We introduce the board packing problem (BoPP). In this problem we are given a rectangular board with a given number of rows and columns. Each position of the board has an integer value representing a gain, or revenue,...
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We introduce the board packing problem (BoPP). In this problem we are given a rectangular board with a given number of rows and columns. Each position of the board has an integer value representing a gain, or revenue, that is obtained if the position is covered. A set of rectangles is also given, each with a given size and cost. The objective is to purchase some rectangles to place on the board so as to maximize the profit, which is the sum of the gain values of the covered cells minus the total cost of purchased rectangles. This problem subsumes several natural optimization problems that arise in practice. A mixedintegerprogramming model for the BoPP problem is provided, along with a proof that BoPP is NP -hard by reduction from the satisfiability problem. An evolutionary algorithm is also developed that can solve large instances of BoPP. We introduce benchmark instances and make extensive computer examinations.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )
Attribute reduction is a difficult topic in rough set theory and knowledge granularity reduction is one of the important types of reduction. However, up to now, its reduction algorithm based on a discernibility matrix...
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Attribute reduction is a difficult topic in rough set theory and knowledge granularity reduction is one of the important types of reduction. However, up to now, its reduction algorithm based on a discernibility matrix has not been given. In this paper, we show that knowledge granularity reduction is equivalent to both positive region reduction and X-absolute reduction, and derive its corresponding algorithm based on a discernibility matrix to fill the gap. Particularly, knowledge granularity reduction is the usual positive region reduction for consistent decision tables. Finally, we provide a simple knowledge granularity reduction algorithm for finding a reduct with the help of binary integer programming, and consider six UCI datasets to illustrate our algorithms.
Phasor measurement unit (PMU) is deemed a pivotal tool in wide-area monitoring, protection, and control of power systems. The optimal allocation of PMUs has recently received more attention. In this paper, binary Inte...
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Phasor measurement unit (PMU) is deemed a pivotal tool in wide-area monitoring, protection, and control of power systems. The optimal allocation of PMUs has recently received more attention. In this paper, binary integer programming (BIP) technique is proposed to optimally allocate PMUs in the power network keeping complete observability of the network and reducing the total numbers of PMUs. The proposed technique is tested and examined through different systems to investigate the effectiveness of BIP. Additionally, the BIP is compared with different techniques to verify its superiority and reveal the main contributions of BIP-based algorithms using different IEEE test systems. The proposed method shows an efficient technique while placing PMUs through direct, simple, and linear formulas regardless of the network scale or configuration;transmission, or distribution systems. Moreover, the whole process consumes the least time slots to hit the intended goal because of the problem formulating criteria. (C) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
This paper tackles management zone delineation and crop planning problems in an integrated precision agriculture framework. The zoning problem defines relatively homogeneous management zones regarding their soil prope...
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This paper tackles management zone delineation and crop planning problems in an integrated precision agriculture framework. The zoning problem defines relatively homogeneous management zones regarding their soil properties, and for which specific rates of agricultural inputs are necessary. From a sustainable point of view, the crop planning problem considers cropping of species from different botanic families in adjacent zones at the same time. With this in mind, we propose a novel linear binaryinteger program for an integrated zoning and crop planning problem with adjacency constraints. In this model, we maximize the incomes of the crop plan subject to zoning constraints and adjacency constraints on crop families. The proposed model has a column-based formulation, and as such, we develop a decomposition-based heuristic which make use of the column generation method with column-dependent rows. The decomposition strategy involves a master problem that deals with ensuring homogeneity of the selected management zones within the field partition and ensuring that the crop plan meets adjacency policies. On the other hand, the pricing problem generates rectangular management zones whose incorporation improves the objective value of the master problem. The algorithm is implemented in JuMP, a modeling language for mathematical optimization embedded in Julia. Results from a set of instances show the relevance of the decomposition-based heuristic.
Canada produces most of its electricity using renewables. However, in remote communities that are not con-nected to Southern Canada's main grid, the quasi-totality of microgrids rely on fossil fuels to ensure elec...
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Canada produces most of its electricity using renewables. However, in remote communities that are not con-nected to Southern Canada's main grid, the quasi-totality of microgrids rely on fossil fuels to ensure electricity supply. How much would it cost to decarbonize all of these microgrids? This paper uses a cost-based approach paired with a binaryinteger optimization model to find the least costly decarbonization solution for each off-grid settlement from now until 2050. By using wind speed and solar irradiance data together with future generation and storage cost estimates, our model determines whether solar or wind is more appropriate for a settlement and at which period it is best to undergo a transition from fossil fuel generation to renewables. Our results show that the cost of decarbonizing Canada's remote microgrids is not prohibitive and which technology and imple-mentation period are cheapest for each settlement. We find that in 2020 wind turbines would be the cheapest option for most settlements, whereas in 2050 solar panels would be the cheapest option for most settlements. Settlements that currently use diesel of heavy fuel to produce electricity should consider undergoing decar-bonization as soon as possible, while those that use natural gas could wait until production and storage tech-nologies become cheaper. Larger settlements and fly-in communities could also be prioritized.
In this paper, we propose a novel joint approach to solve the regeneration placement, routing, modulation level, and spectrum assignment (RP-RMLSA) problem using a binaryinteger program (BIP) model. Using a mock and ...
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ISBN:
(纸本)9789897584855
In this paper, we propose a novel joint approach to solve the regeneration placement, routing, modulation level, and spectrum assignment (RP-RMLSA) problem using a binaryinteger program (BIP) model. Using a mock and real-world network topology, we conduct extensive numerical experiments testing the proposed optimization model's performance and analyzing the characteristics of the solutions found. Our results show that considering only an optimal solution occurs when signals in need of regeneration are concentrated in one regeneration node when considering the regeneration devices' capital and operational expenditure.
