Showing papers on "Integer programming published in 2011"

Sequential model-based optimization for general algorithm configuration

Abstract: State-of-the-art algorithms for hard computational problems often expose many parameters that can be modified to improve empirical performance. However, manually exploring the resulting combinatorial space of parameter settings is tedious and tends to lead to unsatisfactory outcomes. Recently, automated approaches for solving this algorithm configuration problem have led to substantial improvements in the state of the art for solving various problems. One promising approach constructs explicit regression models to describe the dependence of target algorithm performance on parameter settings; however, this approach has so far been limited to the optimization of few numerical algorithm parameters on single instances. In this paper, we extend this paradigm for the first time to general algorithm configuration problems, allowing many categorical parameters and optimization for sets of instances. We experimentally validate our new algorithm configuration procedure by optimizing a local search and a tree search solver for the propositional satisfiability problem (SAT), as well as the commercial mixed integer programming (MIP) solver CPLEX. In these experiments, our procedure yielded state-of-the-art performance, and in many cases outperformed the previous best configuration approach.

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.

Wiley encyclopedia of operations research and management science

Abstract: Use of Lagrange Interpolating Polynomials in RLT. Systems in Series. Parallel Configurations. Spanning trees. Recycling. Split Cuts. Retrial Queues. Horse Racing. MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Dual simplex. History of CP. Procurement Contracts. MRP. Just in Time. Push and Pull Production. MULTIVARIATE INPUT MODELING. Operational Research Society. The M/G/1 Queue. Drama Theory. Hyper-heuristics. Antithetic Variates. Music. Edgeworth market games. Operational Risk. Queueing Notation. Environmental impact. Why variance is not risk. Conjugate gradient methods. Birth-and-Death Processes. Surgery Planning and Scheduling. Large-scale linear models. Standby Systems. Billiards/Pool. AXIOMATIC MEASURES OF RISK AND RISK-VALUE MODELS. Age Replacement Policies. PASTA and Related Results. Collaborative Procurement. LP projection algorithms. R&D risk management. Bioterrorism. Vendor-Managed Inventory. Gomory Cuts. Travel demand modeling. System Availability. Infinite horizon problems. Trust. Bayesian Network Classifiers. Integer Programming Duality. Queueing Disciplines. Stakeholder participation. Models and Basic Properties. Parametric LP analysis. Operations Research and Golfing. Ice Hockey. Clustering. Finite-Population Models. Batch Arrivals and Service. Optimal Monitoring Strategies. Basic Polyhedral Theory. Operations Research and Art. Managing portfolios of risks. Measures of risk equity. Branch and Bound Algorithms. Analytics in Retail. Variational Inequalities. Cross-Entropy Method. TSP heuristics. Capacity allocation. Control Variates. Cover Inequalities. Direct Search Methods. NLP Software. Bilinear optimization. Discrete-Time Martingales. Branch and Price. Column generation. IP Preprocessing. Optimal Reliability Allocation. Simplex-based LP solvers. Instance Formats. Clique generalizations. Availability in Stochastic Models. Evolutionary Algorithms. Basic CP theory: Search. Multimethodology. Branch and Cut. Memetic Algorithms. Urban mass transit. Coherent Systems. Subgradient optimization. Klimov's Model. Credit risk assessment. Branch-width and Tangles. Stochastic Hazard Process. Deterministic Global Optimization. Multistage (stochastic) games. Basis Reduction Methods. ACCIDENT PRECURSORS AND WARNING SYSTEMS MANAGEMENT: A BAYESIAN APPROACH TO MATHEMATICAL MODELS. Genetic Algorithms. Newsvendor models. Parallel Systems. Opportunities in Tennis. Job-shop scheduling. Simplex method and complexity. Geometric programming. Evacuation Planning. The Performance? Allocation Games. Scenario Generation. Robustness Analysis. Dynamic auctions. Neuroeconomics and game theory. Common Random Numbers. Selective Support Vector Machines. Semi-Markov Processes. Risk Averse Models. Sampling Methods. Domination problems. Simulation of Rare Events. Introduction to Tabu Search. Basic Interdiction Models. Introductory Concepts. Remanufacturing. PAUSE procedure. Wardrop equilibria. Mass customization. Ellipsoidal algorithms. Benders decomposition. Dynamic vehicle routing. Warranty Modeling. Design for Network Resiliency. Passenger rail transportation. Vehicle Routing Problem. Supply Chain Outsourcing. Lovasz-Schriver Reformulation. Hazard Rate Function. Lot-sizing. Differential games. Regenerative Processes. Guided Local Search. Preferences for repeated gambles. Percolation Theory. Simulated Annealing. Scoring Rules. Mixing Sets. Cricket. Prospect Theory. Combining Forecasts. Graph search techniques. Quasi-Newton methods. Random search algorithms. Supply chain coordination. Service Outsourcing. Markov Renewal Processes. K-out-of-n Systems.

