Nonlinear goal programming with -ni, -pi and -(n i+pi) goals

Zhiyong Zhang; Shanlin Yang; Xinbao Liu; Jen S. Shang; Jianbo Yang

doi:10.1109/ICIEEM.2009.5344199

Nonlinear goal programming with -n_i, -p_i and -(n _i+p_i) goals

Zhiyong Zhang
, Shanlin Yang
, Xinbao Liu
, Jen S. Shang
, Jianbo Yang

Hefei University of Technology
Beijing Wuzi University
University of Pittsburgh
University of Manchester

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

The (minimizing) achievement function of the traditional Goal Programming (GP) model has five basic forms: n_i, p_i, (n _i+p_i), (n₁-p_i), and (p _i-n_i), where n_i and p_i are nonnegative under and over achievement variables in the i^th goal-constraint. Zhang and Shang (2001) proposed the theory of Goal Programs with -n_i, -p_i, and -(n_i+p_i) goals, which has many interesting and practical applications. This paper extends the theory further into the nonlinear situation and proposes a new algorithm for solving the ensuing nonconvex nonlinear program. Results obtained in this paper shows that the basic conclusions for the linear GP model still hold for the nonlinear case.

Original language	English
Title of host publication	IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management
Pages	894-898
Number of pages	5
DOIs	https://doi.org/10.1109/ICIEEM.2009.5344199
State	Published - 2009
Externally published	Yes
Event	2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management, IE and EM 2009 - Beijing, China Duration: 21 Oct 2009 → 23 Oct 2009

Publication series

Name	IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management

Conference

Conference	2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management, IE and EM 2009
Country/Territory	China
City	Beijing
Period	21/10/09 → 23/10/09

Keywords

Multiobjective algorithm
Nonconvex goal programming
Nonlinear goal programming

Access to Document

10.1109/ICIEEM.2009.5344199

Cite this

Zhang, Z., Yang, S., Liu, X., Shang, J. S., & Yang, J. (2009). Nonlinear goal programming with -n_i, -p_i and -(n _i+p_i) goals. In IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management (pp. 894-898). Article 5344199 (IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management). https://doi.org/10.1109/ICIEEM.2009.5344199

Zhang, Zhiyong ; Yang, Shanlin ; Liu, Xinbao et al. / Nonlinear goal programming with -n_i, -p_i and -(n _i+p_i) goals. IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management. 2009. pp. 894-898 (IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management).

@inproceedings{a970b5acb4994c3f9a3ec603f5ea9a57,

title = "Nonlinear goal programming with -ni, -pi and -(n i+pi) goals",

abstract = "The (minimizing) achievement function of the traditional Goal Programming (GP) model has five basic forms: ni, pi, (n i+pi), (n1-pi), and (p i-ni), where ni and pi are nonnegative under and over achievement variables in the ith goal-constraint. Zhang and Shang (2001) proposed the theory of Goal Programs with -ni, -pi, and -(ni+pi) goals, which has many interesting and practical applications. This paper extends the theory further into the nonlinear situation and proposes a new algorithm for solving the ensuing nonconvex nonlinear program. Results obtained in this paper shows that the basic conclusions for the linear GP model still hold for the nonlinear case.",

keywords = "Multiobjective algorithm, Nonconvex goal programming, Nonlinear goal programming",

author = "Zhiyong Zhang and Shanlin Yang and Xinbao Liu and Shang, \{Jen S.\} and Jianbo Yang",

year = "2009",

doi = "10.1109/ICIEEM.2009.5344199",

language = "英语",

isbn = "9781424436705",

series = "IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management",

pages = "894--898",

booktitle = "IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management",

note = "2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management, IE and EM 2009 ; Conference date: 21-10-2009 Through 23-10-2009",

}

Zhang, Z, Yang, S, Liu, X, Shang, JS & Yang, J 2009, Nonlinear goal programming with -n_i, -p_i and -(n _i+p_i) goals. in IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management., 5344199, IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management, pp. 894-898, 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management, IE and EM 2009, Beijing, China, 21/10/09. https://doi.org/10.1109/ICIEEM.2009.5344199

Nonlinear goal programming with -n_i, -p_i and -(n _i+p_i) goals. / Zhang, Zhiyong; Yang, Shanlin; Liu, Xinbao et al.
IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management. 2009. p. 894-898 5344199 (IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The (minimizing) achievement function of the traditional Goal Programming (GP) model has five basic forms: ni, pi, (n i+pi), (n1-pi), and (p i-ni), where ni and pi are nonnegative under and over achievement variables in the ith goal-constraint. Zhang and Shang (2001) proposed the theory of Goal Programs with -ni, -pi, and -(ni+pi) goals, which has many interesting and practical applications. This paper extends the theory further into the nonlinear situation and proposes a new algorithm for solving the ensuing nonconvex nonlinear program. Results obtained in this paper shows that the basic conclusions for the linear GP model still hold for the nonlinear case.

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Zhang Z, Yang S, Liu X, Shang JS, Yang J. Nonlinear goal programming with -n_i, -p_i and -(n _i+p_i) goals. In IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management. 2009. p. 894-898. 5344199. (IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management). doi: 10.1109/ICIEEM.2009.5344199