Showing papers on "Integer programming published in 2012"

Sizing of Energy Storage for Microgrids

Abstract: This paper presents a new method based on the cost-benefit analysis for optimal sizing of an energy storage system in a microgrid (MG). The unit commitment problem with spinning reserve for MG is considered in this method. Time series and feed-forward neural network techniques are used for forecasting the wind speed and solar radiations respectively and the forecasting errors are also considered in this paper. Two mathematical models have been built for both the islanded and grid-connected modes of MGs. The main problem is formulated as a mixed linear integer problem (MLIP), which is solved in AMPL (A Modeling Language for Mathematical Programming). The effectiveness of the approach is validated by case studies where the optimal system energy storage ratings for the islanded and grid-connected MGs are determined. Quantitative results show that the optimal size of BESS exists and differs for both the grid-connected and islanded MGs in this paper.

ViNEYard: virtual network embedding algorithms with coordinated node and link mapping

Abstract: Network virtualization allows multiple heterogeneous virtual networks (VNs) to coexist on a shared infrastructure. Efficient mapping of virtual nodes and virtual links of a VN request onto substrate network resources, also known as the VN embedding problem, is the first step toward enabling such multiplicity. Since this problem is known to be NP-hard, previous research focused on designing heuristic-based algorithms that had clear separation between the node mapping and the link mapping phases. In this paper, we present ViNEYard-a collection of VN embedding algorithms that leverage better coordination between the two phases. We formulate the VN embedding problem as a mixed integer program through substrate network augmentation. We then relax the integer constraints to obtain a linear program and devise two online VN embedding algorithms D-ViNE and R-ViNE using deterministic and randomized rounding techniques, respectively. We also present a generalized window-based VN embedding algorithm (WiNE) to evaluate the effect of lookahead on VN embedding. Our simulation experiments on a large mix of VN requests show that the proposed algorithms increase the acceptance ratio and the revenue while decreasing the cost incurred by the substrate network in the long run.

Demand Response Optimization for Smart Home Scheduling Under Real-Time Pricing

Abstract: Demand response (DR) is very important in the future smart grid, aiming to encourage consumers to reduce their demand during peak load hours. However, if binary decision variables are needed to specify start-up time of a particular appliance, the resulting mixed integer combinatorial problem is in general difficult to solve. In this paper, we study a versatile convex programming (CP) DR optimization framework for the automatic load management of various household appliances in a smart home. In particular, an L1 regularization technique is proposed to deal with schedule-based appliances (SAs), for which their on/off statuses are governed by binary decision variables. By relaxing these variables from integer to continuous values, the problem is reformulated as a new CP problem with an additional L1 regularization term in the objective. This allows us to transform the original mixed integer problem into a standard CP problem. Its major advantage is that the overall DR optimization problem remains to be convex and therefore the solution can be found efficiently. Moreover, a wide variety of appliances with different characteristics can be flexibly incorporated. Simulation result shows that the energy scheduling of SAs and other appliances can be determined simultaneously using the proposed CP formulation.

Minimum Loss Network Reconfiguration Using Mixed-Integer Convex Programming

Abstract: This paper proposes a mixed-integer conic programming formulation for the minimum loss distribution network reconfiguration problem. This formulation has two features: first, it employs a convex representation of the network model which is based on the conic quadratic format of the power flow equations and second, it optimizes the exact value of the network losses. The use of a convex model in terms of the continuous variables is particularly important because it ensures that an optimal solution obtained by a branch-and-cut algorithm for mixed-integer conic programming is global. In addition, good quality solutions with a relaxed optimality gap can be very efficiently obtained. A polyhedral approximation which is amenable to solution via more widely available mixed-integer linear programming software is also presented. Numerical results on practical test networks including distributed generation show that mixed-integer convex optimization is an effective tool for network reconfiguration.

Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem

Abstract: This paper examines the polytope of feasible power generation schedules in the unit commitment (UC) problem. We provide computational results comparing formulations for the UC problem commonly found in the literature. We introduce a new class of inequalities, giving a tighter description of feasible operating schedules for generators. Computational results show that these inequalities can significantly reduce overall solution times.

