knowledge discovery. While a binary matrix can be decomposed in several ways, however, certain decompositions better characterize the semantics associated with the original matrix in a succinct but comprehensive way. Indeed, one can find different decompositions optimizing different criteria matching various semantics. In this paper, we first present a number of variants to the optimal Boolean matrix decomposition problem that have pragmatic implications. We then present a unified framework for modeling the optimal binary matrix decomposition and its variants using binary integer programming. Such modeling allows us to directly adopt the huge body of heuristic solutions and tools developed for binary integer programming. Although the proposed solutions are applicable to any domain of interest, for providing more meaningful discussions and results, in this paper, we present the binary matrix decomposition problem in a role engineering context, whose goal is to discover an optimal and correct set of roles from existing permissions, referred to as the role mining problem (RMP). This problem has gained significant interest in recent years as role based access control has become a popular means of enforcing security in databases. We consider several variants of the above basic RMP, including the min-noise RMP, delta-approximate RMP and edge-RMP. Solutions to each of them aid security administrators in specific scenarios. We then model these variants as Boolean matrix decomposition and present efficient heuristics to solve them.

Optimal control of Mixed Logical Dynamical systems with Linear Temporal Logic specifications

Abstract: Recently, linear temporal logic (LTL) has been employed as a tool for formal specification in dynamical control systems. With this formal approach, control systems can be designed to provably accomplish a large class of complex tasks specified via LTL. For this purpose, language generating Buchi automata with finite abstractions of dynamical systems have been used in the literature. In this paper, we take a mathematical programming-based approach to control of a broad class of discrete-time dynamical systems, called mixed logic dynamical (MLD) systems, with LTL specifications. MLDs include discontinuous and hybrid piecewise discrete-time linear systems. We apply these tools for model checking and optimal control of MLD systems with LTL specifications. Our algorithms exploit mixed integer linear programming (MILP) as well as, in the appropriate setting, mixed integer quadratic programming (MIQP) techniques. Our solution approach introduces a general technique useful in representing LTL constraints as mixed-integer linear constraints.

An Optimization-Based Heuristic for the Split Delivery Vehicle Routing Problem

Abstract: The split delivery vehicle routing problem is concerned with serving the demand of a set of customers with a fleet of capacitated vehicles at minimum cost. Contrary to what is assumed in the classical vehicle routing problem, a customer can be served by more than one vehicle, if convenient. We present a solution approach that integrates heuristic search with optimization by using an integer program to explore promising parts of the search space identified by a tabu search heuristic. Computational results show that the method improves the solution of the tabu search in all but one instance of a large test set.