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Abstract. Solving a large batch of linear programs (LPs) with varying parameters is needed in stochastic programming and sensitivity analysis, among other modeling frameworks. Solving the LPs for all combinations [...]

Abstract. Intercontinental liner container shipping service connects trades between different continents in the global logistic system. This paper proposes a single intercontinental service design problem that aims to jointly determine [...]

Abstract. We present a new heuristic algorithm to approximately generate the nondominated frontier of bi-objective pure integer linear programs. The proposed algorithm employs a customized version of several existing algorithms [...]

Abstract. We study the parallel machine scheduling problem to minimize the sum of the weighted completion times of the jobs to be scheduled (problem Pm [parallel] [SIGMA] [w.sub.j][C.sub.j] in the [...]

Abstract. The convergence of a column generation algorithm can be improved in practice by using stabilization techniques. Smoothing and proximal methods based on penalizing the deviation from the incumbent dual [...]

Abstract. We study a capacitated multi-item lot sizing problem with nonidentical machines. For the problem, we propose several mathematical formulations and their peritem and per-period Dantzig-Wolfe decompositions, followed by exploring [...]

Abstract. We study a prize-collecting single-machine scheduling problem with hard deadlines, where the objective is to minimize the difference between the total tardiness and the total prize of the selected [...]

Abstract. Whereas much research in the area of optimization is directed toward developing algorithms for optimization of feasible models, the diagnosis of infeasible models has not received as much attention. [...]

Abstract. Operating rooms (ORs) play a substantial role in hospital profitability, and their optimal utilization is conducive to containing the cost of surgical service delivery, shortening surgical patient wait times, [...]

Abstract. We consider the inventory routing problem, in which a supplier has to replenish a set of customers by means of a limited fleet of capacitated vehicles over a discrete [...]

We present a long-term power generation expansion planning model that features a long planning horizon, an hourly time resolution, multiperiod investment and retirement decisions, transmission constraints, start-up restrictions, and short-term demand response. Demand response is the capability of power load to react to short-term changes in electricity prices. It plays an increasingly important role in today's electricity markets but has not been taken into consideration in long-term power generation expansion planning problems, which mostly treat demand as perfectly inelastic. Given mild assumptions for the underlying demand function, the resulting model is a large -scale, concave, linearly constrained maximization problem. We exploit the model structure by developing a new approach to generalized Benders decomposition (GBD). In particular, we present two algorithmic ideas: (1) solving the nonlinear Benders subproblem as a linear programming (LP) problem with the aid of dynamic linear overestimation, referred to as the LP-based method, and (2) directly calculating all necessary optimal primal and dual variable values, referred to as the calculation-based method. We consider three special cases of our expansion planning model and show that solving mathematical programming problems can become entirely obsolete in the calculation-based method. We demonstrate the efficiency of all proposed algorithms for the Texas power system, comparing our tailored decomposition methods to a monolithic approach and a state-of-the -art GBD implementation. Our LP-based method is up to 3,822 times faster than the monolithic approach and up to 55 times faster than the GBD. The calculation-based method dramatically improves the solution time, being an average factor of 20 faster than solving LPs and 107,074 times faster than the monolithic approach (for the largest solvable instance by a commercial solver). The overall largest instance we solve, containing more than 79 million variables and constraints, converges in less than one minute using the calculation-based method. The modeling language GAMS and its latest features were used to efficiently implement all algorithms. History: Accepted by Yinyu Ye, optimization. Supplemental Material: Data are available available at https://doi.org/10.1287/mnsc.2015.2420. Keywords: power generation planning * convex nonlinear programming * Benders decomposition * short-term demand response * Benders cut calculation * Texas power system, 1. Introduction Optimization problems in the power industry can be characterized by their time horizon. Power control problems typically span time horizons of seconds to minutes, short-term optimization problems tend [...]

Abstract. We introduce a framework for finding and analyzing all optimal solutions to a linear-programming-based model for cellular metabolism. The implementation of a pivoting-based method for generating alternate optimal reaction [...]