Distribution System Planning With Incorporating DG Reactive Capability and System Uncertainties

Abstract: Distributed generation (DG) systems are considered an integral part in future distribution system planning. The active and reactive power injections from DG units, typically installed close to the load centers, are seen as a cost-effective solution for distribution system voltage support, energy saving, and reliability improvement. This paper proposes a novel distribution system expansion planning strategy encompassing renewable DG systems with schedulable and intermittent power generation patterns. The reactive capability limits of different renewable DG systems covering wind, solar photovoltaic, and biomass-based generation units are included in the planning model and the system uncertainties such as load demand, wind speed, and solar radiation are also accounted using probabilistic models. The problem of distribution system planning with renewable DG is formulated as constrained mixed integer nonlinear programming, wherein the total cost will be minimized with optimal allocation of various renewable DG systems. A solution algorithm integrating TRIBE particle swarm optimization (TRIBE PSO) and ordinal optimization (OO) is developed to effectively obtain optimal and near-optimal solutions for system planners. TRIBE PSO, OO, and the proposed algorithm are applied to a practical test system and results are compared and presented.

Algorithms and Software for Convex Mixed Integer Nonlinear Programs

Abstract: This paper provides a survey of recent progress and software for solving convex Mixed Integer Nonlinear Programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in recent years. By exploiting analogies to well-known techniques for solving Mixed Integer Linear Programs and incorporating these techniques into software, significant improvements have been made in the ability to solve these problems.

An integer linear programming based optimization for home demand-side management in smart grid

Abstract: We propose a consumption scheduling mechanism for home area load management in smart grid using integer linear programming (ILP) technique. The aim of the proposed scheduling is to minimise the peak hourly load in order to achieve an optimal (balanced) daily load schedule. The proposed mechanism is able to schedule both the optimal power and the optimal operation time for power-shiftable appliances and time-shiftable appliances respectively according to the power consumption patterns of all the individual appliances. Simulation results based on home and neighbourhood area scenarios have been presented to demonstrate the effectiveness of the proposed technique.

Mixed-integer quadratic program trajectory generation for heterogeneous quadrotor teams

Abstract: We present an algorithm for the generation of optimal trajectories for teams of heterogeneous quadrotors in three-dimensional environments with obstacles We formulate the problem using mixed-integer quadratic programs (MIQPs) where the integer constraints are used to enforce collision avoidance The method allows for different sizes, capabilities, and varying dynamic effects between different quadrotors Experimental results illustrate the method applied to teams of up to four quadrotors ranging from 65 to 962 grams and 21 to 67 cm in width following trajectories in three-dimensional environments with obstacles with accelerations approaching 1g

Comparison of Scenario-Based and Interval Optimization Approaches to Stochastic SCUC

Abstract: This paper compares applications of scenario-based and interval optimization approaches to stochastic security-constrained unit commitment (Stochastic SCUC). The uncertainty of wind power generation is considered in this study to compare the two approaches, while other types of uncertainty can be addressed similarly. For the simulation of uncertainty, the scenario-based approach considers the Monte Carlo (MC) method, while lower and upper bounds are adopted in the interval optimization. The Stochastic SCUC problem is formulated as a mixed-integer linear programming (MIP) problem and solved using the two approaches. The scenario-based solutions are insensitive to the number of scenarios, but present additional computation burdens. The interval optimization solution requires less computation and automatically generates lower and upper bounds for the operation cost and generation dispatch, but its optimal solution is very sensitive to the uncertainty interval. The numerical results on a six-bus system and the modified IEEE 118-bus system show the attributes of the two approaches for solving the Stochastic SCUC problem. Several convergence acceleration options are also discussed for overcoming the computation obstacles in the scenario-based approach.

