We introduce the Stochastic Maintenance Fleet Transportation Problem for Offshore wind farms (SMFTPO), in which a maintenance provider determines an optimal, medium-term planning for maintaining multiple wind farms wh...
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We introduce the Stochastic Maintenance Fleet Transportation Problem for Offshore wind farms (SMFTPO), in which a maintenance provider determines an optimal, medium-term planning for maintaining multiple wind farms while controlling for uncertainty in the maintenance tasks and weather conditions. Since the maintenance provider is typically not the owner of a wind farm, it needs to adhere minimum service requirements that specify the required service. We consider three of such settings: (1) perform all maintenance tasks, (2) allow for a fraction of unscheduled tasks, and (3) incentivize to perform maintenance rather quickly. We provide a two-stage stochastic mixed integer programming model for the three SMFTPO settings, and solve it by means of Sample Average Approximation. In addition, we provide an overview of the, what we discovered, non-aligned modeling assumptions in the literature regarding operational decisions. By providing a series of special cases of the second-stage problem resembling the different modeling assumptions, we aim to establish a common consensus regarding the key modeling decisions to be taken in maintenance planning problems for offshore wind farms. We provide newly constructed, and publicly available, benchmark sets. We extensively compare the different SMFTPO settings and its special cases on those benchmark sets, and we show that the special case reformulations are very effective for solving the second-stage problems. In addition, we find that for particular cases, established modeling techniques result in overestimations and increased running times.
A reconfigurable manufacturing system can evolve its configuration to offer exactly the capacity and functionality needed for every demand period. For the reconfigurable manufacturing system with multi-part flow-line ...
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A reconfigurable manufacturing system can evolve its configuration to offer exactly the capacity and functionality needed for every demand period. For the reconfigurable manufacturing system with multi-part flow-line configuration simultaneously producing multiple parts within the same family, the production cost and the delivery time are closely related to its configuration and corresponding scheduling for certain demand period. Although studies on multi-part flow-line configuration design are abundant, studies on concurrent optimization of configuration design and scheduling for reconfigurable manufacturing system are scarce. First, a generic mixedinteger nonlinear programming model for concurrent configuration design and scheduling is established to relax the limitation of the existing model, and then a mixedinteger linear programming model is derived. The decisions of the two generalized models are to decide the amount of stations, the amount of identical machines and machines' configuration for every station, and assign parts to machines along the multi-part flow line together with sequencing assigned parts for each machine. Based on the mixedinteger linear programming model, an exact epsilon-constraint method is developed to obtain the Pareto optimal solutions with tradeoffs between cost and tardiness. The validation of two models and the epsilon-constraint method is verified against two cases adapted from the literature.
Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models, only deal with fitting a continuous function. In this paper, we investigate t...
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Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models, only deal with fitting a continuous function. In this paper, we investigate the problem of fitting a discontinuous piecewise affine function to a given function defined on an arbitrary subset of an integer lattice, where no restriction on the partition of the domain is enforced (i.e., its geometric shape can be nonconvex). This is useful for segmentation and denoising when the given function corresponds to a mapping from pixels of a bitmap image to their color depth values. We propose a novel mixedinteger Program (MIP) formulation for the piecewise affine fitting problem, where binary edge variables determine the boundary between two partitions of the function domain. To obtain a consistent partitioning (e.g., image segmentation), we include multicut constraints in the formulation. The resulting problem is NP-hard, and two techniques are introduced to improve the computation. One is to adopt a cutting plane method to add the exponentially many multicut inequalities on-the-fly. The other is to provide initial feasible solutions using a tailored heuristic algorithm. We show that the MIP formulation on grid graphs is approximate, while on king's graph, it is exact under certain circumstances. We conduct initial experiments on synthetic images as well as real depth images, and discuss the advantages and drawbacks of the two models.
A positive relationship between treatment volume and outcome quality has been demonstrated in the literature and is thus evident for a variety of procedures. Consequently, policy makers have tried to translate this so...
