Showing papers on "Integer programming published in 2014"

Learning surrogate models for simulation‐based optimization

Abstract: A central problem in modeling, namely that of learning an algebraic model from data obtained from simulations or experiments is addressed. A methodology that uses a small number of simulations or experiments to learn models that are as accurate and as simple as possible is proposed. The approach begins by building a low-complexity surrogate model. The model is built using a best subset technique that leverages an integer programming formulation to allow for the efficient consideration of a large number of possible functional components in the model. The model is then improved systematically through the use of derivative-free optimization solvers to adaptively sample new simulation or experimental points. Automated learning of algebraic models for optimization (ALAMO), the computational implementation of the proposed methodology, along with examples and extensive computational comparisons between ALAMO and a variety of machine learning techniques, including Latin hypercube sampling, simple least-squares regression, and the lasso is described. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2211–2227, 2014

A Base Integer Programming Model and Benchmark Suite for Liner-Shipping Network Design

Abstract: The liner-shipping network design problem is to create a set of nonsimple cyclic sailing routes for a designated fleet of container vessels that jointly transports multiple commodities. The objective is to maximize the revenue of cargo transport while minimizing the costs of operation. The potential for making cost-effective and energy-efficient liner-shipping networks using operations research OR is huge and neglected. The implementation of logistic planning tools based upon OR has enhanced performance of airlines, railways, and general transportation companies, but within the field of liner shipping, applications of OR are scarce. We believe that access to domain knowledge and data is a barrier for researchers to approach the important liner-shipping network design problem. The purpose of the benchmark suite and the paper at hand is to provide easy access to the domain and the data sources of liner shipping for OR researchers in general. We describe and analyze the liner-shipping domain applied to network design and present a rich integer programming model based on services that constitute the fixed schedule of a liner shipping company. We prove the liner-shipping network design problem to be strongly NP-hard. A benchmark suite of data instances to reflect the business structure of a global liner shipping network is presented. The design of the benchmark suite is discussed in relation to industry standards, business rules, and mathematical programming. The data are based on real-life data from the largest global liner-shipping company, Maersk Line, and supplemented by data from several industry and public stakeholders. Computational results yielding the first best known solutions for six of the seven benchmark instances is provided using a heuristic combining tabu search and heuristic column generation.

Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables

Abstract: Train dispatching is critical for the punctuality and reliability of rail operations, especially for a complex rail network. This paper develops an innovative integer programming model for the problem of train dispatching on an N -track network by means of simultaneously rerouting and rescheduling trains. Based on a time–space network modeling framework, we first adapt a commonly used big- M method to represent complex “if-then” conditions for train safety headways in a multi-track context. The track occupancy consideration on typical single and double tracks is then reformulated using a vector of cumulative flow variables. This new reformulation technique can provide an efficient decomposition mechanism through modeling track capacities as side constraints which are further dualized through a proposed Lagrangian relaxation solution framework. We further decompose the original complex rerouting and rescheduling problem into a sequence of single train optimization subproblems. For each subproblem, a standard label correcting algorithm is embedded for finding the time dependent least cost path on a time–space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. We present a set of numerical experiments to demonstrate the system-wide performance benefits of simultaneous train rerouting and rescheduling, compared to commonly-used sequential train rerouting and rescheduling approaches.

Integer Programming

Abstract: This book is an elegant and rigorous presentation of integer programming, exposing the subjects mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the readers understanding and serving as a gateway to deeper study.Key topics include:formulationspolyhedral theorycutting planesdecompositionenumerationsemidefinite relaxationsWritten by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.

Operating Strategies for a GB Integrated Gas and Electricity Network Considering the Uncertainty in Wind Power Forecasts

Abstract: In many power systems, in particular in Great Britain (GB), significant wind generation is anticipated and gas-fired generation will continue to play an important role. Gas-fired generating units act as a link between the gas and electricity networks. The variability of wind power is, therefore, transferred to the gas network by influencing the gas demand for electricity generation. Operation of a GB integrated gas and electricity network considering the uncertainty in wind power forecast was investigated using three operational planning methods: deterministic, two-stage stochastic programming, and multistage stochastic programming. These methods were benchmarked against a perfect foresight model which has no uncertainty associated with the wind power forecast. In all the methods, thermal generators were controlled through an integrated unit commitment and economic dispatch algorithm that used mixed integer programming. The nonlinear characteristics of the gas network, including the gas flow along pipes and the operation of compressors, were taken into account and the resultant nonlinear problem was solved using successive linear programming. The operational strategies determined by the stochastic programming methods showed reductions of the operational costs compared to the solution of the deterministic method by almost 1%. Also, using the stochastic programming methods to schedule the thermal units was shown to make a better use of pumped storage plants to mitigate the variability and uncertainty of the net demand.