A Mixed-Integer Linear Programming Approach for Multi-Stage Security-Constrained Transmission Expansion Planning

Abstract: The transmission expansion planning (TEP) problem in modern power systems is a large-scale, mixed-integer, non-linear and non-convex problem. Although remarkable advances have been made in optimization techniques, finding an optimal solution to a problem of this nature can still be extremely challenging. Based on the linearized power flow model, this paper presents a mixed-integer linear programming (MILP) approach that considers losses, generator costs and the N - 1 security constraints for the multi-stage TEP problem. The losses and generator cost are modeled as piecewise linear functions of the line flows and the generator outputs, respectively. The IEEE 24-bus system is used to compare the lossy and the lossless model. The results show that the lossy model provides savings in total cost in the long run. The selection of the best number of piecewise linear sections L is also shown. Then a complete planning framework is presented and a multi-stage TEP is performed on the IEEE 118-bus test system. Simulation results show that the proposed approach is accurate and efficient, and has the potential to be applied to large-scale power system planning problems.

A hybrid approach for efficient Web service composition with end-to-end QoS constraints

Abstract: Dynamic selection of Web services at runtime is important for building flexible and loosely-coupled service-oriented applications. An abstract description of the required services is provided at design-time, and matching service offers are located at runtime. With the growing number of Web services that provide the same functionality but differ in quality parameters (e.g., availability, response time), a decision needs to be made on which services should be selected such that the user's end-to-end QoS requirements are satisfied. Although very efficient, local selection strategy fails short in handling global QoS requirements. Solutions based on global optimization, on the other hand, can handle global constraints, but their poor performance renders them inappropriate for applications with dynamic and realtime requirements. In this article we address this problem and propose a hybrid solution that combines global optimization with local selection techniques to benefit from the advantages of both worlds. The proposed solution consists of two steps: first, we use mixed integer programming (MIP) to find the optimal decomposition of global QoS constraints into local constraints. Second, we use distributed local selection to find the best Web services that satisfy these local constraints. The results of experimental evaluation indicate that our approach significantly outperforms existing solutions in terms of computation time while achieving close-to-optimal results.

Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure After Surgery

Abstract: This article presents a new method for optimal matching in observational studies based on mixed integer programming. Unlike widely used matching methods based on network algorithms, which attempt to achieve covariate balance by minimizing the total sum of distances between treated units and matched controls, this new method achieves covariate balance directly, either by minimizing both the total sum of distances and a weighted sum of specific measures of covariate imbalance, or by minimizing the total sum of distances while constraining the measures of imbalance to be less than or equal to certain tolerances. The inclusion of these extra terms in the objective function or the use of these additional constraints explicitly optimizes or constrains the criteria that will be used to evaluate the quality of the match. For example, the method minimizes or constrains differences in univariate moments, such as means, variances, and skewness; differences in multivariate moments, such as correlations between covari...

Generalized Fisher Score for Feature Selection

Abstract: Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims at finding an subset of features, which maximize the lower bound of traditional Fisher score. The resulting feature selection problem is a mixed integer programming, which can be reformulated as a quadratically constrained linear programming (QCLP). It is solved by cutting plane algorithm, in each iteration of which a multiple kernel learning problem is solved alternatively by multivariate ridge regression and projected gradient descent. Experiments on benchmark data sets indicate that the proposed method outperforms Fisher score as well as many other state-of-the-art feature selection methods.

Energy-Efficient Cooperative Spectrum Sensing by Optimal Scheduling in Sensor-Aided Cognitive Radio Networks

Abstract: A promising technology that tackles the conflict between spectrum scarcity and underutilization is cognitive radio (CR), of which spectrum sensing is one of the most important functionalities. The use of dedicated sensors is an emerging service for spectrum sensing, where multiple sensors perform cooperative spectrum sensing. However, due to the energy constraint of battery-powered sensors, energy efficiency arises as a critical issue in sensor-aided CR networks. An optimal scheduling of each sensor active time can effectively extend the network lifetime. In this paper, we divide the sensors into a number of nondisjoint feasible subsets such that only one subset of sensors is turned on at a period of time while guaranteeing that the necessary detection and false alarm thresholds are satisfied. Each subset is activated successively, and nonactivated sensors are put in a low-energy sleep mode to extend the network lifetime. We formulate such problem of energy-efficient cooperative spectrum sensing in sensor-aided CR networks as a scheduling problem, which is proved to be NP-complete. We employ Greedy Degradation to degrade it into a linear integer programming problem and propose three approaches, namely, Implicit Enumeration (IE), General Greedy (GG), and λ-Greedy (λG), to solve the subproblem. Among them, IE can achieve an optimal solution with the highest computational complexity, whereas GG can provide a solution with the lowest complexity but much poorer performance. To achieve a better tradeoff in terms of network lifetime and computational complexity, a brand new λG is proposed to approach IE with the complexity comparable with GG. Simulation results are presented to verify the performance of our approaches, as well as to study the effect of adjustable parameters on the performance.

