IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v103y2021ics0305048321000013.html
   My bibliography  Save this article

Designing optimal masks for a multi-object spectrometer

Author

Listed:
  • Salazar-González, Juan-José

Abstract

This paper concerns a new optimization problem arising in the management of a multi-object spectrometer with a configurable slit unit. The field of view of the spectrograph is divided into contiguous and parallel spatial bands, each one associated with two opposite sliding metal bars that can be positioned to observe one astronomical object. Thus several objects can be analyzed simultaneously within a configuration of the bars called a mask. Due to the high demand from astronomers, pointing the spectrograph’s field of view to the sky, rotating it, and selecting the objects to conform a mask is a crucial optimization problem for the efficient use of the spectrometer. The paper describes this problem, presents a Mixed Integer Linear Programming formulation for the case where the rotation angle is fixed, presents a non-convex formulation for the case where the rotation angle is unfixed, describes a heuristic approach for the general problem, and discusses computational results on real-world and randomly-generated instances.

Suggested Citation

  • Salazar-González, Juan-José, 2021. "Designing optimal masks for a multi-object spectrometer," Omega, Elsevier, vol. 103(C).
    • Handle: RePEc:eee:jomega:v:103:y:2021:i:c:s0305048321000013
    DOI: 10.1016/j.omega.2021.102392
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048321000013
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2021.102392?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Manfred W. Padberg & M. R. Rao, 1982. "Odd Minimum Cut-Sets and b -Matchings," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 67-80, February.
    2. Matthias Ehrgott & Çiğdem Güler & Horst Hamacher & Lizhen Shao, 2010. "Mathematical optimization in intensity modulated radiation therapy," Annals of Operations Research, Springer, vol. 175(1), pages 309-365, March.
    3. Cacchiani, Valentina & Salazar-González, Juan-José, 2020. "Heuristic approaches for flight retiming in an integrated airline scheduling problem of a regional carrier," Omega, Elsevier, vol. 91(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lisa K. Fleischer & Adam N. Letchford & Andrea Lodi, 2006. "Polynomial-Time Separation of a Superclass of Simple Comb Inequalities," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 696-713, November.
    2. Fan Zhang, 2003. "A Separation Algorithm for b -Matching Degree-Sequence Polyhedra," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 92-102, February.
    3. Danielle A. Ripsman & Thomas G. Purdie & Timothy C. Y. Chan & Houra Mahmoudzadeh, 2022. "Robust Direct Aperture Optimization for Radiation Therapy Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2017-2038, July.
    4. Barbara De Rosa & Gennaro Improta & Gianpaolo Ghiani & Roberto Musmanno, 2002. "The Arc Routing and Scheduling Problem with Transshipment," Transportation Science, INFORMS, vol. 36(3), pages 301-313, August.
    5. Oylum S¸eker & Mucahit Cevik & Merve Bodur & Young Lee & Mark Ruschin, 2023. "A Multiobjective Approach for Sector Duration Optimization in Stereotactic Radiosurgery Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 248-264, January.
    6. Julián Aráoz & Elena Fernández & Carles Franquesa, 2017. "The Generalized Arc Routing Problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 497-525, October.
    7. Xu, Yifan & Wandelt, Sebastian & Sun, Xiaoqian, 2021. "Airline integrated robust scheduling with a variable neighborhood search based heuristic," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 181-203.
    8. Shraddha Ghatkar, 2019. "Optimization of fractionation schemes and beamlet intensities in intensity-modulated radiation therapy with changing cancer tumor properties," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 46(4), pages 385-407, December.
    9. Kelsey Maass & Minsun Kim & Aleksandr Aravkin, 2022. "A Nonconvex Optimization Approach to IMRT Planning with Dose–Volume Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1366-1386, May.
    10. Marc C. Robini & Feng Yang & Yuemin Zhu, 2020. "A stochastic approach to full inverse treatment planning for charged-particle therapy," Journal of Global Optimization, Springer, vol. 77(4), pages 853-893, August.
    11. Michele Conforti & Gérard Cornuéjols & Giacomo Zambelli, 2013. "Extended formulations in combinatorial optimization," Annals of Operations Research, Springer, vol. 204(1), pages 97-143, April.
    12. Quoc Trung Bui & Yves Deville & Quang Dung Pham, 2016. "Exact methods for solving the elementary shortest and longest path problems," Annals of Operations Research, Springer, vol. 244(2), pages 313-348, September.
    13. Luc Muyldermans & Patrick Beullens & Dirk Cattrysse & Dirk Van Oudheusden, 2005. "Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem," Operations Research, INFORMS, vol. 53(6), pages 982-995, December.
    14. Dursun, Pınar & Taşkın, Z. Caner & Altınel, İ. Kuban, 2019. "The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)," European Journal of Operational Research, Elsevier, vol. 272(1), pages 372-388.
    15. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, October.
    16. A N Letchford & J Lysgaard & R W Eglese, 2007. "A branch-and-cut algorithm for the capacitated open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1642-1651, December.
    17. Raith, Andrea & Ehrgott, Matthias & Fauzi, Fariza & Lin, Kuan-Min & Macann, Andrew & Rouse, Paul & Simpson, John, 2022. "Integrating Data Envelopment Analysis into radiotherapy treatment planning for head and neck cancer patients," European Journal of Operational Research, Elsevier, vol. 296(1), pages 289-303.
    18. Neamatian Monemi, Rahimeh & Gelareh, Shahin & Nagih, Anass & Maculan, Nelson & Danach, Kassem, 2021. "Multi-period hub location problem with serial demands: A case study of humanitarian aids distribution in Lebanon," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    19. Turan, Hasan Hüseyin & Jalalvand, Fatemeh & Elsawah, Sondoss & Ryan, Michael J., 2022. "A joint problem of strategic workforce planning and fleet renewal: With an application in defense," European Journal of Operational Research, Elsevier, vol. 296(2), pages 615-634.
    20. Caterina De Simone & Anna Galluccio, 2009. "Edge-colouring of joins of regular graphs, I," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 417-428, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:103:y:2021:i:c:s0305048321000013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.