Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in distribution networks so they can be blended into final products. The uncapacitated...
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Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in distribution networks so they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) studied in this paper captures a core structure encountered in many of these environments. We model the FCTPwB as a mixed-integer linear program, and we derive two classes of facets, both exponential in size, for the convex hull of solutions for the problem with a single consumer and show that they can be separated in polynomial time. Furthermore, we prove that, in certain situations, these classes of facets along with the continuous relaxation of the original constraints yield a description of the convex hull. Finally, we present a computational study that demonstrates that these classes of facets are effective in reducing the integrality gap and solution time for more general instances of the FCTPwB with arc capacities and multiple consumers.
In dense railway traffic, even the small delay of a single train may propagate through the network, causing a sequence of knock-on delays and significant deviations from the timetable. To mitigate the propagation of d...
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In dense railway traffic, even the small delay of a single train may propagate through the network, causing a sequence of knock-on delays and significant deviations from the timetable. To mitigate the propagation of delays, railway infrastructure managers can generally employ two strategies: (i) in real time, train dispatchers can limit delay propagation by rescheduling trains, i.e., by adjusting the timetable in response to disturbances; (ii) in the timetable design phase, train planners can try to build delay-resilient timetables, which requires a complicated and lengthy iterative process. The ability of a timetable to “absorb” delays whenever they occur is known as robustness. While there is no unanimous consensus on a measure to quantify such robustness, it is normally a global measure, and therefore it is unable to highlight whether specific train paths or regions of the railway network are less robust than others. Moreover, only a few academic works incorporate the possibility of mitigating delays in real time through dispatching when evaluating robustness measures. These shortcomings motivate the present work. In this paper, we introduce the concept of fragility as a new practical tool to analyze a given timetable in order to identify the specific sections where a primary delay is most likely to generate knock-on delays, factoring in optimal future dispatching decisions. We also discuss the relationship between the fragility concept and the so-called recovery cost. We present computational results on real-life scenarios from a busy railway line in Norway and discuss several potential uses of fragility to improve decisions at different levels of the railway planning process, including dispatching, timetable design, and network design.
We consider mixed-integer linear programs where free integer variables are expressed in terms of nonnegative continuous variables. When this model only has two integer variables, Dey and Louveaux characterized the int...
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We consider mixed-integer linear programs where free integer variables are expressed in terms of nonnegative continuous variables. When this model only has two integer variables, Dey and Louveaux characterized the intersection cuts that have infinite split rank. We show that, for any number of integer variables, the split rank of an intersection cut generated from a rational lattice-free polytope L is finite if and only if the integer points on the boundary of L satisfy a certain "2-hyperplane property." The Dey-Louveaux characterization is a consequence of this more general result.
Concentrating Solar Power Tower (CSPT) plants rely on heliostat fields to focus sunlight onto a central receiver. Although simple aiming strategies, such as directing all heliostats to the receiver’s equator, can max...
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Concentrating Solar Power Tower (CSPT) plants rely on heliostat fields to focus sunlight onto a central receiver. Although simple aiming strategies, such as directing all heliostats to the receiver’s equator, can maximize energy collection, they often result in uneven flux distributions that cause hotspots, thermal stresses, and reduced receiver lifetimes. This paper presents a novel, data-driven approach that combines constraint learning, neural network-based surrogates, and mathematical optimization to address these challenges. The methodology learns complex heliostat-to-receiver flux interactions from simulation data and embeds the resulting surrogate model in a tractable optimization framework. By maximizing a tailored quality score that balances energy collection with flux uniformity, the approach produces smoothly distributed flux profiles and mitigates excessive thermal peaks. An iterative refinement process, guided by a trust region strategy and progressive data sampling, ensures continual improvement of the surrogate model by exploring new solution spaces at each iteration. Results from a real CSPT case study show that the proposed approach outperforms conventional heuristic methods, delivering flatter flux distributions with nearly a 10% reduction in peak values and safer thermal conditions (reflected by up to a 50% decrease in deviations from safe concentration distributions), without significantly compromising overall energy capture.
We investigate the green resource allocation to minimize the energy consumption of the users in mobile edge computing systems,where task offloading decisions,transmit power,and computation resource allocation are join...