A Brief History of Linear and Mixed-Integer Programming Computation

Abstract: For many of us, modern-day linear programming (LP) started with the work of George Dantzig in 1947. However, it must be said that many other scientists have also made seminal contributions to the subject, and some would argue that the origins of LP predate Dantzig’s contribution. It is matter open to debate [36]. However, what is not open to debate is Dantzig’s key contribution to LP computation. In contrast to the economists of his time, Dantzig viewed LP not just as a qualitative tool in the analysis of economic phenomena, but as a method that could be used to compute actual answers to specific real-world problems. Consistent with that view, he proposed an algorithm for solving LPs, the simplex algorithm [12]. To this day the simplex algorithm remains a primary computational tool in linear and mixed-integer programming (MIP). In [11] it is reported that the first application of Dantzig’s simplex algorithm to the solution of a non-trivial LP was Laderman’s solution of a 21 constraint, 77 variable instance of the classical Stigler Diet Problem [41]. It is reported that the total computation time was 120 man-days! The first computer implementation of an at-least modestly general version of the simplex algorithm is reported to have been on the SEAC computer at the then National Bureau of Standards [25]. (There were apparently some slightly earlier implementations for dealing with models that were “triangular”, that is, where all the linear systems could be solved by simple addition and subtraction.) Orchard-Hays [35] reports that several small instances having as many as 10 constraints and 20 variables were solved with this implementation. The first systematic development of computer codes for the simplex algorithm began very shortly thereafter at the RAND Corporation in Santa Monica, California. Dantzig’s initial LP work occurred at the Air Force following

A Hybrid Heuristic for an Inventory Routing Problem

Abstract: We consider an inventory routing problem in discrete time where a supplier has to serve a set of customers over a multiperiod horizon. A capacity constraint for the inventory is given for each customer, and the service cannot cause any stockout situation. Two different replenishment policies are considered: the order-up-to-level and the maximum-level policies. A single vehicle with a given capacity is available. The transportation cost is proportional to the distance traveled, whereas the inventory holding cost is proportional to the level of the inventory at the customers and at the supplier. The objective is the minimization of the sum of the inventory and transportation costs. We present a heuristic that combines a tabu search scheme with ad hoc designed mixed-integer programming models. The effectiveness of the heuristic is proved over a set of benchmark instances for which the optimal solution is known.

The max-p-regions problem

Abstract: In this paper, we introduce a new spatially constrained clustering problem called the max-p-regions problem. It involves the clustering of a set of geographic areas into the maximum number of homogeneous regions such that the value of a spatially extensive regional attribute is above a predefined threshold value. We formulate the max-p-regions problem as a mixed integer programming (MIP) problem, and propose a heuristic solution.

Cargo routing and empty container repositioning in multiple shipping service routes

Abstract: This paper considers the problem of joint cargo routing and empty container repositioning at the operational level for a shipping network with multiple service routes, multiple deployed vessels and multiple regular voyages. The objective is to minimize the total relevant costs in the planning horizon including: container lifting on/off costs at ports, customer demand backlog costs, the demurrage (or waiting) costs at the transhipment ports for temporarily storing laden containers, the empty container inventory costs at ports, and the empty container transportation costs. The laden container routing from the original port to the destination port is limited with at most three service routes. Two solution methods are proposed to solve the optimization problem. The first is a two-stage shortest-path based integer programming method, which combines a cargo routing algorithm with an integer programming of the dynamic system. The second is a two-stage heuristic-rules based integer programming method, which combines an integer programming of the static system with a heuristic implementation algorithm in dynamic system. The two solution methods are applied to two case studies with 30 different scenarios and compared with a practical policy. The results show that two solution methods perform substantially better than the practical policy. The shortest-path based method is preferable for relatively small-scale problems as it yields slightly better solution than the heuristic-rules based method. However, the heuristic-rules based method has advantages in its applicability to large-scale realistic systems while producing good performance, to which the shortest-path based method may be computationally inapplicable. Moreover, the heuristic-rules based method can also be applied to stochastic situations because its second stage is rule-based and dynamical.

