566 research outputs found
Achieving an optimal trade-off between revenue and energy peak within a smart grid environment
We consider an energy provider whose goal is to simultaneously set
revenue-maximizing prices and meet a peak load constraint. In our bilevel
setting, the provider acts as a leader (upper level) that takes into account a
smart grid (lower level) that minimizes the sum of users' disutilities. The
latter bases its decisions on the hourly prices set by the leader, as well as
the schedule preferences set by the users for each task. Considering both the
monopolistic and competitive situations, we illustrate numerically the validity
of the approach, which achieves an 'optimal' trade-off between three
objectives: revenue, user cost, and peak demand
Contributions to robust and bilevel optimization models for decision-making
Los problemas de optimización combinatorios han sido ampliamente estudiados en la
literatura especializada desde mediados del siglo pasado. No obstante, en las últimas
décadas ha habido un cambio de paradigma en el tratamiento de problemas cada vez
más realistas, en los que se incluyen fuentes de aleatoriedad e incertidumbre en los
datos, múltiples criterios de optimización y múltiples niveles de decisión. Esta tesis
se desarrolla en este contexto. El objetivo principal de la misma es el de construir
modelos de optimización que incorporen aspectos inciertos en los parámetros que
de nen el problema así como el desarrollo de modelos que incluyan múltiples niveles
de decisión. Para dar respuesta a problemas con incertidumbre usaremos los modelos
Minmax Regret de Optimización Robusta, mientras que las situaciones con múltiples
decisiones secuenciales serán analizadas usando Optimización Binivel.
En los Capítulos 2, 3 y 4 se estudian diferentes problemas de decisión bajo incertidumbre
a los que se dará una solución robusta que proteja al decisor minimizando
el máximo regret en el que puede incurrir. El criterio minmax regret analiza el comportamiento
del modelo bajo distintos escenarios posibles, comparando su e ciencia
con la e ciencia óptima bajo cada escenario factible. El resultado es una solución con
una eviciencia lo más próxima posible a la óptima en el conjunto de las posibles realizaciones
de los parámetros desconocidos. En el Capítulo 2 se estudia un problema de
diseño de redes en el que los costes, los pares proveedor-cliente y las demandas pueden
ser inciertos, y además se utilizan poliedros para modelar la incertidumbre, permitiendo
de este modo relaciones de dependencia entre los parámetros. En el Capítulo
3 se proponen, en el contexto de la secuenciación de tareas o la computación grid,
versiones del problema del camino más corto y del problema del viajante de comercio
en el que el coste de recorrer un arco depende de la posición que este ocupa en el
camino, y además algunos de los parámetros que de nen esta función de costes son
inciertos. La combinación de la dependencia en los costes y la incertidumbre en los
parámetros da lugar a dependencias entre los parámetros desconocidos, que obliga a
modelar los posibles escenarios usando conjuntos más generales que los hipercubos,
habitualmente utilizados en este contexto. En este capítulo, usaremos poliedros generales
para este cometido. Para analizar este primer bloque de aplicaciones, en el Capítulo 4, se analiza un modelo de optimización en el que el conjunto de posibles
escenarios puede ser alterado mediante la realización de inversiones en el sistema.
En los problemas estudiados en este primer bloque, cada decisión factible es evaluada
en base a la reacción más desfavorable que pueda darse en el sistema. En los
Capítulos 5 y 6 seguiremos usando esta idea pero ahora se supondrá que esa reacción
a la decisión factible inicial está en manos de un adversario o follower. Estos dos
capítulos se centran en el estudio de diferentes modelos binivel. La Optimización
Binivel aborda problemas en los que existen dos niveles de decisión, con diferentes
decisores en cada uno ellos y la decisión se toma de manera jerárquica. En concreto,
en el Capítulo 5 se estudian distintos modelos de jación de precios en el contexto
de selección de carteras de valores, en los que el intermediario nanciero, que se
convierte en decisor, debe jar los costes de invertir en determinados activos y el
inversor debe seleccionar su cartera de acuerdo a distintos criterios. Finalmente, en
el Capítulo 6 se estudia un problema de localización en el que hay distintos decisores,
con intereses contrapuestos, que deben determinar secuencialmente la ubicación de
distintas localizaciones. Este modelo de localización binivel se puede aplicar en contextos
como la localización de servicios no deseados o peligrosos (plantas de reciclaje,
centrales térmicas, etcétera) o en problemas de ataque-defensa.