Transit route and frequency design:Bi-level modeling and hybrid artificial bee colony algorithm approach

Abstract: This paper proposes a bi-level transit network design problem where the transit routes and frequency settings are determined simultaneously. The upper-level problem is formulated as a mixed integer non-linear program with the objective of minimizing the number of passenger transfers, and the lower-level problem is the transit assignment problem with capacity constraints. A hybrid artificial bee colony (ABC) algorithm is developed to solve the bi-level problem. This algorithm relies on the ABC algorithm to design route structures and a proposed descent direction search method to determine an optimal frequency setting for a given route structure. The descent direction search method is developed by analyzing the optimality conditions of the lower-level problem and using the relationship between the lower- and upper-level objective functions. The step size for updating the frequency setting is determined by solving a linear integer program. To efficiently repair route structures, a node insertion and deletion strategy is proposed based on the average passenger demand for the direct services concerned. To increase the computation speed, a lower bound of the objective value for each route design solution is derived and used in the fitness evaluation of the proposed algorithm. Various experiments are set up to demonstrate the performance of our proposed algorithm and the properties of the problem.

Learning to Search in Branch and Bound Algorithms

Abstract: Branch-and-bound is a widely used method in combinatorial optimization, including mixed integer programming, structured prediction and MAP inference. While most work has been focused on developing problem-specific techniques, little is known about how to systematically design the node searching strategy on a branch-and-bound tree. We address the key challenge of learning an adaptive node searching order for any class of problem solvable by branch-and-bound. Our strategies are learned by imitation learning. We apply our algorithm to linear programming based branch-and-bound for solving mixed integer programs (MIP). We compare our method with one of the fastest open-source solvers, SCIP; and a very efficient commercial solver, Gurobi. We demonstrate that our approach achieves better solutions faster on four MIP libraries.

Modeling and optimizing the integrated problem of closed-loop supply chain network design and disassembly line balancing

Abstract: This paper describes an integrated model that jointly optimizes the strategic and tactical decisions of a closed-loop supply chain (CLSC). The strategic level decisions relate to the amounts of goods flowing on the forward and reverse chains. The tactical level decisions concern balancing disassembly lines in the reverse chain. The objective is to minimize costs of transportation, purchasing, refurbishing, and operating the disassembly workstations. A nonlinear mixed integer programming formulation is described for the problem. Numerical examples are presented using the proposed model.

A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support

Abstract: We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with finite support and random polyhedral constraints. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and most available methods are only able to find provably good solutions in certain very special cases. Our approach uses both decomposition, to enable processing subproblems corresponding to one possible outcome at a time, and integer programming techniques, to combine the results of these subproblems to yield strong valid inequalities. Computational results on a chance-constrained formulation of a resource planning problem inspired by a call center staffing application indicate the approach works significantly better than both an existing mixed-integer programming formulation and a simple decomposition approach that does not use strong valid inequalities. We also demonstrate how the approach can be used to efficiently solve for a sequence of risk levels, as would be done when solving for the efficient frontier of risk and cost.

A Two-Objective Timetable Optimization Model in Subway Systems

Abstract: The train timetable optimization problem in subway systems is to determine arrival and departure times for trains at stations so that the resources can be effectively utilized and the trains can be efficiently operated. Because the energy saving and the service quality are paid more attention, this paper proposes a timetable optimization model to increase the utilization of regenerative energy and, simultaneously, to shorten the passenger waiting time. First, we formulate a two-objective integer programming model with headway time and dwell time control. Second, we design a genetic algorithm with binary encoding to find the optimal solution. Finally, we conduct numerical examples based on the operation data from the Beijing Yizhuang subway line of China. The results illustrate that the proposed model can save energy by 8.86% and reduce passenger waiting time by 3.22% in comparison with the current timetable.

