The n-queens puzzle is a well-known combinatorial problem that requires to place n queens on an n x n chessboard so that no two queens can attack each other. Since the 19th century, this problem was studied by many ma...
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ISBN:
(数字)9783319930312
ISBN:
(纸本)9783319930312;9783319930305
The n-queens puzzle is a well-known combinatorial problem that requires to place n queens on an n x n chessboard so that no two queens can attack each other. Since the 19th century, this problem was studied by many mathematicians and computer scientists. While finding any solution to the n-queens puzzle is rather straightforward, it is very challenging to find the lexicographically first (or smallest) feasible solution. Solutions for this type are known in the literature for n <= 55, while for some larger chessboards only partial solutions are known. The present paper was motivated by the question of whether integer Linear programming (ILP) can be used to compute solutions for some open instances. We describe alternative ILP-based solution approaches, and show that they are indeed able to compute (sometimes in unexpectedly-short computing times) many new lexicographically optimal solutions for n ranging from 56 to 115.
Managing the inherent variability of solar generation is a critical challenge for utility grid operators, particularly as the distribution grid-integrated solar generation is making fast inroads in power systems. This...
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ISBN:
(纸本)9781538671382
Managing the inherent variability of solar generation is a critical challenge for utility grid operators, particularly as the distribution grid-integrated solar generation is making fast inroads in power systems. This paper proposes to leverage Battery Swapping Station (BSS) as an energy storage for mitigating solar photovoltaic (PV) output fluctuations. Using mixed-integer programming, a model for the BSS optimal scheduling is proposed to capture solar generation variability. The proposed model aims at minimizing the BSS total operation cost, which represents the accumulated cost of exchanging power with the utility grid. The model is subject to four sets of constraints associated with the utility grid, the BSS system, individual batteries, and solar variability. Numerical simulations on a test BSS demonstrate the effectiveness of the proposed model and show its viability in helping the utility grids host a higher penetration of solar generation.
This paper addresses the identification of Linear Parameter-Varying (LPV) models through regularized moving-horizon Piece Wise Affine (PWA) regression. Specifically, the scheduling-variable space is partitioned into p...
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This paper addresses the identification of Linear Parameter-Varying (LPV) models through regularized moving-horizon Piece Wise Affine (PWA) regression. Specifically, the scheduling-variable space is partitioned into polyhedral regions, where each region is assigned to a PWA function describing the local affine dependence of the LPV model coefficients on the scheduling variable. The regression approach consists of two stages. In the first stage, the data samples are processed iteratively, and a mixed-integer Quadratic programming (MIQP) problem is solved to cluster the scheduling variable observations and simultaneously fit the model parameters to the training data, within a relatively short moving-horizon window of the past. At the second stage, the polyhedral partition of the scheduling-variable space is computed by separating the estimated clusters through linear multi-category discrimination. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G=(V,E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a mini...
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This paper aims at developing a new tool to support home health care structures in preparing their risk management plan. Evacuation or adaptive home support is the major decision that managers can take in order to sec...
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This paper aims at developing a new tool to support home health care structures in preparing their risk management plan. Evacuation or adaptive home support is the major decision that managers can take in order to secure their patients. Using risk-based clustering (partitioning) and risk assessment of each patient situation, the proposed tool provides an evacuation plan for the critical patients to be evacuated and a home-support plan for the low-level risk patients that will be kept at home. The model combines a dynamic partitioning model based on individual risk evolution and geographical proximity between patients, and an assignment model considering fixed and variable costs. The experiments are performed with the commercial solver CPLEX and the computing time is acceptable for real size instances. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
High school timetabling problems consist in assigning meetings between classes and teachers, with the goal of minimizing the violation of specific soft requisites. This category of problems has been extensively studie...
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High school timetabling problems consist in assigning meetings between classes and teachers, with the goal of minimizing the violation of specific soft requisites. This category of problems has been extensively studied since the 1950s, mostly via mixed-integer programming and metaheuristic techniques. However, the computation of optimal or near-optimal solutions using mixed-integer programs or metaheuristics is still a challenge for most practical problems. In this thesis, we investigate new mixed-integer programming formulations, column generation approaches and parallel metaheuristic based algorithms to compute lower bounds and solutions for high school timetabling problems. Extensive computational experiments conducted with real-world instances demonstrate that our best formulations are competitive with best-known formulations, while our parallel algorithms present superior performance than the state-of-the-art methods.
The reduction of greenhouse gas emissions is a major issue in worldwide govern- mental policy making. The transportation industry is responsible for a considerable part of greenhouse gas emissions. Electrification of ...