A safe supply of blood for transfusion is a critical component of the healthcare system in all countries. Most health systems manage the risk of transfusion-transmissible infections (TTIs) through a portfolio of blood...
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A safe supply of blood for transfusion is a critical component of the healthcare system in all countries. Most health systems manage the risk of transfusion-transmissible infections (TTIs) through a portfolio of blood safety interventions. These portfolios must be updated periodically to reflect shifting epidemiological conditions, emerging infectious diseases, and new technologies. However, the number of available blood safety portfolios grows exponentially with the number of available interventions, making it impossible for policymakers to evaluate all feasible portfolios without the assistance of a computer model. We develop a novel optimization model for evaluating blood safety portfolios that enables systematic comparison of all feasible portfolios of deferral, testing, and modification interventions to identify the portfolio that is preferred from a cost-utility perspective. We present structural properties that reduce the state space and required computation time in certain cases, and we develop a linear approximation of the model. We apply the model to retrospectively evaluate U.S. blood safety policies for Zika and West Nile virus for the years 2017, 2018, and 2019, defining donor groups based on season and geography. We leverage structural properties to efficiently find an optimal solution. We find that the optimal portfolio varies geographically, seasonally, and over time. Additionally, we show that for this problem the approximated model yields the same optimal solution as the exact model. Our method enables systematic identification of the optimal blood safety portfolio in any setting and any time period, thereby supporting decision makers in efforts to ensure the safety of the blood supply.
Recently, wireless power transmission technology (WPT) is used in wireless rechargeable unmanned aerial vehicle (UAV) networks (WRUNs) to replenish energy for UAVs. In WRUN, if UAVs cannot replenish energy in time, th...
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ISBN:
(纸本)9781665443319
Recently, wireless power transmission technology (WPT) is used in wireless rechargeable unmanned aerial vehicle (UAV) networks (WRUNs) to replenish energy for UAVs. In WRUN, if UAVs cannot replenish energy in time, the task will fail or the task completion time will be greatly prolonged. So, when and how long should the wireless static chargers (WSCs) be scheduled to replenish energy for UAVs while the energy utilization rate of WSCs can be optimized is very critical. However, the existing methods only optimize the charging time periods, that is the time durations during which WSCs release energy, ignoring the impact of the adjustable source power of WSCs. In fact, inappropriate source power will lead to the low energy utilization rate of WSCs. This paper takes both the charging time periods and the adjustable source power of WSCs into account and formulates the power-aware charging time scheduling (PACTS) problem as an optimization problem. Namely, how to decide the optimal charging time periods and the appropriate source power in each charging time period simultaneously to improve the energy utilization rate of WSCs. To solve PACTS, we first discretize the flight paths of UAVs spatiotemporally and then present a novel method to reformulate PACTS as a binary integer programming (BIP) problem that can be solved by existing algorithms. Finally, experiments are conducted to evaluate the performance of our scheme.
This paper presents a new phasor measurement unit (PMU) placement methodology to provide the required data for wide-area backup protection scheme. The presented placement method is primarily a binary linear optimizati...
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This paper presents a new phasor measurement unit (PMU) placement methodology to provide the required data for wide-area backup protection scheme. The presented placement method is primarily a binary linear optimization problem whose constraints are defined to detect faults on transmission lines based on the difference between voltage values of a bus obtained from two different paths, while the full observability of the system is also guaranteed. To consider the limitation on the number of PMU channels, a new bi-level approach is also proposed in this paper, in which the upper level is aimed to find the best solution among different submatrices, while the lower level finds the best PMU placement solution for each submatrix. Therefore, the contribution of this paper is to propose a methodology to optimally locate minimum number of PMUs in a power system in a way that while full observability of the system and its wide-area backup protection are assured, the types of each PMU-in terms of its number of channels as well as the lines whose currents should be measured by the PMU to satisfy the constraints-are determined. The performance of the proposed methodology is evaluated on standard test power systems.
Given the increasing frequency, duration, and intensity of heat waves around the globe, more research is needed on the allocation and operations of cooling shelters for efficient heat mitigation. To address this need,...
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Given the increasing frequency, duration, and intensity of heat waves around the globe, more research is needed on the allocation and operations of cooling shelters for efficient heat mitigation. To address this need, this study considers a cooling shelter operating system that uses shuttle buses to transport heat-vulnerable people and presents a binary integer programming model for the multi-depot location routing problem (LRP) that decides optimal locations of cooling shelters and routes of shuttle buses simultaneously with the objective of minimizing the total operating cost for full accommodation of the heat-vulnerable population. Since the LRP is NP-hard, we further present the simulated annealing to efficiently derive a near-optimal solution. We then validate the proposed methodology with an application to the 14 administrative regions of Ulsan Metropolitan City in the Republic of Korea to assign heat-vulnerable residents and provide them with ride services to the associated cooling shelters. The overall results demonstrate the proposed methodology's competitive performance compared with the traditional two-phased solution approach that separately solves the location problem and routing problem. In particular, our results show that the proposed methodology can save up to 49,000 USD in addressing the cooling shelter location routing problem compared to the two-phased solution approach. Subsequently, a sensitivity analysis is conducted regarding three factors that are likely to impact the effectiveness and efficiency of cooling shelter operations: shuttle bus capacity, traveling cost, and maximum walking distance. Our research provides recommendations for policymakers to carry out the best heat mitigation strategy for their unique circumstances and reduce heat-related illness and death.
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