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Resultant Gradient Flow Method for Multiple Objective Programming Based on Efficient Computing

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Parallel Architectures, Algorithms and Programming (PAAP 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1163))

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Abstract

The process of blending gas transmission contains multiple kinds of influence factors that are related with the achievement of maximal overall profit for a refinery gas company. It is, therefore, a multiple objective optimization problems. To maximize overall profit, we proposes a multiple objective resultant gradient descent method (RGDM) to solve fractional, nonlinear, and multiple objective programming problems. Resultant gradient descent requires a proper direction of multiple objective functions. The proper direction in this paper is computed by gradient flow to approach to the global maximum values. Gradient flow is one of the forms of geometric flow, which is widely used in linear programming, least-squares approximation, optimization, and differential equation. It is the first time to be used in mathematical programming. Resultant gradient flow is calculated in linear programming, and the extremum can directly affect the extremum of the our multiple objective functions. Such steps can indirectly simplify the non-linear objective function by separate the single objective functions so that we can use the gradient flow method to solve the multi-objective problem of non-linear programming. It also embodies the stability and efficiency of the proposed gradient flow.

With the case study of a refinery gas company, this paper build a overall profit model. Also, we apply the proposed resultant method to solve this multi-objective problem by a planned strategy of how to supply natural gas to the residential area and schedule the initial coordination. Moreover, its solutions are displayed and compared with a genetic algorithm-based solver in our experimental study.

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Authors and Affiliations

  1. Nanjing University of Finance and Economics, Nanjing, China

    Bao Feng, Peixin He, Yunyao Li, Junfeng Wu & Jing He

  2. Nanjing University of Posts and Telecommunications, Nanjing, China

    Peng Li, Haichang Yao & Yimu Ji

  3. Southwestern Petroleum University, Chengdu, China

    Chao Min, Jing He & Yang Wang

  4. Jingqi Smart Healthcare Pty Ltd., Hefei, China

    Jiekui Zhang & Youtao Li

  5. Research Centre on Fictitious Economy and Data Science, Beijing, China

    Peizhuang Wang & Yong Shi

  6. Swinburne University of Technology, Melbourne, Australia

    Jing He & Hui Zheng

Authors
  1. Bao Feng
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  15. Yang Wang
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Corresponding author

Correspondence to Jing He .

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Editors and Affiliations

  1. Sun Yat-sen University, Guangzhou, China

    Hong Shen

  2. Sun Yat-sen University, Guangzhou, China

    Yingpeng Sang

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Feng, B. et al. (2020). Resultant Gradient Flow Method for Multiple Objective Programming Based on Efficient Computing. In: Shen, H., Sang, Y. (eds) Parallel Architectures, Algorithms and Programming. PAAP 2019. Communications in Computer and Information Science, vol 1163. Springer, Singapore. https://doi.org/10.1007/978-981-15-2767-8_43

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  • DOI: https://doi.org/10.1007/978-981-15-2767-8_43

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  • Print ISBN: 978-981-15-2766-1

  • Online ISBN: 978-981-15-2767-8

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