Academic literature on the topic 'BILEVEL PROGRAMMING FRAMEWORK'

Market power, defined as the ability to raise prices above competitive levels profitably, continues to be a prime concern in the restructured electricity markets. Market power must be mitigated to improve market performance and avoid inefficient generation investment, price volatility, and overpayment in power systems. For this reason, involving market power in the transmission expansion planning (TEP) problem is essential for ensuring the efficient operation of the electricity markets. In this regard, a methodological bilevel stochastic framework for the TEP problem that explicitly includes the market power indices in the upper level is proposed, aiming to restrict the potential market power execution. A mixed-integer linear/quadratic programming (MILP/MIQP) reformulation of the stochastic bilevel model is constructed utilizing Karush−Kuhn−Tucker (KKT) conditions. Wind power and electricity demand uncertainty are incorporated using scenario-based two-stage stochastic programming. The model enables the planner to make a trade-off between the market power indices and the investment cost. Using comparable results of the IEEE 118-bus system, we show that the proposed TEP outperforms the existing models in terms of market power indices and facilitates open access to the transmission network for all market participants.

A conceptual framework is presented for modeling the capacity of multimodal freight transportation networks. A review is provided on the evolution of capacity models for use in transportation systems planning and investment, and recent advances toward a system-oriented, multimodal capacity model are discussed in depth. A logical network capacity model based on bilevel programming is proposed.

High-occupancy vehicle (HOV) lanes, which are designed so as to encourage more people to use high-capacity travel modes and thus move more people in a single roadway lane, have been implemented as a lane management measure to deal with the growing traffic congestion in practice. However, the implementation has shown that some HOV lanes are not able to achieve the expected effects without proper HOV lane settings. In this study, the tradable credits scheme (TCS) is introduced to improve the HOV lane management and an optimal capacity of HOV lanes in a multilane highway is investigated to match TCSs. To approach the investigation, a bilevel programming model is proposed. The upper-level represents the decision of the highway authority and the lower-level follows the commuters’ user equilibrium with deterministic demand. The potential influence of TCSs is further investigated within the proposed framework. A modified genetic algorithm is proposed to solve the bilevel programming model. Numerical examples demonstrate that combining TCSs with the HOV lane management can obviously mitigate traffic congestion.

We present a novel framework for integrating prior knowledge into discriminative classifiers. Our framework allows discriminative classifiers such as Support Vector Machines (SVMs) to utilize prior knowledge specified in the generative setting. The dual objective of fitting the data and respecting prior knowledge is formulated as a bilevel program, which is solved (approximately) via iterative application of second-order cone programming. To test our approach, we consider the problem of using WordNet (a semantic database of English language) to improve low-sample classification accuracy of newsgroup categorization. WordNet is viewed as an approximate, but readily available source of background knowledge, and our framework is capable of utilizing it in a flexible way.

With the rapid development of e-commerce and the dramatic upsurge in direct-to-consumer deliveries, the last-mile problem has become increasingly apparent. With the distinct advantages of bringing economies of scale and providing 24/7 contactless self-service, smart parcel lockers play a critical role in solving the last-mile problem. However, due to a lack of planning, myopia expansion, and an ambiguous profit model, smart parcel locker suppliers in China have been suffering huge economic losses, restricting their further development. In the study, on the basis of an in-depth analysis of the cost elements and major revenue sources of smart parcel lockers, we propose a bilevel programming model to optimize the location of community smart parcel lockers with the upper-level model maximizing the profit of a third-party smart parcel locker supplier and the lower-level model maximizing user satisfaction. Then, a solution algorithm based on the genetic algorithm is proposed. Finally, some numerical experiments are carried out based on a medium-scale residential community in Jiading District, Shanghai. The sensitivity analyses conducted in this study reveal how the user satisfaction evaluation and the investment budget influence the expected profit. The modelling framework and numerical results can provide third-party smart parcel locker suppliers with significant theoretical support and practical guidance on planning the investment budget and optimizing the smart parcel locker locations to maximize their profit.