A study of the routing and spectrum allocation in spectrum-sliced Elastic Optical Path networks

Abstract: In OFDM-based optical networks, multiple subcarriers can be allocated to accommodate various size of traffic demands. By using the multi-carrier modulation technique, subcarriers for the same node-pair can be overlapping in the spectrum domain. Compared to the traditional wavelength routed networks (WRNs), the OFDM-based Spectrum-sliced Elastic Optical Path (SLICE) network has higher spectrum efficiency due to its finer granularity and frequency-resource saving. In this work, for the first time, we comprehensively study the routing and spectrum allocation (RSA) problem in the SLICE network. After proving the NP-hardness of the static RSA problem, we formulate the RSA problem using the Integer Linear Programming (ILP) formulations to optimally minimize the maximum number of sub-carriers required on any fiber of a SLICE network. We then analyze the lower/upper bounds for the sub-carrier number in a network with general or specific topology. We also propose two efficient algorithms, namely, balanced load spectrum allocation (BLSA) algorithm and shortest path with maximum spectrum reuse (SPSR) algorithm to minimize the required sub-carrier number in a SLICE network. The results show that the proposed algorithms can match the analysis and approximate the optimal solutions using the ILP model.

Learning with Whom to Share in Multi-task Feature Learning

Abstract: In multi-task learning (MTL), multiple tasks are learnt jointly. A major assumption for this paradigm is that all those tasks are indeed related so that the joint training is appropriate and beneficial. In this paper, we study the problem of multi-task learning of shared feature representations among tasks, while simultaneously determining "with whom" each task should share. We formulate the problem as a mixed integer programming and provide an alternating minimization technique to solve the optimization problem of jointly identifying grouping structures and parameters. The algorithm mono-tonically decreases the objective function and converges to a local optimum. Compared to the standard MTL paradigm where all tasks are in a single group, our algorithm improves its performance with statistical significance for three out of the four datasets we have studied. We also demonstrate its advantage over other task grouping techniques investigated in literature.

Routing and Spectrum Assignment in Spectrum Sliced Elastic Optical Path Network

Abstract: A spectrum-sliced elastic optical path network (SLICE) architecture has been recently proposed as an efficient solution for a flexible bandwidth allocation in optical networks In SLICE, the problem of Routing and Spectrum Assignment (RSA) emerges In this letter, we both formulate RSA as an Integer Linear Programming (ILP) problem and propose an effective heuristic to be used if the solution of ILP is not attainable

MIPLIB 2010 - Mixed Integer Programming Library version 5

Abstract: This paper reports on the fifth version of theMixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which are all solvable by today’s codes, and also the challenge test set with 164 instances, many of which are currently unsolved. For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to test the accuracy of provided solutions using exact arithmetic.

Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem

Abstract: This paper introduces and studies the maximum k-plex problem, which arises in social network analysis and has wider applicability in several important areas employing graph-based data mining. After establishing NP-completeness of the decision version of the problem on arbitrary graphs, an integer programming formulation is presented, followed by a polyhedral study to identify combinatorial valid inequalities and facets. A branch-and-cut algorithm is implemented and tested on proposed benchmark instances. An algorithmic approach is developed exploiting the graph-theoretic properties of a k-plex that is effective in solving the problem to optimality on very large, sparse graphs such as the power law graphs frequently encountered in the applications of interest.

Efficient Data Collection in Wireless Sensor Networks with Path-Constrained Mobile Sinks

Abstract: Recent work has shown that sink mobility along a constrained path can improve the energy efficiency in wireless sensor networks. However, due to the path constraint, a mobile sink with constant speed has limited communication time to collect data from the sensor nodes deployed randomly. This poses significant challenges in jointly improving the amount of data collected and reducing the energy consumption. To address this issue, we propose a novel data collection scheme, called the Maximum Amount Shortest Path (MASP), that increases network throughput as well as conserves energy by optimizing the assignment of sensor nodes. MASP is formulated as an integer linear programming problem and then solved with the help of a genetic algorithm. A two-phase communication protocol based on zone partition is designed to implement the MASP scheme. We also develop a practical distributed approximate algorithm to solve the MASP problem. In addition, the impact of different overlapping time partition methods is studied. The proposed algorithms and protocols are validated through simulation experiments using OMNET++.