Todos estos modelos se abordan mediante el uso de técnicas de Programación
Matemática. De cada uno de ellos se analizan algunas de sus propiedades y se desarrollan
formulaciones y algoritmos, que son examinados también desde el punto de
vista computacional. Además, se justica la validez de los modelos desde un enfoque
de las aplicaciones prácticas. Los modelos presentados en esta tesis comparten la
peculiaridad de requerir resolver distintos problemas de optimización encajados.Combinatorial optimization problems have been extensively studied in the specialized
literature since the mid-twentieth century. However, in recent decades, there
has been a paradigm shift to the treatment of ever more realistic problems, which
include sources of randomness and uncertainty in the data, multiple optimization
criteria and multiple levels of decision. This thesis concerns the development of such
concepts. Our objective is to study optimization models that incorporate uncertainty
elements in the parameters de ning the model, as well as the development of
optimization models integrating multiple decision levels. In order to consider problems
under uncertainty, we use Minmax Regret models from Robust Optimization;
whereas the multiplicity and hierarchy in the decision levels is addressed using Bilevel
Optimization.
In Chapters 2, 3 and 4, we study di erent decision problems under uncertainty
to which we give a robust solution that protects the decision-maker minimizing the
maximum regret that may occur. This robust criterion analyzes the performance
of the system under multiple possible scenarios, comparing its e ciency with the
optimum one under each feasible scenario. We obtain, as a result, a solution whose
e ciency is as close as possible to the optimal one in the set of feasible realizations
of the uncertain parameters. In Chapter 2, we study a network design problem in
which the costs, the pairs supplier-customer, and the demands can take uncertain
values. Furthermore, the uncertainty in the parameters is modeled via polyhedral
sets, thereby allowing relationships among the uncertain parameters. In Chapter
3, we propose time-dependent versions of the shortest path and traveling salesman
problems in which the costs of traversing an arc depends on the relative position
that the arc occupies in the path. Moreover, we assume that some of the parameters
de ning these costs can be uncertain. These models can be applied in the context of
task sequencing or grid computing. The incorporation of time-dependencies together
with uncertainties in the parameters gives rise to dependencies among the uncertain
parameters, which require modeling the possible scenarios using more general sets
than hypercubes, normally used in this context. In this chapter, we use general
polyhedral sets with this purpose. To nalize this rst block of applications, in Chapter 4, we analyze an optimization model in which the set of possible scenarios
can be modi ed by making some investments in the system.
In the problems studied in this rst block, each feasible decision is evaluated
based on the most unfavorable possible reaction of the system. In Chapters 5 and
6, we will still follow this idea, but assuming that the reaction to the initial feasible
decision will be held by a follower or an adversary, instead of assuming the most
unfavorable one. These two chapters are focused on the study of some bilevel models.
Bilevel Optimization addresses optimization problems with multiple decision
levels, di erent decision-makers in each level and a hierarchical decision order. In
particular, in Chapter 5, we study some price setting problems in the context of
portfolio selection. In these problems, the nancial intermediary becomes a decisionmaker
and sets the transaction costs for investing in some securities, and the investor
chooses her portfolio according to di erent criteria. Finally, in Chapter 6, we study
a location problem with several decision-makers and opposite interests, that must
set, sequentially, some location points. This bilevel location model can be applied
in practical applications such as the location of semi-obnoxious facilities (power or
electricity plants, waste dumps, etc.) or interdiction problems.