Optimal Supervisory Control of Flexible Manufacturing Systems by Petri Nets: A Set Classification Approach

Abstract: Supervisory control is usually considered as an external control mechanism to a system by controlling the occurrences of its controllable events. There exist Petri net models whose legal reachability spaces are nonconvex. In this case, they cannot be optimally controlled by the conjunctions of linear constraints. For Petri net models of flexible manufacturing systems, this work proposes a method to classify the legal markings into several subsets. Each subset is associated with a linear constraint that can forbid all first-met bad markings. Then, the disjunctions of the obtained constraints can make all legal markings reachable and forbid all first-met bad markings, i.e., the controlled net is live and maximally permissive. An integer linear programming model is formulated to minimize the number of the constraints. A supervisory structure is also proposed to implement the disjunctions of the constraints. Finally, examples are provided to illustrate the proposed method.

Energy Efficient Uplink Resource Allocation in LTE Networks with M2M/H2H Co-existence under Statistical QoS Guarantees

Abstract: Recently, energy efficiency in wireless networks has become an important objective. Aside from the growing proliferation of smartphones and other high-end devices in conventional human-to-human (H2H) communication, the introduction of machine-to-machine (M2M) communication or machine-type communication into cellular networks is another contributing factor. In this paper, we investigate quality-of-service (QoS)-driven energy-efficient design for the uplink of long term evolution (LTE) networks in M2M/H2H co-existence scenarios. We formulate the resource allocation problem as a maximization of effective capacity-based bits-per-joule capacity under statistical QoS provisioning. The specific constraints of single carrier frequency division multiple access (uplink air interface in LTE networks) pertaining to power and resource block allocation not only complicate the resource allocation problem, but also render the standard Lagrangian duality techniques inapplicable. We overcome the analytical and computational intractability by first transforming the original problem into a mixed integer programming (MIP) problem and then formulating its dual problem using the canonical duality theory. The proposed energy-efficient design is compared with the spectral efficient design along with round robin (RR) and best channel quality indicator (BCQI) algorithms. Numerical results, which are obtained using the invasive weed optimization (IWO) algorithm, show that the proposed energy-efficient uplink design not only outperforms other algorithms in terms of energy efficiency while satisfying the QoS requirements, but also performs closer to the optimal design.

Hydro Unit Commitment via Mixed Integer Linear Programming: A Case Study of the Three Gorges Project, China

Abstract: This paper develops a methodology for optimizing the hydro unit commitment (HUC) for the Three Gorges Project (TGP) in China. The TGP is the world's largest and most complex hydropower system in operation. The objective is to minimize the total operational cost. The decision variables are the startup or shutdown of each of the available units in the system and the power releases from the online units. The mathematical formulation must take into account the head variation over the operation periods as the net head changes from hour to hour and affects power generation. Additionally, the formulation must consider the operation of 32 heterogeneous generating units and the nonlinear power generation function of each unit. A three-dimensional interpolation technique is used to accurately represent the nonlinear power generation function of each individual unit, taking into account the time-varying head as well as the non-smooth limitations for power output and power release. With the aid of integer variables that represent the on/off and operation partition statuses of a unit, the developed HUC model for the TGP conforms to a standard mixed integer linear programming (MILP) formulation. We demonstrate the performance and utility of the model by analyzing the results from several scenarios for the TGP.

MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics

Abstract: Optimization is the key to solving many problems in computational biology. Global optimization methods, which provide a robust methodology, and metaheuristics in particular have proven to be the most efficient methods for many applications. Despite their utility, there is a limited availability of metaheuristic tools. We present MEIGO, an R and Matlab optimization toolbox (also available in Python via a wrapper of the R version), that implements metaheuristics capable of solving diverse problems arising in systems biology and bioinformatics. The toolbox includes the enhanced scatter search method (eSS) for continuous nonlinear programming (cNLP) and mixed-integer programming (MINLP) problems, and variable neighborhood search (VNS) for Integer Programming (IP) problems. Additionally, the R version includes BayesFit for parameter estimation by Bayesian inference. The eSS and VNS methods can be run on a single-thread or in parallel using a cooperative strategy. The code is supplied under GPLv3 and is available at http://www.iim.csic.es/~gingproc/meigo.html . Documentation and examples are included. The R package has been submitted to BioConductor. We evaluate MEIGO against optimization benchmarks, and illustrate its applicability to a series of case studies in bioinformatics and systems biology where it outperforms other state-of-the-art methods. MEIGO provides a free, open-source platform for optimization that can be applied to multiple domains of systems biology and bioinformatics. It includes efficient state of the art metaheuristics, and its open and modular structure allows the addition of further methods.