Learning to Simplify Sentences with Quasi-Synchronous Grammar and Integer Programming

Abstract: Text simplification aims to rewrite text into simpler versions, and thus make information accessible to a broader audience. Most previous work simplifies sentences using handcrafted rules aimed at splitting long sentences, or substitutes difficult words using a predefined dictionary. This paper presents a data-driven model based on quasi-synchronous grammar, a formalism that can naturally capture structural mismatches and complex rewrite operations. We describe how such a grammar can be induced from Wikipedia and propose an integer linear programming model for selecting the most appropriate simplification from the space of possible rewrites generated by the grammar. We show experimentally that our method creates simplifications that significantly reduce the reading difficulty of the input, while maintaining grammaticality and preserving its meaning.

Contingency-Constrained Unit Commitment With $n - K$ Security Criterion: A Robust Optimization Approach

Abstract: This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an n - K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions.

Scheduling smart home appliances using mixed integer linear programming

Abstract: This paper considers the minimum electricity cost scheduling problem of smart home appliances. Operation characteristics, such as expected duration and peak power consumption of the smart appliances, can be adjusted through a power profile signal. The optimal power profile signal minimizes cost, while satisfying technical operation constraints and consumer preferences. Constraints such as enforcing uninterruptible and sequential operations are modeled in the proposed framework using mixed integer linear programming (MILP). Several realistic scenarios based on actual spot price are considered, and the numerical results provide insight into tariff design. Computational issues and extensions of the proposed scheduling framework are also discussed.

An Integer Optimization Approach to Large-Scale Air Traffic Flow Management

Abstract: This paper presents a new integer programming (IP) model for large-scale instances of the air traffic flow management (ATFM) problem. The model covers all the phases of each flight---i.e., takeoff, en route cruising, and landing---and solves for an optimal combination of flow management actions, including ground-holding, rerouting, speed control, and airborne holding on a flight-by-flight basis. A distinguishing feature of the model is that it allows for rerouting decisions. This is achieved through the imposition of sets of “local” conditions that make it possible to represent rerouting options in a compact way by only introducing some new constraints. Moreover, three classes of valid inequalities are incorporated into the model to strengthen the polyhedral structure of the underlying relaxation. Computational times are short and reasonable for practical application on problem instances of size comparable to that of the entire U.S. air traffic management system. Thus, the proposed model has the potential of serving as the main engine for the preliminary identification, on a daily basis, of promising air traffic flow management interventions on a national scale in the United States or on a continental scale in Europe.

Modeling disjunctive constraints with a logarithmic number of binary variables and constraints

Abstract: Many combinatorial constraints over continuous variables such as SOS1 and SOS2 constraints can be interpreted as disjunctive constraints that restrict the variables to lie in the union of a finite number of specially structured polyhedra. Known mixed integer binary formulations for these constraints have a number of binary variables and extra constraints linear in the number of polyhedra. We give sufficient conditions for constructing formulations for these constraints with a number of binary variables and extra constraints logarithmic in the number of polyhedra. Using these conditions we introduce mixed integer binary formulations for SOS1 and SOS2 constraints that have a number of binary variables and extra constraints logarithmic in the number of continuous variables. We also introduce the first mixed integer binary formulations for piecewise linear functions of one and two variables that use a number of binary variables and extra constraints logarithmic in the number of linear pieces of the functions. We prove that the new formulations for piecewise linear functions have favorable tightness properties and present computational results showing that they can significantly outperform other mixed integer binary formulations.

Layout decomposition for triple patterning lithography

Abstract: As minimum feature size and pitch spacing further decrease, triple patterning lithography (TPL) is a possible 193nm extension along the paradigm of double patterning lithography (DPL). However, there is very little study on TPL layout decomposition. In this paper, we show that TPL layout decomposition is a more difficult problem than that for DPL. We then propose a general integer linear programming formulation for TPL layout decomposition which can simultaneously minimize conflict and stitch numbers. Since ILP has very poor scalability, we propose three acceleration techniques without sacrificing solution quality: independent component computation, layout graph simplification, and bridge computation. For very dense layouts, even with these speedup techniques, ILP formulation may still be too slow. Therefore, we propose a novel vector programming formulation for TPL decomposition, and solve it through effective semidefinite programming (SDP) approximation. Experimental results show that the ILP with acceleration techniques can reduce 82% runtime compared to the baseline ILP. Using SDP based algorithm, the runtime can be further reduced by 42% with some tradeoff in the stitch number (reduced by 7%) and the conflict (9% more). However, for very dense layouts, SDP based algorithm can achieve 140× speed-up even compared with accelerated ILP.