All these models are stated from a Mathematical Programming perspective, analyzing
their properties and developing formulations and algorithms, that are tested
from a computational point of view. Furthermore, we pay special attention to justifying
the validity of the models from the practical applications point of view. The
models presented in this thesis share the characteristic of involving the resolution of
nested optimization problems.Premio Extraordinario de Doctorado U
A new Bi– level production-routing-inventory model for a medicine supply chain under uncertainty
This research presents a new bi-level bi-objective production-routing-inventory model for a medi-cine supply chain. In this case, the production is executed by multi-separated producers in a multi-production line for different kinds of medicines which will be saved in stores for delivering to cus-tomers. The capacitated vehicle routing problem is considered in designing a distribution system from stores to customers. The goal of this model is to make a suitable trade-off between the customer satisfaction and the budget cost. This problem has been formulated in a bi-level form where the first objective function is the minimization of the budget during the scheduled time and the second one is the minimization of the shortage amount associated with the lost sale of medicine demands delivering to drug stores. Uncertainty is considered as a nature of the main parameters of the problem. Then the robust approach was used to handle the associated uncertainty of related parameters and the resulted problem is solved by Benders decomposition algorithm. The results indi-cate that the model make an improvement in medicine supply chain
Optimization Approaches for Electricity Generation Expansion Planning Under Uncertainty
In this dissertation, we study the long-term electricity infrastructure investment planning problems in the electrical power system. These long-term capacity expansion planning problems aim at making the most effective and efficient investment decisions on both thermal and wind power generation units. One of our research focuses are uncertainty modeling in these long-term decision-making problems in power systems, because power systems\u27 infrastructures require a large amount of investments, and need to stay in operation for a long time and accommodate many different scenarios in the future. The uncertainties we are addressing in this dissertation mainly include demands, electricity prices, investment and maintenance costs of power generation units. To address these future uncertainties in the decision-making process, this dissertation adopts two different optimization approaches: decision-dependent stochastic programming and adaptive robust optimization. In the decision-dependent stochastic programming approach, we consider the electricity prices and generation units\u27 investment and maintenance costs being endogenous uncertainties, and then design probability distribution functions of decision variables and input parameters based on well-established econometric theories, such as the discrete-choice theory and the economy-of-scale mechanism. In the adaptive robust optimization approach, we focus on finding the multistage adaptive robust solutions using affine policies while considering uncertain intervals of future demands. This dissertation mainly includes three research projects. The study of each project consists of two main parts, the formulation of its mathematical model and the development of solution algorithms for the model. This first problem concerns a large-scale investment problem on both thermal and wind power generation from an integrated angle without modeling all operational details. In this problem, we take a multistage decision-dependent stochastic programming approach while assuming uncertain electricity prices. We use a quasi-exact solution approach to solve this multistage stochastic nonlinear program. Numerical results show both computational efficient of the solutions approach and benefits of using our decision-dependent model over traditional stochastic programming models. The second problem concerns the long-term investment planning with detailed models of real-time operations. We also take a multistage decision-dependent stochastic programming approach to address endogenous uncertainties such as generation units\u27 investment and maintenance costs. However, the detailed modeling of operations makes the problem a bilevel optimization problem. We then transform it to a Mathematic Program with Equilibrium Constraints (MPEC) problem. We design an efficient algorithm based on Dantzig-Wolfe decomposition to solve this multistage stochastic MPEC problem. The last problem concerns a multistage adaptive investment planning problem while considering uncertain future demand at various locations. To solve this multi-level optimization problem, we take advantage of affine policies to transform it to a single-level optimization problem. Our numerical examples show the benefits of using this multistage adaptive robust planning model over both traditional stochastic programming and single-level robust optimization approaches. Based on numerical studies in the three projects, we conclude that our approaches provide effective and efficient modeling and computational tools for advanced power systems\u27 expansion planning
Optimizing High-Speed Railroad Timetable with Passenger and Station Service Demands: A Case Study in the Wuhan-Guangzhou Corridor
This paper aims to optimize high-speed railroad timetables for a corridor. We propose an integer programming model using a time-space network-based approach to consider passenger service demands, train scheduling, and station service demands simultaneously. A modified branch-and-price algorithm is used for the computation. This algorithm solves the linear relaxation of all nodes in a branch-and-bound tree using a column generation algorithm to derive a lower-bound value (LB) and derive an upper-bound value (UB) using a rapid branching strategy. The optimal solution is derived by iteratively updating the upper- and lower-bound values. Three acceleration strategies, namely, initial solution iteration, delayed constraints, and column removal, were designed to accelerate the computation. The effectiveness and efficiency of the proposed model and algorithm were tested using Wuhan-Guangzhou high-speed railroad data. The results show that the proposed model and algorithm can quickly reduce the defined cost function by 38.2% and improve the average travel speed by 10.7 km/h, which indicates that our proposed model and algorithm can effectively improve the quality of a constructed train timetable and the travel efficiency for passengers.
