Browsing by Subject "Mixed integer linear programming"

Now showing 1 - 6 of 6

Open Access
A new formulation and an effective matheuristic for the airport gate assignment problem
(Elsevier, 2023-03) Karsu, Özlem; Solyalı, Oğuz
This study considers an airport gate assignment problem where a set of aircraft arriving to an airport are assigned to the fixed gates of the airport terminal or to the apron. The aim is to lexicographically minimize the number of aircraft assigned to the apron, and then the total walking distance by passengers. A new mixed integer linear programming formulation and a matheuristic is proposed for the problem. The proposed formulation is based on the idea of flow of passengers and has smaller size compared to the existing formulations in the literature. The proposed matheuristic, which relies on solving a restricted version of the proposed formulation of the problem, is not only easy to implement but is also very effective. A computational study performed on benchmark instances reveals that the proposed formulation and the matheuristic outperform the existing exact and heuristic algorithms in the literature.
Open Access
Exact and heuristic approaches based on noninterfering transmissions for joint gateway selection, time slot allocation, routing and power control for wireless mesh networks
(Elsevier, 2017) Gokbayrak, K.; Yıldırım, E. A.
Wireless mesh networks (WMNs) provide cost-effective alternatives for extending wireless communication over larger geographical areas. In this paper, given a WMN with its nodes and possible wireless links, we consider the problem of gateway node selection for connecting the network to the Internet along with operational problems such as routing, wireless transmission capacity allocation, and transmission power control for efficient use of wired and wireless resources. Under the assumption that each node of the WMN has a fixed traffic rate, our goal is to allocate capacities to the nodes in proportion to their traffic rates so as to maximize the minimum capacity-to-demand ratio, referred to as the service level. We adopt a time division multiple access (TDMA) scheme, in which a time frame on the same frequency channel is divided into several time slots and each node can transmit in one or more time slots. We propose two mixed integer linear programming formulations. The first formulation, which is based on individual transmissions in each time slot, is a straightforward extension of a previous formulation developed by the authors for a related problem under a different set of assumptions. The alternative formulation, on the other hand, is based on sets of noninterfering wireless transmissions. In contrast with the first formulation, the size of the alternative formulation is independent of the number of time slots in a frame. We identify simple necessary and sufficient conditions for simultaneous transmissions on different links of the network in the same time slot without any significant interference. Our characterization, as a byproduct, prescribes a power level for each of the transmitting nodes. Motivated by this characterization, we propose a simple scheme to enumerate all sets of noninterfering transmissions, which is used as an input for the alternative formulation. We also introduce a set of valid inequalities for both formulations. For large instances, we propose a three-stage heuristic approach. In the first stage, we solve a partial relaxation of our alternative optimization model and determine the gateway locations. This stage also provides an upper bound on the optimal service level. In the second stage, a routing tree is constructed for each gateway node computed in the first stage. Finally, in the third stage, the alternative optimization model is solved by fixing the resulting gateway locations and the routing trees from the previous two stages. For even larger networks, we propose a heuristic approach for solving the partial relaxation in the first stage using a neighborhood search on gateway locations. Our computational results demonstrate the promising performance of our exact and heuristic approaches and the valid inequalities
Open Access
Exact and heuristic solution approaches for the airport gate assignment problem
(Elsevier, 2021-01-30) Karsu, Özlem; Azizoğlu, M.; Alanlı, K.
In this study, we consider an airport gate assignment problem that assigns a set of aircraft to a set of gates. The aircraft that cannot be assigned to any gate are directed to an apron. We aim to make aircraft-gate assignments so as to minimize the number of aircraft assigned to apron and among the apron usage minimizing solutions, we aim to minimize total walking distance travelled by all passengers. The problem is formulated as a mixed-integer nonlinear programming model and then it is linearized. A branch and bound algorithm, beam search and filtered beam search algorithms that employ powerful lower and upper bounding mechanisms are developed. The results of the computational experiment have shown the satisfactory performance of the algorithms.
Open Access
Lower hedging of American contingent claims with minimal surplus risk in finite-state financial markets by mixed-integer linear programming
(2014) Pınar, M. Ç.
The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear expected surplus criterion for American contingent claims in finite state markets gives rise to a non-convex bilinear programming formulation which admits an exact linearization. The resulting mixed-integer linear program can be readily processed by available software.
Open Access
Minimum conflict balanced graph coloring problem
(2022-05) Hanoğlu, Nazlı Elif
Graph coloring is an important problem in optimization. The classical vertex coloring problem in graphs asks that the vertices are clustered to groups (colors) having no edge interconnections. In this thesis, we focus on a di erent version of the vertex coloring problem. The vertices have to be partitioned into balanced groups with a minimum number of con icts (inner-group connections). In mobile wireless communications, this version of the problem has several applications. Since the majority of graph coloring problems are NP-hard, only a few exact methods have been introduced in the literature. We propose several mixed-integer linear programming formulations that are solved within a binary search framework and show their e cacy. In order to provide lower and upper bounds to our problem, we use clique inequalities as valid inequalities and a heuristic algorithm, respectively. We perform computational analyses instances from the literature and also on instances that we randomly generate. We compare performances of models/algorithms in terms of their solution times and also conduct sensitivity analyses using di erent parameter settings on randomly generated instances and discuss their e ects on the solution times.
Open Access
Prescriptive modeling for counterfactual inferences
(2024-06) Işık, Elif Sena
In real-life scenarios, conducting experiments or simulations to optimize out-comes can be costly in terms of time and resources. This thesis explores the utilization of trained neural networks for predictive modeling and optimization to address this challenge. The methodology involves training neural networks on historical data or simulated environments to capture complex relationships be-tween input variables and outputs. We then employ optimization techniques to explore parameter/input spaces and identify optimal configurations for desired outputs. Importantly, this approach enables us to conduct counterfactual analyses, allowing us to assess how changes in input parameters would affect outputs. We present case studies utilizing two distinct real-life scenarios: firstly, the public simulation model FluTE, where we demonstrate the effectiveness of our approach in optimizing strategies to alleviate the spread of infectious diseases. Secondly, we tackle an assortment problem and demonstrate how decision-making processes in retail settings can be assisted by trained neural networks to maximize profitability. We then also suggest an improved methodology to control the uncertainty in predicted outputs from neural network. We utilize dropout networks to quantify variability in the output predictions and embed them into the optimization model. Computational experiments are conducted with the two case studies and customized problem specific methodologies are suggested that includes decomposition methods and heuristics.