This paper deals with the problem of positive [L.sub.1]-gain filter design for positive Markovian jump systems with time-varying delay and incomplete transition rates. By implying an appropriate co-positive type Lyapunov function and free-connection weighting vectors, sufficient conditions for stochastic stability of the filtering error system are established. Then, the [L.sub.1]-gain performance is analyzed. Based on the obtained results, a positive full-order filter is designed to ensure that the corresponding filtering error system is positive and stochastically stable with [L.sub.1]-gain performance. All the conditions are derived in linear programming. Finally, the obtained theoretical results are demonstrated by a numerical example. Key words: positive Markovian jump systems, incomplete transition rates, stochastic stability, linear programming. Nous nous penchons ici sur la conception d'un filtre a gain [L.sub.1] positif pour des systemes a saut de Markov positif, avec delai variant dans le temps et taux de transition incomplete. En introduisant des fonctions appropriees de Lyapunov de type copositif et des vecteurs de poids libres de connexions, nous sommes en mesure d'etablir les conditions suffisantes pour la stabilite stochastique du systeme de filtration d'erreurs. Nous analysons ensuite la performance degain [L.sub.1]. Sur la base des resultats obtenus, nous proposons le design d'un filtre d'ordre infini positif pour garantir que le systeme de filtration d'erreurs correspondant est positif et stochastiquement stable avec gain [L.sub.1]. Toutes les conditions sont obtenues par programmation lineaire. Finalement, les resultats theoriques obtenus sont illustres par un exemple en simulation numerique. [Traduit par la Redaction] Mots-cles: systeme a saut de Markov positif, taux de transition incomplete, stabilite stochastique, programmation lineaire., 1. Introduction A positive system is one in which the state and output are nonnegative whenever the initial condition and input are nonnegative [1, 2]. Positive systems have numerous applications [...]

We describe an iterative refinement procedure for computing extended-precision or exact solutions to linear programming (LP) problems. Arbitrarily precise solutions can be computed by solving a sequence of closely related [...]

A new mixed-integer linear programming (MILP) formulation for nonpreemptive single machine scheduling problems is presented. The model is a generalisation of the classical time indexed (TI) model to one in [...]

In this article, we propose a general framework for an algorithm derived from the primal simplex that guarantees a strict improvement in the objective after each iteration. Our approach relies [...]

LU and Cholesky factorizations are computational tools for efficiently solving linear systems that play a central role in solving linear programs and several other classes of mathematical programs. In many [...]

Recent work by Han and Van Roy [Han J, Van Roy B (2011) Control of diffusions via linear programming. Infanger G, ed. Stochastic Programming: The State of the Art, in [...]

In this paper, a cutting-plane neighborhood structure is proposed for the fixed-charge capacitated multicommodity network design (CMND) problem. In the proposed structure, different strategies are used to select an open [...]

We present two decomposition algorithms for single product deep-sea maritime inventory routing problems (MIRPs) that possess a core substructure common in many real-world applications. The problem involves routing vessels, each [...]

Linear active-power-only power flow approximations are pervasive in the planning and control of power systems. However, AC power systems are governed by a system of nonlinear nonconvex power flow equations. [...]

We consider a class of linear programs involving a set of covering constraints of which at most k are allowed to be violated. We show that this covering linear program [...]

Replication is a widely-used technique in information retrieval and database systems for providing fault tolerance and reducing parallelization and processing costs. Combinatorial models based on hypergraph partitioning are proposed for [...]

Models incorporating more realistic models of customer behavior, as customers choosing from an offer set, have recently become popular in assortment optimization and revenue management. The dynamic program for these [...]

We discuss the method recently proposed by S. Chubanov [Chubanov S (2012a) A strongly polynomial algorithm for linear systems having a binary solution. Math. Programming 134(3)533-570] for the linear feasibility problem. We present new, concise proofs and geometric interpretations of some of his results. From our ideas we derive the first strongly polynomial time algorithm based on relaxation method techniques for special classes of linear feasibility problems. Under certain conditions, these results provide new proofs of classical results obtained by Tardos for combinatorial linear programs. The paper ends with some experimental investigations. Keywords: linear programming; relaxation methods; strongly polynomial time algorithms, 1. Introduction In their now classical papers, Agmon (1954) and Motzkin and Schoenberg (1954) introduced the so called relaxation method to determine the feasibility of a system of linear inequalities [...]

We explore the idea of obtaining bounds on the value of an optimization problem from a discrete relaxation based on binary decision diagrams (BDDs). We show how to construct a [...]