An effective iterated greedy algorithm for the mixed no-idle permutation flowshop scheduling problem

Abstract: In the no-idle flowshop, machines cannot be idle after finishing one job and before starting the next one. Therefore, start times of jobs must be delayed to guarantee this constraint. In practice machines show this behavior as it might be technically unfeasible or uneconomical to stop a machine in between jobs. This has important ramifications in the modern industry including fiber glass processing, foundries, production of integrated circuits and the steel making industry, among others. However, to assume that all machines in the shop have this no-idle constraint is not realistic. To the best of our knowledge, this is the first paper to study the mixed no-idle extension where only some machines have the no-idle constraint. We present a mixed integer programming model for this new problem and the equations to calculate the makespan. We also propose a set of formulas to accelerate the calculation of insertions that is used both in heuristics as well as in the local search procedures. An effective iterated greedy (IG) algorithm is proposed. We use an NEH-based heuristic to construct a high quality initial solution. A local search using the proposed accelerations is employed to emphasize intensification and exploration in the IG. A new destruction and construction procedure is also shown. To evaluate the proposed algorithm, we present several adaptations of other well-known and recent metaheuristics for the problem and conduct a comprehensive set of computational and statistical experiments with a total of 1750 instances. The results show that the proposed IG algorithm outperforms existing methods in the no-idle and in the mixed no-idle scenarios by a significant margin.

Two-Stage Robust Generation Expansion Planning: A Mixed Integer Linear Programming Model

Abstract: This paper presents a new uncertainty handling framework for optimal generation expansion planning (GEP) amalgamating the notions of single-stage and two-stage robust optimization (RO) The proposed multiyear robust GEP methodology, as a tractable mixed integer linear programming optimization problem, copes with the inherent planning uncertainties associated with forecasted electricity load demand, as well as estimated investment and operation costs through distribution-free bounded intervals producing polyhedral uncertainty sets The optimal generation expansion plan obtained from the proposed RO approach is immunized against worst-case planning uncertainties considering the adopted degree of conservatism for each uncertainty set Therefore, the proposed methodology is capable of controlling the robustness of the optimal investment schedule regarding the enforced planning uncertainties Simulation results demonstrate the efficacy and efficiency of the proposed RO framework throughout GEP studies

Particle swarm optimization algorithm for the berth allocation problem

Abstract: The berth allocation is one of the major container port optimization problems. In both port operator's and ocean carriers' perspective, the minimization of the time a ship at the berth may be considered as an objective with respect to port operations. This paper focuses on the discrete and dynamic berth allocation problem (BAP), which assigns ships to discrete berth positions and minimizes the total waiting times and handling times for all ships. We formulate a mixed integer programming (MIP) model for the BAP. Since BAP is a NP-hard problem, exact solution approaches cannot solve the instances of realistic size optimally within reasonable time. We propose a particle swarm optimization (PSO) approach to solve the BAP. The proposed PSO is tested with two sets of benchmark instances in different sizes from the literature. Experimental results show that the PSO algorithm is better than the other compared algorithms in terms of solution quality and computation time.

Qubit placement to minimize communication overhead in 2D quantum architectures

Abstract: Regular, local-neighbor topologies of quantum architectures restrict interactions to adjacent qubits, which in turn increases the latency of quantum circuits mapped to these architectures. To alleviate this effect, optimization methods that consider qubit-to-qubit interactions in 2D grid architectures are presented in this paper. The proposed approaches benefit from Mixed Integer Programming (MIP) formulation for the qubit placement problem. Simulation results on various benchmarks show 27% on average reduction in communication overhead between qubits compared to best results of previous work.

Routing, spectrum and core allocation in flexgrid SDM networks with multi-core fibers

Abstract: Space division multiplexing (SDM) over multi-core fiber (MCF) is advocated as a promising technology to overcome the capacity limit of the current single-core optical networks. However, employing the MCF for flexgrid networks necessitates the development of new concepts, such as routing, spectrum and core allocation (RSCA) for traffic demands. The introduction of MCF in the networks mitigates the spectrum continuity constraint of the routing and spectrum assignment (RSA) problem. In fact cores can be switched freely on different links during routing of the network traffic. Similarly, the route disjointness for demands with same allocated spectrum diminishes to core disjointness at the link level. On the other hand, some new issues such as the inter-core crosstalk should be taken into account while solving the RSCA problem. This paper formulates the RSCA network planning problem using the integer linear programming (ILP) formulation. The aim is to optimally minimize the maximum number of spectrum slices required on any core of MCF of a flexgrid SDM network. Furthermore, a scalable and effective heuristic is proposed for the same problem and its performance is compared with the optimal solution. The results show that the proposed algorithm is able to well approximate the optimal solution based on ILP model.