Bayesian network learning with cutting planes

Abstract: The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approach—the search for such cutting planes is effected using a sub-IP. Results show that this is a particularly fast method for exact BN learning.

Unit Commitment With Volatile Node Injections by Using Interval Optimization

Abstract: In response to the challenges brought by uncertain bus load and volatile wind power to power system security, this paper presents a novel unit commitment formulation based on interval number optimization to improve the security as well as economy of power system operation. By using full-scenario analysis, the worst-case impact of volatile node injection on unit commitment is acquired, so that the proposed model can always provide a secure and economical unit commitment result to the operators. Scenarios generation and reduction method based on interval linear programming theory are used to accelerate the solution procedure without loss of optimality. Benders decomposition is also implemented to reduce the complexity of this large-scale interval mixed integer linear programming, and prove the rationality and rigor of our proposed method. The numerical results indicate better secure and economical features of the proposed method comparing with the traditional one.

Spinning Reserve Estimation in Microgrids

Abstract: In this paper, a probabilistic methodology for estimating spinning reserve requirement in microgrids is proposed. The spinning reserve amount is determined by a tradeoff between reliability and economics. The unreliability of units and uncertainties caused by load and nondispatchable units are both considered. In order to reduce computation burden, various uncertainties are aggregated. A multistep method is proposed to efficiently consider the combinatorial characteristic of unit outage events. The computation efficiency of spinning reserve calculations can be greatly improved. The optimization is solved by mixed integer linear programming (MILP). Two case studies are carried out to illustrate the proposed method. Their results and discussions are also presented.

The synchronization of traffic signals by mixed-integer linear programming

Abstract: Traffic signals can be synchronized so that a car, starting at one end of a main artery and traveling at preassigned speeds, can go to the other end without stopping for a red light. The portion of a signal cycle for which this is possible is called the bandwidth for that direction. A mixed-integer linear program is formulated for the following arterial problem: Given 1 an arbitrary number of signals, 2 the red-green split at each signal, 3 upper and lower limits on signal period, 4 upper and lower limits on speed between adjacent signals, and 5 limits on change in speed, find 1 common signal period, 2 speeds between signals, and 3 the relative phasing of the signals, in order to maximize the sum of the bandwidths for the two directions. Several variants of the problem are formulated, including the problem of synchronizing a network of signals. Branch-and-bound algorithms are developed for solving the mixed-integer linear programs by solving sequences of ordinary linear programs. A 10-signal arterial example and a 7-signal network example are worked out.

Fast Model Predictive Control for Urban Road Networks via MILP

Abstract: In this paper, an advanced control strategy, i.e., model predictive control (MPC), is applied to control and coordinate urban traffic networks. However, due to the nonlinearity of the prediction model, the optimization of MPC is a nonlinear nonconvex optimization problem. In this case, the online computational complexity becomes a big challenge for the MPC controller if it is implemented in a real-life traffic network. To overcome this problem, the online optimization problem is reformulated into a mixed-integer linear programming (MILP) optimization problem to increase the real-time feasibility of the MPC control strategy. The new optimization problem can be very efficiently solved by existing MILP solvers, and the global optimum of the problem is guaranteed. Moreover, we propose an approach to reduce the complexity of the MILP optimization problem even further. The simulation results show that the MILP-based MPC controllers can reach the same performance, but the time taken to solve the optimization becomes only a few seconds, which is a significant reduction, compared with the time required by the original MPC controller.

A Scenario-Based Multi-Objective Model for Multi-Stage Transmission Expansion Planning

Abstract: The unbundling of the electricity industry introduced new uncertainties and escalated the existing ones in transmission expansion planning. In this paper, a multi-stage transmission expansion methodology is presented using a multi-objective optimization framework with internal scenario analysis. Total social cost (TSC), maximum regret (robustness criterion), and maximum adjustment cost (flexibility criterion) are considered as three optimization objectives. Uncertainties are considered by defining a number of scenarios. To overcome the difficulties in solving the nonconvex and mixed integer optimization problem, the genetic-based Non-dominated Sorting Genetic Algorithm (NSGA II) is used. Then, fuzzy decision making is applied to obtain the optimal solution. The planning methodology is applied to the Iranian 400-kV transmission grid to show feasibility of the proposed algorithm.

