scholarly journals Mixed-Integer Linear Programming Model by Linear Approximation for a Strike Package-to-Target Assignment Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Heungseob Kim
Keyword(s):  
Linear Programming ◽  
Linear Approximation ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Mixed Integer ◽  
Piecewise Linear Approximation ◽  
Heterogeneous Vehicle Routing Problem ◽  
Target Assignment ◽  
Milp Model

This study deals with an aircraft-to-target assignment (ATA) problem considering the modern air operation environment, such as the strike package concept, multiple targets for a sortie, and the strike packages’ survivability. For the ATA problem, this study introduces a novel mathematical model in which a heterogeneous vehicle routing problem (HVRP) and a weapon-to-target assignment (WTA) problem are conceptually integrated. The HVRP generates the flight routes for strike packages because this study confirms that the survivability of a strike package depends on the path, and the WTA problem evaluates the likelihood of successful target destruction of assigned weapons. Although the first version of the model is developed as a mixed-integer nonlinear programming (MINLP) model, this study attempts to convert it to a mixed-integer linear programming (MILP) model using the logarithmic transformation and piecewise linear approximation methods. For an ATA problem, this activity could provide an opportunity to use the excellent existing algorithms for searching the optimal solution of LP models. To maximize the operational effectiveness, the MILP model simultaneously determines the following for each strike package: (a) composition type, (b) targets, (c) flight route, (d) types, and (e) quantity of weapons for each target.

scholarly journals Spillways Scheduling for Flood Control of Three Gorges Reservoir Using Mixed Integer Linear Programming Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Maoyuan Feng ◽  
Pan Liu
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Three Gorges Reservoir ◽  
Flood Control ◽  
Mixed Integer ◽  
Piecewise Linear Approximation ◽  
Three Gorges ◽  
Reservoir Storage ◽  
Milp Model

This study proposes a mixed integer linear programming (MILP) model to optimize the spillways scheduling for reservoir flood control. Unlike the conventional reservoir operation model, the proposed MILP model specifies the spillways status (including the number of spillways to be open and the degree of the spillway opened) instead of reservoir release, since the release is actually controlled by using the spillway. The piecewise linear approximation is used to formulate the relationship between the reservoir storage and water release for a spillway, which should be open/closed with a status depicted by a binary variable. The control order and symmetry rules of spillways are described and incorporated into the constraints for meeting the practical demand. Thus, a MILP model is set up to minimize the maximum reservoir storage. The General Algebraic Modeling System (GAMS) and IBM ILOG CPLEX Optimization Studio (CPLEX) software are used to find the optimal solution for the proposed MILP model. The China’s Three Gorges Reservoir, whose spillways are of five types with the total number of 80, is selected as the case study. It is shown that the proposed model decreases the flood risk compared with the conventional operation and makes the operation more practical by specifying the spillways status directly.

scholarly journals Optimising the selection of food items for FFQs using Mixed Integer Linear Programming

2014 ◽  
Vol 18 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Johanna C Gerdessen ◽  
Olga W Souverein ◽  
Pieter van ‘t Veer ◽  
Jeanne HM de Vries
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Selection Process ◽  
Saturated Fat ◽  
Mixed Integer ◽  
Monounsaturated Fat ◽  
Food Items ◽  
Milp Model ◽  
Selection Of

AbstractObjectiveTo support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible.DesignSelection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium.ResultsThe food lists generated by the MILP model have good performance in terms of length, coverage and R2 (explained variance) of all nutrients. MILP-generated food lists were 32–40 % shorter than a benchmark food list, whereas their quality in terms of R2 was similar to that of the benchmark.ConclusionsThe results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.

scholarly journals A Mixed Integer Linear Programming Method for Simultaneous Multi-Periodic Train Timetabling and Routing on a High-Speed Rail Network

2020 ◽  
Vol 12 (3) ◽  
pp. 1131
Author(s):  
Wenliang Zhou ◽  
Xiaorong You ◽  
Wenzhuang Fan
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
High Speed ◽  
Programming Model ◽  
Mixed Integer ◽  
High Speed Rail ◽  
Train Timetabling ◽  
Train Timetable ◽  
The Impact

To avoid conflicts among trains at stations and provide passengers with a periodic train timetable to improve service level, this paper mainly focuses on the problem of multi-periodic train timetabling and routing by optimizing the routes of trains at stations and their entering time and leaving time on each chosen arrival–departure track at each visited station. Based on the constructed directed graph, including unidirectional and bidirectional tracks at stations and in sections, a mixed integer linear programming model with the goal of minimizing the total travel time of trains is formulated. Then, a strategy is introduced to reduce the number of constraints for improving the solved efficiency of the model. Finally, the performance, stability and practicability of the proposed method, as well as the impact of some main factors on the model are analyzed by numerous instances on both a constructed railway network and Guang-Zhu inter-city railway; they are solved using the commercial solver WebSphere ILOG CPLEX (International Business Machines Corporation, New York, NY, USA). Experimental results show that integrating multi-periodic train timetabling and routing can be conducive to improving the quality of a train timetable. Hence, good economic and social benefits for high-speed rail can be achieved, thus, further contributing to the sustained development of both high-speed railway systems and society.

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