The journey of this research work got initiated through identification of recent challenges in strategic planning faced by the decision-makers at managerial levels. Through interactions with practitioners of various sectors of the Industry, it started becoming clear that a peculiar situation is predominantly encountered by decision-makers. During a majority of situations of strategic planning, the selection of a move as a course of action by a decision- maker gets a reaction from one or more concerned parties, which in turn affects the objective of the decision-maker under consideration. The introspection of the literature in mathematical programming enabled us to realize that the mathematical modelling of such situations is possible through bilevel programming framework. The industrial interactions and literature review provided the motivation to address these challenges of strategic planning by modelling such decision-making issues as bilevel programming problems. For meticulously and precisely modelling the problems and to test the models with appropriate data, we narrowed down our study to the problems of Railways and supply chain management, due to approachability to the practitioners in these two sectors. Subsequent to the task of modelling the addressed issues, another challenge which we faced during our research is the unavailability of solution algorithms to solve the problems modelled as variants of bilevel programming framework. Wherever any algorithms were available for solving such a problem, we discovered those as incapable of handling the problems of a practical scale of ours. This motivated us to work towards the development of solution algorithms for the variants of bilevel programming problems being dealt with, and thus achieve success in our main objective. In our study, we have addressed both of these challenges collectively and contributed towards the development of decision support for some of the identified challenges of decision-makers which can be categorized within the scope of modelling through the bilevel programming. Further, we have supported our study by an implementation of developed algorithms on the relevant data obtained for appropriate cases from firms facing such problems. This has enabled us to contribute to the society through an optimal utilization of available opportunities. The thesis entitled “Strategic Planning and Decision Making Problems in the Bilevel Programming Framework” comprises of five chapters followed by the bibliography and the list of publications. The precursory Chapter 1 manifests strategic planning and decision-making, and decision-support for the same. The concept of bilevel programming along with its variants is then introduced. A survey of literature on decision-making models using bilevel programming framework developed for assisting managerial decisions of firms from various sectors is presented thereafter. Noting some practical issues in the approaches followed in strategic planning, a scope of research for developing a decision-support is observed to fix the objective of thesis along with the plan of research work. Preliminary concepts from different areas are used in our research work for development of solution algorithms. They need to be introduced with a bit detailed explanation before using them in the presentation of our work in subsequent chapters. All of such relevant concepts are presented in Chapter 2 for providing the readers with a clear understanding of our interdisciplinary work. Additionally, an independent discussion on a special case of a variant of bilevel programming problem is explicated as a ground work for developing a GA-based solution methodology in a later chapter. In Chapter 3, problem of railways is studied for decision-making on an operational issue of running special trains to tackle higher demand on specific routes during seasons of festivals and holidays. The study includes development of decision support for operational decisions on optimal utilization of rolling-stocks and determining optimal fare-price structure in a competitive environment coerced by other travelling service providers. The influence on the demand-shares by the competitors of railways is incorporated in decision making to utilize the rolling-stock accordingly. The problem is modelled as a mixed integer single- leader-multi-follower bilevel programming problem. A diversified-elitist genetic algorithm is introduced to solve the constructed model. The suggested methodology is illustrated by taking a test situation from Indian Railways. The work presented in this chapter has been published as a research paper entitled “A Bilevel Programming Model for Operative Decisions on Special Trains: An Indian Railways Perspective”, in Journal of Rail Transport Planning & Management (Elsevier), 8, (2018), 184-206. doi: 10.1016/j.jrtpm.2018.03.001. xv Chapter 4 develops a decision support for strategic pricing and aggregate production distribution planning for a small scale supplier intending to penetrate into a potential market engendered by a single buyer. A novel mixed integer single-leader-single-follower bilevel programming model is developed to formulate the problem in which the supplier is considered as a leader and the buyer as a follower. The proposed model subsumes the assessment of demand share against the price quotation, enabling the supplier to prepare an aggregate production distribution plan accordingly. An integer coded genetic algorithm is developed to solve the model and its implementation is exhibited through a test scenario. The work presented in this chapter is published as a research paper entitled “A Bilevel Programming Model for a Cohesive Decision Making on Strategic Pricing and Production Distribution Planning for a Small Scale Supplier”, in the journal International Game Theory Review (World Scientific Publishing Company), 22(2), 2020, doi: 10.1142/S0219198920400095. Chapter 5 studies a strategic problem of price negotiation of the buyer with its multiple suppliers in an oligopolistic-monopsony market. The problem is studied to develop a decision support for identifying target prices for negotiation through which the common goal of all stakeholders viz maintaining a sustainable business environment can be achieved. For this purpose it is suggested for the buyer to identify the Nash-equilibrium prices of the suppliers’ oligopolistic-competition as target prices, as adopting this strategy helps in avoiding adverse actions from either side. In order to develop a decision support for this strategic issue a mathematical model is formulated as a multi-leader-single-follower bilevel programming problem. A GA-based solution approach is proposed to solve such a bilevel programming problem. The proposed methodology is demonstrated by an implementation of a case of a manufacturing firm of the FMCG sector. The work presented in this chapter is communicated as a research paper entitled “A Bilevel Game Model for Ascertaining Competitive Target Prices for a Buyer in Negotiation with Multiple Suppliers” to the Journal Omega (Elsevier). A summary followed by future scope of the research work is evinced to conclude the thesis. Finally, two independent results on convex optimization are presented in Appendix, which are referred in Chapter 3 for developing a methodology to solve a problem modelled there.