Optimal Generator Start-Up Strategy for Bulk Power System Restoration

Abstract: During system restoration, it is critical to utilize the available black-start (BS) units to provide cranking power to non-black-start (NBS) units in such a way that the overall system generation capability will be maximized. The corresponding optimization problem is combinatorial with complex practical constraints that can vary with time. This paper provides a new formulation of generator start-up sequencing as a mixed integer linear programming (MILP) problem. The linear formulation leads to an optimal solution to this important problem that clearly outperforms heuristic or enumerative techniques in quality of solutions or computational speed. The proposed generator start-up strategy is intended to provide an initial starting sequence of all BS or NBS units. The method can provide updates on the system MW generation capability as the restoration process progresses. The IEEE 39-Bus system, American Electric Power (AEP), and Entergy test cases are used for validation of the generation capability optimization. Simulation results demonstrate that the proposed MILP-based generator start-up sequencing algorithm is highly efficient.

Design of a Survivable Hybrid Wireless-Optical Broadband-Access Network

Abstract: The hybrid wireless-optical broadband-access network (WOBAN) is a promising architecture for access networks. Although the front-end wireless mesh networks in a WOBAN are self-healing, the back-end passive optical networks do not have survivability due to their tree topology. We propose a cost-effective protection method for WOBAN that deals with network element failures in the optical part of WOBAN. We define the maximum protection with minimum cost (MPMC) problem and show that the problem can be converted to the minimum cost maximum flow (MCMF) problem. We also present an integer linear programming (ILP) model for the MCMF problem. Numerical results are reported for the application of our algorithm to obtain the optimal solutions for different instances of the MPMC problem.

Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach

Abstract: This paper proposes a global optimization algorithm for solving a mixed (continuous/discrete) transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both expansion of existing links and addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. In this paper, we first formulate the UE condition as a variational inequality (VI) problem, which is defined from a finite number of extreme points of a link-flow feasible region. The MNDP is approximated as a piecewise-linear programming (P-LP) problem, which is then transformed into a mixed-integer linear programming (MILP) problem. A global optimization algorithm based on a cutting constraint method is developed for solving the MILP problem. Numerical examples are given to demonstrate the efficiency of the proposed method and to compare the results with alternative algorithms reported in the literature.

Method for the Solution of the Multi-Dimensional 0/1 Knapsack Problem

Abstract: In the knapsack problem, given the desirability of each of a number of items, one seeks to find that subset which satisfies a constraint on total weight. The multidimensional variant imposes constraints on additional variables of the items; the 0/1 specification means that an item is either taken or not, i.e., multiples of the same item are not considered, except possibly indirectly. Traditionally the one-dimensional knapsack problem is solved by means of dynamic programming. The multidimensional problem is usually reduced to a one-dimensional one by use of Lagrangian Multipliers that, however, do not generally yield the exact solution to the problem posed. Here some new algorithms are developed that are applied within a dynamic programming framework. Additionally, the methods make integral use of an interactive computer system in which the heuristics of the problem solver are applied and changed as the character of the solution process evolves. The problem arises in the context of capital budgeting, but has obvious applications in a variety of other areas. The methods have been employed for solving numerical problems with as many as 105 items, the parameters having been obtained from industrial applications.

An Exact Algorithm for the Pickup and Delivery Problem with Time Windows

Abstract: The pickup and delivery problem with time windows (PDPTW) is a generalization of the vehicle routing problem with time windows. In the PDPTW, a set of identical vehicles located at a central depot must be optimally routed to service a set of transportation requests subject to capacity, time window, pairing, and precedence constraints. In this paper, we present a new exact algorithm for the PDPTW based on a set-partitioning--like integer formulation, and we describe a bounding procedure that finds a near-optimal dual solution of the LP-relaxation of the formulation by combining two dual ascent heuristics and a cut-and-column generation procedure. The final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between a known upper bound and the lower bound achieved. If the resulting problem has moderate size, it is solved by an integer programming solver; otherwise, a branch-and-cut-and-price algorithm is used to close the integrality gap. Extensive computational results over the main instances from the literature show the effectiveness of the proposed exact method.