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A positive relationship between treatment volume and outcome quality has been demonstrated in the literature and is thus evident for a variety of procedures. Consequently, policy makers have tried to translate this so-called volume-outcome relationship into minimum volume regulation (MVR) to increase the quality of care-yet with limited success. Until today, the effect of strict MVR application remains unclear as outcome quality gains cannot be estimated adequately and restrictions to application such as patient travel time and utilization of remaining hospital capacity are not considered sufficiently. Accordingly, when defining MVR, its effectiveness cannot be assessed. Thus, we developed a mixed integer programming model to define minimum volume thresholds balancing utility in terms of outcome quality gain and feasibility in terms of restricted patient travel time and utilization of hospital capacity. We applied our model to the German hospital sector and to four surgical procedures. Results showed that effective MVR needs a minimum volume threshold of 125 treatments for cholecystectomy, of 45 and 25 treatments for colon and rectum resection, respectively, of 32 treatments for radical prostatectomy and of 60 treatments for total knee arthroplasty. Depending on procedure type and incidence as well as the procedure's complication rate, outcome quality gain ranged between 287 (radical prostatectomy) and 977 (colon resection) avoidable complications (11.7% and 11.9% of all complications). Ultimately, policy makers can use our model to leverage MVR's intended benefit: concentrating treatment delivery to improve the quality of care.
Presolving is a critical component in modern mixed integer programming (MIP) solvers. In this paper, we propose a new and effective presolving method named inequation-based variable aggregation and develop a combined ...
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Presolving is a critical component in modern mixed integer programming (MIP) solvers. In this paper, we propose a new and effective presolving method named inequation-based variable aggregation and develop a combined variable aggregation (VA) technique with the advantage of significantly reducing the scales of MIP problems. This technique is particularly effective for problems involving semi -continuous variables, such as unit commitment problems. Extensive numerical experiments demonstrate that the combined VA technique can substantially accelerate the solution process of MIP problems. (c) 2024 Elsevier B.V. All rights reserved.
Two essential ingredients of modern mixed-integerprogramming solvers are diving heuristics, which simulate a partial depth-first search in a branch-and-bound tree, and conflict analysis, which learns valid constraint...
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Two essential ingredients of modern mixed-integerprogramming solvers are diving heuristics, which simulate a partial depth-first search in a branch-and-bound tree, and conflict analysis, which learns valid constraints from infeasible subproblems. So far, these techniques have mostly been studied independently: primal heuristics for finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. In this paper, we pose the question of whether and how the orthogonal goals of proving infeasibility and generating improving solutions can be pursued in a combined manner such that a state-of-the-art solver can benefit. To do so, we integrate both concepts in two different ways. First, we develop a diving heuristic that simultaneously targets the generation of valid conflict constraints from the Farkas dual and the generation of improving solutions. We show that, in the primal, this is equivalent to the optimistic strategy of diving toward the best bound with respect to the objective function. Second, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classic coefficient diving. In a detailed computational study, both methods are evaluated on the basis of an implementation in the source-open-solver SCIP. The experimental results underline the potential of combining both diving heuristics and conflict analysis. Summary of Contribution. This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed-integer linear programs. It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be combined successfully with diving heuristics that aim at finding primal solutions. For two newly designed diving heuristics, this paper features a thoroughly computational study regarding their impact on the
This study proposes a model predictive control framework using a mixed integer programming for the deep neural network (DNN) model with rectified linear unit (ReLU). The accurate DNN model with ReLU using the past inp...
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This study proposes a model predictive control framework using a mixed integer programming for the deep neural network (DNN) model with rectified linear unit (ReLU). The accurate DNN model with ReLU using the past input time series for the diesel engine is constructed. In this method, the ReLU is represented by inequalities including 0-1 variables (binaries). The model predictive control problem is formulated as a mixed integer programming problem and is applied to the control problem of the diesel engine. Dynamical DNN model of a diesel engine is constructed using the experimental data. This model can represent complicate engine phenomena such as strong nonlinearity and delay. Simulation results of the worldwide harmonized transient cycle (WHTC) verify the effectiveness of the proposed method. The difficulties of non-linearity, delay, and interference in the control problem of the diesel engine are solved by using a systematic model predictive control of the DNN model.
Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate fac...
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Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be finite sets. In this work, we study the set-covering location problem when both candidate locations and demand points are continuous on a network. This variant has received little attention, and the scarce existing approaches have focused on particular cases, such as tree networks and integer covering radius. Here we study the general problem and present a mixedinteger Linear programming formulation (MILP) for networks with edge lengths no greater than the covering radius. The model does not lose generality, as any edge not satisfying this condition can be partitioned into subedges of appropriate lengths without changing the problem. We propose a preprocessing algorithm to reduce the size of the MILP, and devise tight big-M constants and valid inequalities to strengthen our formulations. Moreover, a second MILP is proposed, which admits edge lengths greater than the covering radius. As opposed to existing formulations of the problem (including the first MILP proposed herein), the number of variables and constraints of this second model does not depend on the lengths of the network's edges. This second model represents a scalable approach that particularly suits real-world networks, whose edges are usually greater than the covering radius. Our computational experiments show the strengths and limitations of our exact approach to both real-world and random networks. Our formulations are also tested against an existing exact method. & COPY;2023 Elsevier Ltd. All rights reserved.
作者：
Van Engeland, JensBelien, JeroenKatholieke Univ Leuven
Ctr Econ & Corp Sustainabil Fac Econ & Business Campus BrusselsWarmoesberg 26 B-1000 Brussels Belgium Katholieke Univ Leuven
Ctr Informat Management Modeling & Simulat Fac Econ & Business Campus BrusselsWarmoesberg 26 B-1000 Brussels Belgium Katholieke Univ Leuven
Res Ctr Operat Management Fac Econ & Business Campus LeuvenNaamsestr 69 B-3000 Leuven Belgium
Environmental considerations and corresponding legislation cause a shift from waste management to materials management, requiring efficient collection of these flows. This paper develops a model for building tactical ...
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Environmental considerations and corresponding legislation cause a shift from waste management to materials management, requiring efficient collection of these flows. This paper develops a model for building tactical waste collection schemes in which a set of capacitated vehicles visits a set of customers during a given time period. Each vehicle must visit the disposal facility to discharge the waste after each customer visit. This is motivated by the fact that the waste of each customer has to be weighed at the disposal facility. The goal is to find a set of routes for each vehicle that satisfy both the demand and the frequency constraints and minimize the total cost. Since a state-of-the-art solver could not find a solution with a reasonable gap within an acceptable time limit, a column generation and a mixed integer programming-based heuristic are proposed. While the mixed integer programming-based heuristic outperforms the column generation heuristic in terms of solution quality, the lower bound provided by column generation allows to prove the small optimality gaps of the solutions obtained. Moreover, by applying both heuristics on instances derived from real-life data, they proved to be capable of finding good quality solutions in small computation times.
Correspondence analysis (CA) is a dimension reduction technique for categorical data in a two-way contingency table. The low-dimensional CA solution optimally depicts the relationship between the categorical variables...
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Correspondence analysis (CA) is a dimension reduction technique for categorical data in a two-way contingency table. The low-dimensional CA solution optimally depicts the relationship between the categorical variables. We consider the inverse correspondence analysis (ICA) problem, where we use the low-dimensional representation in order to retrieve the original data table. We propose a mixed integer programming formulation for the ICA problem based on transition formulas, which link the row and column coordinates in a CA solution. We show that our formulation has better theoretical characteristics than the existing formulation in the literature and is able to model a generalised ICA problem, which requires less input. In addition, we introduce an iterative method, which uses the fit of individual points in the low-dimensional CA solution. By incorporating statistical information on the quality of CA solutions into our methodology, we are able to retrieve the original data for larger ICA instances.
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