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We investigate the green resource allocation to minimize the energy consumption of the users in mobile edge computing systems,where task offloading decisions,transmit power,and computation resource allocation are jointly *** considered energy consumption minimization problem is a non-convex mixed-integer nonlinear programming problem,which is challenging to ***,we develop a joint search and Successive Convex Approximation(SCA)scheme to optimize the non-integer variables and integer variables in the inner loop and outer loop,***,in the inner loop,we solve the optimization problem with fixed task offloading *** to the non-convex objective function and constraints,this optimization problem is still non-convex,and thus we employ the SCA method to obtain a solution satisfying the Karush-Kuhn-Tucker *** the outer loop,we optimize the offloading decisions through exhaustive ***,the computational complexity of the exhaustive search method is greatly *** reduce the complexity,a heuristic scheme is proposed to obtain a sub-optimal *** results demonstrate the effectiveness of the developed schemes.
Extensive penetration of distribution energy resources(DERs)brings increasing uncertainties to distribution *** topology identification is a critical basis to guarantee robust distribution network *** algorithms that ...
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Extensive penetration of distribution energy resources(DERs)brings increasing uncertainties to distribution *** topology identification is a critical basis to guarantee robust distribution network *** algorithms that estimate distribution network topology have already been ***,most are based on data-driven alone method and are hard to deal with ever-changing distribution network physical *** these backgrounds,this paper proposes a data-model hybrid driven topology identification scheme for distribution ***,a data-driven method based on a deep belief network(DBN)and random forest(RF)algorithm is used to realize the distribution network topology rough ***,the rough identification results in the previous step are used to make a model of distribution network *** model transforms the topology identification problem into a mixedintegerprogramming problem to correct the rough topology *** of the proposed method is verified in an IEEE 33-bus test system and modified 292-bus system.
This paper presents a mixed-integer programming model for a multi-floor layout design of cellular manufacturing systems (CMSs) in a dynamic environment. A novel aspect of this model is to concurrently determine the ce...
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This paper presents a mixed-integer programming model for a multi-floor layout design of cellular manufacturing systems (CMSs) in a dynamic environment. A novel aspect of this model is to concurrently determine the cell formation (CF) and group layout (GL) as the interrelated decisions involved in the design of a CMS in order to achieve an optimal (or near-optimal) design solution for a multi-floor factory in a multi-period planning horizon. Other design aspects are to design a multi-floor layout to form cells in different floors, a multi-rows layout of equal area facilities in each cell, flexible reconfigurations of cells during successive periods, distance-based material handling cost, and machine depot keeping idle machines. This model incorporates with an extensive coverage of important manufacturing features used in the design of CMSs. The objective is to minimize the total costs of intra-cell, inter-cell, and inter-floor material handling, purchasing machines, machine processing, machine overhead, and machine relocation. Two numerical examples are solved by the CPLEX software to verify the performance of the presented model and illustrate the model features. Since this model belongs to NP-hard class, an efficient genetic algorithm (GA) with a matrix-based chromosome structure is proposed to derive near-optimal solutions. To verify its computational efficiency in comparison to the CPLEX software, several test problems with different sizes and settings are implemented. The efficiency of the proposed GA in terms of the objective function value and computational time is proved by the obtained results. (C) 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the ef...
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Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to use slight shifts in the departure times from the stations to avoid too many simultaneous departures. This limits peak consumption and can help to improve the stability of the power supply. To this end, we derive efficient formulations for the problem of an optimal timetable adjustment based on a given timetable draft, two of which even allow for totally unimodular polyhedral descriptions. The proper choice of the objective function allows the incorporation of the priorities of either the train operating companies or the infrastructure manager. These include the avoidance of large peaks in average or instantaneous consumption and the improved use of recuperated braking energy. To solve the arising optimization models efficiently, we develop specially tailored exact Benders decomposition schemes that allow for the computation of high-quality solutions within a very short time. In an extensive case study for German railway passenger traffic, we show that our methods are capable of solving the problem on a nationwide scale. We see that the optimal adjustment of timetables entails a tremendous potential for reducing energy consumption.
In this paper, we introduce a deep learning aided constraint encoding method to tackle the frequency-constraint microgrid scheduling problem. The nonlinear function between system operating condition and frequency nad...
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In this paper, we introduce a deep learning aided constraint encoding method to tackle the frequency-constraint microgrid scheduling problem. The nonlinear function between system operating condition and frequency nadir is approximated by using a neural network, which admits an exact mixed-integer formulation (MIP). This formulation is then integrated with the scheduling problem to encode the frequency constraint. With the stronger representation power of the neural network, the resulting commands can ensure adequate frequency response in a realistic setting in addition to islanding success. The proposed method is validated on a modified 33-node system. Successful islanding with a secure response is simulated under the scheduled commands using a detailed three-phase model in Simulink. The advantages of our model are particularly remarkable when the inertia emulation functions from wind turbine generators are considered.
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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