Optimal PMU Placement by an Equivalent Linear Formulation for Exhaustive Search

Abstract: Observability of bulk power transmission network by means of minimum number of phasor measurement units (PMUs), with the aid of the network topology, is a great challenge. This paper presents a novel equivalent integer linear programming method (EILPM) for the exhaustive search-based PMU placement. The state estimation implemented based on such a placement is completely linear, thereby eliminating drawbacks of the conventional SCADA-based state estimation. Additional constraints for observability preservation following single PMU or line outages can easily be implemented in the proposed EILPM. Furthermore, the limitation of communication channels is dealt with by translation of nonlinear terms into linear ones. Optimal PMU placement is carried out on the IEEE 118-bus test system in different scenarios. The comparison between obtained results of EILPM and those of other methods reveals optimality of the solutions. Moreover, the proposed method is successfully applied on the Iranian National Grid, which demonstrates it can effectively be employed for practical power networks.

COLIN: planning with continuous linear numeric change

Abstract: In this paper we describe COLIN, a forward-chaining heuristic search planner, capable of reasoning with COntinuous LINear numeric change, in addition to the full temporal semantics of PDDL2.1. Through this work we make two advances to the state-of-the-art in terms of expressive reasoning capabilities of planners: the handling of continuous linear change, and the handling of duration-dependent effects in combination with duration inequalities, both of which require tightly coupled temporal and numeric reasoning during planning. COLIN combines FF-style forward chaining search, with the use of a Linear Program (LP) to check the consistency of the interacting temporal and numeric constraints at each state. The LP is used to compute bounds on the values of variables in each state, reducing the range of actions that need to be considered for application. In addition, we develop an extension of the Temporal Relaxed Planning Graph heuristic of CRIKEY3, to support reasoning directly with continuous change. We extend the range of task variables considered to be suitable candidates for specifying the gradient of the continuous numeric change effected by an action. Finally, we explore the potential for employing mixed integer programming as a tool for optimising the timestamps of the actions in the plan, once a solution has been found. To support this, we further contribute a selection of extended benchmark domains that include continuous numeric effects. We present results for COLIN that demonstrate its scalability on a range of benchmarks, and compare to existing state-of-the-art planners.

Pricing Non-Convexities in an Electricity Pool

Abstract: Electricity pools are generally cleared through auctions that are conveniently formulated as mixed-integer linear programming problems. Since a mixed-integer linear programming problem is non-continuous and non-convex, marginal prices cannot be easily derived. However, to trade electricity, prices are needed. Thus, a relevant question arises: how does one generate appropriate prices? This paper addresses this important issue and proposes a primal-dual approach to derive efficient revenue adequate uniform prices that guarantee that dispatched producers are willing to remain in the market. Such prices may not significantly deviate from the marginal prices obtained if integrality conditions are relaxed in the original mixed-integer linear programming problem. Two case studies illustrate the functioning of the proposed pricing scheme.

Recent advances on support vector machines research

Abstract: Support vector machines (SVMs), with their roots in Statistical Learning Theory (SLT) and optimization methods, have become powerful tools for problem solution in machine learning. SVMs reduce most machine learning problems to optimization problems and optimization lies at the heart of SVMs. Lots of SVM algorithms involve solving not only convex problems, such as linear programming, quadratic programming, second order cone programming, semi-definite programming, but also non-convex and more general optimization problems, such as integer programming, semi-infinite programming, bi-level programming and so on. The purpose of this paper is to understand SVM from the optimization point of view, review several representative optimization models in SVMs, their applications in economics, in order to promote the research interests in both optimization-based SVMs theory and economics applications. This paper starts with summarizing and explaining the nature of SVMs. It then proceeds to discuss optimization...