Document type: Articl
Benders' decomposition algorithm to solve bi-level bi-objective scheduling of aircrafts and gate assignment under uncertainty
Abstract Management and scheduling of flights and assignment of gates to aircraft play a significant role in improving the procedure of the airport, due to the growing number of flights, decreasing the flight times. This research addresses assigning and scheduling of runways and gates in the main airport simultaneously. Moreover, this research considers the unavailability of runway's constraint and the uncertain parameters relating to both areas of runway and gate assignment. The proposed model is formulated as a comprehensive bi-level bi-objective problem.The leader's objective function minimizes the total waiting time for runways and gates for all aircrafts based on their importance coefficient. Meanwhile, the total distance traveled by all passengers in the airport terminal is minimized by a follower's objective function. To solve the proposed model, the decomposition approach based on Benders' decomposition method is applied. Empirical data are used to show the validation and application of our model. A comparison shows the effectiveness of the proposed model and its significant impact on cost decreasing
Optimal Energy and Flexibility Dispatch of Grid-Connected Microgrids
This thesis proposes an optimization model to efficiently schedule energy and flexibilities of a grid-connected microgrid (MG) with non-dispatchable renewable energy sources and battery energy storages (BESs). The model can also be used to coordinate the MG operation with the connected upstream distribution grid and to assess the MG flexibility considering economic viability, technical feasibility, and BES degradation. The performance of the model was tested for both deterministic and stochastic formulations using two solution approaches i.e., day-ahead and rolling horizon, in different simulation and demonstration test cases. In these test cases, the model optimizes the schedule of the MG resources and the energy exchange with the connected main grid, while satisfying the constraints and operational objectives of the MG. The flexibilities from the MG would also be optimized when the MG provided flexibility services (FSs) to the distribution systems. The coordination with the distribution system operator (DSO) was proposed to ensure that the microgrid operation would not violate the technical constraints of the distribution grid. \ua0Two types of test systems were used for the simulations studies: 1) distribution grids with grid-connected MGs and 2) building MGs (BMGs). The distribution test systems included the 12-kV electrical distribution grid of the Chalmers campus and a 12.6-kV 33-bus standard test system, while the BMGs were based on real residential buildings i.e., the HSB LL building and the Brf Viva buildings. Results of the Chalmers’ test case showed that the MGs’ economic optimization could reduce the annual cost for the DSO by up to 2%. Centralized coordination, where the MG resources were scheduled by the DSO, led to an even higher reduction, although it also led to sub-optimal solutions for the MGs. Decentralized coordination was applied on the 33-bus network with a bilevel optimization framework for energy and flexibility dispatch. Two types of FSs were integrated in the bilevel model i.e., the baseline (FS-B) and the capacity limitation (FS-C). The latter has found to be more promising, as it could offer economic incentives for both the DSO and the MGs. In the studies of the BMGs, the BESs were modeled considering both degradation and real-life operation characteristics derived from measurements conducted at the buildings. Results showed that the annual building energy and BES degradation cost could be reduced by up to 3% compared to when the impact of BES degradation was neglected in the energy scheduling. With the participation of the BMG in FS-C provision, the building’s operation cost could be further reduced depending on the flexibility price. A 24-h simulation of the BMG’s operation yielded an economic value of flexibility of at least 7% of its daily energy and peak power cost, while the DSO could benefit from the FS assuming that the dispatched flexibility could be used to reduce the subscription fee that guarantees a certain power level. For frequent flexibility provision i.e., multiple times within a year, the value of flexibility for the MG operator could be reduced due to the BES degradation.\ua0To demonstrate the practical use of the proposed model, an energy management system was designed to integrate the model and employ it to optimize the energy schedule of the BMGs’ BESs and energy exchange with the main grid. The energy dispatch was performed in real-time based on the model’s decisions in real demonstration cases. The demonstration results showed the benefits of the model in that it helped reduce the energy cost of the BMG both in short term and in long term. The model can also be used by the MG operators to quantify the potential and assess the value of microgrid flexibility. Moreover, with the help of this model, the MG can be employed as a flexible resource and reduce the operation cost of the connected distribution grid
A Two-Level Approach to Large Mixed-Integer Programs with Application to Cogeneration in Energy-Efficient Buildings
We study a two-stage mixed-integer linear program (MILP) with more than 1
million binary variables in the second stage. We develop a two-level approach
by constructing a semi-coarse model (coarsened with respect to variables) and a
coarse model (coarsened with respect to both variables and constraints). We
coarsen binary variables by selecting a small number of pre-specified daily
on/off profiles. We aggregate constraints by partitioning them into groups and
summing over each group. With an appropriate choice of coarsened profiles, the
semi-coarse model is guaranteed to find a feasible solution of the original
problem and hence provides an upper bound on the optimal solution. We show that
solving a sequence of coarse models converges to the same upper bound with
proven finite steps. This is achieved by adding violated constraints to coarse
models until all constraints in the semi-coarse model are satisfied. We
demonstrate the effectiveness of our approach in cogeneration for buildings.
The coarsened models allow us to obtain good approximate solutions at a
fraction of the time required by solving the original problem. Extensive
numerical experiments show that the two-level approach scales to large problems
that are beyond the capacity of state-of-the-art commercial MILP solvers
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