<b>Puzzle</b>—Solving the <i>Battleship</i> Puzzle as an Integer Programming Problem

Meuffels, W.J.M.; Hertog, Dick den

doi:10.1287/ited.1100.0047

Cited by 13 publications

(12 citation statements)

References 11 publications

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“…For instance, Chlond proposes an IP formulation for well-known puzzles such as the minesweeper (Chlond 2011), a card trick puzzle (Chlond 2009), and Su Doku puzzles (Chlond 2005). Another example is the battleship puzzle in Meuffels and den Hertog (2010) that is solved by IP. According to DePuy and Taylor (2007), puzzle games are a useful tool to help students learn creative formulation and solution techniques.…”

Section: Case Studies and Gamesmentioning

confidence: 99%

“…Students playing the game typically try to find a feasible solution (mix of plants) based on a trial-and-error approach. Note that as compared to other operations research (OR) games and puzzles (see, e.g., Chlond 2005Chlond , 2009Chlond , 2011Meuffels and den Hertog 2010;Beliën et al 2011), the input data of the optimization model are not given to the student in a very straightforward and clear way but have to be extracted out of the game by the students themselves.…”

Section: Introductionmentioning

confidence: 99%

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Teaching Integer Programming Starting From an Energy Supply Game

Beliën

Colpaert

Boeck

et al. 2013

INFORMS Transactions on Education

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T his paper presents an integer programming (IP) model for solving an online energy supply game. Instead of a traditional approach in which students are given a problem statement and asked to develop an IP model, both the problem and data are hidden in the game. The energy supply game can be used to illustrate many mathematical programming concepts including blending constraints, multiobjective programming, and the branch-and-bound method. In addition to developing IP modeling skills, students become familiar with the properties of several energy supply systems. The results of two experiments and the related evaluation questionnaires indicate that the game component motivates students more to build IP models as compared to classic approaches.

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Section: Case Studies and Gamesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Teaching Integer Programming Starting From an Energy Supply Game

Beliën

Colpaert

Boeck

et al. 2013

INFORMS Transactions on Education

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“…Synthetic Aperture Radar (SAR) can acquire images all day and all night without being affected by the weather and light conditions [1], which is a tremendous advantage that optical remote sensing images cannot offer. Therefore, it plays an increasingly important role in military and civilian applications.…”

Section: Introductionmentioning

confidence: 99%

A New Framework for Automatic Airports Extraction from SAR Images Using Multi-Level Dual Attention Mechanism

et al. 2020

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The detection of airports from Synthetic Aperture Radar (SAR) images is of great significance in various research fields. However, it is challenging to distinguish the airport from surrounding objects in SAR images. In this paper, a new framework, multi-level and densely dual attention (MDDA) network is proposed to extract airport runway areas (runways, taxiways, and parking lots) in SAR images to achieve automatic airport detection. The framework consists of three parts: down-sampling of original SAR images, MDDA network for feature extraction and classification, and up-sampling of airports extraction results. First, down-sampling is employed to obtain a medium-resolution SAR image from the high-resolution SAR images to ensure the samples (500 × 500) can contain adequate information about airports. The dataset is then input to the MDDA network, which contains an encoder and a decoder. The encoder uses ResNet_101 to extract four-level features with different resolutions, and the decoder performs fusion and further feature extraction on these features. The decoder integrates the chained residual pooling network (CRP_Net) and the dual attention fusion and extraction (DAFE) module. The CRP_Net module mainly uses chained residual pooling and multi-feature fusion to extract advanced semantic features. In the DAFE module, position attention module (PAM) and channel attention mechanism (CAM) are combined with weighted filtering. The entire decoding network is constructed in a densely connected manner to enhance the gradient transmission among features and take full advantage of them. Finally, the airport results extracted by the decoding network were up-sampled by bilinear interpolation to accomplish airport extraction from high-resolution SAR images. To verify the proposed framework, experiments were performed using Gaofen-3 SAR images with 1 m resolution, and three different airports were selected for accuracy evaluation. The results showed that the mean pixels accuracy (MPA) and mean intersection over union (MIoU) of the MDDA network was 0.98 and 0.97, respectively, which is much higher than RefineNet and DeepLabV3. Therefore, MDDA can achieve automatic airport extraction from high-resolution SAR images with satisfying accuracy.

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“…They are an opportunity for students to test their modelling skills on a different style of problem, and some puzzles even require advanced techniques to become tractable. Puzzles are also typically modelled as integer programs (IP), for example, crossword construction (Wilson 1989), Su Doku and the Log Pile puzzle (Chlond 2005), Rummikub (den Hertog and Hulshof 2006), the Battleship problem (Meuffels and den Hertog 2010) and more.…”

Section: Introductionmentioning

confidence: 99%

Puzzle—The Fillomino Puzzle

Pearce

Forbes

2017

INFORMS Transactions on Education

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Abstract. Logic puzzles form an excellent set of problems for the teaching of advanced solution techniques in operations research. They are an opportunity for students to test their modelling skills on a different style of problem, and some puzzles even require advanced techniques to become tractable. Fillomino is a puzzle in which the player must enter integers into a grid to satisfy certain rules. This puzzle is a good exercise in using lazy constraints and composite variables to solve difficult problems.

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Puzzle—Solving the Battleship Puzzle as an Integer Programming Problem

Cited by 13 publications

References 11 publications

Teaching Integer Programming Starting From an Energy Supply Game

Teaching Integer Programming Starting From an Energy Supply Game

A New Framework for Automatic Airports Extraction from SAR Images Using Multi-Level Dual Attention Mechanism

Puzzle—The Fillomino Puzzle

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