We present a semidefinite programming (SDP) approach for the problem of ordering vertices of a layered graph such that the edges of the graph are drawn as vertical as possible. [...]

Split cuts constitute a class of cutting planes that has been successfully employed by the majority of branch-and-cut solvers for mixed-integer linear programs. Given a basis of the linear programming [...]

Motivated by addressing probabilistic 0-1 programs we study the conic quadratic knapsack polytope with generalized upper bound (CUB) constraints. In particular, we investigate separating and extending CUB cover inequalities. We [...]

The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce [...]

With the emergence of thread-level parallelism as the primary means for continued performance improvement, the programmability issue has reemerged as an obstacle to the use of architectural advances. We argue that evolving legacy libraries for dense and banded linear algebra is not a viable solution due to constraints imposed by early design decisions. We propose a philosophy of abstraction and separation of concerns that provides a promising solution in this problem domain. The first abstraction, FLASH, allows algorithms to express computation with matrices consisting of contiguous blocks, facilitating algorithms-by-blocks. Operand descriptions are registered for a particular operation a priori by the library implementor. A runtime system, SuperMatrix, uses this information to identify data dependencies between suboperations, allowing them to be scheduled to threads out-of-order and executed in parallel. But not all classical algorithms in linear algebra lend themselves to conversion to algorithms-by-blocks. We show how our recently proposed LU factorization with incremental pivoting and a closely related algorithm-by-blocks for the QR factorization, both originally designed for out-of-core computation, overcome this difficulty. Anecdotal evidence regarding the development of routines with a core functionality demonstrates how the methodology supports high productivity while experimental results suggest that high performance is abundantly achievable. Categories and Subject Descriptors: G.4 [Mathematical Software]: Efficiency General Terms: Algorithms, Performance Additional Key Words and Phrases: Linear algebra, libraries, high-performance, multithreaded architectures DOI 10.1145/1527286.1527288

We design and implement an intensity-modulated radiation therapy plan generation technology that effectively and efficiently optimizes beam geometry as well as beam intensities. Our approach is based on an existing [...]

At IBM's 300 mm semiconductor plant in East Fishkill, New York, we developed and implemented the Enterprise Production Planning and Optimization System (EPOS), an advanced queueing network model for capacity [...]

ABSTRACT In this study, a radial-interval linear programming (RILP) approach was developed for supporting waste management under uncertainty. RILP improved interval-parameter linear programming and its extensions in terms of input [...]

Passenger airline delays have received increasing attention over the past several years as air space congestion, severe weather, mechanical problems, and other sources cause substantial disruptions to a planned flight schedule. Adding to this challenge is the fact that each flight delay can propagate to disrupt subsequent downstream flights that await the delayed flight's aircraft and crew. This potential for delays to propagate is exacerbated by a fundamental conflict: slack in the planned schedule is often viewed as undesirable, as it implies missed opportunities to utilize costly perishable resources, whereas slack is critical in operations as a means for absorbing disruption. This article shows how delay propagation can be reduced by redistributing existing slack in the planning process, making minor modifications to the flight schedule while leaving the original fleeting and crew scheduling decisions unchanged. Computational results based on data from a major U.S. carrier are presented that show that significant improvements in operational performance can be achieved without increasing planned costs. Keywords: Airline planning, robust planning, linear programming, delay propagation, 1. Introduction Airline plans are made up of several costly and constrained resources such as aircraft and crews. These resources link flights across the network, with each resource flowing from [...]

The civil and environmental decision-making processes are plagued with uncertain, vague, and incomplete information. Interval linear programming (ILP) is a widely applied mathematical programming method in assisting civil and environmental decision making under uncertainty. However, the existing ILP decision approach is found to be ineffective in generating operational schemes for practical decision support due to a lack of linkage between decision risk and system return. In addition, the interpretation of the ILP solutions represented as the lower and upper bounds of decision variables can cause problems of infeasibility and nonoptimality in the resulted implementation schemes. This study proposed a risk explicit ILP (REILP) approach to overcome the limitations of existing ILP approaches. The REILP explicitly reflects the tradeoffs between risk and system return for a decision-making problem under an interval-type uncertainty environment. A risk function was defined to enable finding solutions which maximize system return while minimizing system risk, hence leading to crisp solutions that are feasible and optimal for practical decision making. A numerical experiment on land-use decision making under total maximum daily load was conducted to illustrate the REILP approach. The model results show that the REILP approach is able to efficiently explore the interval uncertainty space and generate an optimal decision front that directly reflects the tradeoff between decision risks and system return, allowing decision makers to make effective decision based on the risk-reward information generated by the REILP modeling analysis. DOI: 10.1061/(ASCE)CP.1943-5487.0000037 CE Database subject headings: Computer programming; Risk management; Decision making; Environmental engineering. Author keywords: Interval linear programming (ILP); Risk explicit ILP (REILP); Decision making; Risk function; Aspiration level; Normalized risk level (NRL); Civil engineering.