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The reduction of greenhouse gas emissions is a major issue in worldwide govern- mental policy making. The transportation industry is responsible for a considerable part of greenhouse gas emissions. Electrification of the sector is a viable approach to reduce these emissions, as even electric cars powered by coal-generated electricity could cut emissions of the sector in half. In public transport electric transportation is currently mainly implemented with visually polluting catenary-powered trams or buses. Recent innovations in battery technology allow for public transport buses to be battery-driven and recharged at distinguished stops, rather than powered by catenary wires. Various trial projects have shown this technology is feasible for pub- lic transport operations and the contribution to gas emission control in urban areas is significant. Creating a network for an electrical catenary-free public transport system is very costly due to their battery usage and installing high-tech charging stations. Cost optimization is therefore key for the promotion of battery-driven buses. In recent years, several papers have addressed designing such networks from technological as well as operational aspects. The operational decisions have a major impact on battery degradation in such systems. In order to achieve accurate cost optimization the maximization of battery life is crucial. In this paper, we introduce a linearized battery degradation model incorporated in an MILP for the design of such electrical public transport networks. Two commonly used approaches are applied for design- ing a Multicriteria Optimization Problem, weighted sum and ε-constraint. A case study with semi-real data is conducted to compare the impact of incorpo- rating battery aging on the costs and battery life with the results of a model without battery lifetime optimization.
Under the envisioned smart city paradigm, there is an increasing demand for the coordinated operation of our infrastructure networks. In this context, this thesis puts forth a comprehen- sive toolbox for the optimizat...
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Under the envisioned smart city paradigm, there is an increasing demand for the coordinated operation of our infrastructure networks. In this context, this thesis puts forth a comprehen- sive toolbox for the optimization of electric power and water distribution networks. On the analytical front, the toolbox consists of novel mixed-integer (non)-linear program (MINLP) formulations; convex relaxations with optimality guarantees; and the powerful technique of McCormick linearization. On the application side, the developed tools support the operation of each of the infrastructure networks independently, but also towards their joint operation. Starting with water distribution networks, the main difficulty in solving any (optimal-) water flow problem stems from a piecewise quadratic pressure drop law. To efficiently handle these constraints, we have first formulated a novel MINLP, and then proposed a relaxation of the pressure drop constraints to yield a mixed-integer second-order cone program. Further, a novel penalty term is appended to the cost that guarantees optimality and exactness under pre-defined network conditions. This contribution can be used to solve the WF problem; the OWF task of minimizing the pumping cost satisfying operational constraints; and the task of scheduling the operation of tanks to maximize the water service time in an area experienc- ing electric power outage. Regarding electric power systems, a novel MILP formulation for distribution restoration using binary indicator vectors on graph properties alongside exact McCormick linearization is proposed. This can be used to minimize the restoration time of an electric system under critical operational constraints, and to enable a coordinated response with the water utilities during outages.
This thesis is composed of two essays that investigate whole farm planning and crop marketing in western Kentucky. In the first essay, contracting decisions between food corn producers and a mill are analyzed to obser...
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This thesis is composed of two essays that investigate whole farm planning and crop marketing in western Kentucky. In the first essay, contracting decisions between food corn producers and a mill are analyzed to observe factors affecting the bushel amount farmers contract. Unbalanced panel data containing seven years' worth of pricing and contract information are used with a fixed-effects model to generate parameter estimates and quantify their effect on bushels contracted. It was found that contract attributes, market condition, and relationship-specific assets had a significant effect on producers' food corn contracting decisions. The second essay utilizes mixed-integer programming to optimize resource allocation and marketing strategy for a hypothetical farm. Post-optimal analysis is performed to determine non-binding capacities for drying and storage equipment. The model is re-run with these non-binding capacities to observe changes in net returns as well as planting, harvesting, and marketing strategies. New equipment and associated costs are identified, and the change in net returns from the base case is used as net cash flow in a net present value investment analysis. Results of the investment analysis indicate increasing drying and storage capacity is a wise investment given the scenario modeled.
Examination timetabling problem (ETP) is one of the hardest administrative tasks that has to be undertaken at each semester in all faculties. Although the major structure of the problem remains intact, requirements ma...
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Examination timetabling problem (ETP) is one of the hardest administrative tasks that has to be undertaken at each semester in all faculties. Although the major structure of the problem remains intact, requirements may change from faculty to faculty causing major changes in the solution procedures. The number of academic staff and the level of infrastructures of newly established universities cannot keep up with the increasing number of departments and students. This scarcity brings several additional constraints to the ETP. In this study, we propose a two stage solution procedure for the ETP of such universities. We apply our solution method to a real problem. We show that better feasible solutions can be found in shorter computation times compared to commercial softwares. Moreover we show that the total examination period length can be reduced from seven days to six days with the proposed method.
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