Learning graph structure for graph neural networks (GNNs) is crucial to facilitate the GNN-based downstream learning tasks. It is challenging due to the non-differentiable discrete graph structure and lack of ground-truth. In this paper, we address these problems and propose a novel graph structure learning framework for GNNs. Firstly, we directly model the continuous graph structure with dual-normalization, which implicitly imposes sparse constraint and reduces the influence of noisy edges. Secondly, we formulate the whole training process as a bilevel programming problem, where the inner objective is to optimize the GNNs given learned graphs, while the outer objective is to optimize the graph structure to minimize the generalization error of downstream task. Moreover, for bilevel optimization, we propose an improved Neumann-IFT algorithm to obtain an approximate solution, which is more stable and accurate than existing optimization methods. Besides, it makes the bilevel optimization process memory-efficient and scalable to large graphs. Experiments on node classification and scene graph generation show that our method can outperform related methods, especially with noisy graphs.

In our previous paper,[1] we have integrated the Robust Optimization framework with the Real Options model to evaluate flexibility, introducing the Flexible-Robust Objective. Flexibility is defined as the energy left to allocate after meeting daily demands. This integration proved more efficient in risk evaluation in energy allocation problems. However, the integration has some limitations in applying operational and physical constraints of the reservoirs. In this paper, an in-depth analysis of all the limitations is discussed. To overcome those limitations and ensure a conceptually correct approach, a bilevel programming approach has been introduced in the second stage of the model to solve the energy allocation problem. We define the proposed model in this paper as Two-Stage, Bi-Level Flexible-Robust Optimization. Stage 1 provides the maximum total flexibility that can be allocated throughout the optimization period. Stage 2 uses bi-level optimization. The Stage 2 upper level sets the target allocation of flexibility in each iteration and maximizes net revenue along with the evaluation of allocated flexibility by the real options model. The Stage 2 lower level minimizes the deviation between the level 1 target and the achievable solution, ensuring no violation in physical and operational constraints of the reservoirs. Some compatibility issues have been identified in integrating the two levels, which have been discussed and solved successfully; the model provides an optimal achievable allocation of flexibility by maximizing net revenue and minimizing violation of constraints. Uncertainty in the objective function and constraints has been handled by converting into a robust objective and probabilistic constraints, respectively. Both classical methods (SQP) and evolutionary methods (GA) with continuous decision variables have been applied to solving the optimization problem, and the results are compared. Also, the result has been compared with the simplified version in previous paper, which was limited to randomly generate discrete decision variables. The new results provided an 8% improvement over the previous simplified model.