We propose a new separation scheme for micrometer-sized particles combining acoustic forces and gravitational field in split-flaw lateral-transport thin (SPLITT)-like fractionation channels. Acoustic forces are generated by ultrasonic standing waves set up in the channel thickness. We report on the separation of latex particles of two different sizes in a preliminary experiment using this proposed hydrodynamic acoustic sorter, HAS. Total binary separation of 5 and 10 [micro]m diameter particles has been achieved. Numerical simulations of trajectories of particles flowing through a step-SPLITT under the conditions which combine acoustic standing waves and gravity show a very good agreement with the experiment. Calculations in order to compare separations obtained by the acoustic programming s-SPLITT fractionation and the conventional SPLITT fractionation show that the improvement in separation time is around 1 order of magnitude and could still be improved; this is the major finding of this work. This separation technique can be extended to biomimetic particles and blood cells. 10.1021/ac902357b

Decomposition-based strategies, such as analytical target cascading (ATC), are often employed in design optimization of complex systems. Achieving convergence and computational efficiency in the coordination strategy that solves the partitioned problem is a key challenge. A new convergent strategy is proposed for ATC that coordinates interactions among subproblems using sequential linearizations. The linearity of subproblems is maintained using infinity norms to measure deviations between targets and responses. A subproblem suspension strategy is used to suspend temporarily inclusion of subproblems that do not need significant redesign, based on trust region and target value step size. An individual subproblem trust region method is introduced for faster convergence. The proposed strategy is intended for use in design optimization problems where sequential linearizations are typically effective, such as problems with extensive monotonicities, a large number of constraints relative to variables, and propagation of probabilities with normal distributions. Experiments with test problems show that, relative to standard ATC coordination, the number of subproblem evaluations is reduced considerably while the solution accuracy depends on the degree of monotonicity and nonlinearity. [DOI: 10.1115/1.4000758]

The allocation of water in a multicountry river system necessarily involves conflicting objectives, where increasing water benefits for one country entails losses for other countries. This paper presents the formulation and application of a multiobjective linear programming model, where each objective represents the benefits for a country from using water for agriculture, urban consumption, and energy production, net of conveyance costs. This model is applied to the Euphrates and Tigris River basin and its three riparian countries--Turkey, Syria, and Iraq. The model is used to delineate the set of nondominated solutions (Pareto frontier), and is extended to include political factors and distributional constraints, leading to an allocation of basin water and resulting benefits. CE Database subject headings: Water resources; Economic factors; Computer programming; Water management. Author keywords: Water resources allocation; Economic benefits; Multiobjective programming; Pareto frontier. DOI: 10.1061/(ASCE)0733-9496(2010)136:1(95)

Compressed sensing aims to undersample certain high-dimensional signals yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a known basis. Currently, the best known sparsity--undersampling tradeoff is achieved when reconstructing by convex optimization, which is expensive in important large-scale applications. Fast iterative thresholding algorithms have been intensively studied as alternatives to convex optimization for large-scale problems. Unfortunately known fast algorithms offer substantially worse sparsity--undersampling tradeoffs than convex optimization. We introduce a simple costless modification to iterative thresholding making the sparsity--undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures. The new iterative-thresholding algorithms are inspired by belief propagation in graphical models. Our empirical measurements of the sparsity--undersampling tradeoff for the new algorithms agree with theoretical calculations. We show that a state evolution formalism correctly derives the true sparsity--undersampling tradeoff. There is a surprising agreement between earlier calculations based on random convex polytopes and this apparently very different theoretical formalism. combinatorial geometry | phase transitions | linear programming | iterative thresholding algorithms | state evolution www.pnas.org/cgi/doi/10.1073/pnas.0909892106